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Abstract
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Introduction Sy Sy Co
Experimental Verification of Load Angle
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Electrical Engineering

Determination of Load Angle for Salient-pole Synchronous Machine

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https://doi.org/10.2478/V10048-010-0018-2
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Abstract

This paper presents two methods for load angle determination for salient-pole synchronous generator. The first method uses optical encoder to detect the rotor position. In some cases the end of the rotor shaft is not free to be used and mounting of an encoder is impossible. Therefore, the second method proposes estimation of the load angle based on the measured electrical values that have been already used in excitation control system of the synchronous generator. Estimation method uses corresponding voltage-current vector diagram and parameters of the synchronous generator, transformer and transmission lines. Both methods were experimentally verified on the digital control system and synchronous generator connected to power system. The estimation and measured results were compared. The accuracy of load angle estimation method depends on voltage and current measurement accuracy as well as generator, transformer and transmission line parameter accuracy. The estimation method gives satisfactory accuracy for load angles less than 120º el. Thus, it can be applied in excitation control system to provide stable work of synchronous generator in under-excitation operating area.

Figures (21)
The load angle of a synchronous generator is the essential variable for the transient stability studies of power systems [1]. In recent years, an application of the load angle as an input variable in the excitation control and protection systems of synchronous generators and power systems has been investigated [8], [9], [10]. Therefore, real-time measurement of the load angle is required for these applications.
The load angle of a synchronous generator is the essential variable for the transient stability studies of power systems [1]. In recent years, an application of the load angle as an input variable in the excitation control and protection systems of synchronous generators and power systems has been investigated [8], [9], [10]. Therefore, real-time measurement of the load angle is required for these applications.
The load angle was measured using optical encoder and the digital control system. The load angle was measured at the exact moment of the network’s phase voltage passing through zero, which means that for the power system’s frequency of 50 Hz the sampling frequency is 100 Hz. The angle is measured based on the difference between the momentary position of the rotor and the network phase voltage. Fig.3 shows the principle of operation for measuring the load angle. From the optical encoder, two pulse trains are connected to the digital control system. The first pulse train
The load angle was measured using optical encoder and the digital control system. The load angle was measured at the exact moment of the network’s phase voltage passing through zero, which means that for the power system’s frequency of 50 Hz the sampling frequency is 100 Hz. The angle is measured based on the difference between the momentary position of the rotor and the network phase voltage. Fig.3 shows the principle of operation for measuring the load angle. From the optical encoder, two pulse trains are connected to the digital control system. The first pulse train
This paper presents a load angle measurement using the optical encoder. It also presents the load angle estimation method for synchronous generator connected over the transformer and transmission line to the power system Fig.2). The proposed estimation method uses the available measured values that have already been introduced for the purpose of the control system excitation. This method has been implemented in the digital control system and requires knowledge of generator and the equivalent network parameters. Fig.2. Synchronous generator connected to power system
This paper presents a load angle measurement using the optical encoder. It also presents the load angle estimation method for synchronous generator connected over the transformer and transmission line to the power system Fig.2). The proposed estimation method uses the available measured values that have already been introduced for the purpose of the control system excitation. This method has been implemented in the digital control system and requires knowledge of generator and the equivalent network parameters. Fig.2. Synchronous generator connected to power system
Usua ly, the characteristic values of a synchronous machine are obtained from a short-circuit test at no load genera or operation. This test implies risks and it cannot be performed every time, so the DC decay test is an alternative method. It determines the characteristic values of a synchronous machine for two axes in function of the saturation state of the leakage paths. In general, the DC decay [18]. est is done for positions of the rotor in d- and q- axis Fig.5. Experimental setup for DC decay test
