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In Equation (24), the term inside the brackets corresponds to the fast Fourier transform algorithm; this allows computing time savings if N is equal to an integer power of two. Finally, by implementing the odd sampling presented in (21) and including a window function Om, the Laplace transform in (20) can be numerically approximated by:

Figure 74 In Equation (24), the term inside the brackets corresponds to the fast Fourier transform algorithm; this allows computing time savings if N is equal to an integer power of two. Finally, by implementing the odd sampling presented in (21) and including a window function Om, the Laplace transform in (20) can be numerically approximated by:

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Figure 1. Integral fingerprint for quality control during the manufacturing, transportation, and installation of offshore power cables. As offshore cables are often produced in very long lengths compared to onshore cables and a lot of typical handling is taken place from manufacturing up to the offshore installation, there are the risks of cable damages. Those can be related to manufacturing, transportation, and the installation stages of the cable. Therefore, there is a need to use an integral approach where the condition of the cables will be verified. Having such fingerprints as obtained during these stages, a comparison could be made to verify the cable quality. This can also be used as a good basis for the cable maintenance activity later on, see Figure 1.
Figure 1. Integral fingerprint for quality control during the manufacturing, transportation, and installation of offshore power cables. As offshore cables are often produced in very long lengths compared to onshore cables and a lot of typical handling is taken place from manufacturing up to the offshore installation, there are the risks of cable damages. Those can be related to manufacturing, transportation, and the installation stages of the cable. Therefore, there is a need to use an integral approach where the condition of the cables will be verified. Having such fingerprints as obtained during these stages, a comparison could be made to verify the cable quality. This can also be used as a good basis for the cable maintenance activity later on, see Figure 1.
ACRT—AC Resonance Test; VLF—Very Low Frequency; DAC—Damped AC; PD—Partial Discharges. 1 when connecting a second resonance reactor; 2 when lowering the VLF test frequency to e.g., 0.01 Hz; 3 Voltage source produces high interference during the PD measurement (>10 pC). Table 1. Overview of test technologies for monitored withstand test of 66 kV subsea inter-array cables.
ACRT—AC Resonance Test; VLF—Very Low Frequency; DAC—Damped AC; PD—Partial Discharges. 1 when connecting a second resonance reactor; 2 when lowering the VLF test frequency to e.g., 0.01 Hz; 3 Voltage source produces high interference during the PD measurement (>10 pC). Table 1. Overview of test technologies for monitored withstand test of 66 kV subsea inter-array cables.
Figure 2. Schematic overview of a damped AC (DAC) system connected to a power cable, with U the high voltage source, R the protective resistor, S the semiconductor switch, L the air core inductor, M the voltage divider, and coupling capacitor and Cro the cable under test. The energizing time depends on the maximum available load current of the high voltage power supply, the test voltage, and the capacitance of the test object and has to stay below 100 s [2]. During a number of AC voltage cycles (of several hundred milliseconds), the PD signals are initiated in a way similar to 50/60 Hz inception conditions [5,20-22]. In accordance with [5], no DC stresses are applied to the test object, and the DAC stress can be considered similar to factory partial discharge testing conditions, i.e., a 50 Hz AC test combined with a PD measurement. Due to the continuous voltage increase and immediate transition to the DAC voltage after the maximum test voltage is reached, no steady-state condition occurs, and the low electric field strength in the insulation (typically <20 kV/mm), and short durations (less than a second up to tens of seconds) of bipolar stresses ensures no space charge accumulation.
Figure 2. Schematic overview of a damped AC (DAC) system connected to a power cable, with U the high voltage source, R the protective resistor, S the semiconductor switch, L the air core inductor, M the voltage divider, and coupling capacitor and Cro the cable under test. The energizing time depends on the maximum available load current of the high voltage power supply, the test voltage, and the capacitance of the test object and has to stay below 100 s [2]. During a number of AC voltage cycles (of several hundred milliseconds), the PD signals are initiated in a way similar to 50/60 Hz inception conditions [5,20-22]. In accordance with [5], no DC stresses are applied to the test object, and the DAC stress can be considered similar to factory partial discharge testing conditions, i.e., a 50 Hz AC test combined with a PD measurement. Due to the continuous voltage increase and immediate transition to the DAC voltage after the maximum test voltage is reached, no steady-state condition occurs, and the low electric field strength in the insulation (typically <20 kV/mm), and short durations (less than a second up to tens of seconds) of bipolar stresses ensures no space charge accumulation.
Figure 3. Example of damped AC voltage excitations monitored by partial discharge (PD) detection. The PD activity can be used to localize the breakdown site. During the AC resonance phase, the DAC voltage is characterized by a decaying sine wave with a frequency given by the inductance used and the capacitance of the cable under test. Inductor values of DAC systems are chosen such that the DAC voltage frequency is in the near power frequency range of 10-500 Hz, see Figure 3. The maximum cable length is only limited by the energizing time and the maximum current capabilities of the semiconductor switch, therefore DAC systems can be easily used to test cable lengths up to tens of kilometers.
Figure 3. Example of damped AC voltage excitations monitored by partial discharge (PD) detection. The PD activity can be used to localize the breakdown site. During the AC resonance phase, the DAC voltage is characterized by a decaying sine wave with a frequency given by the inductance used and the capacitance of the cable under test. Inductor values of DAC systems are chosen such that the DAC voltage frequency is in the near power frequency range of 10-500 Hz, see Figure 3. The maximum cable length is only limited by the energizing time and the maximum current capabilities of the semiconductor switch, therefore DAC systems can be easily used to test cable lengths up to tens of kilometers.
Figure 4. Monitored voltages withstand testing of a 150 kV XLPE cable underground circuit (4.5 km) up to 1.7 Uo. Example of PD mapping as obtained during DAC voltage testing up to 1.0 Uo shows that joint No. 5 has concentrated PD activity at operating voltage level. Figure 4. Monitored voltages withstand testing of a 150 kV XLPE cable underground circuit (4.5 km) test results obtained may differ from those obtained by continuous AC withstand voltage testing [5]. Assuming that testing should not necessarily be destructive and that the PD inception indicates presence of defects, this difference in the time until breakdown has to be considered as an advantage of DAC testing. In practice, a monitored damped AC hold test is performed to determine whether the cable passes or fails the damped AC test. Due to additional information as provided by PD detection, the monitoring insulation properties during a damped AC withstand test, and the effect of the test voltage during its application can improve the evaluation of the insulation condition.
Figure 4. Monitored voltages withstand testing of a 150 kV XLPE cable underground circuit (4.5 km) up to 1.7 Uo. Example of PD mapping as obtained during DAC voltage testing up to 1.0 Uo shows that joint No. 5 has concentrated PD activity at operating voltage level. Figure 4. Monitored voltages withstand testing of a 150 kV XLPE cable underground circuit (4.5 km) test results obtained may differ from those obtained by continuous AC withstand voltage testing [5]. Assuming that testing should not necessarily be destructive and that the PD inception indicates presence of defects, this difference in the time until breakdown has to be considered as an advantage of DAC testing. In practice, a monitored damped AC hold test is performed to determine whether the cable passes or fails the damped AC test. Due to additional information as provided by PD detection, the monitoring insulation properties during a damped AC withstand test, and the effect of the test voltage during its application can improve the evaluation of the insulation condition.
Figure 5. Example of dissipation factor diagnosis data as obtained for two different cable circuits: (a,b) A 150 kV power cable with self-contained fluid-filled (SCFF) insulation, length: 850 m, aged 49 years, (c,d) A 230 kV power cable with low-pressure fluid-filled (LPFF) insulation, length 13.3 km, aged 33 years.
Figure 5. Example of dissipation factor diagnosis data as obtained for two different cable circuits: (a,b) A 150 kV power cable with self-contained fluid-filled (SCFF) insulation, length: 850 m, aged 49 years, (c,d) A 230 kV power cable with low-pressure fluid-filled (LPFF) insulation, length 13.3 km, aged 33 years.
Figure 6. Setup for dual-sided PD monitored on-site testing techniques for offshore export cables of long lengths: DAC excitation circuit and synchronized PD detector units supported by PD measurement with localization feasibility with C, the coupling capacitor (1-2 nF), Ling is the air core inductance (5-9 H). Detection and localization of PD in export cable system with long lengths e.g., 30 km can b improved by performing PD measurements at both sides of the cable circuit. This will, for th worst-case situation (PD at the near end), reduce the traveling distance for PD pulses by a factor of 4 In a single-sided measurement setup, a near end partial discharge has to travel through the whol cable length to the far end and the whole cable length back to the near end. The overall travelin; distance is, therefore, two times the cable length. In a dual-sided measurement, the near end PL only has to travel to the far end to be detected there, so it only has to travel the cable length once For this dual-sided measurement system, a damped AC system for energizing the cable system is usec see Figure 6. This system uses a coupling capacitor with PD detector on the near end side and a secon« PD detector at the far end side [11]. Figure 6. Setup for dual-sided PD monitored on-site testing techniques for offshore export cables of long
Figure 6. Setup for dual-sided PD monitored on-site testing techniques for offshore export cables of long lengths: DAC excitation circuit and synchronized PD detector units supported by PD measurement with localization feasibility with C, the coupling capacitor (1-2 nF), Ling is the air core inductance (5-9 H). Detection and localization of PD in export cable system with long lengths e.g., 30 km can b improved by performing PD measurements at both sides of the cable circuit. This will, for th worst-case situation (PD at the near end), reduce the traveling distance for PD pulses by a factor of 4 In a single-sided measurement setup, a near end partial discharge has to travel through the whol cable length to the far end and the whole cable length back to the near end. The overall travelin; distance is, therefore, two times the cable length. In a dual-sided measurement, the near end PL only has to travel to the far end to be detected there, so it only has to travel the cable length once For this dual-sided measurement system, a damped AC system for energizing the cable system is usec see Figure 6. This system uses a coupling capacitor with PD detector on the near end side and a secon« PD detector at the far end side [11]. Figure 6. Setup for dual-sided PD monitored on-site testing techniques for offshore export cables of long
Figure 7. The layout of the array cable strings, each string consist of a total of nine wind turbine generators (WTGs). DAC test was performed from the offshore substation (OSS).
Figure 7. The layout of the array cable strings, each string consist of a total of nine wind turbine generators (WTGs). DAC test was performed from the offshore substation (OSS).
SSE See Sipe eae ene In a string of 8.4 km length of inter-array cables between the OSS and nine wind turbines, partial discharges were detected and localized. Each phase was individually tested using a damped AC offshore system with a DAC frequency of 100 Hz (total cable capacitance 1.85 uF). The test voltage level was ramped up in steps up to the maximum applied test voltage level of 1.4 Uo. PD was monitored during the voltage ramp-up phase and during the withstand testing of 50 DAC excitations at the maximum test voltage. No breakdown was observed during the withstand test, however as the damped AC test voltage was increased up to 1.4 Uo, PD activity was observed in phases L2 and L3 ot the string, see Figure 8. PD mapping revealed the PD concentration at WTG 5 in phase L3 and at WTG 6 km in phase L2. Figure 8. Phase-resolved PD pattern at 1.4 Uo (left), PD mapping showing the complete string length with the localized PD concentrations at the wind turbines (WTG) at WTG 5 and WTG 6. The squares are the locations of the WTGs in the string (right).
SSE See Sipe eae ene In a string of 8.4 km length of inter-array cables between the OSS and nine wind turbines, partial discharges were detected and localized. Each phase was individually tested using a damped AC offshore system with a DAC frequency of 100 Hz (total cable capacitance 1.85 uF). The test voltage level was ramped up in steps up to the maximum applied test voltage level of 1.4 Uo. PD was monitored during the voltage ramp-up phase and during the withstand testing of 50 DAC excitations at the maximum test voltage. No breakdown was observed during the withstand test, however as the damped AC test voltage was increased up to 1.4 Uo, PD activity was observed in phases L2 and L3 ot the string, see Figure 8. PD mapping revealed the PD concentration at WTG 5 in phase L3 and at WTG 6 km in phase L2. Figure 8. Phase-resolved PD pattern at 1.4 Uo (left), PD mapping showing the complete string length with the localized PD concentrations at the wind turbines (WTG) at WTG 5 and WTG 6. The squares are the locations of the WTGs in the string (right).
Figure 9. On-site testing of a 220 kV 13.3 km long XLPE cable circuit: The damped AC system HV300 i: connected to one of the cable section phases (left) and the transition point between land and submarin cable (right).
Figure 9. On-site testing of a 220 kV 13.3 km long XLPE cable circuit: The damped AC system HV300 i: connected to one of the cable section phases (left) and the transition point between land and submarin cable (right).
Figure 10. Damped AC voltages and PD patterns as observed during withstand testing of a 220 kV XLPE cable underground circuit (13.3 km): (a) example of PD pattern at 0.2 Uo of phase L1, (b) example of PD pattern at breakdown voltage of 0.4 Uo of phase L1, (c) PD pattern at 1.3 Uo of phases L2 and L3. Figure 10. Damped AC voltages and PD patterns as observed during withstand testing of a 220 kV
Figure 10. Damped AC voltages and PD patterns as observed during withstand testing of a 220 kV XLPE cable underground circuit (13.3 km): (a) example of PD pattern at 0.2 Uo of phase L1, (b) example of PD pattern at breakdown voltage of 0.4 Uo of phase L1, (c) PD pattern at 1.3 Uo of phases L2 and L3. Figure 10. Damped AC voltages and PD patterns as observed during withstand testing of a 220 kV
Figure 11. PD Mapping as made up to 1.3 Uo during DAC testing of a 220 kV 13.3 km long cable circuit. The PD concentration at 5.2 km distance indicates the breakdown site of phase L1 (left). Measurement from the other end confirmed this location at 8.1 km (right).
Figure 11. PD Mapping as made up to 1.3 Uo during DAC testing of a 220 kV 13.3 km long cable circuit. The PD concentration at 5.2 km distance indicates the breakdown site of phase L1 (left). Measurement from the other end confirmed this location at 8.1 km (right).
Table 2. Results of DAC condition assessment on an offshore wind farm (OSWF). It can be concluded that a considerable number of wind turbines have increased risk of a failure due to the presence of PD at voltages higher than Uo. These PD sites are probably related to poor workmanship during the installation.
Table 2. Results of DAC condition assessment on an offshore wind farm (OSWF). It can be concluded that a considerable number of wind turbines have increased risk of a failure due to the presence of PD at voltages higher than Uo. These PD sites are probably related to poor workmanship during the installation.
* Depending on the complexity of the repair. Table 3. Losses of a single inter-array 33 kV or 66 kV termination failures. Approximate failure costs for a 100 WTG (800 MW) wind farm: (German calculation taking average 50% efficiency of the wind farm with a price of EUR 0.16 kWh). However, the size (i.e., the power rating) of the turbine also plays an important role. In the future, larger turbines will be built were a termination fault will lead quickly to higher financial loss due to the greater loss of energy. As a result, a proper after-installation testing program is beneficial to verify the cable quality and can prevent costly failures during operation. The economic impact of an HVAC or HVDC export cable failure can be examined under the following categories:
* Depending on the complexity of the repair. Table 3. Losses of a single inter-array 33 kV or 66 kV termination failures. Approximate failure costs for a 100 WTG (800 MW) wind farm: (German calculation taking average 50% efficiency of the wind farm with a price of EUR 0.16 kWh). However, the size (i.e., the power rating) of the turbine also plays an important role. In the future, larger turbines will be built were a termination fault will lead quickly to higher financial loss due to the greater loss of energy. As a result, a proper after-installation testing program is beneficial to verify the cable quality and can prevent costly failures during operation. The economic impact of an HVAC or HVDC export cable failure can be examined under the following categories:
Figure 1. Structure chart of the Multi-frequency ultrasonic device. As shown in Figure 1, the multi frequency ultrasonic detection system consists of three parts, namely, an Ultrasonic Measurement Device (Yucoya Energy Safety GmbH, GER), an Ultrasonic Sensor and Measurement Software (Yucoya Ultrasound Manager, Yucoya Energy Safety GmbH, GER). The internal state information of transformer oil was reflected by these ultrasonic parameters that were obtained by continuous scanning at the molecular level.
Figure 1. Structure chart of the Multi-frequency ultrasonic device. As shown in Figure 1, the multi frequency ultrasonic detection system consists of three parts, namely, an Ultrasonic Measurement Device (Yucoya Energy Safety GmbH, GER), an Ultrasonic Sensor and Measurement Software (Yucoya Ultrasound Manager, Yucoya Energy Safety GmbH, GER). The internal state information of transformer oil was reflected by these ultrasonic parameters that were obtained by continuous scanning at the molecular level.
Figure 2. Principle structure diagram of ultrasonic sensor. The structure of the ultrasonic sensor is shown in Figure 2. At the time of detection, the ultrasonic sensor was dipped into the transformer oil, except for the mounting bracket and the external connectors to fill the measurement chamber with the oil. Meanwhile, the ultrasonic transmitter Tx emits an ultrasound signal, including 20 frequencies within the range of 600 kHz—1000 kHz and the central resonance frequency was about 750 kHz. A part of this signal is first reflected at the interface between the reference medium and the measurement chamber. This reflected signal travels back to ultrasonic receiver Rx1 where it is measured. This signal is called L1. The other part of the signal emitted by ultrasonic transmitter Tx is transmitted through the interface of the reference medium and the measurement chamber. It travels to ultrasonic receiver Rx2, where it is measured. This part of the signal is called L3. Finally, at ultrasonic receiver Rx2, a part of the signal is reflected again and travels back to ultrasonic receiver Rx1. This signal is called L2. The received signals which are called L1, L2 and L3 can be written as:
Figure 2. Principle structure diagram of ultrasonic sensor. The structure of the ultrasonic sensor is shown in Figure 2. At the time of detection, the ultrasonic sensor was dipped into the transformer oil, except for the mounting bracket and the external connectors to fill the measurement chamber with the oil. Meanwhile, the ultrasonic transmitter Tx emits an ultrasound signal, including 20 frequencies within the range of 600 kHz—1000 kHz and the central resonance frequency was about 750 kHz. A part of this signal is first reflected at the interface between the reference medium and the measurement chamber. This reflected signal travels back to ultrasonic receiver Rx1 where it is measured. This signal is called L1. The other part of the signal emitted by ultrasonic transmitter Tx is transmitted through the interface of the reference medium and the measurement chamber. It travels to ultrasonic receiver Rx2, where it is measured. This part of the signal is called L3. Finally, at ultrasonic receiver Rx2, a part of the signal is reflected again and travels back to ultrasonic receiver Rx1. This signal is called L2. The received signals which are called L1, L2 and L3 can be written as:
The six samples oil response spectrum are shown in Figure 3, where the legend is the moisture content of the sample in mg/L. It can be seen that, as the moisture content fell, the amplitude response of each frequency fell, and the increase in amplitude response was maintained in L1 phase and L2 phase. In L3 phase, there was a “basin” inside the amplitude response within the scope of the frequency range 700 kHz to 850 kHz. An oil sample with a moisture content of 1.51 mg/L exhibited the lowest amplitude response in L1 phase, L2 phase and In L3 phase. Figure 3. Spectrum curve of ultrasonic signal. (a) Amplitude response of L1 phase of multi-frequency ultrasonic detection; (b) Amplitude response of L2 phase of multi-frequency ultrasonic detection; (c) Amplitude response of L3 phase of multi-frequency ultrasonic detection.
The six samples oil response spectrum are shown in Figure 3, where the legend is the moisture content of the sample in mg/L. It can be seen that, as the moisture content fell, the amplitude response of each frequency fell, and the increase in amplitude response was maintained in L1 phase and L2 phase. In L3 phase, there was a “basin” inside the amplitude response within the scope of the frequency range 700 kHz to 850 kHz. An oil sample with a moisture content of 1.51 mg/L exhibited the lowest amplitude response in L1 phase, L2 phase and In L3 phase. Figure 3. Spectrum curve of ultrasonic signal. (a) Amplitude response of L1 phase of multi-frequency ultrasonic detection; (b) Amplitude response of L2 phase of multi-frequency ultrasonic detection; (c) Amplitude response of L3 phase of multi-frequency ultrasonic detection.
Figure 5. Flow chart of back propagation neural network training. The flow chart of model training and learning is shown in Figure 5.
Figure 5. Flow chart of back propagation neural network training. The flow chart of model training and learning is shown in Figure 5.
Figure 6. Flow chart of optimizing the BP neural network parameters with a GA. 4.4. PCA-GA-BPNN Prediction Model
Figure 6. Flow chart of optimizing the BP neural network parameters with a GA. 4.4. PCA-GA-BPNN Prediction Model
Figure 7. The MSE of BP neural network recheck. where / is the number of input layer neurons, 1 is the number of hidden layer neurons, and m is the number of output layer neurons. a is in the range of 1-10. Therefore, in this paper, the number of hidden layer neurons was between 1 and 16. The back-check diagnosis was performed using the network of 1-16 hidden neurons, and the mean square error (MSE) of recheck was calculated. The variation of MSE with the number of neurons in the hidden layer as shown in Figure 7.
Figure 7. The MSE of BP neural network recheck. where / is the number of input layer neurons, 1 is the number of hidden layer neurons, and m is the number of output layer neurons. a is in the range of 1-10. Therefore, in this paper, the number of hidden layer neurons was between 1 and 16. The back-check diagnosis was performed using the network of 1-16 hidden neurons, and the mean square error (MSE) of recheck was calculated. The variation of MSE with the number of neurons in the hidden layer as shown in Figure 7.
Figure 9. The regression fitting curve of GA-BPNN. The optimal weights and the optimal thresholds obtained from the optimization of GA were assigned to the BPNN. Then, the model was trained with the training set. The regression curve of the model is shown in Figure 9. Figure 9 shows that the correlation coefficient of the PCA-GA-BPNN model was about 0.98, indicating that the model has a good regression fit.
Figure 9. The regression fitting curve of GA-BPNN. The optimal weights and the optimal thresholds obtained from the optimization of GA were assigned to the BPNN. Then, the model was trained with the training set. The regression curve of the model is shown in Figure 9. Figure 9 shows that the correlation coefficient of the PCA-GA-BPNN model was about 0.98, indicating that the model has a good regression fit.
Figure 8. The fitness curve of Genetic algorithms.
Figure 8. The fitness curve of Genetic algorithms.
Figure 10. The training process of GA-BPNN.
Figure 10. The training process of GA-BPNN.
Table 1. Prediction results of water content. In order to quantitatively analyze the predictive effect of the three models, the mean absolute percent error (MAPE) was used to compare the prediction errors of the BPNN model, the GA-BPNN
Table 1. Prediction results of water content. In order to quantitatively analyze the predictive effect of the three models, the mean absolute percent error (MAPE) was used to compare the prediction errors of the BPNN model, the GA-BPNN
Figure 1. The microstructures of metal particles (a) and cellulose particles (b). Viscous drag force (Fyragi) acts on the metal particle, as shown in Formula (2). Because of the nonlinearity of the viscous drag force, the correction factor (Cy) related to the Reynolds coefficient (Re) should be used to correct the viscous drag force.
Figure 1. The microstructures of metal particles (a) and cellulose particles (b). Viscous drag force (Fyragi) acts on the metal particle, as shown in Formula (2). Because of the nonlinearity of the viscous drag force, the correction factor (Cy) related to the Reynolds coefficient (Re) should be used to correct the viscous drag force.
where €,, and ép tepresent the permittivity of insulation oil and cellulose impurities, and d and | stand for the diameter and length of the cellulose particle. Using Formulas (8)—(15), the velocity of the cellulose particle vpy2 can be attained using
where €,, and ép tepresent the permittivity of insulation oil and cellulose impurities, and d and | stand for the diameter and length of the cellulose particle. Using Formulas (8)—(15), the velocity of the cellulose particle vpy2 can be attained using
Figure 2. The experimental platform for the particle accumulation and DC breakdown test. A standard oil cup containing a sphere-sphere electrode made of copper material with a diameter of 13 mm was used in the experiments. In accordance with IEC 60156, an electrode distance of 2.5 mm was used in the DC breakdown experiments. To study the accumulation characteristics of the three kinds of particles, 7.5 mm and 12.5 kV were utilized. The oil cup was situated under a digital camera which recorded the process of particle accumulation. The current was measured by a Keithley electrometer (6517B). The experimental setup for the DC breakdown voltage testing is shown in Figure 2. HCDJC-100kV/5kVA was utilized to provide high DC voltage. The signal together with data was controlled and attained by the computer system.
Figure 2. The experimental platform for the particle accumulation and DC breakdown test. A standard oil cup containing a sphere-sphere electrode made of copper material with a diameter of 13 mm was used in the experiments. In accordance with IEC 60156, an electrode distance of 2.5 mm was used in the DC breakdown experiments. To study the accumulation characteristics of the three kinds of particles, 7.5 mm and 12.5 kV were utilized. The oil cup was situated under a digital camera which recorded the process of particle accumulation. The current was measured by a Keithley electrometer (6517B). The experimental setup for the DC breakdown voltage testing is shown in Figure 2. HCDJC-100kV/5kVA was utilized to provide high DC voltage. The signal together with data was controlled and attained by the computer system.
