Experimental Studies of Generalized Neuron Based Power System Stabilizer

Transcription

1 Dayalbagh Educational Institute From the SelectedWorks of D. K. Chaturvedi Dr. August, 2004 Experimental Studies of Generalized Neuron Based Power System Stabilizer D. K. Chaturvedi, Dayalbagh Educational Institute O. P. Malik, University of Calgary, Canada P. K. Kalra Available at:

2 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST Experimental Studies With a Generalized Neuron-Based Power System Stabilizer D. K. Chaturvedi, O. P. Malik, Life Fellow, IEEE, and P. K. Kalra Abstract Artificial neural networks (ANNs) can be used as intelligent controllers to control nonlinear, dynamic systems through learning, which can easily accommodate the nonlinearities and time dependencies. However, they require large training time and large number of neurons to deal with complex problems. To overcome these drawbacks, a generalized neuron (GN) has been developed that requires much smaller training data and shorter training time. Taking benefit of these characteristics of the GN, a new power system stabilizer (PSS) is proposed. Results show that the proposed GN-based PSS can provide a consistently good dynamic performance of the system over a wide range of operating conditions. Index Terms Back-propagation, generalized neuron controller, neural network, power system stabilizer. I. INTRODUCTION USE of a supplementary control signal in the excitation system and/or the governor system of a generating unit can provide extra damping for the system and thus improve the unit s dynamic performance [1]. Power system stabilizers (PSSs) aid in maintaining power system stability and improving dynamic performance by providing a supplementary signal to the excitation system. This is an easy, economical and flexible way to improve power system stability. Over the past few decades, PSSs have been extensively studied and successfully used in the industry. The conventional PSS (CPSS) was first proposed in the 1950s based on a linear model of the power system at some operating point to damp the low frequency oscillations in the system. Linear control theory was employed as the design tool for the CPSS. After decades of theoretical studies and field experiments, this type of PSS has made a great contribution in enhancing the operating quality of the power system [2], [3]. With the development of power systems and increasing demand for quality electricity, it is worthwhile looking into the possibility of using modern control techniques. The linear optimal control strategy is one possibility that has been proposed for supplementary excitation controllers [4]. Preciseness of the Manuscript received December 16, This work was supported by The Department of Science and Technology, Government of India, New Delhi, under a BOYSCAST Fellowship awarded to the first author. D. K. Chaturvedi is with the University of Calgary, Calgary AB T3G 1V4, Canada ( chaturve@ucalgary.ca), on leave from the Faculty of Engineering, Dayalbagh Educational Institute, Agra , India ( dkc_foe@rediffmail.com). O. P. Malik is with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada ( malik@enel.ucalgary.ca). P. K. Kalra is with the Electrical Engineering Department, Indian Institute of Technology, Kanpur U.P , India ( kalra@iitk.ac.in). Digital Object Identifier /TPWRS linear model to represent the actual system and the measurement of some variables are major obstacles to the application of the optimal controller in practice. A more reasonable design of the PSS is based on the adaptive control theory as it takes into consideration the nonlinear and stochastic characteristics of the power systems [5], [6]. This type of stabilizer can adjust its parameters online according to the operating condition. Many years of intensive studies have shown that the adaptive stabilizer can not only provide good damping over a wide operating range but more importantly, also can solve the coordination problem among stabilizers. Power systems being dynamic systems, the response time of the controller is the key to a good closed loop performance. Many adaptive control algorithms have been proposed in the recent years. Generally speaking, the better the closed loop system performance is desired, the more complicated the control algorithm becomes, thus needing more online computation time to calculate the control signal. More recently, ANNs and fuzzy set theoretic approach have been proposed for power system stabilization problems. A number of papers have been published in the last decade. An illustrative list is given in [6] [13]. Both techniques have their own advantages and disadvantage. The integration of these approaches can give improved results. The common neuron model has been modified to obtain a generalized neuron (GN) model using fuzzy compensatory operators as aggregation operators to overcome the problems such as large number of neurons and layers required for complex function approximation, which not only affect the training time but also the fault tolerant capabilities of the artificial neural network (ANN) [14]. Application of this GN as a PSS is described in this paper. II. EXISTING NEURON MODEL The general structure of the common neuron is an aggregation function and its transformation through a filter. It is shown in the literature [15] [17] that the ANNs can be universal function approximators for given input-output data. The common neuron structure has summation as the aggregation function with sigmoidal, radial basis, tangent hyperbolic or linear limiters as the thresholding function as shown in Fig. 1. III. DEVELOPMENT OF A GN MODEL The aggregation operators used in the neurons are generally crisp. However, they overlook the fact that most of the processing in the neural networks is done with incomplete information at hand. Thus, a GN model approach has been adopted /04$ IEEE

