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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,

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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.

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 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 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 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).

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 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.

* 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 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.

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 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 8. The fitness curve of Genetic algorithms.

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

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

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 3. Abbreviations of samples analyzed in the experiments. 3. Experimental Results and Discussion

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 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.

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 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 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 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.

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).

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:

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.

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 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 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.

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 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.

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 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 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 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 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 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.

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 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.

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 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.

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:

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:

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 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 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 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 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].

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.

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.

Table 3. Mean relative difference of transient voltage in example 3.2. Table 4. Mean relative difference of transient voltage in example 3.3.

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.

Figure 2. Comparison of measured [14] and computed radio interference (RI) profiles.

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].

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.

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 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 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 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.

Figure 73 – uploaded by Issouf Fofana

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