Table 1. Parameters of mineral oil. Table 2. Parameters of mineral oil.
Table 1. Parameters of mineral oil. Table 2. Parameters of mineral oil.
Table 3. Abbreviations of samples analyzed in the experiments. 3. Experimental Results and Discussion
Table 3. Abbreviations of samples analyzed in the experiments. 3. Experimental Results and Discussion
Table 4. Parameters of the particle accumulation model.
Table 4. Parameters of the particle accumulation model.
Figure 3. Simulation results of different kinds of particle accumulation in mineral oil at different times.
Figure 3. Simulation results of different kinds of particle accumulation in mineral oil at different times.
Figure 4. Particle accumulation status under the same DC voltage in mineral oil at different time Figure 4 illustrates the dynamic behavior of particle accumulation under DC voltage, in which the concentration levels of cellulose particles, metal particles, and mixed particles were respectively 0.009% by weight, 0.1 g/L, and the sum of both. The distance and DC voltage between the spherical electrodes were 7.5 mm and 11.25 kV, respectively. The left electrode was a cathode, and the right one was an anode.
Figure 4. Particle accumulation status under the same DC voltage in mineral oil at different time Figure 4 illustrates the dynamic behavior of particle accumulation under DC voltage, in which the concentration levels of cellulose particles, metal particles, and mixed particles were respectively 0.009% by weight, 0.1 g/L, and the sum of both. The distance and DC voltage between the spherical electrodes were 7.5 mm and 11.25 kV, respectively. The left electrode was a cathode, and the right one was an anode.
Figure 5. Motion trajectory of cellulose particles (a) and metal particles (b) under DC voltage in mineral oil. ae - As shown in Figure 4 (sample DMCP) a thin fiber bridge was observed after 30 s in mineral oil containing cellulose particles. After that, the thickness of cellulose bridges increased gradually The complete bridge formed until approximately 600 s. Then, notable changes in the cellulose bridge were not seen. For mineral oil contaminated by metal particles, most metal particles sunk down owing to their larger densities. A filamentous bridge formed at about 500 s (Figure 4, sample DMMP) which was so unstable that it migrated back and forth between electrodes, which may be attributed to the impact of the strong electrical field. The ultimate metal bridge appeared until 1200 s. As for mixed particles (Figure 4, sample DMCP), the complete bridge formed more quickly than those for single impurities. Furthermore, it was observed that the complete bridge was densest when the transverse force among thin bridges made up of mixed particles was larger. It can be inferred that the simulation model depicting the changing course of particles aggregation is in agreement with the actual process Thus, the simulation model can accurately describe the impact of impurities on motion as well as on the accumulation characteristics of particles. Different attributes of particles determined the difference in the trajectory. The trajectories of cellulose particles and metal particles under DC electrical field observed from Figure 4 is shown in Figure 5.
Figure 5. Motion trajectory of cellulose particles (a) and metal particles (b) under DC voltage in mineral oil. ae - As shown in Figure 4 (sample DMCP) a thin fiber bridge was observed after 30 s in mineral oil containing cellulose particles. After that, the thickness of cellulose bridges increased gradually The complete bridge formed until approximately 600 s. Then, notable changes in the cellulose bridge were not seen. For mineral oil contaminated by metal particles, most metal particles sunk down owing to their larger densities. A filamentous bridge formed at about 500 s (Figure 4, sample DMMP) which was so unstable that it migrated back and forth between electrodes, which may be attributed to the impact of the strong electrical field. The ultimate metal bridge appeared until 1200 s. As for mixed particles (Figure 4, sample DMCP), the complete bridge formed more quickly than those for single impurities. Furthermore, it was observed that the complete bridge was densest when the transverse force among thin bridges made up of mixed particles was larger. It can be inferred that the simulation model depicting the changing course of particles aggregation is in agreement with the actual process Thus, the simulation model can accurately describe the impact of impurities on motion as well as on the accumulation characteristics of particles. Different attributes of particles determined the difference in the trajectory. The trajectories of cellulose particles and metal particles under DC electrical field observed from Figure 4 is shown in Figure 5.
ifferent samples under the DC breakdown voltage. With an increase in the concentration of particles, ne Weibull curve moved to the left. Namely, the average breakdown values of samples reduced as the article concentration increased. The relationship between the average breakdown voltages of mineral il containing cellulose particles, metal particles, and mixed particles and the particles concentration re shown in Figure 7. The DC breakdown voltages of oil samples contaminated with metal particles nd mixed particles were found to be lower than those of mineral oil containing cellulose particles. n summary, metal impurities and mixed particles have more significant impacts on the DC breakdown haracteristics of mineral oil: Figure 6. Weibull probability distribution plot of DC breakdown voltage for different samples DMCP (a), DMMP (b) and DMCM (c).
ifferent samples under the DC breakdown voltage. With an increase in the concentration of particles, ne Weibull curve moved to the left. Namely, the average breakdown values of samples reduced as the article concentration increased. The relationship between the average breakdown voltages of mineral il containing cellulose particles, metal particles, and mixed particles and the particles concentration re shown in Figure 7. The DC breakdown voltages of oil samples contaminated with metal particles nd mixed particles were found to be lower than those of mineral oil containing cellulose particles. n summary, metal impurities and mixed particles have more significant impacts on the DC breakdown haracteristics of mineral oil: Figure 6. Weibull probability distribution plot of DC breakdown voltage for different samples DMCP (a), DMMP (b) and DMCM (c).
Figure 7. Average DC breakdown voltage of mineral oil with cellulose or metal particles (a), and mixed particles (b).
Figure 7. Average DC breakdown voltage of mineral oil with cellulose or metal particles (a), and mixed particles (b).
Figure 8. Changes in the current in mineral oil containing different particles under the same DC voltage. decreasing order for mixed particles, metal particles, and cellulose particles. The saturated current in mineral oil containing mixed particles is the largest, almost seven times larger than that of clean oil followed by copper particles (5.5 times) and cellulose particles (2.8 times). As a result, metal particles o1 mixed particles more easily cause insulation oil to partially discharge and even break down. Since the sum of the saturated current of cellulose particles and metal particles is not equal to the saturated current of mixed particles, cellulose particles coupled with metal particles cannot have a superposition effect on the conductivity of oil. There is no doubt that the bridge formation of particles under a DC electrical field can significantly improve the conductivity of mineral oil, which is one of main reasons for the decrease in the breakdown strength of oil. Furthermore, there is a corresponding relation between current and particle aggregation state, which is shown in Figure 9.
Figure 8. Changes in the current in mineral oil containing different particles under the same DC voltage. decreasing order for mixed particles, metal particles, and cellulose particles. The saturated current in mineral oil containing mixed particles is the largest, almost seven times larger than that of clean oil followed by copper particles (5.5 times) and cellulose particles (2.8 times). As a result, metal particles o1 mixed particles more easily cause insulation oil to partially discharge and even break down. Since the sum of the saturated current of cellulose particles and metal particles is not equal to the saturated current of mixed particles, cellulose particles coupled with metal particles cannot have a superposition effect on the conductivity of oil. There is no doubt that the bridge formation of particles under a DC electrical field can significantly improve the conductivity of mineral oil, which is one of main reasons for the decrease in the breakdown strength of oil. Furthermore, there is a corresponding relation between current and particle aggregation state, which is shown in Figure 9.
Figure 9. Relationship between oil conductivity current and particle aggregation.
Figure 9. Relationship between oil conductivity current and particle aggregation.
Figure 10. Particle accumulation patterns under three different initial concentrations for cellulose particles (a), copper particles (b) and mixed particles (c) at 600 s. Then, taking advantage of the effective simulation model shown in Section 3.1, relationships among concentrations, particles properties, and the variation in electrical field strength were analyzed in order to explain the DC breakdown results. Figures 10 and 11 display three dimensional particle accumulation patterns as well as the DC electric field distribution of insulation oil under three different initial concentrations at 600 s. It can be observed that firstly, accumulation degrees increase as the initial concentration increases. Secondly, the range of electrical field distortion caused by particle accumulation is also gradually enlarged.
Figure 10. Particle accumulation patterns under three different initial concentrations for cellulose particles (a), copper particles (b) and mixed particles (c) at 600 s. Then, taking advantage of the effective simulation model shown in Section 3.1, relationships among concentrations, particles properties, and the variation in electrical field strength were analyzed in order to explain the DC breakdown results. Figures 10 and 11 display three dimensional particle accumulation patterns as well as the DC electric field distribution of insulation oil under three different initial concentrations at 600 s. It can be observed that firstly, accumulation degrees increase as the initial concentration increases. Secondly, the range of electrical field distortion caused by particle accumulation is also gradually enlarged.
Figure 12. Ej; qx of mineral oil and natural ester containing different particles under three different initial concentrations at 600 s. Figure 12 shows the influence of the particle concentration on the maximum electrical field strength (Emax) of contaminated mineral oil at 600 s. It can be seen that metal particles almost play a more prominent part in electrical field distortion than cellulose particles. Additionally, the saturated current of metal particles is larger than that for cellulose impurities, so the breakdown voltage of mineral oil polluted by metal particles is smaller than that contaminated by cellulose particles. Figures 10 and 11 also imply that cellulose particles as well as metal particles cannot have a superposition effect on the electric field distortion of insulation oil. For mineral oil contaminated by cellulose or metal particles, Emax increases as the particle concentration increases, which indicates that electrical field distortion combined with the conductivity variation leads to degradation of the insulation strength of mineral oil. As for mineral oil containing mixed particles, though electrical field distortion weakens with an increasing concentration, conductivity obviously increases because of the increasing accumulation degree. Hence, changes in the electrical field distribution together with an increase in conductivity collectively affects the DC breakdown characteristics of mineral oil.
Figure 12. Ej; qx of mineral oil and natural ester containing different particles under three different initial concentrations at 600 s. Figure 12 shows the influence of the particle concentration on the maximum electrical field strength (Emax) of contaminated mineral oil at 600 s. It can be seen that metal particles almost play a more prominent part in electrical field distortion than cellulose particles. Additionally, the saturated current of metal particles is larger than that for cellulose impurities, so the breakdown voltage of mineral oil polluted by metal particles is smaller than that contaminated by cellulose particles. Figures 10 and 11 also imply that cellulose particles as well as metal particles cannot have a superposition effect on the electric field distortion of insulation oil. For mineral oil contaminated by cellulose or metal particles, Emax increases as the particle concentration increases, which indicates that electrical field distortion combined with the conductivity variation leads to degradation of the insulation strength of mineral oil. As for mineral oil containing mixed particles, though electrical field distortion weakens with an increasing concentration, conductivity obviously increases because of the increasing accumulation degree. Hence, changes in the electrical field distribution together with an increase in conductivity collectively affects the DC breakdown characteristics of mineral oil.
Figure 1. Size distribution diagram based on dynamic light scattering measurement of the colloidal magnetic iron oxides nanoparticles (MIONs) in the oil matrix and digital image colloidal nanofluid (colNF) after 2 months of storage (inset).
Figure 1. Size distribution diagram based on dynamic light scattering measurement of the colloidal magnetic iron oxides nanoparticles (MIONs) in the oil matrix and digital image colloidal nanofluid (colNF) after 2 months of storage (inset).
Figure 2. TEM micrograph from the oleate-coated MION colloids.
Figure 2. TEM micrograph from the oleate-coated MION colloids.
Table 1. Breakdown voltage probabilities. According to Table 1, the two nanofluids show differences not only in the mean value of BDV but also in standard deviation. The BDV values of sNF are more scattered at all ranges of concentrations and standard deviation varies from 9.5 kV up to 14.1 kV. The standard deviation of colNF is also large for a nanoparticle concentration of 0.008% or less, but above this value it declines sharply. A 2 85 aaa | LASS thcelamlarltitme AE lett bed Axio Sraltea cn. del Ake A Mlermkal HALA Se. Dantawncne
Table 1. Breakdown voltage probabilities. According to Table 1, the two nanofluids show differences not only in the mean value of BDV but also in standard deviation. The BDV values of sNF are more scattered at all ranges of concentrations and standard deviation varies from 9.5 kV up to 14.1 kV. The standard deviation of colNF is also large for a nanoparticle concentration of 0.008% or less, but above this value it declines sharply. A 2 85 aaa | LASS thcelamlarltitme AE lett bed Axio Sraltea cn. del Ake A Mlermkal HALA Se. Dantawncne
Figure 3. Mean AC breakdown voltage (BDV) versus nanoparticles concentration (colNF and silica NF).
Figure 3. Mean AC breakdown voltage (BDV) versus nanoparticles concentration (colNF and silica NF).
Table 2. Relaxation time of indicative nanoparticles adapted from Hwang et al. [20]. where, €1 and €2 are the permittivity of transformer oil and nanoparticle, respectively and o; and 62 are the conductivities of transformer oil and nanoparticle respectively. Conductive NPs, such as Fe3O,4 or ZnO, have a very small relaxation time of the order of 10-!_10-14 s [20] as can be seen in Table 2. Non-conductive NPs on the other hand have large relaxation times. However, bound charges are formed on their surface due to polarization. Electronic and ionic displacement polarizations are generated very quickly in 10-5 s to 10-2 s. It should be noted that conductive NPs with large dielectric permittivity contain both induced and polarized charges on their surface.
Table 2. Relaxation time of indicative nanoparticles adapted from Hwang et al. [20]. where, €1 and €2 are the permittivity of transformer oil and nanoparticle, respectively and o; and 62 are the conductivities of transformer oil and nanoparticle respectively. Conductive NPs, such as Fe3O,4 or ZnO, have a very small relaxation time of the order of 10-!_10-14 s [20] as can be seen in Table 2. Non-conductive NPs on the other hand have large relaxation times. However, bound charges are formed on their surface due to polarization. Electronic and ionic displacement polarizations are generated very quickly in 10-5 s to 10-2 s. It should be noted that conductive NPs with large dielectric permittivity contain both induced and polarized charges on their surface.
Table 3. Breakdown voltage probabilities. The electric field, Eg, for colNF is calculated as 31.12 x 10° V/m and for sNF as 23.88 x 10° V/m considering that the breakdown voltage for colNF and sNF is 77.8 kV and 59.7 kV, respectively, for a gap of 2.5 mm. Substituting these values of electric field Ey, as well as the values of average nanoparticle diameter R from Table 3, into Equations (4) and (5) for the coIMIONs and SiO) NPs, respectively, their saturation charges are:
Table 3. Breakdown voltage probabilities. The electric field, Eg, for colNF is calculated as 31.12 x 10° V/m and for sNF as 23.88 x 10° V/m considering that the breakdown voltage for colNF and sNF is 77.8 kV and 59.7 kV, respectively, for a gap of 2.5 mm. Substituting these values of electric field Ey, as well as the values of average nanoparticle diameter R from Table 3, into Equations (4) and (5) for the coIMIONs and SiO) NPs, respectively, their saturation charges are:
Figure 4. Potential well distribution of oleate-coated colloidal magnetic iron oxide nanocrystals (colMION) and SiOz nanoparticles versus the distance from the nanoparticle’s surface. Accordingly, substituting the above electric field values Eg into Equations (6) and (7), the potentiz well as a function of the distance from the nanoparticles’ surface before breakdown occurs is given i Figure 4 for both nanoparticles in question.
Figure 4. Potential well distribution of oleate-coated colloidal magnetic iron oxide nanocrystals (colMION) and SiOz nanoparticles versus the distance from the nanoparticle’s surface. Accordingly, substituting the above electric field values Eg into Equations (6) and (7), the potentiz well as a function of the distance from the nanoparticles’ surface before breakdown occurs is given i Figure 4 for both nanoparticles in question.
Figure 5. Dielectric losses (tand) for natural ester oil and colNF 0.012% at 20 °C and 100 °C. The results from dielectric relaxation spectroscopy study for natural ester oil and colNF 0.012% w/w at 20 °C and 100 °C for a frequency range of 10-!-10° Hz are given in Figure 5. Figure 4 shows the difference in the potential well between colIMIONs and sNF and especially near the nanoparticle’s surface. The saturation charges of nanoparticles Equation (8) with respect to the potential well of colMIONs (Figure 4), indicate their higher capability to trap electrons generated from ionization or injection in the bulk of dielectric liquid which can affect the streamer early development. The above is an indication of the better dielectric performance of colNF as compared to sNF which is due to the increased potential well of the colNF.
Figure 5. Dielectric losses (tand) for natural ester oil and colNF 0.012% at 20 °C and 100 °C. The results from dielectric relaxation spectroscopy study for natural ester oil and colNF 0.012% w/w at 20 °C and 100 °C for a frequency range of 10-!-10° Hz are given in Figure 5. Figure 4 shows the difference in the potential well between colIMIONs and sNF and especially near the nanoparticle’s surface. The saturation charges of nanoparticles Equation (8) with respect to the potential well of colMIONs (Figure 4), indicate their higher capability to trap electrons generated from ionization or injection in the bulk of dielectric liquid which can affect the streamer early development. The above is an indication of the better dielectric performance of colNF as compared to sNF which is due to the increased potential well of the colNF.
Table 1. Insulator designs. During the laboratory tests, video and images were recorded with a high-definition camcorder and a still camera to obtain signs of the discharge phenomena in the trunk areas. Unfortunately, the faint discharges were not clearly visible, and they could be observed only using long-time exposure techniques. Simultaneously, a FLIR A325 camera was adopted and fixed on the same tripod of the visual camera in order to achieve a close focal point between the two recordings. IR pictures were recorded using a 1 Hz frame rate to minimize memory storage requirement. The IR camera offers the capability to monitor the temperature at a frequency rate up to 60 Hz and with a precision of 0.5 °C These capabilities are clearly not sufficient to record the instantaneous maximum temperature of the discharge. However, the IR records can show with good precision the maximum temperature of any area of the insulator. The camera does not offer any triggering signal, and only by using the time stamp associated with each IR frame recorded was it possible to synchronize the temperature with all the other data recorded during the test, such as electrical parameters and visual records, with a precision of 1 ms [14].
Table 1. Insulator designs. During the laboratory tests, video and images were recorded with a high-definition camcorder and a still camera to obtain signs of the discharge phenomena in the trunk areas. Unfortunately, the faint discharges were not clearly visible, and they could be observed only using long-time exposure techniques. Simultaneously, a FLIR A325 camera was adopted and fixed on the same tripod of the visual camera in order to achieve a close focal point between the two recordings. IR pictures were recorded using a 1 Hz frame rate to minimize memory storage requirement. The IR camera offers the capability to monitor the temperature at a frequency rate up to 60 Hz and with a precision of 0.5 °C These capabilities are clearly not sufficient to record the instantaneous maximum temperature of the discharge. However, the IR records can show with good precision the maximum temperature of any area of the insulator. The camera does not offer any triggering signal, and only by using the time stamp associated with each IR frame recorded was it possible to synchronize the temperature with all the other data recorded during the test, such as electrical parameters and visual records, with a precision of 1 ms [14].
Figure 1. Schematic diagram of the measurement set-up used in the experiment [15].
Figure 1. Schematic diagram of the measurement set-up used in the experiment [15].
Figure 2. Visual frame before fog application (a), visual frame using long-exposure acquisition (b) and the IR frame (c) during the constant voltage test on sample TT4; equivalent salt deposit density (ESDD) was 0.64 mg/cm? with a fog spray rate of 3 L/h. camera, as shown in Figure 2c. The visual photos were post-processed in order to enhance the spark visibility. A second type of discharge, the streamer discharges, are shown by a red/orange colour crossing an extended area than that of the dry band.
Figure 2. Visual frame before fog application (a), visual frame using long-exposure acquisition (b) and the IR frame (c) during the constant voltage test on sample TT4; equivalent salt deposit density (ESDD) was 0.64 mg/cm? with a fog spray rate of 3 L/h. camera, as shown in Figure 2c. The visual photos were post-processed in order to enhance the spark visibility. A second type of discharge, the streamer discharges, are shown by a red/orange colour crossing an extended area than that of the dry band.
Figure 3. Temperature difference between the insulator surface and the surrounding fog. we «ee A differential temperature between the insulator surface and the surrounding fog along a vertical segment has been calculated for each test. After preliminary tests, using constant voltage, a fixed threshold of 5.5 °C appeared to be a quick identification method. However, if this methodology would be simply applied to the all extended ramp voltage tests the results would be not correct. In fact, a lower extension of dry bands would have been detected, with the temperature profile presented in Figure 3 as example. Moreover, the identification of the dry band is very time consuming if performed by the user by manually examining a significant number of frames and series of tests and this suggested the need for developing an automatic procedure. aa a Se aR” Ca a Ei a
Figure 3. Temperature difference between the insulator surface and the surrounding fog. we «ee A differential temperature between the insulator surface and the surrounding fog along a vertical segment has been calculated for each test. After preliminary tests, using constant voltage, a fixed threshold of 5.5 °C appeared to be a quick identification method. However, if this methodology would be simply applied to the all extended ramp voltage tests the results would be not correct. In fact, a lower extension of dry bands would have been detected, with the temperature profile presented in Figure 3 as example. Moreover, the identification of the dry band is very time consuming if performed by the user by manually examining a significant number of frames and series of tests and this suggested the need for developing an automatic procedure. aa a Se aR” Ca a Ei a
Figure 4. Schematic diagram of the procedure adopted. The precise identification of the insulator location and its perimeter on the thermal frame is a fundamental feature of the proposed analysis. The authors developed a MATLAB procedure to automatically detect the profile boundary of the insulator. This procedure is based on the analysis of the small variations between the ambient air surrounding the insulator and the insulator surface. Since the temperature difference between the insulator and the fog is quite small at the start of each test, the automatic identification is not a trivial task. In addition, possible reflections on the object can cause significant error in the outline identifications. A schematic diagram of the procedure adopted is shown in Figure 4.
Figure 4. Schematic diagram of the procedure adopted. The precise identification of the insulator location and its perimeter on the thermal frame is a fundamental feature of the proposed analysis. The authors developed a MATLAB procedure to automatically detect the profile boundary of the insulator. This procedure is based on the analysis of the small variations between the ambient air surrounding the insulator and the insulator surface. Since the temperature difference between the insulator and the fog is quite small at the start of each test, the automatic identification is not a trivial task. In addition, possible reflections on the object can cause significant error in the outline identifications. A schematic diagram of the procedure adopted is shown in Figure 4.
Figure 5. Automatic boundaries recognition and area selection applied to (a) a conventional and (b) a textured design. of the fog temperature and the hotter area indicating the insulator position within the frame. Once the perimeter is extracted, it is subdivided in two sections, the left- and right-hand boundaries, as can be seen in Figure 4 with the red and blue colours, respectively. Then, they are plotted over the frame for final acceptance by the user. As shown in Figure 5b, the boundaries are not always identified completely, and the user can decide to modify the thresholds or introduce some corrections. However, despite some uncertainty on sheds areas, the areas of interest, the trunks are correctly identified in most cases.
Figure 5. Automatic boundaries recognition and area selection applied to (a) a conventional and (b) a textured design. of the fog temperature and the hotter area indicating the insulator position within the frame. Once the perimeter is extracted, it is subdivided in two sections, the left- and right-hand boundaries, as can be seen in Figure 4 with the red and blue colours, respectively. Then, they are plotted over the frame for final acceptance by the user. As shown in Figure 5b, the boundaries are not always identified completely, and the user can decide to modify the thresholds or introduce some corrections. However, despite some uncertainty on sheds areas, the areas of interest, the trunks are correctly identified in most cases.
ATle POUULEG HlsulatOr PreviOUsly stOlred al laDOratOlry lEMIPEralure 1s Placed UL Ule LOs CrlalllDer WIICLE, as the test begins, the fog cools the insulator surface until the discharge activity heats up the surface. In particular, the temperature of area 5, which is the trunk close to the ground termination, is observed to increase in many tests of the conventional design. The increment of temperature in the graph confirms the presence of a dry band and discharge activity. This trend is not followed for the textured design, indicating no significant activity in this area. The area 1, which is the trunk area close to the high voltage termination, shows no discharge activity for both designs.
ATle POUULEG HlsulatOr PreviOUsly stOlred al laDOratOlry lEMIPEralure 1s Placed UL Ule LOs CrlalllDer WIICLE, as the test begins, the fog cools the insulator surface until the discharge activity heats up the surface. In particular, the temperature of area 5, which is the trunk close to the ground termination, is observed to increase in many tests of the conventional design. The increment of temperature in the graph confirms the presence of a dry band and discharge activity. This trend is not followed for the textured design, indicating no significant activity in this area. The area 1, which is the trunk area close to the high voltage termination, shows no discharge activity for both designs.
Figure 7. Average temperature of right and left trunk areas during the whole test.
Figure 7. Average temperature of right and left trunk areas during the whole test.
Figure 8. Cumulative dry-band extension on all the trunks. Ramp-test: Design CONV, ESDD = 0.64 mg/cm, and a fog rate of 3 L/hr.
Figure 8. Cumulative dry-band extension on all the trunks. Ramp-test: Design CONV, ESDD = 0.64 mg/cm, and a fog rate of 3 L/hr.