3 1446 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST 2004 Fig. 1. Simple neuron model. training time is significantly reduced by optimally selecting the number of aggregation functions and thresholding functions. In this paper, summation and product are used at the aggregation level for simplification, but one can take other fuzzy aggregation operators such as max, min, or compensatory operators too. Similarly, the thresholding functions are only sigmoidal and Gaussian functions for the proposed GN, but other functions like straight line, sine, cosine, etc. can also be used. The weighting factor may be associated with each aggregation function and thresholding function. During training, these weights change and decide the best functions for the GN. C. Learning Algorithm of a GN The following steps are involved in the training of a GN. Step 1) The output of the part of the GN is (1) Fig. 2. GN model. Step 2) The output of the art of the GN is that uses the fuzzy compensatory operators [18], that are partly sum and partly product to take into account the vagueness involved. A. GN Model Use of the sigmoidal thresholding function and ordinary summation or product as aggregation functions in the existing models fails to cope with the nonlinearities involved in real life problems. To deal with these, the proposed model has both sigmoidal and Gaussian functions with weight sharing. The GN model has flexibility at both the aggregation and threshold function level to cope with the nonlinearity involved in the type of applications dealt with. The neuron has both and aggregation functions. The aggregation function has been used with the sigmoidal characteristic function while the aggregation function has been used with the Gaussian function as a characteristic function. The final output of the neuron is a function of the two outputs and with the weights W and (1-W), respectively, as shown in Fig. 2. The neuron model described above is known as the summation type compensatory neuron model, since the outputs of the sigmoidal and Gaussian functions are summed up. Similarly, the product type compensatory neuron models may also be developed. It is found that in most of the applications summation type compensatory neuron model works well [18] and is the one used for the development of the PSS. B. Advantages of GN The number of weights in the case of a GN is equal to twice the number of inputs plus one, which is very low in comparison to a multi-layer feed-forward ANN. The weights are determined through training. Hence, by reducing the number of unknown weights, training time as well as minimum number of patterns required for training can be reduced. In the proposed GN the The output of the GN can be written as (2) (3) After calculating the output of the GN in the forward pass, as in the feed-forward neural network, it is compared with the desired output to find the error. Using back-propagation algorithm the GN is trained to minimize the error. In this step, the output of the single flexible GN is compared with the desired output to get error for the ith set of inputs: (4) Then, the sum-squared error for convergence of all the patterns is A multiplication factor of 0.5 has been taken to simplify the calculations. Step 3) Reverse pass for modifying the connection strength. a) Weight associated with the and part of the GN is b) Weights associated with the inputs of the part of the GN are (5) (6) (7)