Usua ly, the characteristic values of a synchronous machine are obtained from a short-circuit test at no load genera or operation. This test implies risks and it cannot be performed every time, so the DC decay test is an alternative method. It determines the characteristic values of a synchronous machine for two axes in function of the saturation state of the leakage paths. In general, the DC decay [18]. est is done for positions of the rotor in d- and q- axis Fig.5. Experimental setup for DC decay test
where 6 is the load angle, J is the armature current, P is the active power, U,, is the power system voltage, Q is the reactive power and S is the apparent power. The values of the quadrature-axis synchronous reactance X,, equivalen resistance R and reactance X, must be known for this estimation method. Measurement of the quadrature-axis synchronous reactance X, is presented in the nex subsection. Reactance X, is calculated and in p.u. system is equal to 0.1 p.u. and equivalent resistance is equal to 0.01 p.u. In section III it was determined that estimation method in dynamic operations is not significantly dependent on the change of reactance X,. Fig.4 Vector diagram of the synchronous generator connected to AC network
where 6 is the load angle, J is the armature current, P is the active power, U,, is the power system voltage, Q is the reactive power and S is the apparent power. The values of the quadrature-axis synchronous reactance X,, equivalen resistance R and reactance X, must be known for this estimation method. Measurement of the quadrature-axis synchronous reactance X, is presented in the nex subsection. Reactance X, is calculated and in p.u. system is equal to 0.1 p.u. and equivalent resistance is equal to 0.01 p.u. In section III it was determined that estimation method in dynamic operations is not significantly dependent on the change of reactance X,. Fig.4 Vector diagram of the synchronous generator connected to AC network
where the coefficients A, B, C, a and # are functions of time-constants and reactances for each of the axes [18]. The identification procedure starts from a mathematical model, which consists of the machine voltage equations for the d- and q-axis. The d- and q- axis current time-variation is considered as being given by a sum of exponential functions, which means, in a per-unit (p.u.):
where the coefficients A, B, C, a and # are functions of time-constants and reactances for each of the axes [18]. The identification procedure starts from a mathematical model, which consists of the machine voltage equations for the d- and q-axis. The d- and q- axis current time-variation is considered as being given by a sum of exponential functions, which means, in a per-unit (p.u.):
Fig.6. Structure of identification procedure The identification method gives following results: X,=0.! p.u and X,=0.59 p.u.
Fig.6. Structure of identification procedure The identification method gives following results: X,=0.! p.u and X,=0.59 p.u.
Digital control system (Fig.7) based on NI cRIO-9012 [13] was used for excitation control of synchronous generator, as well as to implement the load angle determination methods. The cRIO-9012 controller operates the National Instruments LabVIEW Real-Time Module, while the connectivity to sensors and actuators was obtained with four I/O modules, two NI-9215 (16-bit analog input, (digital I/O, 100 ns) and NI-9263 (16 100KS/s) [20]. NI LabVIEW graphical can be used for easier modeling of con testing purposes a software monitori 0OKS/s), NI-9401 -bit analog output, programming tools rol algorithms. For ng tool was also developed. It enables regulator parameters optimization as well as displaying and recording of the testing results via PC. Experimental setup is presented in Fig.8. Fig.7. Digital control system
Digital control system (Fig.7) based on NI cRIO-9012 [13] was used for excitation control of synchronous generator, as well as to implement the load angle determination methods. The cRIO-9012 controller operates the National Instruments LabVIEW Real-Time Module, while the connectivity to sensors and actuators was obtained with four I/O modules, two NI-9215 (16-bit analog input, (digital I/O, 100 ns) and NI-9263 (16 100KS/s) [20]. NI LabVIEW graphical can be used for easier modeling of con testing purposes a software monitori 0OKS/s), NI-9401 -bit analog output, programming tools rol algorithms. For ng tool was also developed. It enables regulator parameters optimization as well as displaying and recording of the testing results via PC. Experimental setup is presented in Fig.8. Fig.7. Digital control system
Fig.9. Measured and estimated load angle, and estimation error with reactive power of 0 p.u. during active power change from 0 p.u. to 1.0 p.u. The static comparison of the measured and estimated load angle was performed by three appropriate experiments. Active power was changed from 0 p.u. to 1.0 p.u. with the step change of 0.2 p.u. In the first experiment (Fig.9), reactive power of the generator is zero.