Figure 9. Dry-band extension as function of time and dry-band temperature range for the (a) conventional design and (b) textured TT4 insulator examples.
Figure 9. Dry-band extension as function of time and dry-band temperature range for the (a) conventional design and (b) textured TT4 insulator examples.
earlier than textured insulators. As early as after 1 min, the conventional (CONV) samples start to develop dry bands which continue to extend with increasing applied voltage. This trend is significantly delayed on textured (TT) samples, where the total dry-band length starts to be significant only afte1 4 min. The curves before flashover shows different trends. In fact, the dry-band dimensions on the TT¢ design increases sharply, whereas for TT4 and TTS4 a delayed increase and a lower maximum width is observed before the flashover event. If the analysis was limited to only flashover voltage levels the test results would not have highlighted any other details such as the clearly visible differences ir this graph [10]. This suggests that the new procedure can offer a valuable tool to analyse and compare insulator performance under pollution. Figure 10. Comparison of the dry-band extension on all the trunks for the five designs, with ESDD = 0.64 mg/cm, and a fog spray rate of 3 L/h.
earlier than textured insulators. As early as after 1 min, the conventional (CONV) samples start to develop dry bands which continue to extend with increasing applied voltage. This trend is significantly delayed on textured (TT) samples, where the total dry-band length starts to be significant only afte1 4 min. The curves before flashover shows different trends. In fact, the dry-band dimensions on the TT¢ design increases sharply, whereas for TT4 and TTS4 a delayed increase and a lower maximum width is observed before the flashover event. If the analysis was limited to only flashover voltage levels the test results would not have highlighted any other details such as the clearly visible differences ir this graph [10]. This suggests that the new procedure can offer a valuable tool to analyse and compare insulator performance under pollution. Figure 10. Comparison of the dry-band extension on all the trunks for the five designs, with ESDD = 0.64 mg/cm, and a fog spray rate of 3 L/h.
Figure A1. Average temperature of the main trunk areas during the whole test (left and right zones). Design CONV, ESDD = 0.42 mg/cm, and a fog rate of 3 L/hr. Appendix A shows an example of ramp test performed on insulator design CONV, with applied pollution of ESDD 0.42 mg/cm? and a fog rate 3 L/hr. Figures Al and A2 shows the average temperature of the main trunk and top and lower trunk areas during the whole test respectively. Figure A3 shows the total dry-band length computed for the same selected test. Figure A4 shows the dry-band development on each trunk as a maximum temperature profile on a 3D plot versus time and vertical axis position.
Figure A1. Average temperature of the main trunk areas during the whole test (left and right zones). Design CONV, ESDD = 0.42 mg/cm, and a fog rate of 3 L/hr. Appendix A shows an example of ramp test performed on insulator design CONV, with applied pollution of ESDD 0.42 mg/cm? and a fog rate 3 L/hr. Figures Al and A2 shows the average temperature of the main trunk and top and lower trunk areas during the whole test respectively. Figure A3 shows the total dry-band length computed for the same selected test. Figure A4 shows the dry-band development on each trunk as a maximum temperature profile on a 3D plot versus time and vertical axis position.
Figure A2. Average temperature of top and lower trunk areas during the whole test (left and right zones). Design CONV, ESDD = 0.42 mg/cm?, and a fog rate of 3 L/hr.
Figure A2. Average temperature of top and lower trunk areas during the whole test (left and right zones). Design CONV, ESDD = 0.42 mg/cm?, and a fog rate of 3 L/hr.
Figure A3. Total dry-band length. Ramp-test: Design CONV, ESDD = 0.42 meg/cm?, and a fog rate of 3 L/hr.
Figure A3. Total dry-band length. Ramp-test: Design CONV, ESDD = 0.42 meg/cm?, and a fog rate of 3 L/hr.
Figure A4. 3D representation of dry-band development on each trunk. Ramp-test: Design CONV ESDD = 0.42 mg/cm, and a fog rate of 3 L/hr.
Figure A4. 3D representation of dry-band development on each trunk. Ramp-test: Design CONV ESDD = 0.42 mg/cm, and a fog rate of 3 L/hr.
Figure 1. Experimental arrangement of typical vegetation combustion and measurement. It is necessary to obtain the statistical law of the shape and size of vegetation combustion particles for simulation. The heat release rate and temperature distribution of vegetation combustion also need to be measured. The experimental arrangement of typical vegetation combustion and measurement is shown in Figure 1. The vegetation is placed on a plate electrode. A weight sensor is placed below the plate electrode to measure the rate of vegetation mass loss during combustion. Then the heat release rate can be calculated by combining the burning calorific value of different vegetation. The varied process of flame shape and height change is photographed and recorded, combined with a digital camera and ruler. An infrared thermal imager can be used to photograph the temperature distribution of the whole flame. At the same time, the thermocouple array can record the temperature values at different heights in the flame. Rod electrodes are suspended directly above the vegetation and applied with DC voltage.
Figure 1. Experimental arrangement of typical vegetation combustion and measurement. It is necessary to obtain the statistical law of the shape and size of vegetation combustion particles for simulation. The heat release rate and temperature distribution of vegetation combustion also need to be measured. The experimental arrangement of typical vegetation combustion and measurement is shown in Figure 1. The vegetation is placed on a plate electrode. A weight sensor is placed below the plate electrode to measure the rate of vegetation mass loss during combustion. Then the heat release rate can be calculated by combining the burning calorific value of different vegetation. The varied process of flame shape and height change is photographed and recorded, combined with a digital camera and ruler. An infrared thermal imager can be used to photograph the temperature distribution of the whole flame. At the same time, the thermocouple array can record the temperature values at different heights in the flame. Rod electrodes are suspended directly above the vegetation and applied with DC voltage.
Figure 2. Arrangement of typical vegetation. The arrangement of the wooden crib is simple and repeatable. Most of the previous studies for reakdown characteristics of clearance under flame conditions use this wooden crib. However, due to he difference of component content, the combustion effect of branches and leaves is quite different rom that of the wooden crib. It shows that the breakdown voltage of clearance under the branch nd leaf combustion is significantly lower than that of a wooden stack. Therefore, reed, straw and fir ranches were selected as three typical plants to cause the trip of transmission lines due to a vegetation ire. At the same time, the wooden crib test was carried out as a comparison. As shown in Figure 2, ne vegetation or wooden crib is arranged in a square stack of 21 cm x 21 cm x 10 cm. In order to ensure he same burning intensity each time, the typical vegetation was assigned with the same quality in epeated experiments. Typical vegetation is exposed to the sun for several days before the experiment ) ensure dryness, as in nature. The effect of different moisture content on combustion is avoided.
Figure 2. Arrangement of typical vegetation. The arrangement of the wooden crib is simple and repeatable. Most of the previous studies for reakdown characteristics of clearance under flame conditions use this wooden crib. However, due to he difference of component content, the combustion effect of branches and leaves is quite different rom that of the wooden crib. It shows that the breakdown voltage of clearance under the branch nd leaf combustion is significantly lower than that of a wooden stack. Therefore, reed, straw and fir ranches were selected as three typical plants to cause the trip of transmission lines due to a vegetation ire. At the same time, the wooden crib test was carried out as a comparison. As shown in Figure 2, ne vegetation or wooden crib is arranged in a square stack of 21 cm x 21 cm x 10 cm. In order to ensure he same burning intensity each time, the typical vegetation was assigned with the same quality in epeated experiments. Typical vegetation is exposed to the sun for several days before the experiment ) ensure dryness, as in nature. The effect of different moisture content on combustion is avoided.
Figure 3. Comparison of flame temperature distribution between the wooden crib and straw Temperature variations at different heights on the axis of each planting flame are obtained by temperature sensors. The burning time of the wooden crib is the longest, being about 14 min. After ignition, the temperature of each thermocouple is recorded every minute. The burning time of reed, straw and fir branches is relatively short, so the thermocouple readings are recorded every 10s after ignition. For instance, comparison of the flame temperature distribution between the wooden crib and straw is shown in Figure 3. With the increase of flame, the temperature increases gradually. When the maximum fire is reached, the combustion will remain stable for a period of time, and the temperature will reach the maximum. The maximum flame temperature of wood is 747 °C, while that of straw is 518 °C. The maximum temperatures of reed and fir branches are 306 °C and 273 °C, respectively. According to vegetation combustion, the gap can be divided into a continuous area, an oscillating area and a smoky area. The continuous area is about 0~30 cm above the vegetation. The highest temperature is found in the continuous flame area about 15 cm above the wood. The height of the oscillating area is about 30~55 cm. In the oscillating area, the flame will oscillate up and down, and the flame does not always exist. The smoky area is filled with particles and smoke generated by combustion, and the temperature is low.
Figure 3. Comparison of flame temperature distribution between the wooden crib and straw Temperature variations at different heights on the axis of each planting flame are obtained by temperature sensors. The burning time of the wooden crib is the longest, being about 14 min. After ignition, the temperature of each thermocouple is recorded every minute. The burning time of reed, straw and fir branches is relatively short, so the thermocouple readings are recorded every 10s after ignition. For instance, comparison of the flame temperature distribution between the wooden crib and straw is shown in Figure 3. With the increase of flame, the temperature increases gradually. When the maximum fire is reached, the combustion will remain stable for a period of time, and the temperature will reach the maximum. The maximum flame temperature of wood is 747 °C, while that of straw is 518 °C. The maximum temperatures of reed and fir branches are 306 °C and 273 °C, respectively. According to vegetation combustion, the gap can be divided into a continuous area, an oscillating area and a smoky area. The continuous area is about 0~30 cm above the vegetation. The highest temperature is found in the continuous flame area about 15 cm above the wood. The height of the oscillating area is about 30~55 cm. In the oscillating area, the flame will oscillate up and down, and the flame does not always exist. The smoky area is filled with particles and smoke generated by combustion, and the temperature is low.
Figure 4. The stable combustion flames of four combustible materials. LL LIICGOULOIIICILE LCOULLS OLLUVV Lilcit CLIC LICGL OMS GEM do ut ov a ce aaa VVitiL LILO ERA eR The stable combustion flames of the four combustible materials are shown in Figure 4. The smoke concentration produced during combustion is small. Because the burning material has been exposed to the sun for a week, the water content is low, and the burning is sufficient. The combustion products of vegetation in the experiment mainly consist of carbon black particles of micron magnitude and ashes of large size. A differential motion particle size meter (DMPS) was used to analyze the size of these carbon black particles. The particle size of carbon black is about 0.02-0.05 um. These carbon black particles will aggregate into spherical or chain-like particles with a size of about 10-300 um. For instance, the size of aggregated carbon black particles produced by the wooden crib combustion is from 0.01 um to more than 43 um. The two peaks of the contents of different sizes are 0.3 um and 43 um, respectively. These carbon black particles are charged, and may be adsorbed onto large size ashes. They further distort the space electric field and lead to trigger discharge.
Figure 4. The stable combustion flames of four combustible materials. LL LIICGOULOIIICILE LCOULLS OLLUVV Lilcit CLIC LICGL OMS GEM do ut ov a ce aaa VVitiL LILO ERA eR The stable combustion flames of the four combustible materials are shown in Figure 4. The smoke concentration produced during combustion is small. Because the burning material has been exposed to the sun for a week, the water content is low, and the burning is sufficient. The combustion products of vegetation in the experiment mainly consist of carbon black particles of micron magnitude and ashes of large size. A differential motion particle size meter (DMPS) was used to analyze the size of these carbon black particles. The particle size of carbon black is about 0.02-0.05 um. These carbon black particles will aggregate into spherical or chain-like particles with a size of about 10-300 um. For instance, the size of aggregated carbon black particles produced by the wooden crib combustion is from 0.01 um to more than 43 um. The two peaks of the contents of different sizes are 0.3 um and 43 um, respectively. These carbon black particles are charged, and may be adsorbed onto large size ashes. They further distort the space electric field and lead to trigger discharge.
Figure 5. Typical ashes of four kinds of combustions. 3. Simulation Mechanism and Model Establishment The generation of charged particles in a vegetation fire mainly includes chemical reaction, collision ionization, thermal dissociation, etc. The main component of vegetation is cellulose, which is similar to hydrocarbons. The process of generating electrons and ions in the reaction of hydrocarbons is shown in Formula (1) [9]. During combustion, alkali metal and alkaline-earth metal salts can react with the combustion byproduct CO to produce electrons and CO, such as in Formula (2). Flame is a kind of plasma (ionized gas). The ion concentration in the reaction zone of mixed hydrocarbon and air flame is 10°-10!2/cm3, and the typical ion concentration of flame is 10!°/cm>.
Figure 5. Typical ashes of four kinds of combustions. 3. Simulation Mechanism and Model Establishment The generation of charged particles in a vegetation fire mainly includes chemical reaction, collision ionization, thermal dissociation, etc. The main component of vegetation is cellulose, which is similar to hydrocarbons. The process of generating electrons and ions in the reaction of hydrocarbons is shown in Formula (1) [9]. During combustion, alkali metal and alkaline-earth metal salts can react with the combustion byproduct CO to produce electrons and CO, such as in Formula (2). Flame is a kind of plasma (ionized gas). The ion concentration in the reaction zone of mixed hydrocarbon and air flame is 10°-10!2/cm3, and the typical ion concentration of flame is 10!°/cm>.
Figure 6. Equivalent Model of the Vegetation Flame Gap under Direct Current (DC) Voltage.
Figure 6. Equivalent Model of the Vegetation Flame Gap under Direct Current (DC) Voltage.
The flow chart of the multi-physical field coupling analysis is shown in Figure 7. Firstly, the temperature field and fluid field are strongly coupled and simulated according to the heat release rate obtained from the experiment. The simulation model is improved by comparing it with the temperature distribution. Then, according to the statistical data of combustion particle size, the charge of particles is set. The maximum charge of particles does not exceed the saturated charge. Finally, the coupling simulation of particle motion, fluid field and electric field is carried out. The forces on particles and movement of the particles are simulated and analyzed. Figure 7. Flow chart of the multi-physical field coupling simulation.
The flow chart of the multi-physical field coupling analysis is shown in Figure 7. Firstly, the temperature field and fluid field are strongly coupled and simulated according to the heat release rate obtained from the experiment. The simulation model is improved by comparing it with the temperature distribution. Then, according to the statistical data of combustion particle size, the charge of particles is set. The maximum charge of particles does not exceed the saturated charge. Finally, the coupling simulation of particle motion, fluid field and electric field is carried out. The forces on particles and movement of the particles are simulated and analyzed. Figure 7. Flow chart of the multi-physical field coupling simulation.
Table 1. Comparison of temperature data between experiment and simulation. 4.2. Analysis of Force and Motion Characteristics of Combustion Particles
Table 1. Comparison of temperature data between experiment and simulation. 4.2. Analysis of Force and Motion Characteristics of Combustion Particles
Figure 8. Coupled simulation results of temperature and fluid field in straw combustion. For instance, when straw burns steadily, the heat release rate is set at 15.93 kJ/s. The heat release rate is applied to the vegetation area and the equivalent flame area, correspondingly. By adjusting the equivalent flame area, the temperature distribution is closer to the experimental situation. The flame will oscillate in the process of steady combustion. The simulation results are shown in Figure 8.
Figure 8. Coupled simulation results of temperature and fluid field in straw combustion. For instance, when straw burns steadily, the heat release rate is set at 15.93 kJ/s. The heat release rate is applied to the vegetation area and the equivalent flame area, correspondingly. By adjusting the equivalent flame area, the temperature distribution is closer to the experimental situation. The flame will oscillate in the process of steady combustion. The simulation results are shown in Figure 8.
Figure 9. The overall trajectory of the combustion particles. particles is the same as that of the electrode, the particles are mainly affected by the drag force of the fluid in the initial drift stage.
Figure 9. The overall trajectory of the combustion particles. particles is the same as that of the electrode, the particles are mainly affected by the drag force of the fluid in the initial drift stage.
When the particle size is large, the distance between the particle and the center has little effect on the drag force.
When the particle size is large, the distance between the particle and the center has little effect on the drag force.
Figure 10. Force analysis of combustion particles. As shown in Figure 12a, the particles are easily adsorbed by electrodes when the charge of particles is large. Although the drag force decreases with the distance from the electrode, the electric field force decreases more. The farther away from the electrode, the harder the charge is to be absorbed. As shown in Figure 12b, the farther away from the electrode, the larger the critical charge-mass ratio
Figure 10. Force analysis of combustion particles. As shown in Figure 12a, the particles are easily adsorbed by electrodes when the charge of particles is large. Although the drag force decreases with the distance from the electrode, the electric field force decreases more. The farther away from the electrode, the harder the charge is to be absorbed. As shown in Figure 12b, the farther away from the electrode, the larger the critical charge-mass ratio
Figure 12. Force analysis of particles under different polarities. required for particles to be adsorbed by the electrode, and the critical charge-mass ratio decreases with the increase of particle size. Under the same charge-mass ratio, larger particles are easier to be adsorbed by the electrode. 5. Conclusions
Figure 12. Force analysis of particles under different polarities. required for particles to be adsorbed by the electrode, and the critical charge-mass ratio decreases with the increase of particle size. Under the same charge-mass ratio, larger particles are easier to be adsorbed by the electrode. 5. Conclusions
Figure 1. Uniform transmission line representation. Vg and V, are the voltages of the sending and receiving node, and Ip and I; are the injected currents at the sending and receiving node, respectively, and L is the line’s length. In Equation (2) Zo, Yo, Z, Y, and L are the line’s characteristic impedance, characteristic admittance, series impedance, shunt admittance and length, respectively. Additionally, the Laplace variable is defined as s = c + jw, where w is given by 2rf. By changing the direction of I, in Figure 1, Equation (1) is modified in the following manner:
Figure 1. Uniform transmission line representation. Vg and V, are the voltages of the sending and receiving node, and Ip and I; are the injected currents at the sending and receiving node, respectively, and L is the line’s length. In Equation (2) Zo, Yo, Z, Y, and L are the line’s characteristic impedance, characteristic admittance, series impedance, shunt admittance and length, respectively. Additionally, the Laplace variable is defined as s = c + jw, where w is given by 2rf. By changing the direction of I, in Figure 1, Equation (1) is modified in the following manner:
Matrix ® in Equation (4) is the chain matrix of the transmission line. Due to the fact that the currents at both ends of the line have the same direction, multiple transmission lines can be cascade-connected by using their corresponding chain matrices, as it can be seen in Figure 2.
Matrix ® in Equation (4) is the chain matrix of the transmission line. Due to the fact that the currents at both ends of the line have the same direction, multiple transmission lines can be cascade-connected by using their corresponding chain matrices, as it can be seen in Figure 2.
Figure 2. Cascaded connection of chain matrices, where ®,, V,,, and I, are the chain matrix, sending voltage, and sending current of the n-th cascade-connected line, respectively.
Figure 2. Cascaded connection of chain matrices, where ®,, V,,, and I, are the chain matrix, sending voltage, and sending current of the n-th cascade-connected line, respectively.
Equation (6) can be used to compute the voltage and current profiles along a nonuniform transmission line. The transient profiles are computed in a sequential manner, obtaining the voltage and current at the end of the first line segment from the chain matrix and from the voltages and currents at the beginning of the same segment; this process is repeated until the voltage and current along the whole line have been computed. It can also be observed in Equation (6) that Vo and Ip are required as initial values of the algorithm; in order to compute such values, a two-port admittance representation of the complete transmission line from the chain matrix ®f, is defined as: Figure 2 can also be interpreted as one transmission line subdivided into several smaller line segments, where each segment is represented by a unique chain matrix with its own independent electrical properties. Using this approach, it is possible to build a transmission line model that includes nonuniformities. With this consideration in mind, it can be deduced from Figure 2 that the voltage and current at the beginning of each line segment and the chain matrix of the same segment can be used to compute the voltage and current of the next segment:
Equation (6) can be used to compute the voltage and current profiles along a nonuniform transmission line. The transient profiles are computed in a sequential manner, obtaining the voltage and current at the end of the first line segment from the chain matrix and from the voltages and currents at the beginning of the same segment; this process is repeated until the voltage and current along the whole line have been computed. It can also be observed in Equation (6) that Vo and Ip are required as initial values of the algorithm; in order to compute such values, a two-port admittance representation of the complete transmission line from the chain matrix ®f, is defined as: Figure 2 can also be interpreted as one transmission line subdivided into several smaller line segments, where each segment is represented by a unique chain matrix with its own independent electrical properties. Using this approach, it is possible to build a transmission line model that includes nonuniformities. With this consideration in mind, it can be deduced from Figure 2 that the voltage and current at the beginning of each line segment and the chain matrix of the same segment can be used to compute the voltage and current of the next segment:
Figure 3. (a) Transmission line before the closing operation of a switch connected at the sending node. (b) Transmission line after the closing operation of a switch connected at the sending node. and can be obtained from the following expression [11]: In Equation (12), Ybusg is the nodal admittance matrix before the switch closing (Figure 3a), Ybus, is the admittance matrix modified by the closing operation (Figure 3b), INo contains the initially injected currents, and In is the injection current vector due to the switch operation. An example of the construction of the nodal admittance matrices Ybusg and Ybus for the transmission line in Figure 3 is presented below:
Figure 3. (a) Transmission line before the closing operation of a switch connected at the sending node. (b) Transmission line after the closing operation of a switch connected at the sending node. and can be obtained from the following expression [11]: In Equation (12), Ybusg is the nodal admittance matrix before the switch closing (Figure 3a), Ybus, is the admittance matrix modified by the closing operation (Figure 3b), INo contains the initially injected currents, and In is the injection current vector due to the switch operation. An example of the construction of the nodal admittance matrices Ybusg and Ybus for the transmission line in Figure 3 is presented below:
Figure 4. Five-segment piece-wise approximation of a nonlinear v-i characteristic curve [11]. The element R,, of the n-th linear element from Figure 4 and the voltage V;, are computed as follows:
Figure 4. Five-segment piece-wise approximation of a nonlinear v-i characteristic curve [11]. The element R,, of the n-th linear element from Figure 4 and the voltage V;, are computed as follows:
Figure 5. Circuital representation of the piecewise approximation for the characteristic curve of a nonlinear element presented in Figure 5 [11]. In the circuit presented in Figure 5, the switch in the n-th branch operates according to the reference voltage; it closes when the voltage across nodes j and k goes above Vrefin and it opens when the voltage drops below V,,4,. It is important to mention that the switches must operate in a successive manner,
Figure 5. Circuital representation of the piecewise approximation for the characteristic curve of a nonlinear element presented in Figure 5 [11]. In the circuit presented in Figure 5, the switch in the n-th branch operates according to the reference voltage; it closes when the voltage across nodes j and k goes above Vrefin and it opens when the voltage drops below V,,4,. It is important to mention that the switches must operate in a successive manner,
Figure 6. Three-phase non-uniform transmission line used in the example in Section 3.1. A second-degree polynomial equation was utilized to approximate the conductors’ height, as presented in [23]. There was a 10 m separation between the conductors.
Figure 6. Three-phase non-uniform transmission line used in the example in Section 3.1. A second-degree polynomial equation was utilized to approximate the conductors’ height, as presented in [23]. There was a 10 m separation between the conductors.
Figure 7. Computed voltage profile along phase A (example 3.1). Additionally, a comparison at the middle of the line between the transient voltage waveforms obtained with the proposed method and results from ATP simulations is presented (Figure 8). The simulations performed with ATP required a time step 10 times smaller than the proposed method to achieve similar results.
Figure 7. Computed voltage profile along phase A (example 3.1). Additionally, a comparison at the middle of the line between the transient voltage waveforms obtained with the proposed method and results from ATP simulations is presented (Figure 8). The simulations performed with ATP required a time step 10 times smaller than the proposed method to achieve similar results.
Figure 8. Comparison of transient voltage waveforms at two specific distances between the computed results with the proposed method (solid lines) and results obtained with ATP simulations (dashed lines). The solid blue and dashed red lines correspond to voltage measurements at 150 m from the sending node; the solid green and the dashed orange lines were obtained at 450 m. The oscillations observed in the results from the ATP simulations are attributed to the error accumulation due to the discretization of the transmission line [2].
Figure 8. Comparison of transient voltage waveforms at two specific distances between the computed results with the proposed method (solid lines) and results obtained with ATP simulations (dashed lines). The solid blue and dashed red lines correspond to voltage measurements at 150 m from the sending node; the solid green and the dashed orange lines were obtained at 450 m. The oscillations observed in the results from the ATP simulations are attributed to the error accumulation due to the discretization of the transmission line [2].
Figure 9. Comparison of transient voltage waveforms at the middle point of the line computed with different numbers of chain matrices. The curve computed with 20 chain matrices is not as smooth as the ones computed with 40 and 80.
Figure 9. Comparison of transient voltage waveforms at the middle point of the line computed with different numbers of chain matrices. The curve computed with 20 chain matrices is not as smooth as the ones computed with 40 and 80.
Figure 10. Voltage profile computed along phase A (example 3.2).
Figure 10. Voltage profile computed along phase A (example 3.2).
Figure 11. Transient voltage profile along phase B in example 3.2. The complete voltage profile induced in phase B due to the energization of phase A can be observed. This type of detailed information cannot be easily achieved using ATP-like simulation software.