4 CHATURVEDI et al.: EXPERIMENTAL STUDIES WITH A GENERALIZED NEURON-BASED POWER SYSTEM STABILIZER 1447 The output of the GN is the control signal u, which is a function of the angular speed and past control signals. Training data for the GN is acquired from the system controlled by the CPSS, which is tuned for each operating condition. The GN is trained offline over a wide working range of the generator operating conditions (i.e., output ranging from 0.1 p.u. to 1.0 p.u. and the power factor ranging from 0.7 lag to 0.8 lead). Similarly, a variety of disturbances is also included in the training, like change in reference voltage, governor input torque variation, one transmission line outage, and three-phase fault on one circuit of the double circuit transmission line. Fig. 3. Block diagram of GN-based PSS. c) Weights associated with the input of the part of the GN are where is the momentum factor for better convergence, and is the learning rate. Range of these factors is from 0 to 1 and is determined by experience. IV. CONVENTIONAL PSS The most commonly used PSS, referred to as the CPSS, is a fixed parameter device. The input of the CPSS, usually obtained from speed or a related signal such as the frequency, is processed through a suitable network to obtain the desired phase relationship [19], [20]. A practical CPSS [6] with the shaft speed input may take the form as shown in the Appendix. V. GN-BASED PSS AND ITS TRAINING A block diagram of the GN controller and power system is shown in Fig. 3. The power system consists of a single machine connected to infinite bus through a double circuit transmission line. The angular speed of synchronous machine, sensed at a fixed time intervals is used as input to the GN based PSS (GNPSS). The GNPSS calculates the output or control action. The dynamic model of the synchronous machine infinite bus system and its parameters are given in the Appendix. Training of an ANN is a major exercise. Performance of GN-based PSS depends upon the training of the GN. Data used for training must cover most of the working range and working conditions in order to get good performance. Of course, it is impossible to train any GN under all working conditions that the controller is likely to meet. Still most of the working conditions must be included in the training. The current and past three generator speed signals (i.e.,, and, where T is the sampling period), and past three values of the PSS output are used as inputs to the GN. Hence, the input vector for the GN can be written as where is the angular speed in radians per second. (8) (9) VI. COMPARISON OF GN AND ANN PSS The GN model is much less complex compared to a three-layered ANN proposed earlier for PSS [22] [25]. These ANNs were [22], [23], [24], and 35-1 [25]. Taking, for illustration purposes, an ANN with one hidden layer and much smaller number of neurons, a comparison of structural complexity associated with ANN and GN model is given in Table I. It is clear from Table I that the number of interconnections for a GNM is very small as compared to ANN. Hence, the number of unknown weights is reduced drastically, which ultimately reduces the training time and training data required. A comparison of the performance of the GN and ANN based PSS is given in Fig. 4. VII. SIMULATION RESULTS OF GN-BASED PSS A number of simulation studies were first performed to study the performance of the GNPSS. A. CPSS Parameter Tuning With the generator operating at p.u. and p.u. lag, a 100-ms three-phase-to-ground fault is applied at 0.5 s at the generator bus. The CPSS is carefully tuned under the above conditions to yield the best performance and its parameters are kept fixed for all studies. B. Performance Under Three-Phase-to-Ground Fault The results have been compared for the GNPSS and conventional PSS for a 100-ms three-phase-to-ground fault at generator bus under the following operating conditions: 1) p.u. and -p.u. lag; 2) p.u. and -p.u. lead; 3) p.u. and -p.u. lead. The results are shown in Fig. 5 for deviation in angular speed. Because CPSS has been tuned for p.u., -p.u. lag, performance at this operating condition as shown in Fig. 5(a) is practically the same for both the GNPSS and the CPSS. System performance at other operating conditions, as given in Fig. 5(b) and (c), is better with GNPSS than a fixed parameter CPSS. C. Performance With One Line Removed The results have been compared under different operating conditions such as and -p.u. lead, p.u. and -p.u. lead, p.u. and -p.u. lag when

5 1448 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST 2004 Fig. 4. Comparison of the performance of ANN and GN-based PSSs. TABLE I COMPARISON OF NETWORK COMPLEXITY INVOLVED IN ANN AND GNM Fig. 5. Performance of GN-PSS and CPSS for a three-phase ground fault. D. Performance Under Reference Operating Point Changes one line is removed from the system with two parallel transmission lines operating initially. It can be seen from Fig. 6 that the GNPSS damps out the oscillations very effectively. Because the GNPSS is trained for a wide range of operating conditions, it is able to adjust the control output to that suitable for the working conditions. Applying the change in several small steps instead of a large step can reduce the severity of reference changes. It is also possible to apply a ramp with a small gradient in order to change the system reference settings. Both these things are done by the GNPSS to reduce the severity of reference changes. The performance of GNPSS has been evaluated for step changes in reference setting in Vref and Pref. 1) Step Change in Governor Reference (Pref): The GNPSS performance is studied for a sudden change in the governor reference by 20% to its initial value. The results given in Fig. 7