Fig.9. Measured and estimated load angle, and estimation error with reactive power of 0 p.u. during active power change from 0 p.u. to 1.0 p.u. The static comparison of the measured and estimated load angle was performed by three appropriate experiments. Active power was changed from 0 p.u. to 1.0 p.u. with the step change of 0.2 p.u. In the first experiment (Fig.9), reactive power of the generator is zero.
Fig. 8 Experimental setup A. Static comparison of the measured and estimated load angle
Fig. 8 Experimental setup A. Static comparison of the measured and estimated load angle
Fig.10. Measured and estimated load angle, and estimation error with inductive reactive power of 1.0 p.u. during active power change from 0 p.u. to 1.0 p.u.
Fig.10. Measured and estimated load angle, and estimation error with inductive reactive power of 1.0 p.u. during active power change from 0 p.u. to 1.0 p.u.
Fig.11. Measured and estimated load angle and estimation error with capacitive reactive power of 1.0 p.u. during active power change from 0 p.u. to 1.0 p.u.
Fig.11. Measured and estimated load angle and estimation error with capacitive reactive power of 1.0 p.u. during active power change from 0 p.u. to 1.0 p.u.
Fig.13. Measured and estimated load angle for active power step change and inductive reactive power of 1.0 p.u. Fig 14. Measured and estimated load angle for active power step change and capacitive reactive power of 1.0 p.u.
Fig.13. Measured and estimated load angle for active power step change and inductive reactive power of 1.0 p.u. Fig 14. Measured and estimated load angle for active power step change and capacitive reactive power of 1.0 p.u.
Fig.12._ Measured and estimated load angle for active power step change and reactive power of 0 p.u.
Fig.12._ Measured and estimated load angle for active power step change and reactive power of 0 p.u.
seconds. Stator resistance R, quadrature-axis reactance X, and equivalent reactance X, in estimator are changed from 50 % to 150 % of nominal value with step of 50 %. In the first set of experiments, value of stator resistance in estimator is changed (Fig.15). Two different validation criterions are used to determine sensitivity of estimation method to parameter change. The first criterion is the mean absolute error (MAE) between the measured and estimated load angle. Second criterion is static error (STAT). This error is defined as the absolute error between the measured and estimated load angle 3 seconds after step change of active power. MAE and STAT criterions for stator resistance change are shown in Fig.16. In the second experiment, value of reactance X, in estimator is changed (Fig.17). MAE and STAT criterions for this set of experiments are shown in Fig.18. In the third experiment, value of reactance X, in estimator is changed (Fig.19). MAE and STAT criterions for this set of experiments are shown in Fig.20. Fig.15. The measured and estimated load angle with different stator resistance R in load angle estimator
seconds. Stator resistance R, quadrature-axis reactance X, and equivalent reactance X, in estimator are changed from 50 % to 150 % of nominal value with step of 50 %. In the first set of experiments, value of stator resistance in estimator is changed (Fig.15). Two different validation criterions are used to determine sensitivity of estimation method to parameter change. The first criterion is the mean absolute error (MAE) between the measured and estimated load angle. Second criterion is static error (STAT). This error is defined as the absolute error between the measured and estimated load angle 3 seconds after step change of active power. MAE and STAT criterions for stator resistance change are shown in Fig.16. In the second experiment, value of reactance X, in estimator is changed (Fig.17). MAE and STAT criterions for this set of experiments are shown in Fig.18. In the third experiment, value of reactance X, in estimator is changed (Fig.19). MAE and STAT criterions for this set of experiments are shown in Fig.20. Fig.15. The measured and estimated load angle with different stator resistance R in load angle estimator
Fig.16. MAE and STAT criterions due to different stator resistance R in estimator
Fig.16. MAE and STAT criterions due to different stator resistance R in estimator
Fig.17. The measured and estimated load angle with different quadrature-axis reactance X, in load angle estimator
Fig.17. The measured and estimated load angle with different quadrature-axis reactance X, in load angle estimator
Fig.19. The measured and estimated load angle with different equivalent reactance X, in load angle estimator Fig.18. MAE and STAT criterions due to different quadrature-axis reactance X, in estimator
Fig.19. The measured and estimated load angle with different equivalent reactance X, in load angle estimator Fig.18. MAE and STAT criterions due to different quadrature-axis reactance X, in estimator
Fig.20. MAE and STAT error of load angle estimation due to different equivalent reactance X, in estimator
Fig.20. MAE and STAT error of load angle estimation due to different equivalent reactance X, in estimator

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