Figure 11. Transient voltage profile along phase B in example 3.2. The complete voltage profile induced in phase B due to the energization of phase A can be observed. This type of detailed information cannot be easily achieved using ATP-like simulation software.
Figure 12. Comparison between the transient voltage computed with the proposed method (blue and green lines) and those obtained with ATP simulations (red and orange lines) in example 3.2. The comparisons are made at the middle of the transmission line (2500 m from the sending node) in phases A and B. A good level of agreement can be observed, but the ATP simulations needed a time step 50 times smaller than the proposed method in order to achieve such results.
Figure 12. Comparison between the transient voltage computed with the proposed method (blue and green lines) and those obtained with ATP simulations (red and orange lines) in example 3.2. The comparisons are made at the middle of the transmission line (2500 m from the sending node) in phases A and B. A good level of agreement can be observed, but the ATP simulations needed a time step 50 times smaller than the proposed method in order to achieve such results.
Table 1. Nonlinear v-i characteristic of the arresters [27].
Table 1. Nonlinear v-i characteristic of the arresters [27].
Figure 13. Computed transient voltage profile along phase A when there were no surge arresters connected at the receiving end of the line (example 3.3). First, a simulation was performed without surge arresters connected to the line. Figure 13 presents the transient voltage profile along phase A computed in this simulation. On the other hand, Figure 14 shows the voltage profile along phase A when the arresters were connected at the receiving node of the line. By comparing Figures 13 and 14, the influence that the surge arresters’ operation had on the magnitude of the voltages along the line is easily observed. The voltage along the line in Figure 14 was considerably lower in comparison with the transient profile in Figure 13. Additionally, a comparison is presented with results obtained from ATP simulations (Figure 15). In a similar way to the example in Section 3.1, the time step required by ATP was 10 times smaller than the proposed method in order to obtain similar results.
Figure 13. Computed transient voltage profile along phase A when there were no surge arresters connected at the receiving end of the line (example 3.3). First, a simulation was performed without surge arresters connected to the line. Figure 13 presents the transient voltage profile along phase A computed in this simulation. On the other hand, Figure 14 shows the voltage profile along phase A when the arresters were connected at the receiving node of the line. By comparing Figures 13 and 14, the influence that the surge arresters’ operation had on the magnitude of the voltages along the line is easily observed. The voltage along the line in Figure 14 was considerably lower in comparison with the transient profile in Figure 13. Additionally, a comparison is presented with results obtained from ATP simulations (Figure 15). In a similar way to the example in Section 3.1, the time step required by ATP was 10 times smaller than the proposed method in order to obtain similar results.
Figure 14. Computed transient voltage profile along phase A with surge arresters connected at the receiving node (example 3.3). The voltage magnitude significantly decreased along the transmission line compared to the transient profile presented in Figure 13.
Figure 14. Computed transient voltage profile along phase A with surge arresters connected at the receiving node (example 3.3). The voltage magnitude significantly decreased along the transmission line compared to the transient profile presented in Figure 13.
Table 2. Mean relative difference of transient voltage in example 3.1.
Table 2. Mean relative difference of transient voltage in example 3.1.
Figure 15. Voltage comparison between the results from the proposed method (solid lines) and those obtained from ATP simulations (dashed lines) for example 3.3. The comparisons were made at the middle point of the line (300 m from the sending node) for phases A, B, and C.
Figure 15. Voltage comparison between the results from the proposed method (solid lines) and those obtained from ATP simulations (dashed lines) for example 3.3. The comparisons were made at the middle point of the line (300 m from the sending node) for phases A, B, and C.
Table 3. Mean relative difference of transient voltage in example 3.2. Table 4. Mean relative difference of transient voltage in example 3.3.
Table 3. Mean relative difference of transient voltage in example 3.2. Table 4. Mean relative difference of transient voltage in example 3.3.
5. Conclusions
5. Conclusions
Figure 1. Per unit length equivalent transmission line circuit with corona. The line model used to simulate the propagation of the corona current along a multiconductor transmission line is derived from the per unit length equivalent circuit for a Az section, presented in Figure 1. The transmission line is considered to be infinitely long with uniform corona current density injections per unit length (J).
Figure 1. Per unit length equivalent transmission line circuit with corona. The line model used to simulate the propagation of the corona current along a multiconductor transmission line is derived from the per unit length equivalent circuit for a Az section, presented in Figure 1. The transmission line is considered to be infinitely long with uniform corona current density injections per unit length (J).
Table 1. Data of the high voltage direct current (HVDC) test line considered in the calculations. The RI levels are given in dB with 1 1V/m as base magnitude. The profiles are plotted 80 m from each side of the center of the tower at 1.5 m above ground level. The altitude correction factor fo! HVDC lines proposed in [16] was applied. In this section, the RI values produced by an HVDC test line of +800 kV are computed using the method described in the previous section. Then, the computed values are compared with measurement: reported in [14,15]. This test line is located in the National Engineering Laboratory for UHV Technology in Kunming, China, with an altitude of 2100 m. The length of the test line is 800 m and the terminal: are open ends. The measurement system consists of radio receivers connected to loop antennas with z height of 1.5 m and bandwidth of 9 kHz-30 MHz. Additionally, two wave trappers were installed between generators and the test line in order to suppress RI noises. The measuring frequency was 0.5 MHz and the measurements were made under good weather in fall. The measured RI levels are represented by quasi-peak values (QP). The data of the test line considered in the calculations are presented in Table 1. HVDC lines proposed in [16] was applied. In Figure 2, both measured and computed RI profiles are shown. The position zero of the horizontal axis corresponds to the center of the tower and the positive direction is towards the positive pole. It can be seen that the computed RI values are in good agreement with the measurements principally for the measurements made on the direction of the positive pole. The maximum measured RI value is 66.3 dB while the maximum computed RI value is 65.03 dB, corresponding to a difference of 1.27 dB. Also, it can be observed the asymmetric shape of the profiles that confirms the assumption of the positive pole as the source of RI [9]. The biggest differences between measured and computed values (3-4 dB) appeared for distances longer than 60 m in the direction of the negative pole.
Table 1. Data of the high voltage direct current (HVDC) test line considered in the calculations. The RI levels are given in dB with 1 1V/m as base magnitude. The profiles are plotted 80 m from each side of the center of the tower at 1.5 m above ground level. The altitude correction factor fo! HVDC lines proposed in [16] was applied. In this section, the RI values produced by an HVDC test line of +800 kV are computed using the method described in the previous section. Then, the computed values are compared with measurement: reported in [14,15]. This test line is located in the National Engineering Laboratory for UHV Technology in Kunming, China, with an altitude of 2100 m. The length of the test line is 800 m and the terminal: are open ends. The measurement system consists of radio receivers connected to loop antennas with z height of 1.5 m and bandwidth of 9 kHz-30 MHz. Additionally, two wave trappers were installed between generators and the test line in order to suppress RI noises. The measuring frequency was 0.5 MHz and the measurements were made under good weather in fall. The measured RI levels are represented by quasi-peak values (QP). The data of the test line considered in the calculations are presented in Table 1. HVDC lines proposed in [16] was applied. In Figure 2, both measured and computed RI profiles are shown. The position zero of the horizontal axis corresponds to the center of the tower and the positive direction is towards the positive pole. It can be seen that the computed RI values are in good agreement with the measurements principally for the measurements made on the direction of the positive pole. The maximum measured RI value is 66.3 dB while the maximum computed RI value is 65.03 dB, corresponding to a difference of 1.27 dB. Also, it can be observed the asymmetric shape of the profiles that confirms the assumption of the positive pole as the source of RI [9]. The biggest differences between measured and computed values (3-4 dB) appeared for distances longer than 60 m in the direction of the negative pole.
Figure 2. Comparison of measured [14] and computed radio interference (RI) profiles.
Figure 2. Comparison of measured [14] and computed radio interference (RI) profiles.
Figure 3. Tower geometry of a bipolar HVDC transmission line.
Figure 3. Tower geometry of a bipolar HVDC transmission line.
Table 2. Data of the HVDC lines considered in the simulations. The parameters used for the excitation formula (7) were those corresponding to fair weather condition in summer (Ig = 27, k; = 1.83, and ky = 45.8), which is assumed to be the most critical condition for the generation of radio interference voltages in HVDC lines [5]. In the simulations, ground resistivity was considered with a value of 100 Qm, and the RIV frequency was taken as 0.5 MHz, the frequency that is usually considered in the RI measurements [15,17].
Table 2. Data of the HVDC lines considered in the simulations. The parameters used for the excitation formula (7) were those corresponding to fair weather condition in summer (Ig = 27, k; = 1.83, and ky = 45.8), which is assumed to be the most critical condition for the generation of radio interference voltages in HVDC lines [5]. In the simulations, ground resistivity was considered with a value of 100 Qm, and the RIV frequency was taken as 0.5 MHz, the frequency that is usually considered in the RI measurements [15,17].
Figure 4. RI lateral profiles of the two HVDC transmission lines. As can be seen in Figure 4, the maximum values of RI are placed closer to the positive pole because of the higher amplitude of the positive streamers in comparison with the Trichel pulses in negative polarity. In fact, the streamer pulses from positive corona are considered as the dominant source of the RI in DC transmission lines [9].
Figure 4. RI lateral profiles of the two HVDC transmission lines. As can be seen in Figure 4, the maximum values of RI are placed closer to the positive pole because of the higher amplitude of the positive streamers in comparison with the Trichel pulses in negative polarity. In fact, the streamer pulses from positive corona are considered as the dominant source of the RI in DC transmission lines [9].
Table 3. Results of the calculations for the bipolar HVDC lines. 4.2. Parametric Sweeps In this section, parametric sweeps of five variables that affect the RI levels are presented. Both the RI and the maximum bundle electric field (¢max) are calculated as a function of sub-conductor radius, bundle spacing, and the number of sub-conductors in the bundle and, additionally, the RI levels are also calculated as a function of the soil resistivity and RIV frequency. In the parametric sweeps, the reported RI level was computed considering a measurement point at (x, y) = (23 m, 1.0 m). The previous consideration is taken according to the Canadian Standards Association that specifies tolerable limits for RI in a reference point placed at 15 m from the outermost conductor of the power line [18]. For this case, the reference point is assigned as (23 m, 1.0 m), i.e., 23 m from the center of the tower and 1 m above the ground.
Table 3. Results of the calculations for the bipolar HVDC lines. 4.2. Parametric Sweeps In this section, parametric sweeps of five variables that affect the RI levels are presented. Both the RI and the maximum bundle electric field (¢max) are calculated as a function of sub-conductor radius, bundle spacing, and the number of sub-conductors in the bundle and, additionally, the RI levels are also calculated as a function of the soil resistivity and RIV frequency. In the parametric sweeps, the reported RI level was computed considering a measurement point at (x, y) = (23 m, 1.0 m). The previous consideration is taken according to the Canadian Standards Association that specifies tolerable limits for RI in a reference point placed at 15 m from the outermost conductor of the power line [18]. For this case, the reference point is assigned as (23 m, 1.0 m), i.e., 23 m from the center of the tower and 1 m above the ground.
Figure 5. Parametric sweeps: (a) RI as a function of sub-conductor radius; (b) Maximum bundle electric field (gmax) as a function of sub-conductor radius.
Figure 5. Parametric sweeps: (a) RI as a function of sub-conductor radius; (b) Maximum bundle electric field (gmax) as a function of sub-conductor radius.
Figure 6. Parametric sweeps: (a) RI as a function of bundle spacing; (b) Maximum bundle electric field (Smax) as a function of bundle spacing.
Figure 6. Parametric sweeps: (a) RI as a function of bundle spacing; (b) Maximum bundle electric field (Smax) as a function of bundle spacing.
Figure 7. Parametric sweeps: (a) RI as a function of the number of sub-conductors in the bundle; (b) Maximum bundle electric field (gmax) as a function of the number of sub-conductors in the bundle. Simulation results show that the RI levels go through a minimum value for a certain number of conductors in the bundle (Figure 7a), whereas gmax decreases continuously with the increment in the number of conductors in the bundle (Figure 7b). The lowest RI value for the +500 and +600 kV lines are achieved with five and six sub-conductors in a bundle, respectively. The sensitivity of RI levels to the number of conductors in the bundle is lower around the optimal point in the +600 kV lines, which provides flexibility in the choice of the number of conductors. In fact, the increment in the RI levels—observed when the number of sub-conductors in a bundle is higher than six—can be due to the reference value of ng = 6 used in the excitation function. It is clear that the third term in Equation (7) becomes positive for values of n, greater than 6.
Figure 7. Parametric sweeps: (a) RI as a function of the number of sub-conductors in the bundle; (b) Maximum bundle electric field (gmax) as a function of the number of sub-conductors in the bundle. Simulation results show that the RI levels go through a minimum value for a certain number of conductors in the bundle (Figure 7a), whereas gmax decreases continuously with the increment in the number of conductors in the bundle (Figure 7b). The lowest RI value for the +500 and +600 kV lines are achieved with five and six sub-conductors in a bundle, respectively. The sensitivity of RI levels to the number of conductors in the bundle is lower around the optimal point in the +600 kV lines, which provides flexibility in the choice of the number of conductors. In fact, the increment in the RI levels—observed when the number of sub-conductors in a bundle is higher than six—can be due to the reference value of ng = 6 used in the excitation function. It is clear that the third term in Equation (7) becomes positive for values of n, greater than 6.
Figure 8. RI as a function of the soil resistivity.
Figure 8. RI as a function of the soil resistivity.
Figure 9. RI as a function of the RIV frequency. Finally, the impact of RIV frequency on RI levels is illustrated in Figure 9. It can be seen how the RI values tend to decrease while the measuring frequency increases. This behavior is attributed to the increment in the modal attenuation constants with the frequency. gmax is not a function of the RIV frequency.
Figure 9. RI as a function of the RIV frequency. Finally, the impact of RIV frequency on RI levels is illustrated in Figure 9. It can be seen how the RI values tend to decrease while the measuring frequency increases. This behavior is attributed to the increment in the modal attenuation constants with the frequency. gmax is not a function of the RIV frequency.
Table 4. Genetic algorithm parameters for the MATLAB optimization toolbox. Based on the previous simulations, lower and upper limits are specified for each independent geometric variable. Optimization results are presented together with the variable limits in Tables 5 and 6 for the +500 and +600 kV HVDC lines, respectively.
Table 4. Genetic algorithm parameters for the MATLAB optimization toolbox. Based on the previous simulations, lower and upper limits are specified for each independent geometric variable. Optimization results are presented together with the variable limits in Tables 5 and 6 for the +500 and +600 kV HVDC lines, respectively.
Table 5. Optimal geometric parameters for +500 kV HVDC line. Table 6. Optimal geometric parameters for +600 kV HVDC line.
Table 5. Optimal geometric parameters for +500 kV HVDC line. Table 6. Optimal geometric parameters for +600 kV HVDC line.
According to the optimization results shown in Table 5 for the +500 kV line, increasing the sub-conductor radius from 1.71 to 2.21 cm, reducing the bundle spacing from 45 to 42 cm, and reducing the number of sub-conductors from 4 to 3, the RI value calculated at the reference point (x, y) = (23 m, 1.0 m) is reduced from 53.85 dB with the nominal parameters to 50.23 dB with the optimal parameters. In Figure 10, the comparison of nominal and optimized RI lateral profiles for the +500 kV line is shown. An almost constant reduction of 3.62 dB can be observed along the complete profile. Due to the increment in the sub-conductor radius, the total mass of the bundle increased from 8540 to 10,293 kg/km. The increment of 1753 kg/km should be evaluated from an economical point of view as well as from the strength of the tower to support this new load.
According to the optimization results shown in Table 5 for the +500 kV line, increasing the sub-conductor radius from 1.71 to 2.21 cm, reducing the bundle spacing from 45 to 42 cm, and reducing the number of sub-conductors from 4 to 3, the RI value calculated at the reference point (x, y) = (23 m, 1.0 m) is reduced from 53.85 dB with the nominal parameters to 50.23 dB with the optimal parameters. In Figure 10, the comparison of nominal and optimized RI lateral profiles for the +500 kV line is shown. An almost constant reduction of 3.62 dB can be observed along the complete profile. Due to the increment in the sub-conductor radius, the total mass of the bundle increased from 8540 to 10,293 kg/km. The increment of 1753 kg/km should be evaluated from an economical point of view as well as from the strength of the tower to support this new load.
Figure 10. Comparison of nominal and optimized RI lateral profiles for +500 kV line.
Figure 10. Comparison of nominal and optimized RI lateral profiles for +500 kV line.
Figure 11. Comparison of nominal and optimized RI lateral profiles for +600 kV line. According to the optimization results for the +600 kV line shown in Table 6, by increasing the sub-conductors radius from 1.71 to 2.21 cm, reducing the bundle spacing from 45 to 38 cm, and keeping the number of sub-conductors as 4, the RI value computed at the measuring point was reduced from 61.27 dB for the nominal parameters to 58.88 dB for the optimal parameters. In Figure 11, the comparison of nominal and optimized RI lateral profiles for the +600 kV line is shown. The increment in the sub-conductor radius produces an increment in the total mass of the conductor bundle from 8540 to 13,724 kg/km. Similar to the +500 kV line case, the increment of 5184 kg/km should be evaluated from the economical and mechanical point of view.
Figure 11. Comparison of nominal and optimized RI lateral profiles for +600 kV line. According to the optimization results for the +600 kV line shown in Table 6, by increasing the sub-conductors radius from 1.71 to 2.21 cm, reducing the bundle spacing from 45 to 38 cm, and keeping the number of sub-conductors as 4, the RI value computed at the measuring point was reduced from 61.27 dB for the nominal parameters to 58.88 dB for the optimal parameters. In Figure 11, the comparison of nominal and optimized RI lateral profiles for the +600 kV line is shown. The increment in the sub-conductor radius produces an increment in the total mass of the conductor bundle from 8540 to 13,724 kg/km. Similar to the +500 kV line case, the increment of 5184 kg/km should be evaluated from the economical and mechanical point of view.
As mentioned in the previous section, the aim of the test procedure is to replicate triple junction conditions in the vicinity of a dielectric insulator surface surrounded by a gaseous insulating medium. For that reason, a needle-plane electrode configuration is employed. A two-dimensional illustration along with an actual picture of the electrode configuration, showing the disc-shaped insulator sample under test conditions are shown in Figure 1.
As mentioned in the previous section, the aim of the test procedure is to replicate triple junction conditions in the vicinity of a dielectric insulator surface surrounded by a gaseous insulating medium. For that reason, a needle-plane electrode configuration is employed. A two-dimensional illustration along with an actual picture of the electrode configuration, showing the disc-shaped insulator sample under test conditions are shown in Figure 1.
Figure 2. Finite Element Method (FEM) simulation model: (a) Full geometry including electrodes arrangement and surrounding volume; (b) Three-dimensional equipotential surfaces (isosurfaces) within the half symmetrical volume of the initial geometry. nee a ee ee eee eee eee eee The described design is further examined from the numerical electric field perspective using Finite Element Method (FEM) simulation model. The detailed geometry is transferred to COMSC Multiphysics® through its integrated three-dimensional geometry builder, with some geomet simplifications that can improve significantly the computational time without affecting the quali and reliability of the generated result. As the design is largely symmetrical around the central ax of the entire configuration, only half of the geometry needs to be computationally solved witho affecting the accuracy of the computed results. It is expected that the maximum electric field stress w appear at the needle tip because of its small diameter and short distance from the zero potential pla electrode. Figure 2 shows the simulated full geometry of the test system, as designed within COMSC Multiphysics®, together with a generated illustration of the three-dimensional equipotential surfac (isosurfaces) after solving the simulation model. For the example shown in Figure 2b, the considere insulator sample is made of PTFE with a 4mm thickness; the insulating gaseous medium being air standard atmospheric conditions. The applied voltage is set to 1 V.
Figure 2. Finite Element Method (FEM) simulation model: (a) Full geometry including electrodes arrangement and surrounding volume; (b) Three-dimensional equipotential surfaces (isosurfaces) within the half symmetrical volume of the initial geometry. nee a ee ee eee eee eee eee The described design is further examined from the numerical electric field perspective using Finite Element Method (FEM) simulation model. The detailed geometry is transferred to COMSC Multiphysics® through its integrated three-dimensional geometry builder, with some geomet simplifications that can improve significantly the computational time without affecting the quali and reliability of the generated result. As the design is largely symmetrical around the central ax of the entire configuration, only half of the geometry needs to be computationally solved witho affecting the accuracy of the computed results. It is expected that the maximum electric field stress w appear at the needle tip because of its small diameter and short distance from the zero potential pla electrode. Figure 2 shows the simulated full geometry of the test system, as designed within COMSC Multiphysics®, together with a generated illustration of the three-dimensional equipotential surfac (isosurfaces) after solving the simulation model. For the example shown in Figure 2b, the considere insulator sample is made of PTFE with a 4mm thickness; the insulating gaseous medium being air standard atmospheric conditions. The applied voltage is set to 1 V.
Figure 3. Electric field distribution along insulator surface. Here, 0mm represents the center of the top surface of the insulator sample while +50 mm the edges of it. The presented values are normalised based on the maximum computed value.
Figure 3. Electric field distribution along insulator surface. Here, 0mm represents the center of the top surface of the insulator sample while +50 mm the edges of it. The presented values are normalised based on the maximum computed value.
Figure 4. Experimental set-up for AC voltage application to the needle-plane configuration and insulator samples. Figure 4 summarises the main parts of the experimental configuration used for the purposes of this work. For the AC voltage application, a 50 kV/3.75 kVA transformer is used, which is controlled through an isolating transformer and a voltage regulator with adjustment of the voltage level on the low-voltage side. An RC voltage divider of ratio 3750:1 is used to scale down the generated voltage to safe measurable levels. Voltage is applied to the pressure vessel through a bushing rated up to 39 kV AC rms. As described previously, the electrodes configuration, together with the insulator samples under test, are vertically and horizontally centered inside the cylindrical stainless-steel dull polished chamber. The side apertures are covered with stainless-steel blanking plates, preventing ambient light entering into the pressure vessel.
Figure 4. Experimental set-up for AC voltage application to the needle-plane configuration and insulator samples. Figure 4 summarises the main parts of the experimental configuration used for the purposes of this work. For the AC voltage application, a 50 kV/3.75 kVA transformer is used, which is controlled through an isolating transformer and a voltage regulator with adjustment of the voltage level on the low-voltage side. An RC voltage divider of ratio 3750:1 is used to scale down the generated voltage to safe measurable levels. Voltage is applied to the pressure vessel through a bushing rated up to 39 kV AC rms. As described previously, the electrodes configuration, together with the insulator samples under test, are vertically and horizontally centered inside the cylindrical stainless-steel dull polished chamber. The side apertures are covered with stainless-steel blanking plates, preventing ambient light entering into the pressure vessel.
Figure 5. HFCT enclosure configuration. Two SMA connectors are mounted on the top and bottom of a C101 alloy copper rod. The diameter of this central conductor was calculated based on the 50 O coaxial characteristic impedance principle using Equation (1) [15],
Figure 5. HFCT enclosure configuration. Two SMA connectors are mounted on the top and bottom of a C101 alloy copper rod. The diameter of this central conductor was calculated based on the 50 O coaxial characteristic impedance principle using Equation (1) [15],
Figure 6. S-parameters of the configuration shown in Figure 5, for the frequency range corresponding to the rating of the used HFCT. where, Zo is the characteristic impedance, d; the diameter of the HFCT aperture, dz the diameter of the copper conductor and ¢,;, the relative permittivity of atmospheric air. The entire configuration is enclosed in an EMI/RFI shielded aluminium enclosure. The scattering parameters of the configuration were measured using an R&S® ZVL Vector Network Analyzer (9 kHz — 6 GHz), following a 500 two-port calibration, and the results are presented in Figure 6. As shown, the upper cut-off frequency is measured at 359.46 MHz, which is quite close to the bandwidth rating of the HFCT. The output side is terminated through a short-circuited 20 dB/50 W, DC-8.5 GHz, high-power fixed attenuator, preventing possible reflections reaching the sensing configuration.
Figure 6. S-parameters of the configuration shown in Figure 5, for the frequency range corresponding to the rating of the used HFCT. where, Zo is the characteristic impedance, d; the diameter of the HFCT aperture, dz the diameter of the copper conductor and ¢,;, the relative permittivity of atmospheric air. The entire configuration is enclosed in an EMI/RFI shielded aluminium enclosure. The scattering parameters of the configuration were measured using an R&S® ZVL Vector Network Analyzer (9 kHz — 6 GHz), following a 500 two-port calibration, and the results are presented in Figure 6. As shown, the upper cut-off frequency is measured at 359.46 MHz, which is quite close to the bandwidth rating of the HFCT. The output side is terminated through a short-circuited 20 dB/50 W, DC-8.5 GHz, high-power fixed attenuator, preventing possible reflections reaching the sensing configuration.