6 CHATURVEDI et al.: EXPERIMENTAL STUDIES WITH A GENERALIZED NEURON-BASED POWER SYSTEM STABILIZER 1449 Fig. 7. Performance of GN-based PSS when 20% step change in Pref at P= 0:9 p.u. and Q = 0:4-p.u. lag. Fig. 8. Performance of GN-based PSS when 5% step change in Vref at P= 0:9 p.u. and Q = 0:4-p.u. lag. Fig. 6. Performance of GN-PSS-based PSS when one line is removed from the circuit. show that the angular speed deviations are damped quickly with the GNPSS. 2) Step Change in Voltage Reference (Vref) of AVR: A step change of 5% to its initial value was applied to Vref under the same operating condition as in the case of Pref change. The variation in angular speed is shown in Fig. 8. E. Performance Under Different H Values Performance of the GNPSS under different H values varying from 5 to 25 for a 20% step change in Pref is shown in Fig. 9. The results are consistently good. Fig. 9. Performance of GN-based PSS for different values of H under step change in Pref. VIII. EXPERIMENTAL TEST The behavior of the proposed GNPSS has been further investigated on a physical model in the Power System Research Laboratory at the University of Calgary, Alberta, Canada. The physical model consists of a three-phase 3-kVA microsynchronous generator connected to a constant voltage bus through a double

7 1450 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST 2004 Fig. 10. Experimental setup for Laboratory Power System model. circuit transmission line model. The transmission lines are modeled by six sections, each section is equivalent of 50-km length. The transmission line parameters are the equivalent of 1000 MVA, 300 km, and 500 kv. A field time constant regulator has been employed to adjust the transient field time constant (Tdo ) to the desired value [21]. The governor turbine characteristics are simulated using the micro-machine prime mover. It can be achieved by dc motor which is controlled as a linear voltage to torque converter. An overall schematic diagram of this physical model is given in Fig. 10. The Laboratory model mainly consists of the turbine M, the generator G, the transmission line model, the AVR, digital signal processor (DSP) board and Man-machine interface. The GNPSS control algorithm is implemented on a single board computer, which uses a Texas Instruments TMS320C31 DSP to provide the necessary computational power. The DSP board is installed in a personal computer (PC) with the corresponding development software and debugging application program. The analog to digital input channel of DSP board receives the input signal and control signal output is converted by the digital to analog converter. The IEEE type PSS1A CPSS is also implemented on the same DSP, with a 1-ms sampling period. The following tests have been performed on the experimental set up to study the performance of the GNPSS and CPSS. A. Step Change in Power Reference (Pref) The experiment is performed on the micro-synchronous generator under the following operating conditions: 1) 0.67-p.u. active power and 0.9 lagging power factor; 2) 0.25-p.u. active power and 0.8 leading power factor. A disturbance of 30% step decrease in reference power was applied at 0.5 and again increased to the same initial value at 4.5. The change in generator electrical power with GNPSS and CPSS is shown in Fig. 11. The proposed controller exhibits fast and well-controlled damping. B. Transient Faults To investigate the performance of the GNPSS under transient conditions caused by transmission line faults, various tests on the experimental set up have been conducted. Fig. 11. (Pref). Experimental results under 30% step change in power reference 1) Single-Phase to Ground Fault Test: In this experiment, the generator was operated at p.u. and -pf lag. At this operating condition and with both lines in operation, a single-phase to ground fault was applied in the middle of one transmission line for 100 ms. The system performance is shown in Fig. 12. It can be observed that the GNPSS provides faster settling. 2) Two-Phase to Ground Fault Test: The two-phase to ground fault test has been performed for the following two operating conditions: 1) p.u. and lagging power factor; 2) p.u. and leading power factor; at the middle of one transmission line. The results of these experiments shown in Fig. 13 are consistently better with the GNPSS. 3) Three-Phase to Ground Fault Test: A 100-ms three-phase to ground fault was applied at different operating conditions at the middle of one transmission line at 0.5. Illustratative results for two tests at p.u., 0.8-pf lead, and p.u.,