Figure 7. Flashover voltage (FOV) test results for six different insulator samples in dry air, nitrogen (N2) and carbon dioxide (COy), all at 1 bar absolute pressure. Here, arithmetic mean values are depicted together with the corresponding standard deviations after 10 voltage applications. ER stands for epoxy resin while SR for silicone rubber.
Figure 7. Flashover voltage (FOV) test results for six different insulator samples in dry air, nitrogen (N2) and carbon dioxide (COy), all at 1 bar absolute pressure. Here, arithmetic mean values are depicted together with the corresponding standard deviations after 10 voltage applications. ER stands for epoxy resin while SR for silicone rubber.
Figure 8. Computed electric field (black curves) and measured flashover voltages over dielectric permittivity variation. All the curves are normalised over the corresponding value of ¢, = 2.1 for PTFE.
Figure 8. Computed electric field (black curves) and measured flashover voltages over dielectric permittivity variation. All the curves are normalised over the corresponding value of ¢, = 2.1 for PTFE.
Figure 9. PTFE of 4mm thickness in (a) dry air at 1 bar absolute pressure and 31.74 kV rms applied voltage, (b) N> at 1 bar absolute pressure and 17.74kV rms applied voltage and (c) CO? at 1 bar absolute pressure and 21.61 kV rms applied voltage. High-resolution recordings were obtained through single trigger events of the recording device at dual-channel, sampling at 1.25GS/s rate. Two signals of 40ms duration each were captured, corresponding to two full AC-cycles. The applied voltage levels considered for each case correspond to 85% of the flashover levels presented in previous section. That way, it is possible to compare between the different cases, where the variations in the FOVs do not allow the application of the same test voltage levels. Additionally, a 15% safety margin from flashover events was maintained, avoiding unwanted stress of the test configuration in case of flashover. Figure 9 shows the obtained recordings for PTFE of 4mm thickness in dry air, nitrogen (N2) and carbon dioxide (CO?) at 1 bar absolute pressure. Because similar patterns were observed for the remaining insulator samples types, only the above selected results were shown here.
Figure 9. PTFE of 4mm thickness in (a) dry air at 1 bar absolute pressure and 31.74 kV rms applied voltage, (b) N> at 1 bar absolute pressure and 17.74kV rms applied voltage and (c) CO? at 1 bar absolute pressure and 21.61 kV rms applied voltage. High-resolution recordings were obtained through single trigger events of the recording device at dual-channel, sampling at 1.25GS/s rate. Two signals of 40ms duration each were captured, corresponding to two full AC-cycles. The applied voltage levels considered for each case correspond to 85% of the flashover levels presented in previous section. That way, it is possible to compare between the different cases, where the variations in the FOVs do not allow the application of the same test voltage levels. Additionally, a 15% safety margin from flashover events was maintained, avoiding unwanted stress of the test configuration in case of flashover. Figure 9 shows the obtained recordings for PTFE of 4mm thickness in dry air, nitrogen (N2) and carbon dioxide (CO?) at 1 bar absolute pressure. Because similar patterns were observed for the remaining insulator samples types, only the above selected results were shown here.
Figure 10. Positive polarity current pulses and calculated apparent charge for PTFE of 4mm thickness in: (a) dry air, (b) nitrogen (Nz) and (c) carbon dioxide (CO2). Wide bandwidth sensing and recording devices combined with high sampling rates allow the capturing of current pulses corresponding to creeping discharge events. For the presented test results, applied voltages were very close to the FOVs and most of the recordings consist of superimposed pulses, indicating multiple discharge events occurring in very fast time frames on the surface of the insulator sample. Single streamer current pulses are also present however, less frequent. Current pulses are classified into two different categories: those having the same polarity as the applied voltage and those with opposite polarity. Positive polarity pulses during the positive half cycle of the AC voltage application are present for all the cases with varying amplitudes and characteristics. Examples of positive polarity pulses exported from the recordings in Figure 9 are shown in Figure 10 with their time resolved characteristics being summarised in Table 1. Negative polarity current pulses are also detected, the recordings of which are shown in Figure 11, with their corresponding characteristics summarised in Table 2. Similar pulse shapes were observed for all the insulator sample materials. The apparent charge, which is also depicted, was calculated by integrating the recorded pulse over the corresponding time domain.
Figure 10. Positive polarity current pulses and calculated apparent charge for PTFE of 4mm thickness in: (a) dry air, (b) nitrogen (Nz) and (c) carbon dioxide (CO2). Wide bandwidth sensing and recording devices combined with high sampling rates allow the capturing of current pulses corresponding to creeping discharge events. For the presented test results, applied voltages were very close to the FOVs and most of the recordings consist of superimposed pulses, indicating multiple discharge events occurring in very fast time frames on the surface of the insulator sample. Single streamer current pulses are also present however, less frequent. Current pulses are classified into two different categories: those having the same polarity as the applied voltage and those with opposite polarity. Positive polarity pulses during the positive half cycle of the AC voltage application are present for all the cases with varying amplitudes and characteristics. Examples of positive polarity pulses exported from the recordings in Figure 9 are shown in Figure 10 with their time resolved characteristics being summarised in Table 1. Negative polarity current pulses are also detected, the recordings of which are shown in Figure 11, with their corresponding characteristics summarised in Table 2. Similar pulse shapes were observed for all the insulator sample materials. The apparent charge, which is also depicted, was calculated by integrating the recorded pulse over the corresponding time domain.
Table 2. Negative polarity current pulses characteristics. Significant differences in the measured rise and fall times are observed. For all the tests performed for the purposes of the presented work, the fastest rise and fall times, for these kinds of pulses, were observed in carbon dioxide (CO2) while the slowest were seen in nitrogen (Nz). The calculated apparent charge appears to be dependent and proportional to these values, with the highest charge being observed for the case of N2 in Figure 10b. In [22], the authors describe the correlation between rise and fall times with the electron avalanche process during partial discharge (PD) and electron drift after the full extension of the discharge activity. For the single double-exponential shaped pulses, such an approach can provide valuable information. Figure 11 includes captures of negative polarity current pulses during the negative half cycle of the AC applied voltage for dry air and CO, while for nitrogen the negative polarity current pulse appears during the positive AC half cycle. Pulses of opposite polarity to that of the applied voltage were observed in all measurements. Similar findings, using the Pockels effect optical method, were reported in [9] and identified as back-discharges. Following the provided description for the negative discharges during positive polarity of the applied voltage, the negative charge expands uniformly on the positively charged surface neutralizing the positive charges. The opposite process occurs for positive discharges during the negative half cycles.
Table 2. Negative polarity current pulses characteristics. Significant differences in the measured rise and fall times are observed. For all the tests performed for the purposes of the presented work, the fastest rise and fall times, for these kinds of pulses, were observed in carbon dioxide (CO2) while the slowest were seen in nitrogen (Nz). The calculated apparent charge appears to be dependent and proportional to these values, with the highest charge being observed for the case of N2 in Figure 10b. In [22], the authors describe the correlation between rise and fall times with the electron avalanche process during partial discharge (PD) and electron drift after the full extension of the discharge activity. For the single double-exponential shaped pulses, such an approach can provide valuable information. Figure 11 includes captures of negative polarity current pulses during the negative half cycle of the AC applied voltage for dry air and CO, while for nitrogen the negative polarity current pulse appears during the positive AC half cycle. Pulses of opposite polarity to that of the applied voltage were observed in all measurements. Similar findings, using the Pockels effect optical method, were reported in [9] and identified as back-discharges. Following the provided description for the negative discharges during positive polarity of the applied voltage, the negative charge expands uniformly on the positively charged surface neutralizing the positive charges. The opposite process occurs for positive discharges during the negative half cycles.
Figure 11. Negative polarity current pulses and calculated apparent charge for PTFE of 4mm thickness in: (a) dry air, (b) nitrogen (N2) and (c) carbon dioxide (CO>). Table 1. Positive polarity current pulses characteristics.
Figure 11. Negative polarity current pulses and calculated apparent charge for PTFE of 4mm thickness in: (a) dry air, (b) nitrogen (N2) and (c) carbon dioxide (CO>). Table 1. Positive polarity current pulses characteristics.
Figure 12. Current peaks densities for 4mm thickness insulator samples in dry air at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber. High resolution recordings, within the Go/s sampling rate levels, usually do not allow capturing of multiple trigger events which are able to demonstrate the repeatability of the generated phenomena, during the same applied voltage test. For that purpose, a lower sampling rate, larger buffer size, fast-triggering device was employed. In this way, the quick recording of multiple full AC-cycle trigger events for the same applied voltage attempt was possible without overstressing the test object. Post-processing of these recordings involves isolating the peak values of the current pulses within the time domain and incorporate them in a concatenating plot where colour grading was applied based on the density of these peaks. The colour identification was normalised over the total number of detected peaks based on their polarity. Figures 12-14 illustrate part of the results using the described technique for the cases of 4mm thickness insulator samples while Figure 15 includes selected datasets for 6mm thick samples. Here, 25 trigger events of 20 ms duration each are considered, resulting in a total duration of 500 ms for each case. For all the presented measurements, the applied voltage is approximately equal to the 85% of the corresponding FOV.
Figure 12. Current peaks densities for 4mm thickness insulator samples in dry air at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber. High resolution recordings, within the Go/s sampling rate levels, usually do not allow capturing of multiple trigger events which are able to demonstrate the repeatability of the generated phenomena, during the same applied voltage test. For that purpose, a lower sampling rate, larger buffer size, fast-triggering device was employed. In this way, the quick recording of multiple full AC-cycle trigger events for the same applied voltage attempt was possible without overstressing the test object. Post-processing of these recordings involves isolating the peak values of the current pulses within the time domain and incorporate them in a concatenating plot where colour grading was applied based on the density of these peaks. The colour identification was normalised over the total number of detected peaks based on their polarity. Figures 12-14 illustrate part of the results using the described technique for the cases of 4mm thickness insulator samples while Figure 15 includes selected datasets for 6mm thick samples. Here, 25 trigger events of 20 ms duration each are considered, resulting in a total duration of 500 ms for each case. For all the presented measurements, the applied voltage is approximately equal to the 85% of the corresponding FOV.
Figure 13. Current peaks densities for 4mm thickness insulator samples in nitrogen (N2) at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber. peaks and high repeatability for the 6mm samples compared to the 4mm. Silicone rubber of 6mm thickness in dry air shows increased resistance to creeping discharge activity in comparison with the 4mm sample of the same material, especially when the polarity of the applied voltage is positive. Overall, the dependence of the insulator sample thickness is visible for the presented cases. For tests with epoxy resin of 4mm thickness in COy, the applied voltage margin for occurrence of the discharge activity in the negative half cycle until flashover is small. Results of Nz combined with 4mm thickness samples need further investigation, especially for the case of epoxy resin.
Figure 13. Current peaks densities for 4mm thickness insulator samples in nitrogen (N2) at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber. peaks and high repeatability for the 6mm samples compared to the 4mm. Silicone rubber of 6mm thickness in dry air shows increased resistance to creeping discharge activity in comparison with the 4mm sample of the same material, especially when the polarity of the applied voltage is positive. Overall, the dependence of the insulator sample thickness is visible for the presented cases. For tests with epoxy resin of 4mm thickness in COy, the applied voltage margin for occurrence of the discharge activity in the negative half cycle until flashover is small. Results of Nz combined with 4mm thickness samples need further investigation, especially for the case of epoxy resin.
Figure 14. Current peaks densities for 4mm thickness insulator samples in carbon dioxide (CO?) at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber.
Figure 14. Current peaks densities for 4mm thickness insulator samples in carbon dioxide (CO?) at 1 bar absolute pressure: (a) PTFE, (b) epoxy resin and (c) silicone rubber.
Figure 15. Current peaks densities for 6mm thickness insulator samples: (a) PTFE in CO2 at 1 bar absolute pressure, (b) epoxy resin in N» at 1 bar absolute pressure and (c) silicone rubber in dry air at 1 bar absolute pressure.
Figure 15. Current peaks densities for 6mm thickness insulator samples: (a) PTFE in CO2 at 1 bar absolute pressure, (b) epoxy resin in N» at 1 bar absolute pressure and (c) silicone rubber in dry air at 1 bar absolute pressure.
Figure 1. Molecular structures of polycyclic compounds.
Figure 1. Molecular structures of polycyclic compounds.
Table 1. Tree structure distribution at 1 min.
Table 1. Tree structure distribution at 1 min.
Figure 2. Schematic diagram of experimental setup. and the trap density (Nf) are calculated to analyze the electrical property behaviors [34]. The carrier mobility was also calculated [35], which can obtain the characteristics of charge transportation.
Figure 2. Schematic diagram of experimental setup. and the trap density (Nf) are calculated to analyze the electrical property behaviors [34]. The carrier mobility was also calculated [35], which can obtain the characteristics of charge transportation.
Figure 3. The electrical tree structures of the neat cross-linked polyethylene (XLPE) and XLPE—A composite.
Figure 3. The electrical tree structures of the neat cross-linked polyethylene (XLPE) and XLPE—A composite.
Figure 4. Electrical treeing characteristics with opposite polarity DC-impulse voltage.
Figure 4. Electrical treeing characteristics with opposite polarity DC-impulse voltage.
Figure 5. Electrical treeing characteristics with the same polarity DC-impulse voltage. compound A has the best effect, which is consistent with the results that have an opposite polarity DC-impulse voltage. The effect of temperature on the polycyclic compound is still the same as tha’ with the opposite polarity. As the temperature increases, the suppression effect of the three polycyclic compounds becomes weak. It can be concluded that the suppression effect of the three types o! polycyclic compounds with the same polarity is worse than with the opposite polarity.
Figure 5. Electrical treeing characteristics with the same polarity DC-impulse voltage. compound A has the best effect, which is consistent with the results that have an opposite polarity DC-impulse voltage. The effect of temperature on the polycyclic compound is still the same as tha’ with the opposite polarity. As the temperature increases, the suppression effect of the three polycyclic compounds becomes weak. It can be concluded that the suppression effect of the three types o! polycyclic compounds with the same polarity is worse than with the opposite polarity.
Table 2. Cross-linked polyethylene (XLPE) and its polycyclic compounds composites trap depth.
Table 2. Cross-linked polyethylene (XLPE) and its polycyclic compounds composites trap depth.
Figure 6. Trap distribution and carrier mobility behaviors of XLPE and its polycyclic compounds composites.
Figure 6. Trap distribution and carrier mobility behaviors of XLPE and its polycyclic compounds composites.
Figure A1. The equivalent circuit of the experimental configuration. Figure Al shows the equivalent circuit of the experimental configuration. Figure A2 shows the electrical tree structures of XLPE-B and XLPE-C.
Figure A1. The equivalent circuit of the experimental configuration. Figure Al shows the equivalent circuit of the experimental configuration. Figure A2 shows the electrical tree structures of XLPE-B and XLPE-C.
Figure A2. The electrical tree structures of XLPE—B and XLPE-C composite.
Figure A2. The electrical tree structures of XLPE—B and XLPE-C composite.
1 Part by weight. 2 Treated stands for rounded surface of particle. ry welg. Pi Table 1. Physical properties of samples.
1 Part by weight. 2 Treated stands for rounded surface of particle. ry welg. Pi Table 1. Physical properties of samples.
+ In the present study, samples were not tested under the same partial discharge conditions (for example, amount of charge, and number of pulses). The magnitude of applied voltage was fixed instead, considering the actual usage condition of polymer insulators at the site. It result in different partial discharge activities among samples because localized electric field in the air gap depends on permittivity and conductivity of the sample.
+ In the present study, samples were not tested under the same partial discharge conditions (for example, amount of charge, and number of pulses). The magnitude of applied voltage was fixed instead, considering the actual usage condition of polymer insulators at the site. It result in different partial discharge activities among samples because localized electric field in the air gap depends on permittivity and conductivity of the sample.
Table 2. Number of cycles of sample breakdown. 3.2. Contact Angle No arc discharge was observed during the experiments. Samples C, D, and E were broken-down under some conditions as shown in Table 2. Higher relative permittivity of these samples compared with samples A and B as shown in Table 1 generates higher localized electric field in the air gap, resulting in active partial discharge and shorter lifetime to breakdown. Also, lower resistivity of these samples may have some relation to breakdown. Figure 3a,b shows the change in contact angle with number of cycle just before voltage application and just after voltage interruption in the 50-cycle test with 2 mm air gap spacing, respectively. Characteristics obtained in the 100-cycle test with 2 mm gap spacing are shown in Figure 4a,b. The initial value of contact angle is about 100 degrees for any sample. After 8-h voltage application, it decreased at most 20 degrees due to reduction of hydrophobicity of sample surface by partial discharge. Reduction in contact angle of Sample A is much lower than those of other samples. This corresponds to lower surface erosion of Sample A as described below. Recovery of contact angle to almost the initial value is confirmed after 16-h voltage interruption. It is considered that 16 h in the present experimental procedures are appropriate for low-molecular weight silicone oil to migrate from the bulk to the surface of a sample and to recover hydrophobicity. No remarkable reduction is observed with the number of cycle. Samples A and B are superior to the other samples when repeating cycles. Large fluctuation of contact angle may be attributed to microscopic uneven surface caused by partial discharge, not only erosion like pitting but also accumulation of discharge by-product on the
Table 2. Number of cycles of sample breakdown. 3.2. Contact Angle No arc discharge was observed during the experiments. Samples C, D, and E were broken-down under some conditions as shown in Table 2. Higher relative permittivity of these samples compared with samples A and B as shown in Table 1 generates higher localized electric field in the air gap, resulting in active partial discharge and shorter lifetime to breakdown. Also, lower resistivity of these samples may have some relation to breakdown. Figure 3a,b shows the change in contact angle with number of cycle just before voltage application and just after voltage interruption in the 50-cycle test with 2 mm air gap spacing, respectively. Characteristics obtained in the 100-cycle test with 2 mm gap spacing are shown in Figure 4a,b. The initial value of contact angle is about 100 degrees for any sample. After 8-h voltage application, it decreased at most 20 degrees due to reduction of hydrophobicity of sample surface by partial discharge. Reduction in contact angle of Sample A is much lower than those of other samples. This corresponds to lower surface erosion of Sample A as described below. Recovery of contact angle to almost the initial value is confirmed after 16-h voltage interruption. It is considered that 16 h in the present experimental procedures are appropriate for low-molecular weight silicone oil to migrate from the bulk to the surface of a sample and to recover hydrophobicity. No remarkable reduction is observed with the number of cycle. Samples A and B are superior to the other samples when repeating cycles. Large fluctuation of contact angle may be attributed to microscopic uneven surface caused by partial discharge, not only erosion like pitting but also accumulation of discharge by-product on the
Figure 3. Change in contact angle with number of cycles in 50-cycle test with gap spacing 2 mm. (a) Just before commencement of voltage application. (b) Just after voltage interruption.
Figure 3. Change in contact angle with number of cycles in 50-cycle test with gap spacing 2 mm. (a) Just before commencement of voltage application. (b) Just after voltage interruption.
Figure 4. Change in contact angle with number of cycles in 100-cycle test with gap spacing 2 mm. (a) Just before commencement of voltage application. (b) Just after voltage interruption.
Figure 4. Change in contact angle with number of cycles in 100-cycle test with gap spacing 2 mm. (a) Just before commencement of voltage application. (b) Just after voltage interruption.
Figure 5. Optical and confocal microscope images of surface of samples A and E obtained in the 100-cycle test with 1 mm air gap.
Figure 5. Optical and confocal microscope images of surface of samples A and E obtained in the 100-cycle test with 1 mm air gap.
Figure 6. Confocal microscope images of sample surface obtained after completing 80 cycles in the 100-cycle test with 1 mm air gap. (a) Sample A; (b) Sample B; (c) Sample C; (d) Sample D; (e) Sample E
Figure 6. Confocal microscope images of sample surface obtained after completing 80 cycles in the 100-cycle test with 1 mm air gap. (a) Sample A; (b) Sample B; (c) Sample C; (d) Sample D; (e) Sample E
Figure 7. Examples of surface roughness profiles obtained with surface roughness meter in the 100-cycle test with 1 mm air gap. Ra obtained in the 100-cycle test is shown in Figure 9 for 1 mm air gap. Ra increases gradually with the number of cycle except sample A. The characteristics of samples B and C are similar to each other. The same can be said of samples D and E. The result for 2 mm air gap are not shown because only limited data were available due to failure of the measuring instrument. Comparing Figure 9 with Figure 8a, obtained under the same applied voltage and the same gap spacing, surface roughness after completing 40 cycles, for example, is almost the same for any sample. This shows a good repeatability of results, suggesting the proposed experimental procedures are suitable to investigate partial discharge degradation of silicone rubber.
Figure 7. Examples of surface roughness profiles obtained with surface roughness meter in the 100-cycle test with 1 mm air gap. Ra obtained in the 100-cycle test is shown in Figure 9 for 1 mm air gap. Ra increases gradually with the number of cycle except sample A. The characteristics of samples B and C are similar to each other. The same can be said of samples D and E. The result for 2 mm air gap are not shown because only limited data were available due to failure of the measuring instrument. Comparing Figure 9 with Figure 8a, obtained under the same applied voltage and the same gap spacing, surface roughness after completing 40 cycles, for example, is almost the same for any sample. This shows a good repeatability of results, suggesting the proposed experimental procedures are suitable to investigate partial discharge degradation of silicone rubber.
Figure 8. Change in Ra with number of cycle in the 50-cycle tests. (a) 1 mm air ga; (b) 2 mm air gap.
Figure 8. Change in Ra with number of cycle in the 50-cycle tests. (a) 1 mm air ga; (b) 2 mm air gap.
Figure 9. Change in Ra with number of cycle in the 100-cycle test with 1 mm air gap.
Figure 9. Change in Ra with number of cycle in the 100-cycle test with 1 mm air gap.
Figure 10. Change in Ra with number of cycle in the 100-cycle tests. (a) 1 mm air gap; (b) 2 mm air gap.
Figure 10. Change in Ra with number of cycle in the 100-cycle tests. (a) 1 mm air gap; (b) 2 mm air gap.
Figure 11. Change in FTIR spectra with the number of cycle obtained in the 100-cycle test with 2 mm air gap. (a) Sample A; (b) Sample B; (c) Sample C; (d) Sample D; (e) Sample E.
Figure 11. Change in FTIR spectra with the number of cycle obtained in the 100-cycle test with 2 mm air gap. (a) Sample A; (b) Sample B; (c) Sample C; (d) Sample D; (e) Sample E.
Figure 12. Change in normalized absorption of Si-CH3 and O-Si-O with the number of cycle obtained in the 100-cycle test with 2 mm air gap. (a) Sample A; (b) Sample E.
Figure 12. Change in normalized absorption of Si-CH3 and O-Si-O with the number of cycle obtained in the 100-cycle test with 2 mm air gap. (a) Sample A; (b) Sample E.
I ne Surface erosion of a sample increases gradually by partial discharge with the number of cycle in samples D and E, decrease in hydrophobic Si-CH3 and Si-O-Si of main chain is confirmed by FTII inalysis. This is a possible reason for low contact angle, sever surface erosion, and consequently shor -ycles to breakdown. Samples D and E contain ATH, which is considered effective to enhance resistanc ‘o tracking and erosion by discharge because heat is absorbed by releasing the water of hydration fron ATH molecule when the temperature of an ATH filled polymer reaches ~200 degrees [1,14]. This role o ATH seems effective for partial discharge because decrease in ATH is suggested through FTIR analysi: n the present study. Nevertheless, surface erosion of samples D and E containing ATH is seriou: “compared with sample A without ATH. This is attributed to intensified partial discharge activities ir he air gap for samples D and E because their higher permittivity generates higher localized electri ‘ield in the air gap of the electrode system. Lower resistivity of samples D and E may also relate t shorter lifetime to breakdown.
I ne Surface erosion of a sample increases gradually by partial discharge with the number of cycle in samples D and E, decrease in hydrophobic Si-CH3 and Si-O-Si of main chain is confirmed by FTII inalysis. This is a possible reason for low contact angle, sever surface erosion, and consequently shor -ycles to breakdown. Samples D and E contain ATH, which is considered effective to enhance resistanc ‘o tracking and erosion by discharge because heat is absorbed by releasing the water of hydration fron ATH molecule when the temperature of an ATH filled polymer reaches ~200 degrees [1,14]. This role o ATH seems effective for partial discharge because decrease in ATH is suggested through FTIR analysi: n the present study. Nevertheless, surface erosion of samples D and E containing ATH is seriou: “compared with sample A without ATH. This is attributed to intensified partial discharge activities ir he air gap for samples D and E because their higher permittivity generates higher localized electri ‘ield in the air gap of the electrode system. Lower resistivity of samples D and E may also relate t shorter lifetime to breakdown.
Figure 1. (a) geometry of a planplanar insulation; (b) geometry of a cylindrical insulation [10]. where k = 1.38 x 10723 J/K is the Boltzmann constant, T is the temperature, |Jo| is a current density constant, Ea is the activation energy, and y is a constant to describe the dependency on the electric field [13]. These constants are determined by a fit of Equation (4) to measured data. The constants of XLPE insulations are approximately |Jo| = 1 x 10! A/m2, E, = 1.48 eV and y=2x 10-7 m/V (see [13]). For an LDPE insulation, the constants are |Jo| = 0.04224 A/m2, E, = 0.84 eV and y =4.251 x 10-7 m/V (see [14-16]). Analogously to [9], hetero charge accumulation in the vicinity of both electrodes is described by conductivity gradient with two sigmoid functions. The total electric conductivity o inside a cylindrical nsulation is modeled by
Figure 1. (a) geometry of a planplanar insulation; (b) geometry of a cylindrical insulation [10]. where k = 1.38 x 10723 J/K is the Boltzmann constant, T is the temperature, |Jo| is a current density constant, Ea is the activation energy, and y is a constant to describe the dependency on the electric field [13]. These constants are determined by a fit of Equation (4) to measured data. The constants of XLPE insulations are approximately |Jo| = 1 x 10! A/m2, E, = 1.48 eV and y=2x 10-7 m/V (see [13]). For an LDPE insulation, the constants are |Jo| = 0.04224 A/m2, E, = 0.84 eV and y =4.251 x 10-7 m/V (see [14-16]). Analogously to [9], hetero charge accumulation in the vicinity of both electrodes is described by conductivity gradient with two sigmoid functions. The total electric conductivity o inside a cylindrical nsulation is modeled by
Figure 2. Influence of distance constant 7 on conductivity gradient and resulting space charge distribution p. (a) normalized conductivity o/og; (b) normalized stationary space charge distribution [10]. A conductivity increase is described with Kj, resulting in negative charges at the anode and Ky is describing a conductivity decrease, resulting in positive charges at the cathode. This relationship is obtained from the analytic solution of the stationary charge and electric field distribution, using a conductivity gradient. where K describes the conductivity variations at the inner conductor (anode) and K> the conductivity variations at the outer sheath (cathode); in (6) and (7), rx is the distance between 1, and the position of the highest gradient (o/op(r = rx) = 0.5). If a planplanar insulation is considered, r > x, r, = 0 and ra = L holds.
Figure 2. Influence of distance constant 7 on conductivity gradient and resulting space charge distribution p. (a) normalized conductivity o/og; (b) normalized stationary space charge distribution [10]. A conductivity increase is described with Kj, resulting in negative charges at the anode and Ky is describing a conductivity decrease, resulting in positive charges at the cathode. This relationship is obtained from the analytic solution of the stationary charge and electric field distribution, using a conductivity gradient. where K describes the conductivity variations at the inner conductor (anode) and K> the conductivity variations at the outer sheath (cathode); in (6) and (7), rx is the distance between 1, and the position of the highest gradient (o/op(r = rx) = 0.5). If a planplanar insulation is considered, r > x, r, = 0 and ra = L holds.
Figure 3. (a) Gradient region A, where the conductivity gradient is present. The position r = r, = A/2 has the highest gradient; (b) to determine yx by A, a straight line f(x) = a(x — rx) + 0.5 = (1/A)(x — rx) + 0.5 is used, where the best approximation is shown by A = 10y [10]. the measurement technique itself filters the surface charges, whereby they spread out and look like a Gaussian curve [8]. Consequently, a measured space charge distribution has its maximum hetero charge values in the vicinity of both electrodes, instead of a position immediately at the electrodes. To compare a measured and simulated space charge distribution, the surface charges have to be considered. With an applied voltage and accumulated space charges, surface charge (5+ and 5_) accumulate at both electrodes. These charges are derived from [18] and are approximately described by
Figure 3. (a) Gradient region A, where the conductivity gradient is present. The position r = r, = A/2 has the highest gradient; (b) to determine yx by A, a straight line f(x) = a(x — rx) + 0.5 = (1/A)(x — rx) + 0.5 is used, where the best approximation is shown by A = 10y [10]. the measurement technique itself filters the surface charges, whereby they spread out and look like a Gaussian curve [8]. Consequently, a measured space charge distribution has its maximum hetero charge values in the vicinity of both electrodes, instead of a position immediately at the electrodes. To compare a measured and simulated space charge distribution, the surface charges have to be considered. With an applied voltage and accumulated space charges, surface charge (5+ and 5_) accumulate at both electrodes. These charges are derived from [18] and are approximately described by
Table 1. Used constants for the simulation results in Figures 4 and 5 [10,19-21]. The constant A is determined by minimizing the least squares problem the insulation material. The filter is calibrated by minimizing the difference between the measurement: and the filtered simulation results at t ~ 0s.
Table 1. Used constants for the simulation results in Figures 4 and 5 [10,19-21]. The constant A is determined by minimizing the least squares problem the insulation material. The filter is calibrated by minimizing the difference between the measurement: and the filtered simulation results at t ~ 0s.
Figure 4. (a) Measured and simulated charge distribution in a planplanar cross-linked polyethylene (XLPE) insulation [20]; (b) Measured and simulated charge distribution in a cylindrical XLPE insulation. Three different XLPE cable measurements, labeled with numbers “1”—“3”, are seen [10,19]. Space charge measurements in planplanar and cylindrical XLPE insulations are found in references [6,19,20]. Here, the measured hetero charge distribution, including the surface charges, is positioned in about one third of the insulation thickness in the vicinity of both electrodes, while the magnitude varies with a varying temperature and electric field strength. With a constant magnitude of the applied voltage and the opposite polarity, the charge density also changes the polarity, but shape and magnitude remain the same. This so called “mirror image effect” is reported and discussed e.g., in [23]. The inversion of the equilibrium space charge distribution is explained e.g., with a spatially inhomogeneous polarization of the dielectric and the injection of charges at the electrodes [24,25]. Steady state charge distributions in a planplanar insulation configuration (Figure 4a) and in
Figure 4. (a) Measured and simulated charge distribution in a planplanar cross-linked polyethylene (XLPE) insulation [20]; (b) Measured and simulated charge distribution in a cylindrical XLPE insulation. Three different XLPE cable measurements, labeled with numbers “1”—“3”, are seen [10,19]. Space charge measurements in planplanar and cylindrical XLPE insulations are found in references [6,19,20]. Here, the measured hetero charge distribution, including the surface charges, is positioned in about one third of the insulation thickness in the vicinity of both electrodes, while the magnitude varies with a varying temperature and electric field strength. With a constant magnitude of the applied voltage and the opposite polarity, the charge density also changes the polarity, but shape and magnitude remain the same. This so called “mirror image effect” is reported and discussed e.g., in [23]. The inversion of the equilibrium space charge distribution is explained e.g., with a spatially inhomogeneous polarization of the dielectric and the injection of charges at the electrodes [24,25]. Steady state charge distributions in a planplanar insulation configuration (Figure 4a) and in
Figure 5. Measured and simulated charge distribution in a planplanar low-density polyethylene (LDPE) insulation [10,21]. In Figures 4 and 5, the defined region of accumulated space charges is equal to the region of the conductivity gradient in Figure 2. Differences between the charge distribution in Figures 4 and 5, 3.2. Measurements of LDPE Insulation In Figure 4a, differences are observable especially at the anode and the cathode, which is a result of the filtering process. The computed surface charges (9) and (10) depend on the accumulated space charges and the local electric field. The local electric field depend on the space charges as well. If the simulated space charges differ in comparison to the measurement, the electric field and the surface charges also differ.
Figure 5. Measured and simulated charge distribution in a planplanar low-density polyethylene (LDPE) insulation [10,21]. In Figures 4 and 5, the defined region of accumulated space charges is equal to the region of the conductivity gradient in Figure 2. Differences between the charge distribution in Figures 4 and 5, 3.2. Measurements of LDPE Insulation In Figure 4a, differences are observable especially at the anode and the cathode, which is a result of the filtering process. The computed surface charges (9) and (10) depend on the accumulated space charges and the local electric field. The local electric field depend on the space charges as well. If the simulated space charges differ in comparison to the measurement, the electric field and the surface charges also differ.
Table 2. Distance constants y and positions rx for the simulation of space charge measurements in [6,19-21]. The absolute value of the applied voltage is |U| = 20 kV. Using a temperature and electric field dependent electric conductivity, e.g., (4), only charges within the bulk are simulated, which are mainly a result of the temperature gradient. Thus, comparing the measurements and the simulations, high differences are observable in the vicinity of the electrodes For example, Figure 7 shows a space charge measurement and the simulating results using a commonly utilized conductivity Equation (4) and using (5). The applied constants are equal to the constants for Figure 4a,b and are seen in Table 1. Without a temperature gradient and electric field gradient, (4) is constant within the insulation and the simulated space charge density p = 0 C/m° (see (8)). The surface — charges (17) and (18) are reduced to 64 = egér(ri)|E(ri)| and 6- = €9ér(ra)|E(ra)| (See Figure 7a) A temperature gradient along the insulation results in accumulated bulk space charges, which are ower in the vicinity of the electrodes, compared to the measurements (see Figure 7b). Ln a: re ey a, CS ee: i i a a ce Cn ie of ee fe i. a
Table 2. Distance constants y and positions rx for the simulation of space charge measurements in [6,19-21]. The absolute value of the applied voltage is |U| = 20 kV. Using a temperature and electric field dependent electric conductivity, e.g., (4), only charges within the bulk are simulated, which are mainly a result of the temperature gradient. Thus, comparing the measurements and the simulations, high differences are observable in the vicinity of the electrodes For example, Figure 7 shows a space charge measurement and the simulating results using a commonly utilized conductivity Equation (4) and using (5). The applied constants are equal to the constants for Figure 4a,b and are seen in Table 1. Without a temperature gradient and electric field gradient, (4) is constant within the insulation and the simulated space charge density p = 0 C/m° (see (8)). The surface — charges (17) and (18) are reduced to 64 = egér(ri)|E(ri)| and 6- = €9ér(ra)|E(ra)| (See Figure 7a) A temperature gradient along the insulation results in accumulated bulk space charges, which are ower in the vicinity of the electrodes, compared to the measurements (see Figure 7b). Ln a: re ey a, CS ee: i i a a ce Cn ie of ee fe i. a
Figure 6. Measured and simulated charge distribution in a XLPE and LDPE insulation [6]. (a) XLPE, planplanar, +U; (b) XLPE, planplanar, —U; (c) XLPE, cylindrical, +U; (d) XLPE, cylindrical, —U; (e) LDPE, planplanar, +U; (f) LDPE, planplanar, —U. The absolute value of the applied voltage is |U| = 20 kV.
Figure 6. Measured and simulated charge distribution in a XLPE and LDPE insulation [6]. (a) XLPE, planplanar, +U; (b) XLPE, planplanar, —U; (c) XLPE, cylindrical, +U; (d) XLPE, cylindrical, —U; (e) LDPE, planplanar, +U; (f) LDPE, planplanar, —U. The absolute value of the applied voltage is |U| = 20 kV.
Figure 7. (a) Measured and simulated charge distribution, using a common conductivity equation in literature (4) and the developed conductivity equation (5) in a planplanar XLPE insulation [20]; (b) Measured and simulated charge distribution, using (4) and (5) in a cylindrical XLPE insulation [19]. Figure 7. (a) Measured and simulated charge distribution, using a common conductivity equation
Figure 7. (a) Measured and simulated charge distribution, using a common conductivity equation in literature (4) and the developed conductivity equation (5) in a planplanar XLPE insulation [20]; (b) Measured and simulated charge distribution, using (4) and (5) in a cylindrical XLPE insulation [19]. Figure 7. (a) Measured and simulated charge distribution, using a common conductivity equation
1- DC power supply 2- protective resistance 3- coupling capacitor 4- needle-plate model 5- non inductive resistance 6- oscilloscope The schematic diagram of the experiment platform is shown in Figure 1. DC voltages are generated by the high voltage (HV) DC power supply Matsusada AU-30R2, whose output voltage range is +30 kV. PD pulse acquisition adopts pulse current method. Oscilloscope is adapted to measure the voltage pulse signals on the 50 O non-inductive resistance. The needle-plate model is set in a cylindrical organic glass box (radius of 0.1 m), which is filled with air and blocks air flow. The curvature radius of needle tip r is 0.5 mm, and the distance between the needle and plate d is 15 mm. d/r is greater than 4, and the needle-plate electrical field is extremely uneven [20].
1- DC power supply 2- protective resistance 3- coupling capacitor 4- needle-plate model 5- non inductive resistance 6- oscilloscope The schematic diagram of the experiment platform is shown in Figure 1. DC voltages are generated by the high voltage (HV) DC power supply Matsusada AU-30R2, whose output voltage range is +30 kV. PD pulse acquisition adopts pulse current method. Oscilloscope is adapted to measure the voltage pulse signals on the 50 O non-inductive resistance. The needle-plate model is set in a cylindrical organic glass box (radius of 0.1 m), which is filled with air and blocks air flow. The curvature radius of needle tip r is 0.5 mm, and the distance between the needle and plate d is 15 mm. d/r is greater than 4, and the needle-plate electrical field is extremely uneven [20].
Figure 2. Single pulse under positive or negative polarity DC voltage. (a) Positive pulse; (b) Negative pulse. 3. Statistic Rules and Stage Characteristics of Positive PD
Figure 2. Single pulse under positive or negative polarity DC voltage. (a) Positive pulse; (b) Negative pulse. 3. Statistic Rules and Stage Characteristics of Positive PD
Figure 3. Average value diagram of n, V and At on positive polarity. — - ~ - * * “ The initial streamer stage is 8.8 kV to 9 kV. The density of retained cations at this stage is relatively low and is close to the needle tip, so the effect of cation electric field is weak. E of outer regions is below Eo. Thus the development degrees of streamers are similar, and the generated space charge amounts of each discharge are close. Thus, V basically retains unchanged. Under initial discharge voltage, the high-intensity electric field region is tiny. The discharges is random, thus At is large (84.44 ms, not shown in Figure 3). With the increase of applied voltage, amount of retained cations increases. Because the cations group is close to the tip, thus their main effect is enhancing original E near the needle tip. The amount of produced cations and anions is relatively small, so when E increases, the electric field recovers quickly, thus 7 rises. Nine kV to 9.5 kV is the transition stage, where the cation group gradually becomes intensive and moves away from the needle tip. For the electric field between cations and the needle tip, the cation group generates an opposite electric field and weakens the original one. In some regions, E is weakened to the value below Ey, so some streamers are weakened and stopped inside cation group. While in some regions, the lowest E in cation group is higher than Eg, and even stronger more outside, streamers are enhanced. So on average, V changes little. Weakened E inside results in the increasing of electric field recovery time. So Af increases. The glow-like discharge stage is about 9.5 kV to 13.5 kV. At this stage, the development of streamer is significantly inhibited by the cations group. The cations group stays at a certain distance from the tip and tho nnnncite olactric field ie mare roamarkahlo Moainrity af ectroamore are ctanned incida the cratinn discharges, ion densities reaches an equilibrium state. The cation density near the needle tip should be higher than the average. When the density reaches a certain level, the ionic electric field will distort to the original electric field.
Figure 3. Average value diagram of n, V and At on positive polarity. — - ~ - * * “ The initial streamer stage is 8.8 kV to 9 kV. The density of retained cations at this stage is relatively low and is close to the needle tip, so the effect of cation electric field is weak. E of outer regions is below Eo. Thus the development degrees of streamers are similar, and the generated space charge amounts of each discharge are close. Thus, V basically retains unchanged. Under initial discharge voltage, the high-intensity electric field region is tiny. The discharges is random, thus At is large (84.44 ms, not shown in Figure 3). With the increase of applied voltage, amount of retained cations increases. Because the cations group is close to the tip, thus their main effect is enhancing original E near the needle tip. The amount of produced cations and anions is relatively small, so when E increases, the electric field recovers quickly, thus 7 rises. Nine kV to 9.5 kV is the transition stage, where the cation group gradually becomes intensive and moves away from the needle tip. For the electric field between cations and the needle tip, the cation group generates an opposite electric field and weakens the original one. In some regions, E is weakened to the value below Ey, so some streamers are weakened and stopped inside cation group. While in some regions, the lowest E in cation group is higher than Eg, and even stronger more outside, streamers are enhanced. So on average, V changes little. Weakened E inside results in the increasing of electric field recovery time. So Af increases. The glow-like discharge stage is about 9.5 kV to 13.5 kV. At this stage, the development of streamer is significantly inhibited by the cations group. The cations group stays at a certain distance from the tip and tho nnnncite olactric field ie mare roamarkahlo Moainrity af ectroamore are ctanned incida the cratinn discharges, ion densities reaches an equilibrium state. The cation density near the needle tip should be higher than the average. When the density reaches a certain level, the ionic electric field will distort to the original electric field.
Figure 4. Equivalent charge quantity diagram of positive PD. where tw denotes single PD pulse width, which is set as 50 ns. R denotes the sampling resistance value. Equivalent charge quantities of positive PD are shown in Figure 4. At the initial streamer stage, there is an obvious q, while at the glow-like discharge stage q is close to 0. Then in the breakdown streamer stage, q increases obviously, especially near breakdown. It indicates that the discharges of glow-like stage are obviously inhibited under the action of space charges, which also means that the electric field variation is little, and the discharges consume less energy. gq is obvious at breakdown streamer stage.
Figure 4. Equivalent charge quantity diagram of positive PD. where tw denotes single PD pulse width, which is set as 50 ns. R denotes the sampling resistance value. Equivalent charge quantities of positive PD are shown in Figure 4. At the initial streamer stage, there is an obvious q, while at the glow-like discharge stage q is close to 0. Then in the breakdown streamer stage, q increases obviously, especially near breakdown. It indicates that the discharges of glow-like stage are obviously inhibited under the action of space charges, which also means that the electric field variation is little, and the discharges consume less energy. gq is obvious at breakdown streamer stage.
Figure 5. Variation coefficients diagram of positive polarity. The VC of V and At under different voltages are shown in Figure 5. VC for V basically remains unchanged at the initial streamer stage. Then VC decreases at the early stage of glow-like discharge and reaches the lowest value. It rises at the end of glow-like discharge stage, and reaches a higher value at the breakdown streamer stage and then retains. When approaching breakdown, VC has a small increase. Amplitude fluctuation in the glow-like discharge stage are relatively smaller, indicating that the streamers are relatively regular, and the electric field distribution of discharge regions is even at this stage because of the cation group. Especially at the initial stage of glow-like discharge, the space charge electric field plays an obvious role. The VC for At increases at the initial streamer stage where space charges are few, and decreases at the transition stage with the increasing density of cations. Then VC sustains in glow-like discharge stage. At last, it decreases again near breakdown. It can be seen that the fluctuation of At will be lower with certain cation density, because space charges retained after a single discharge have less effect on the electric field. The cation group contributes to a relatively stable electric field in discharge regions, thus ions migrate regularly and the fluctuation of discharge recovery time is low.
Figure 5. Variation coefficients diagram of positive polarity. The VC of V and At under different voltages are shown in Figure 5. VC for V basically remains unchanged at the initial streamer stage. Then VC decreases at the early stage of glow-like discharge and reaches the lowest value. It rises at the end of glow-like discharge stage, and reaches a higher value at the breakdown streamer stage and then retains. When approaching breakdown, VC has a small increase. Amplitude fluctuation in the glow-like discharge stage are relatively smaller, indicating that the streamers are relatively regular, and the electric field distribution of discharge regions is even at this stage because of the cation group. Especially at the initial stage of glow-like discharge, the space charge electric field plays an obvious role. The VC for At increases at the initial streamer stage where space charges are few, and decreases at the transition stage with the increasing density of cations. Then VC sustains in glow-like discharge stage. At last, it decreases again near breakdown. It can be seen that the fluctuation of At will be lower with certain cation density, because space charges retained after a single discharge have less effect on the electric field. The cation group contributes to a relatively stable electric field in discharge regions, thus ions migrate regularly and the fluctuation of discharge recovery time is low.
Figure 6. At—V distribution of 9 kV at the transition stage. distribute in a horizontal ribbon basically. Figure 9a,b show the proportion distributions of V and At. At the beginning, V is relatively concentrated (10 kV-11 kV). But at later stage, V gradually distributes dispersedly. The abscissa of the peak point is larger. For At, the abscissa of the highest proportion point and the abscissa ranges of each proportion curve are basically the same. It can be observed that the distribution curves of At can be divided into two parts. One part is of peak shape in abscissa of 0 to 0.005 s. Another part is of flat shape in 0.005 s to 0.01 s. The flat part may represent the At after the streamers that pass though the cation group region, since the ions take a long time to migrate because of the low E in this region. For At, their distribution are dispersed at the early stage. The abscissa of the highest proportion point decreases with applied voltage rises, reaching the lowest value under 11 kV. The At points then become more concentrated at the later stage, and the highest proportion value rises.
Figure 6. At—V distribution of 9 kV at the transition stage. distribute in a horizontal ribbon basically. Figure 9a,b show the proportion distributions of V and At. At the beginning, V is relatively concentrated (10 kV-11 kV). But at later stage, V gradually distributes dispersedly. The abscissa of the peak point is larger. For At, the abscissa of the highest proportion point and the abscissa ranges of each proportion curve are basically the same. It can be observed that the distribution curves of At can be divided into two parts. One part is of peak shape in abscissa of 0 to 0.005 s. Another part is of flat shape in 0.005 s to 0.01 s. The flat part may represent the At after the streamers that pass though the cation group region, since the ions take a long time to migrate because of the low E in this region. For At, their distribution are dispersed at the early stage. The abscissa of the highest proportion point decreases with applied voltage rises, reaching the lowest value under 11 kV. The At points then become more concentrated at the later stage, and the highest proportion value rises.
Figure 8. At—V distribution of glow-like discharge stage. (a) At-V distribution of 10 kV; (b) At-V distribution of 13 kV.
Figure 8. At—V distribution of glow-like discharge stage. (a) At-V distribution of 10 kV; (b) At-V distribution of 13 kV.
Figure 9. Proportion distribution diagrams at the glow-like discharge stage. (a) Proportion distribution of V; (b) Proportion distribution of At.
Figure 9. Proportion distribution diagrams at the glow-like discharge stage. (a) Proportion distribution of V; (b) Proportion distribution of At.
Figure 10. At—V distribution of breakdown streamer stage. (a) At-V distribution of 15 kV; (b) At-V distribution of 16 kV. At breakdown streamer stage, E in the cation group region can satisfy self-sustaining condition ind majority of streamers can pass through the cation region. As shown in Figure 10a, the main \t-V points form a triangular. When At abscissa is small, the density of points is large and V range s wide. With the increase of At, density of point and V range are decreased. Compared Figure 10a o Figure 10b, with the increase of applied voltage, the range of V increases, and the At decreases. ‘igure 11a,b show the V and At distribution proportions. For V, the shapes of the proportion curves are imilar in the beginning, and the abscissa of the highest proportion point gradually increases. While ’ overall increases, and V range expands significantly near breakdown. For At, with the increase of pplied voltage, the concentration degree of At is significantly increased. The highest proposition of he curve increases, and the abscissa of highest proposition point decreases. Similarly, the variations re especially obvious near the breakdown. It can be concluded that breakdown streamers in positive olarity are strong and intensive.
Figure 10. At—V distribution of breakdown streamer stage. (a) At-V distribution of 15 kV; (b) At-V distribution of 16 kV. At breakdown streamer stage, E in the cation group region can satisfy self-sustaining condition ind majority of streamers can pass through the cation region. As shown in Figure 10a, the main \t-V points form a triangular. When At abscissa is small, the density of points is large and V range s wide. With the increase of At, density of point and V range are decreased. Compared Figure 10a o Figure 10b, with the increase of applied voltage, the range of V increases, and the At decreases. ‘igure 11a,b show the V and At distribution proportions. For V, the shapes of the proportion curves are imilar in the beginning, and the abscissa of the highest proportion point gradually increases. While ’ overall increases, and V range expands significantly near breakdown. For At, with the increase of pplied voltage, the concentration degree of At is significantly increased. The highest proposition of he curve increases, and the abscissa of highest proposition point decreases. Similarly, the variations re especially obvious near the breakdown. It can be concluded that breakdown streamers in positive olarity are strong and intensive.
Figure 11. Proportion distribution diagrams at breakdown streamer. (a) Proportion distribution of V; (b) Proportion distribution of At.
Figure 11. Proportion distribution diagrams at breakdown streamer. (a) Proportion distribution of V; (b) Proportion distribution of At.
Figure 12. Average value diagram of n, V and At on negative polarity. The initial streamer stage is —8.5 kV to —9.0 kV. At the initial discharge voltage, E is low and the streamers are weak. V is low and At is large. With the increase of the applied voltage, the amount of cations increases, and E between needle tip and cations increased slightly. Recovery time of the electric field becomes shorter; thus n rises. Streamers are strengthened, and the space charges generated by a single discharge are also slightly increased, so V increased slightly.
Figure 12. Average value diagram of n, V and At on negative polarity. The initial streamer stage is —8.5 kV to —9.0 kV. At the initial discharge voltage, E is low and the streamers are weak. V is low and At is large. With the increase of the applied voltage, the amount of cations increases, and E between needle tip and cations increased slightly. Recovery time of the electric field becomes shorter; thus n rises. Streamers are strengthened, and the space charges generated by a single discharge are also slightly increased, so V increased slightly.
Figure 13. Equivalent charge quantity diagram of negative PD. The q diagram of negative polarity discharge pulse is shown in Figure 13. At initial streamer stage, q is small. Then, in the Trichel discharge stage, q increases linearly throughout the stage, which is verified in Figure 14b. The linear increase of q in the Trichel discharge stage also indicates that the electric field inside the cations layer is relatively flat. Subsequently, in glow discharge stage, q is approximately 0. When it comes to the breakdown streamer stage, g rises again.
Figure 13. Equivalent charge quantity diagram of negative PD. The q diagram of negative polarity discharge pulse is shown in Figure 13. At initial streamer stage, q is small. Then, in the Trichel discharge stage, q increases linearly throughout the stage, which is verified in Figure 14b. The linear increase of q in the Trichel discharge stage also indicates that the electric field inside the cations layer is relatively flat. Subsequently, in glow discharge stage, q is approximately 0. When it comes to the breakdown streamer stage, g rises again.
Figure 14. Linear fit analysis of n, q at Trichel discharge stage. (a) Linear fit of n; (b) Linear fit of q.
Figure 14. Linear fit analysis of n, q at Trichel discharge stage. (a) Linear fit of n; (b) Linear fit of q.
Figure 15. Variation coefficients diagram of negative polarity. PD fluctuation is researched by VC. As shown in Figure 15, for V, VC increases at initial streamet stage, has a sudden rise in —9 kV and then stable at the initial stage of Trichel discharge. It indicates that the gradually formed cation layer makes the electric field distribution uniform. At the later stage of Trichel discharge, VC remains stable after rising to a certain extent. It is because with the increase of plasma, E between the needle tip and the plasma layer is quicker strengthened. The electric field intensity in a certain region is all higher than Eg, so the streamer may develop in many paths withir the region. The development degree of the streamer varies, and the fluctuation of V is relatively large At the glow discharge stage, only few PD happen in peripheral regions of plasma. Few PD pulses with small V are achieved in tiny peripheral regions. So VC basically remains stable at glow discharge stage and it slightly decreases at the streamer breakdown stage.
Figure 15. Variation coefficients diagram of negative polarity. PD fluctuation is researched by VC. As shown in Figure 15, for V, VC increases at initial streamet stage, has a sudden rise in —9 kV and then stable at the initial stage of Trichel discharge. It indicates that the gradually formed cation layer makes the electric field distribution uniform. At the later stage of Trichel discharge, VC remains stable after rising to a certain extent. It is because with the increase of plasma, E between the needle tip and the plasma layer is quicker strengthened. The electric field intensity in a certain region is all higher than Eg, so the streamer may develop in many paths withir the region. The development degree of the streamer varies, and the fluctuation of V is relatively large At the glow discharge stage, only few PD happen in peripheral regions of plasma. Few PD pulses with small V are achieved in tiny peripheral regions. So VC basically remains stable at glow discharge stage and it slightly decreases at the streamer breakdown stage.
Figure 16. At-V distribution diagram of —8.75 kV at initial streamer stage. a a aI a I a aa aaa The typical At-V scatter diagram of the Trichel discharge stage is shown in Figure 18. Some At-V points form an inclined spindle. It indicates there is an approximate proportional relationship between V and At, which confirms the analysis in Section 2.3. In Figure 18a, at the initial stage, the points in high At abscissas are relatively intensive. In Figure 18b, the points in low At abscissas are intensive. The density of the points outside the spindle rises because plasma layers form in some regions. The weaken effect of cation layer for electric field outside decrease because of the plasma. So regions where E is higher than Eo were enhanced in some directions. Some At-V points in low-At abscissas have higher V, and their distribution does not follow the original proportional relationship.
Figure 16. At-V distribution diagram of —8.75 kV at initial streamer stage. a a aI a I a aa aaa The typical At-V scatter diagram of the Trichel discharge stage is shown in Figure 18. Some At-V points form an inclined spindle. It indicates there is an approximate proportional relationship between V and At, which confirms the analysis in Section 2.3. In Figure 18a, at the initial stage, the points in high At abscissas are relatively intensive. In Figure 18b, the points in low At abscissas are intensive. The density of the points outside the spindle rises because plasma layers form in some regions. The weaken effect of cation layer for electric field outside decrease because of the plasma. So regions where E is higher than Eo were enhanced in some directions. Some At-V points in low-At abscissas have higher V, and their distribution does not follow the original proportional relationship.
Figure 17. Proportion distribution diagrams of V at the initial streamer stage.
Figure 17. Proportion distribution diagrams of V at the initial streamer stage.
Figure 18. At—V distribution diagrams at Trichel discharge stage. (a) At-V distribution of —10 kV; (b) At-V distribution of —12 kV.
Figure 18. At—V distribution diagrams at Trichel discharge stage. (a) At-V distribution of —10 kV; (b) At-V distribution of —12 kV.
Figure 19. Proportion distribution diagrams at the initial stage of Trichel discharge. (a) Proportion distribution of V; (b) Proportion distribution of At. At the initial stage, the proportion distribution of V under different applied voltage are approximately similar, as shown in Figure 19a. At the later stage, the distribution curve of V overall moves to lower V abscissas gradually, and the highest proportion gradually increases, as shown in Figure 20a.
Figure 19. Proportion distribution diagrams at the initial stage of Trichel discharge. (a) Proportion distribution of V; (b) Proportion distribution of At. At the initial stage, the proportion distribution of V under different applied voltage are approximately similar, as shown in Figure 19a. At the later stage, the distribution curve of V overall moves to lower V abscissas gradually, and the highest proportion gradually increases, as shown in Figure 20a.
Figure 20. Proportion distribution diagrams at the last stage of Trichel discharge. (a) Proportion distribution of V; (b) Proportion distribution of Af.
Figure 20. Proportion distribution diagrams at the last stage of Trichel discharge. (a) Proportion distribution of V; (b) Proportion distribution of Af.
Figure 21. At-V distribution diagrams of glow discharge stage. (a) At-V distribution of —13 kV; (b) At-V distribution of —24 kV. Since PD in the glow-discharge stage are very few, only At-V distribution of the transition stages before and after glow-discharge stage are analyzed. The typical At-V scatter diagrams are shown in Figure 21a,b. The At—V points basically distribute in a horizontal band, which means V changes little, because PD can be measured are only generated in tiny regions. At-V distribution is similar to that of initial streamer stage.
Figure 21. At-V distribution diagrams of glow discharge stage. (a) At-V distribution of —13 kV; (b) At-V distribution of —24 kV. Since PD in the glow-discharge stage are very few, only At-V distribution of the transition stages before and after glow-discharge stage are analyzed. The typical At-V scatter diagrams are shown in Figure 21a,b. The At—V points basically distribute in a horizontal band, which means V changes little, because PD can be measured are only generated in tiny regions. At-V distribution is similar to that of initial streamer stage.
Figure 22. Proportion distribution diagrams at glow discharge stage. (a) Proportion distribution of V; (b) Proportion distribution of At. Proportion distributions of V and At at glow discharge stage are shown in Figure 22. In Figure 22a it can be found that the V proportion curves at transition stage after glow discharge have double peak The points in low-V abscissas peak should link to PD in few peripheral regions of cation layer where E drops below Ep after a streamer. So the low V abscissas peak in proportion curves of transition stage after the glow discharge, are similar to the single peak in proportion curves of transition stage before the glow discharge. The points in high V peak link to PD starting from the outer edge of plasma layer The two forms of discharge streamers have obvious difference, thus form the double peaks.
Figure 22. Proportion distribution diagrams at glow discharge stage. (a) Proportion distribution of V; (b) Proportion distribution of At. Proportion distributions of V and At at glow discharge stage are shown in Figure 22. In Figure 22a it can be found that the V proportion curves at transition stage after glow discharge have double peak The points in low-V abscissas peak should link to PD in few peripheral regions of cation layer where E drops below Ep after a streamer. So the low V abscissas peak in proportion curves of transition stage after the glow discharge, are similar to the single peak in proportion curves of transition stage before the glow discharge. The points in high V peak link to PD starting from the outer edge of plasma layer The two forms of discharge streamers have obvious difference, thus form the double peaks.
Figure 23. At-V distribution of —26 kV at breakdown streamer stage. At breakdown streamer stage, At significantly decreases. The typical At—V scatter diagram is shown in Figure 23. The distribution of At-V points form a sharp cone like shape. In this situation, the discharge region is close to the plate, and the axial electric field is stronger than other directions. In axial direction streamers are continuously produced. Therefore, low At and high V discharge pulses account for the main proportion. Proportion distribution characteristics of V and At at breakdown discharge stage are also shown in Figure 24. In Figure 24b, it can be observed that the concentration degree of At is significantly increased as it approaches breakdown.
Figure 23. At-V distribution of —26 kV at breakdown streamer stage. At breakdown streamer stage, At significantly decreases. The typical At—V scatter diagram is shown in Figure 23. The distribution of At-V points form a sharp cone like shape. In this situation, the discharge region is close to the plate, and the axial electric field is stronger than other directions. In axial direction streamers are continuously produced. Therefore, low At and high V discharge pulses account for the main proportion. Proportion distribution characteristics of V and At at breakdown discharge stage are also shown in Figure 24. In Figure 24b, it can be observed that the concentration degree of At is significantly increased as it approaches breakdown.
Figure 24. Proportion distribution diagrams at breakdown streamer stage. (a) Proportion distribution of V; (b) Proportion distribution of At. 5. Discussion
Figure 24. Proportion distribution diagrams at breakdown streamer stage. (a) Proportion distribution of V; (b) Proportion distribution of At. 5. Discussion
Figure 1. Electric field in the vicinity of the shield discontinuity [11]. To carry out the installation in field or breakdown voltage tests in insulated cables, it is necessary to remove a part of the cable insulation. While the electric field inside the effective length has a predictable distribution, with a radial direction and logarithmical behavior [1,2,10], there is a great field intensification at the cable ends. The electric field in the vicinity of the shield end is illustrated in Figure 1. Thus, such a predictable distribution should be guaranteed to allow successful tests.
Figure 1. Electric field in the vicinity of the shield discontinuity [11]. To carry out the installation in field or breakdown voltage tests in insulated cables, it is necessary to remove a part of the cable insulation. While the electric field inside the effective length has a predictable distribution, with a radial direction and logarithmical behavior [1,2,10], there is a great field intensification at the cable ends. The electric field in the vicinity of the shield end is illustrated in Figure 1. Thus, such a predictable distribution should be guaranteed to allow successful tests.
Figure 2. Cable layers.
Figure 2. Cable layers.
Table 1. Termination and cable materials.
Table 1. Termination and cable materials.
Figure 3. (a) Detail of the cable termination and (b) field intensification on the same area. With the selected physics and material properties, the initial geometry of the cable termination that presented external discharges was modeled and simulated in order to identify the points where the electric field exceeded the breakdown’s stipulated limits for the air. Figure 3 shows that the intensification of the electric field occurred at the cable termination. Due to the high-intensity electric field at the external shielding end, it was necessary to build a termination model for the cable to accomplish successful overvoltage tests. By applying the steps presented for preparing the simulation environment, we simulated successive cable termination geometries from the concept of the stress relief cone. Several models were created and tested until a final configuration was established. The main objectives of the simulations were to minimize the electric field near the cutting region of the semiconductor layer and in the air region between the termination and the high-voltage electrode, in order to minimize corona and reduce the possibility of discharges between the high-voltage electrode and the external grounded shield. Thus, in an overvoltage test, the insulation evaluated was guaranteed to be the internal one, since it was subjected to greater electrical stresses.
Figure 3. (a) Detail of the cable termination and (b) field intensification on the same area. With the selected physics and material properties, the initial geometry of the cable termination that presented external discharges was modeled and simulated in order to identify the points where the electric field exceeded the breakdown’s stipulated limits for the air. Figure 3 shows that the intensification of the electric field occurred at the cable termination. Due to the high-intensity electric field at the external shielding end, it was necessary to build a termination model for the cable to accomplish successful overvoltage tests. By applying the steps presented for preparing the simulation environment, we simulated successive cable termination geometries from the concept of the stress relief cone. Several models were created and tested until a final configuration was established. The main objectives of the simulations were to minimize the electric field near the cutting region of the semiconductor layer and in the air region between the termination and the high-voltage electrode, in order to minimize corona and reduce the possibility of discharges between the high-voltage electrode and the external grounded shield. Thus, in an overvoltage test, the insulation evaluated was guaranteed to be the internal one, since it was subjected to greater electrical stresses.
Figure 4. Main intermediate stages of the termination design: (a) initial stress cone; (b) enhanced stress cone and corona ring inserted; (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position. Initially, the main intermediate stages of the termination design are shown in Figure 4.
Figure 4. Main intermediate stages of the termination design: (a) initial stress cone; (b) enhanced stress cone and corona ring inserted; (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position. Initially, the main intermediate stages of the termination design are shown in Figure 4.
Figure 5. Cont. a conductive material with a metal ring for improving the field distribution was applied to the d termination on the outer surface of the cone. A corona ring was also added to the high-voltage rode. In the Figure 4c configuration, the cone length was increased, the geometry was improved the corona ring position was modified. In Figure 4d, the portion of the stress cone in which the nal shield ends was modified again, and the position of the corona ring was optimized. In Figures 5 and 6, the potential distribution and maximum electric field around the termination hawn in the camo nrdor ac the fair intermediate ctacec nrecented jin Fiore 4
Figure 5. Cont. a conductive material with a metal ring for improving the field distribution was applied to the d termination on the outer surface of the cone. A corona ring was also added to the high-voltage rode. In the Figure 4c configuration, the cone length was increased, the geometry was improved the corona ring position was modified. In Figure 4d, the portion of the stress cone in which the nal shield ends was modified again, and the position of the corona ring was optimized. In Figures 5 and 6, the potential distribution and maximum electric field around the termination hawn in the camo nrdor ac the fair intermediate ctacec nrecented jin Fiore 4
Figure 5. Potential distribution and electric field lines for the configurations of cable termination shown in Figure 4: (a) initial stress cone, (b) enhanced stress cone and corona ring inserted, (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position.
Figure 5. Potential distribution and electric field lines for the configurations of cable termination shown in Figure 4: (a) initial stress cone, (b) enhanced stress cone and corona ring inserted, (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position.
Figure 6. Cont. As can be observed in Figure 5, a progressive change in the potential distribution was achieve: due to modifications in the geometry. Moreover, as indicated in Figure 6, there was a progressiv' decrease of the maximum electric field in the air as the termination was being improved.
Figure 6. Cont. As can be observed in Figure 5, a progressive change in the potential distribution was achieve: due to modifications in the geometry. Moreover, as indicated in Figure 6, there was a progressiv' decrease of the maximum electric field in the air as the termination was being improved.
Figure 6. Electric field distribution and position of its maximum value for the configurations of cable termination shown in Figure 4: (a) initial stress cone; (b) enhanced stress cone and corona ring inserted; (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position. Figure 6. Electric field distribution and position of its maximum value for the configurations of cable
Figure 6. Electric field distribution and position of its maximum value for the configurations of cable termination shown in Figure 4: (a) initial stress cone; (b) enhanced stress cone and corona ring inserted; (c) elongated stress cone with terminal away and (d) improvement in external shield and corona ring position. Figure 6. Electric field distribution and position of its maximum value for the configurations of cable
Figure 7. Drawing of the proposed model geometry. In the final version of the proposed termination, a rubber-composed stress relief cone and a termination electrode with a round end were designed. Near the cone, the termination also had rubber sheds to prevent the formation of a superficial discharge. At the end of the termination itself, a sphere-shaped corona ring was used for decreasing the electric field enhancement at the cable end. A drawing of the final termination design is shown in Figure 7.
Figure 7. Drawing of the proposed model geometry. In the final version of the proposed termination, a rubber-composed stress relief cone and a termination electrode with a round end were designed. Near the cone, the termination also had rubber sheds to prevent the formation of a superficial discharge. At the end of the termination itself, a sphere-shaped corona ring was used for decreasing the electric field enhancement at the cable end. A drawing of the final termination design is shown in Figure 7.
Table 2. Maximum electric field calculated for the analyzed termination designs. The results shown hereafter refer to the final termination design. The obtained result for the inner electric field on the termination is presented in the color plot in Figure 10.
Table 2. Maximum electric field calculated for the analyzed termination designs. The results shown hereafter refer to the final termination design. The obtained result for the inner electric field on the termination is presented in the color plot in Figure 10.
Figure 8. 3D drawing views of the designed termination. After the design definition, its dimensions were obtained, and an 2D-revolution form of the termination was drawn by using AutoCAD® computer-aided design software (2018 student version, AutoDesk, Inc., San Rafael, CA, USA). 3D drawing views of the designed termination are shown in Figure 8.
Figure 8. 3D drawing views of the designed termination. After the design definition, its dimensions were obtained, and an 2D-revolution form of the termination was drawn by using AutoCAD® computer-aided design software (2018 student version, AutoDesk, Inc., San Rafael, CA, USA). 3D drawing views of the designed termination are shown in Figure 8.
Figure 9. (a) Potential distribution and (b) external electric field distribution for the final version of the proposed cable termination.
Figure 9. (a) Potential distribution and (b) external electric field distribution for the final version of the proposed cable termination.
Figure 10. Electric field on the effective length end.
Figure 10. Electric field on the effective length end.
Figure 11. Paths for analysis of the electric field distribution.
Figure 11. Paths for analysis of the electric field distribution.
Figure 12. Distribution of electric fields over the termination. In Figure 12, the distribution of the electric field over the points of Figure 11 is presented. Figure 12 curves represent the electric field decay along the insulating material radius. It is expected that a discharge must begin from a point where the field intensification is maximum. According to the standards, this point shall be inside the effective length of the cable, far enough from the external shield end.
Figure 12. Distribution of electric fields over the termination. In Figure 12, the distribution of the electric field over the points of Figure 11 is presented. Figure 12 curves represent the electric field decay along the insulating material radius. It is expected that a discharge must begin from a point where the field intensification is maximum. According to the standards, this point shall be inside the effective length of the cable, far enough from the external shield end.
Figure 13. Electric field along the inner conductor length.
Figure 13. Electric field along the inner conductor length.
Figure 14. Outer path for external electric field analysis.
Figure 14. Outer path for external electric field analysis.
Figure 15. Simulated electric field along a path adjacent to the termination surface, highlighted in red in Figure 14.
Figure 15. Simulated electric field along a path adjacent to the termination surface, highlighted in red in Figure 14.
Table 1. Dimension of the 363 kV VCB. Table 2. Parameters of the 40.5 kV VCB.
Table 1. Dimension of the 363 kV VCB. Table 2. Parameters of the 40.5 kV VCB.
The vacuum interrupter worked with a fast short circuit current prediction algorithm and a phase control system. The moving contact was driven by an ultrafast electromagnetic repulsion mechanism, so the opening time (500 ts) and opening velocity (up to 5 m/s) could be achieved [6,15]. It adopted a fiber-controlled system to synchronize the VCBs. The open dispersibility (i.e., the time delay of the
The vacuum interrupter worked with a fast short circuit current prediction algorithm and a phase control system. The moving contact was driven by an ultrafast electromagnetic repulsion mechanism, so the opening time (500 ts) and opening velocity (up to 5 m/s) could be achieved [6,15]. It adopted a fiber-controlled system to synchronize the VCBs. The open dispersibility (i.e., the time delay of the
Figure 1. Topology of a 363 kV sextuple-break vacuum circuit breaker (VCB). Notes: QF means VCB; C means grading capacitor. 40.5 kV VCB is 2500 A, so a parallel structure of two branches is needed for a rated current of 5000 A and a rated breaking current of 63 kA. To allow for sufficient breaking capacity and sufficient margin sextuple-break with two branches of parallel structure was adopted. Consequently, the physical structure of the proposed 363 kV VCB was formed by 1240.5 kV VCBs in a series-parallel structure with grading capacitors and inductors (see Figure 1). Series inductors were used to share the current for each phase and grading capacitors were used to share the voltage for each break.
Figure 1. Topology of a 363 kV sextuple-break vacuum circuit breaker (VCB). Notes: QF means VCB; C means grading capacitor. 40.5 kV VCB is 2500 A, so a parallel structure of two branches is needed for a rated current of 5000 A and a rated breaking current of 63 kA. To allow for sufficient breaking capacity and sufficient margin sextuple-break with two branches of parallel structure was adopted. Consequently, the physical structure of the proposed 363 kV VCB was formed by 1240.5 kV VCBs in a series-parallel structure with grading capacitors and inductors (see Figure 1). Series inductors were used to share the current for each phase and grading capacitors were used to share the voltage for each break.
operation of all VCBs) of these VCBs was shorter than 0.1 ms, and the closed dispersibility was shorter than 0.2 ms. Thus, combined with the above components, a quick current interruption within a short arcing time (3 ms) was achieved. Compared to typical high-voltage circuit breakers 30-60 ms, the total interruption time was reduced to 10-20 ms.
operation of all VCBs) of these VCBs was shorter than 0.1 ms, and the closed dispersibility was shorter than 0.2 ms. Thus, combined with the above components, a quick current interruption within a short arcing time (3 ms) was achieved. Compared to typical high-voltage circuit breakers 30-60 ms, the total interruption time was reduced to 10-20 ms.
Note: V1 to V6 denote the first to sixth breaks. Table 3. Voltage sharing of each break.
Note: V1 to V6 denote the first to sixth breaks. Table 3. Voltage sharing of each break.
Figure 3. The mesh of the simulation model.
Figure 3. The mesh of the simulation model.
Figure 4. The static voltage and electric field distribution of the 363 kV VCB.
Figure 4. The static voltage and electric field distribution of the 363 kV VCB.
Figure 5. The conductor definitions. system 1s determined by the seli-capacitance and mutual capacitance of these conductors. The commercial COMSOL software can easily obtain the distributed capacitance and extract a capacitance matrix by defining the conductors successively. As shown in Figure 5, all of the 13 conductors were defined, where the incoming busbar, the upper terminal of the first break, and the static contact were defined as conductor 1; the main shield, which is the floating potential, of the first VCB as conductor 2; the lower terminal of the first break, lower busbar, and the lower terminal of the second break as conductor 3; and so forth, and the exterior tank was grounded. Among the conductors, conductor 13 was composed of the last connecting terminal, last busbar, and outside tank. The capacitances between the moving contact and the static contact, and the capacitance between the conductor and the tank made a greater difference. Therefore, other stray capacitances between the conductors that were at a great distance from each other, such as the capacitance between the main shields of different VCBs, were ignored. According to the calculated capacitance matrix, the stray capacitances to the earth were greater than the capacitance of the break of the VCB, which makes the voltage of each break unequal, indicating the need for a voltage sharing design. A grading capacitor was an effective and low-cost measure to balance the voltage of each break. To analyze the influence of the grading capacitor, the equivalent circuit model can be used. Figure 6a illustrates the equivalent capacitance network and the simulation model with a grading capacitor in PSCAD of the 363 kV VCB, where C1 was the capacitance between the moving contact and the static contact of the first break, and C10 was the capacitance between conductor 1 and the tank. Cg was the grading capacitor. The capacitance between the main shield and nearby conductors, which was very small, was attributed to the capacitance nearby to simplify the equivalent capacitor network under the criterion that the voltage of each break equals the results of the FEM simulation. Finally, parameters for the equivalent circuit simulation model were as follows: C1 =C2=C3 =C4=C5 = C6 = 14.7 pF; C20 = C40 = C60 = 80 pF; C30 = C50 = 76 pF.
Figure 5. The conductor definitions. system 1s determined by the seli-capacitance and mutual capacitance of these conductors. The commercial COMSOL software can easily obtain the distributed capacitance and extract a capacitance matrix by defining the conductors successively. As shown in Figure 5, all of the 13 conductors were defined, where the incoming busbar, the upper terminal of the first break, and the static contact were defined as conductor 1; the main shield, which is the floating potential, of the first VCB as conductor 2; the lower terminal of the first break, lower busbar, and the lower terminal of the second break as conductor 3; and so forth, and the exterior tank was grounded. Among the conductors, conductor 13 was composed of the last connecting terminal, last busbar, and outside tank. The capacitances between the moving contact and the static contact, and the capacitance between the conductor and the tank made a greater difference. Therefore, other stray capacitances between the conductors that were at a great distance from each other, such as the capacitance between the main shields of different VCBs, were ignored. According to the calculated capacitance matrix, the stray capacitances to the earth were greater than the capacitance of the break of the VCB, which makes the voltage of each break unequal, indicating the need for a voltage sharing design. A grading capacitor was an effective and low-cost measure to balance the voltage of each break. To analyze the influence of the grading capacitor, the equivalent circuit model can be used. Figure 6a illustrates the equivalent capacitance network and the simulation model with a grading capacitor in PSCAD of the 363 kV VCB, where C1 was the capacitance between the moving contact and the static contact of the first break, and C10 was the capacitance between conductor 1 and the tank. Cg was the grading capacitor. The capacitance between the main shield and nearby conductors, which was very small, was attributed to the capacitance nearby to simplify the equivalent capacitor network under the criterion that the voltage of each break equals the results of the FEM simulation. Finally, parameters for the equivalent circuit simulation model were as follows: C1 =C2=C3 =C4=C5 = C6 = 14.7 pF; C20 = C40 = C60 = 80 pF; C30 = C50 = 76 pF.
Table 4. Voltage of the first break at different grading capacitor values.
Table 4. Voltage of the first break at different grading capacitor values.
Figure 6. The equivalent circuit model of the 363 kV VCB with a grading capacitor.
Figure 6. The equivalent circuit model of the 363 kV VCB with a grading capacitor.
Figure 7. Influence of grading capacitors for the 363 kV VCB. The voltage unbalance coefficient (K) is defined as:
Figure 7. Influence of grading capacitors for the 363 kV VCB. The voltage unbalance coefficient (K) is defined as:
Figure 8. Breaking test circuit for the 363 kV VCB.G, generator; GB, generator breaker; MS, make switch; MB, master breaker; L, reactor; PT, power transformer; R, resistor; C, capacitor; To, test object; R, arc prolonging circuit; V, voltage measurement; GP, gap; I, current measurement; AB, auxiliary breaker.
Figure 8. Breaking test circuit for the 363 kV VCB.G, generator; GB, generator breaker; MS, make switch; MB, master breaker; L, reactor; PT, power transformer; R, resistor; C, capacitor; To, test object; R, arc prolonging circuit; V, voltage measurement; GP, gap; I, current measurement; AB, auxiliary breaker.
Figure 9. Test waveforms of the synthetic breaking test at 63 kA. The prototype of the 363 kV sextuple-break VCB interrupted the short circuit current (symmetrical and asymmetrical) successfully in a high-voltage apparatus quality supervision and inspection test center as a preliminary research test. The key information is summarized in Table 5, and all recorded waveforms of the breaking current and the TRV are shown in Figures 9 and 10. In Figures 9 and 10, Tis the test current, Ih is the small zero crossing current of synthetic test circuit, Ur is the total transient recovery voltage, Ucs is the voltage of the current source, HFUcs is the high-frequency voltage of the current source, and HFUr is the high-frequency transient recovery voltage. The recovery voltage is less than 258 kV and the TRV peak is less than 544 kV, which indicates that the grading capacitors of 10 nF can meet the requirement of the voltage sharing design and breaking capacity.
Figure 9. Test waveforms of the synthetic breaking test at 63 kA. The prototype of the 363 kV sextuple-break VCB interrupted the short circuit current (symmetrical and asymmetrical) successfully in a high-voltage apparatus quality supervision and inspection test center as a preliminary research test. The key information is summarized in Table 5, and all recorded waveforms of the breaking current and the TRV are shown in Figures 9 and 10. In Figures 9 and 10, Tis the test current, Ih is the small zero crossing current of synthetic test circuit, Ur is the total transient recovery voltage, Ucs is the voltage of the current source, HFUcs is the high-frequency voltage of the current source, and HFUr is the high-frequency transient recovery voltage. The recovery voltage is less than 258 kV and the TRV peak is less than 544 kV, which indicates that the grading capacitors of 10 nF can meet the requirement of the voltage sharing design and breaking capacity.
Table 5. Results of the breaking test. 6. Summary and Conclusions
Table 5. Results of the breaking test. 6. Summary and Conclusions
Figure 10. Test waveforms of the synthetic breaking test at 80 kA.
Figure 10. Test waveforms of the synthetic breaking test at 80 kA.
Figure 1. Measurement topologies for D/I and divider methods. Component values for D/I are such that the receiving cable end represents the time derivative of phase voltage Uyy and the waveform is restored by integration (the open-air sensor design is shown on the left); For standard dividers this signal directly represents the phase voltage Upy. The fraction of Upy arising at the receiving end of the cable is a division over the impedances at both ends as shown in the right side of Figure 2. For the D/I concept this is rather a small fraction,
Figure 1. Measurement topologies for D/I and divider methods. Component values for D/I are such that the receiving cable end represents the time derivative of phase voltage Uyy and the waveform is restored by integration (the open-air sensor design is shown on the left); For standard dividers this signal directly represents the phase voltage Upy. The fraction of Upy arising at the receiving end of the cable is a division over the impedances at both ends as shown in the right side of Figure 2. For the D/I concept this is rather a small fraction,
Figure 2. Effect of induced ground currents along the measurement cable (left); Through the cable transfer impedance the resulting common mode current Icjy causes a differential mode voltage Up which divides over the impedances at the cable ends (right). whereas for a divider it is the major part. In addition, the integration step in the D/I system reduces high frequency interference, which may have entered the measurement cable. Results will be presented comparing the D/I approach with results from pre-installed dividers near underground power cables at their transition points to overhead lines. 3. Results
Figure 2. Effect of induced ground currents along the measurement cable (left); Through the cable transfer impedance the resulting common mode current Icjy causes a differential mode voltage Up which divides over the impedances at the cable ends (right). whereas for a divider it is the major part. In addition, the integration step in the D/I system reduces high frequency interference, which may have entered the measurement cable. Results will be presented comparing the D/I approach with results from pre-installed dividers near underground power cables at their transition points to overhead lines. 3. Results
This equation is applied for each measured sample point. The square roots of the diagonal components in Ey provide the standard deviations for each phase (per sample point). Adding and subtracting the deviations provide the confidence intervals of the reconstructed waveforms. The matrix Oj, represents a linearization of how component y; of the inverted matrix depends on a variation in the value x; of the original coupling matrix. Its calculation can conveniently be implemented by slightly varying numerically each coupling matrix component Mj separately. Next, the phase voltage waveforms are reconstructed by matrix multiplication for each sample in the measurement recordings. The propagation of the error is described by means of matrix O2 which provides information on how each of the three reconstructed phase voltages varies upon variation in each of the inverted matrix components. The reconstructed phase waveforms are evaluated with [13,14]: 3.1.1. Substation The configuration with a line ending at a GIS substation is depicted in Figure 3a. The chosen sensor positioning leaves a reflection symmetric configuration. This leads to equal coupling of the central sensor to the outer phase voltages. Similarly, the coupling of the outer sensors to the central phase conductors are equal. A fundamental problem, as mentioned above, relates to the fact that from calibrating by means of symmetric phase voltages it is impossible to distinguish the contribution of the
This equation is applied for each measured sample point. The square roots of the diagonal components in Ey provide the standard deviations for each phase (per sample point). Adding and subtracting the deviations provide the confidence intervals of the reconstructed waveforms. The matrix Oj, represents a linearization of how component y; of the inverted matrix depends on a variation in the value x; of the original coupling matrix. Its calculation can conveniently be implemented by slightly varying numerically each coupling matrix component Mj separately. Next, the phase voltage waveforms are reconstructed by matrix multiplication for each sample in the measurement recordings. The propagation of the error is described by means of matrix O2 which provides information on how each of the three reconstructed phase voltages varies upon variation in each of the inverted matrix components. The reconstructed phase waveforms are evaluated with [13,14]: 3.1.1. Substation The configuration with a line ending at a GIS substation is depicted in Figure 3a. The chosen sensor positioning leaves a reflection symmetric configuration. This leads to equal coupling of the central sensor to the outer phase voltages. Similarly, the coupling of the outer sensors to the central phase conductors are equal. A fundamental problem, as mentioned above, relates to the fact that from calibrating by means of symmetric phase voltages it is impossible to distinguish the contribution of the
Figure 3. Topologies and sensor (u;) positioning with respect to phase voltages Uj: (a) Overhead line ending at a substation, photo shows the installation of the sensors; (b) Overhead line to underground power cable transition (with termination T, surge arrester S.arr. and voltage transformer V.tr.), photos show the sensor (as seen from below) and its positioning in between two terminations belonging to the same phase. The sensor heights (indicated with arrows) are always chosen such, that they remain below the height reached by the supporting structures of the terminations. The parameters a; and b; are obtained from fitting sinusoidal functions to the last five cycles in the recordings as shown in Figure 4a (left). Equation (10) is solved numerically in @9 and subsequently all matrix components M; can be calculated. The solution depends on the stochastic variable Aj. The other stochastic variables do not affect the solution of (1) and their effect on the coupling matrix elements can be added afterwards.
Figure 3. Topologies and sensor (u;) positioning with respect to phase voltages Uj: (a) Overhead line ending at a substation, photo shows the installation of the sensors; (b) Overhead line to underground power cable transition (with termination T, surge arrester S.arr. and voltage transformer V.tr.), photos show the sensor (as seen from below) and its positioning in between two terminations belonging to the same phase. The sensor heights (indicated with arrows) are always chosen such, that they remain below the height reached by the supporting structures of the terminations. The parameters a; and b; are obtained from fitting sinusoidal functions to the last five cycles in the recordings as shown in Figure 4a (left). Equation (10) is solved numerically in @9 and subsequently all matrix components M; can be calculated. The solution depends on the stochastic variable Aj. The other stochastic variables do not affect the solution of (1) and their effect on the coupling matrix elements can be added afterwards.
Figure 4. Reconstructed waveforms for substation measurements recorded with 5 Msample/s over a duration corresponding to ten power cycles. The curves in colour represent the three phases with confidence margins in black: (a) Full and 10 times zoomed waveform showing overvoltages during the first cycle from energization at the far end of the connection; (b) Waveform with overvoltages during the first power cycle from energization at the near end and 10 times zoomed waveform revealing initial travelling waves along the connection. The extrapolated power cycles (dash-dotted lines) indicate the 50 Hz phase angles at the moments of contact. Figure 4. Reconstructed waveforms for substation measurements recorded with 5 Msample/s over Figure 4 shows the results upon line energization from the far end of the connection and from the substation where the measurements are taken. The black lines indicate one standard deviation confidence margin and the dash-dotted lines are extrapolated steady state phase voltages. The complete waveform in Figure 4a includes the recording of the steady state power frequency established after the switching transient. The last five cycles are employed for determining the coupling matrix. The zoomed figure shows that within the confidence bounds the overvoltage magnitude remains clearly below 2 pu. The switching event in Figure 4b contains steep transients as energization takes place near the measurement location. The zoomed waveform indicates that these relate to travelling waves, which reflect on the line to cable transition point at 6.8 km distance. Also here no serious overvoltages were observed.
Figure 4. Reconstructed waveforms for substation measurements recorded with 5 Msample/s over a duration corresponding to ten power cycles. The curves in colour represent the three phases with confidence margins in black: (a) Full and 10 times zoomed waveform showing overvoltages during the first cycle from energization at the far end of the connection; (b) Waveform with overvoltages during the first power cycle from energization at the near end and 10 times zoomed waveform revealing initial travelling waves along the connection. The extrapolated power cycles (dash-dotted lines) indicate the 50 Hz phase angles at the moments of contact. Figure 4. Reconstructed waveforms for substation measurements recorded with 5 Msample/s over Figure 4 shows the results upon line energization from the far end of the connection and from the substation where the measurements are taken. The black lines indicate one standard deviation confidence margin and the dash-dotted lines are extrapolated steady state phase voltages. The complete waveform in Figure 4a includes the recording of the steady state power frequency established after the switching transient. The last five cycles are employed for determining the coupling matrix. The zoomed figure shows that within the confidence bounds the overvoltage magnitude remains clearly below 2 pu. The switching event in Figure 4b contains steep transients as energization takes place near the measurement location. The zoomed waveform indicates that these relate to travelling waves, which reflect on the line to cable transition point at 6.8 km distance. Also here no serious overvoltages were observed.
Figure 5. Part of the reconstructed waveforms (covering 10 cycles recorded with 5 Msample/s) around the switching moment for measurement at transition points. Coloured curves represent the phase voltages with one standard deviation confidence margins indicated in black: (a) Overvoltages from energization at the substation connected by 4.4 km overhead line to the transition point; (b) Overvoltages from energization at the substation connected via 6.8 km overhead line. Moments of contact can be observed from the extrapolated power frequency waveforms (dash-dotted lines). Figure 5. Part of the reconstructed waveforms (covering 10 cycles recorded with 5 Msample/s) around ALARA VVC VEE ee Figure 5 shows the results obtained at the transition points. In both cases the overhead line leaving from the measurement location was energized at its far end. The confidence bounds are significantly smaller compared to those obtained in the substation measurements. Apparently, shielding by the terminations at either side of the sensors reduce cross-coupling significantly. Uncertainties in the cross-coupling therefore have minor effect on the reconstructed waveforms. Also here it was confirmed that the maximum voltages remain within safe limits.
Figure 5. Part of the reconstructed waveforms (covering 10 cycles recorded with 5 Msample/s) around the switching moment for measurement at transition points. Coloured curves represent the phase voltages with one standard deviation confidence margins indicated in black: (a) Overvoltages from energization at the substation connected by 4.4 km overhead line to the transition point; (b) Overvoltages from energization at the substation connected via 6.8 km overhead line. Moments of contact can be observed from the extrapolated power frequency waveforms (dash-dotted lines). Figure 5. Part of the reconstructed waveforms (covering 10 cycles recorded with 5 Msample/s) around ALARA VVC VEE ee Figure 5 shows the results obtained at the transition points. In both cases the overhead line leaving from the measurement location was energized at its far end. The confidence bounds are significantly smaller compared to those obtained in the substation measurements. Apparently, shielding by the terminations at either side of the sensors reduce cross-coupling significantly. Uncertainties in the cross-coupling therefore have minor effect on the reconstructed waveforms. Also here it was confirmed that the maximum voltages remain within safe limits.
Figure 6. Comparison between D/I measurement (continuous lines in colour for the three phases) and PSCAD simulations (dash-dotted black lines). Generally, the maximum overvoltage value observed for each switching event and phase agree well with calculations for: (a) Recording at substation with energization from far end substation; (b) Recording and energization at the same substation; (c) Energization at substation 4.4 km from the observed transition point; (d) Energization from substation at 6.8 km from the observed transition point. Figure 6. Comparison between D/I measurement (continuous lines in colour for the three phases) and Measurements were conducted at both line to cable transition points and at one of the substations. At each location six switching actions were performed differing in the side from which the connection was energized, the operation state of the parallel circuit and the choice of the parallel circuits to be energized. A selection is presented in Figure 6, corresponding to the results in Figures 4 and 5, with the parallel circuit de-energized.
Figure 6. Comparison between D/I measurement (continuous lines in colour for the three phases) and PSCAD simulations (dash-dotted black lines). Generally, the maximum overvoltage value observed for each switching event and phase agree well with calculations for: (a) Recording at substation with energization from far end substation; (b) Recording and energization at the same substation; (c) Energization at substation 4.4 km from the observed transition point; (d) Energization from substation at 6.8 km from the observed transition point. Figure 6. Comparison between D/I measurement (continuous lines in colour for the three phases) and Measurements were conducted at both line to cable transition points and at one of the substations. At each location six switching actions were performed differing in the side from which the connection was energized, the operation state of the parallel circuit and the choice of the parallel circuits to be energized. A selection is presented in Figure 6, corresponding to the results in Figures 4 and 5, with the parallel circuit de-energized.
Figure 7. Comparison of results from D/I methodology (top figures, black lines indicate the uncertainty margins caused by uncertainty in decoupling), PSCAD simulation (middle figures) and RC-divider results (bottom figures): (a) Energization from substation connected by 4.4 km overhead line to the transition point; (b) Energization from substation connected via 6.8 km overhead line. For both switching events the high frequency oscillations are overrepresented in the divider measurement as compared to both D/I measurement and simulation. Figure 7 shows the result from simultaneous measurement with the D/I method (top figures) and an RC divider (bottom figures). In between, the PSCAD simulations are presented. The measurements are taken at both transition points with the parallel circuit in service. It is observed that oscillations occur in the divider response, which are far more severe than found in both the simulation and the D/I response. It should be noted that, although simulation and D/I response are quite similar, also here the measured oscillation immediately after energizing is somewhat stronger than simulated.
Figure 7. Comparison of results from D/I methodology (top figures, black lines indicate the uncertainty margins caused by uncertainty in decoupling), PSCAD simulation (middle figures) and RC-divider results (bottom figures): (a) Energization from substation connected by 4.4 km overhead line to the transition point; (b) Energization from substation connected via 6.8 km overhead line. For both switching events the high frequency oscillations are overrepresented in the divider measurement as compared to both D/I measurement and simulation. Figure 7 shows the result from simultaneous measurement with the D/I method (top figures) and an RC divider (bottom figures). In between, the PSCAD simulations are presented. The measurements are taken at both transition points with the parallel circuit in service. It is observed that oscillations occur in the divider response, which are far more severe than found in both the simulation and the D/I response. It should be noted that, although simulation and D/I response are quite similar, also here the measured oscillation immediately after energizing is somewhat stronger than simulated.
Figure 8. Comparison of measurement and simulation for transition overvoltages upon energizing from nearby substation: (a) Results for the substation; (b) Results for the two transition points. 5.8%, Figure 8a) is only slightly larger as compared to the width for the two transition points (6.0%, igure 8b). On one hand, this shows that the modelling method is adequate and predicts observations vell. On the other hand, it does not represent the difference in measurement accuracy expected from oth locations. Apparently, the simulations also contribute to deviations. This is not surprising as, Ithough the complete Dutch EHV grid was simulated in large detail, a number of simplifications vere made. Connections to downstream networks (110, 150, 220 kV) were replaced by equivalent mpedances based on active and reactive power consumption by the loads according to powerflow alculations [7]. Moreover, connections abroad were not modelled in detail.
Figure 8. Comparison of measurement and simulation for transition overvoltages upon energizing from nearby substation: (a) Results for the substation; (b) Results for the two transition points. 5.8%, Figure 8a) is only slightly larger as compared to the width for the two transition points (6.0%, igure 8b). On one hand, this shows that the modelling method is adequate and predicts observations vell. On the other hand, it does not represent the difference in measurement accuracy expected from oth locations. Apparently, the simulations also contribute to deviations. This is not surprising as, Ithough the complete Dutch EHV grid was simulated in large detail, a number of simplifications vere made. Connections to downstream networks (110, 150, 220 kV) were replaced by equivalent mpedances based on active and reactive power consumption by the loads according to powerflow alculations [7]. Moreover, connections abroad were not modelled in detail.
Figure 1. Element lenght in per-unit grounding wire illustration of implementation. The element length in per-unit model of the grounding wire is implemented in Matlab as a T-section of the transmission line model. The grounding wire implementation is illustrated with fundamental electrical elements and measurement nodes in Figure 1 which forms a horizontal buried grounding wire. From the grounding wire t-section development, the grounding system is implemented by an appropriate number of T-sections and additional nodes using Simulink graphical block elements. The grounding system layout with formation strategy is illustrated Figure 2 which gives references to the simulation database is found in Appendix B. To assure a smooth representation of the interconnection between elements, and to possibly extend the model functionality to include mutual couplings, the T-section represent one meter of ground wire (in per-unit) [4]. Consequently, the model can be extended to arbitrary lengths and configurations.
Figure 1. Element lenght in per-unit grounding wire illustration of implementation. The element length in per-unit model of the grounding wire is implemented in Matlab as a T-section of the transmission line model. The grounding wire implementation is illustrated with fundamental electrical elements and measurement nodes in Figure 1 which forms a horizontal buried grounding wire. From the grounding wire t-section development, the grounding system is implemented by an appropriate number of T-sections and additional nodes using Simulink graphical block elements. The grounding system layout with formation strategy is illustrated Figure 2 which gives references to the simulation database is found in Appendix B. To assure a smooth representation of the interconnection between elements, and to possibly extend the model functionality to include mutual couplings, the T-section represent one meter of ground wire (in per-unit) [4]. Consequently, the model can be extended to arbitrary lengths and configurations.
Figure 2. The grounding system layout with formation strategy.
Figure 2. The grounding system layout with formation strategy.
Table 1. Required number of logged variables for grounding grid of two different square mesh sizes and total area values.
Table 1. Required number of logged variables for grounding grid of two different square mesh sizes and total area values.
Figure 3. Voltage distribution along an horizontal copper wire in ground (length / = 15 m, conductor radius a = 0.012 m, at soil depth d = 0.6 m) in soil of (si) = 70 Om and eri) = 15: (a) the reproduced results for comparison from the research given in [11] (p. 818); and (b) results from implemented model with excitation current f = 36 A of double exponential waveform (a = 32 x 10°, B =7.6 x 10°). radius a = 0.012 m, at soil depth d = 0.6 m) in soil of (si) = 70 Om and eri) = 15: (a) the reproduced
Figure 3. Voltage distribution along an horizontal copper wire in ground (length / = 15 m, conductor radius a = 0.012 m, at soil depth d = 0.6 m) in soil of (si) = 70 Om and eri) = 15: (a) the reproduced results for comparison from the research given in [11] (p. 818); and (b) results from implemented model with excitation current f = 36 A of double exponential waveform (a = 32 x 10°, B =7.6 x 10°). radius a = 0.012 m, at soil depth d = 0.6 m) in soil of (si) = 70 Om and eri) = 15: (a) the reproduced
Figure 4. Voltage distribution in a grounding grid consisting of 6 x 6 meshes of 10 m size. The grounding grid consist of copper conductors of AWG 2/0, buried at d = 0.6 m in soil of Psoit = 100 Om and er,,;, = 36: (a) the reproduced results for comparison from research given in [7] (p. 31); and (b) results from implemented model with excitation current f =1kA of double exponential waveform (a = 38 x 10°, B = 2.54 x 10°).
Figure 4. Voltage distribution in a grounding grid consisting of 6 x 6 meshes of 10 m size. The grounding grid consist of copper conductors of AWG 2/0, buried at d = 0.6 m in soil of Psoit = 100 Om and er,,;, = 36: (a) the reproduced results for comparison from research given in [7] (p. 31); and (b) results from implemented model with excitation current f =1kA of double exponential waveform (a = 38 x 10°, B = 2.54 x 10°).
Figure 5. Schematic overview of the integration between grounding and transmission system. grounding system lies in the preprocessing of large data-sets. A schematic overview of the model integration is illustrated in Figure 5.
Figure 5. Schematic overview of the integration between grounding and transmission system. grounding system lies in the preprocessing of large data-sets. A schematic overview of the model integration is illustrated in Figure 5.
Figure 6. Simplified illustration of implemented transmission and grounding system. A simplified transmission system network is shown in Figure 6 with the grounding system model interfaced in Matlab. In this model the transmission line, the cable, the transformer and the surge arrester are selected from the standard EMTP-RV software library. At 10 km distance from a substation, a lightning strikes the 300 kV overhead transmission line (Zc, = 400 Q). A shielding failure causes an injected current with a magnitude of 1 kA and 1.2/50 us of CIGRE waveform stroke to flow towards the substation. In the substation, the cable (Zc,) between the surge arrester (Appendix C) and transformer are 10 m. Figure 7 shows the simulation results of the transmission system when the grounding system is ignored, thus giving a peak voltage of 171 kV at the transformer.
Figure 6. Simplified illustration of implemented transmission and grounding system. A simplified transmission system network is shown in Figure 6 with the grounding system model interfaced in Matlab. In this model the transmission line, the cable, the transformer and the surge arrester are selected from the standard EMTP-RV software library. At 10 km distance from a substation, a lightning strikes the 300 kV overhead transmission line (Zc, = 400 Q). A shielding failure causes an injected current with a magnitude of 1 kA and 1.2/50 us of CIGRE waveform stroke to flow towards the substation. In the substation, the cable (Zc,) between the surge arrester (Appendix C) and transformer are 10 m. Figure 7 shows the simulation results of the transmission system when the grounding system is ignored, thus giving a peak voltage of 171 kV at the transformer.
Figure 7. Ignoring grounding system: transmission system nodal voltages and CIGRE 1.2/50 us injected current stroke in far-end (1; = 10 km).
Figure 7. Ignoring grounding system: transmission system nodal voltages and CIGRE 1.2/50 us injected current stroke in far-end (1; = 10 km).
Figure 8. Application case when the grounding system is added: (a) the effect in the transmission system; and (b) the results at the surge arrester injection point.
Figure 8. Application case when the grounding system is added: (a) the effect in the transmission system; and (b) the results at the surge arrester injection point.
Figure 9. Application case when the grounding system is added: (a) nodal voltage measurement values for selected points in the grounding grid; (b) the overall voltage distribution in the grounding grid at peak; and (c) the overall voltage distribution in the grounding grid at corner peak.
Figure 9. Application case when the grounding system is added: (a) nodal voltage measurement values for selected points in the grounding grid; (b) the overall voltage distribution in the grounding grid at peak; and (c) the overall voltage distribution in the grounding grid at corner peak.
Figure 11. Application case: peak field.
Figure 11. Application case: peak field.
Figure 10. Application case: used area.
Figure 10. Application case: used area.
Figure A1. The Matlab /Simulink FMI interface to EMTP-RV with the signals transferred between the softwares and block representation of the integration.
Figure A1. The Matlab /Simulink FMI interface to EMTP-RV with the signals transferred between the softwares and block representation of the integration.
Table A2. EMTP-RV ZnO surge arrester V-I parameters, adopted from [19] (p. 9).
Table A2. EMTP-RV ZnO surge arrester V-I parameters, adopted from [19] (p. 9).
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