8 CHATURVEDI et al.: EXPERIMENTAL STUDIES WITH A GENERALIZED NEURON-BASED POWER SYSTEM STABILIZER 1451 Fig. 12. Experimental results of single-phase fault at P = 0:25 p.u. and Power factor = 0:8 lagging. Fig. 14. Experimental results of three-phase to ground fault. Fig. 13. Experimental results of two-phase ground fault. Fig. 15. Successful re-closing at P=0:5 p.u. and pf = 0:8 leading. 0.8-pf lag are given in Fig. 14. The results show that the GNPSS provides consistently good performance. 4) Successful Re-Closing: A three-phase to ground fault is applied on one of the transmission lines and the faulty line is

9 1452 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 19, NO. 3, AUGUST ) Fig. 16. Removal of one line and reconnected at P=0:5 p.u. and pf = 0:8 lagging. 2) The AVR and exciter used in the system have the transfer functions, respectively opened. After clearing the fault, transmission line is automatically re-closed. The results are shown in Fig. 15. Both the overshoot and settling time for GNPSS are smaller. 5) Removal of One Line: One line is removed at 0.5 s and again connected at 5.8 s. Fig. 16 shows that in this type of fault also the system performance with the GNPSS is very good in terms of damping the oscillations. 3) The governor used in the system has the transfer function IX. CONCLUSION A GN, adaptive in nature and having learning capabilities is described in the paper. It can incorporate the nonlinearities involved in the system. It uses only one neuron and is trained using back-propagation learning algorithm. Because it has a much smaller number of weights than the common multi-layer feed-forward ANN, the training data required is drastically reduced. Training time is also significantly reduced, because the number of weights to be determined is much less than an ANN. GN has been employed to perform the function of a PSS to improve the stability and dynamic performance of the power system. Computer simulation studies described in the paper show that the performance of the GN-based PSS can provide very good performance over a wide range of operating conditions. The proposed GN-based PSS has been implemented on a DSP and its performance investigated on a physical model of a single machine infinite bus system under various operating conditions and disturbances such as transient faults, one line removal from double circuit transmission, change in reference point, etc. It is found that the system performance with the GN-based PSS is consistently good indicating that it can adapt to changing operating conditions. 4) The conventional PSS has the following transfer function: 5) Parameters used in the simulation studies are given below: 5.1 Machine parameters 5.2 Governor parameters 5.3 AVR and exciter parameters 5.4 CPSS parameters 5.5 GNN-based PSS parameters APPENDIX The generating unit is modeled by seven first order nonlinear differential equations given below.

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Hope, An artificial neural network based adaptive power system stabilizer, IEEE Trans. Energy Conversion, vol. 8, pp , Mar [25], A multi-input power system stabilizer based on artificial neural networks, in Proc. IEEE WESCANEX, Saskatoon, SK, Canada, May 17 18, 1993, pp D. K. Chaturvedi is born in Madhya Pradesh, India, on August 3, He graduated in electrical engineering from Government Engineering College, Ujjain, India, in He received the M.Tech degree in engineering systems and management and the Ph.D. degree in electrical power systems from Dayalbagh Educational Institute (D.E.I.), Agra, India. He is currently pursuing Postdoctoral Research at the University of Calgary, Calgary AB, Canada. He is a Reader with the Faculty of Engineering at D.E.I. O. P. Malik (M 66 SM 69 LF 00) received the National Diploma in electrical engineering from Delhi Polytechnic, Delhi, India, the M.E. degree in electrical machine design from Roorkee University, Roorkee, India, in 1962, the Ph.D. degree from the University of London, London,. U.K., and the D.I.C. from the Imperial College, London, U.K., in Currently, he is a Professor in the Department of Electrical and Computer Engineering at the University of Calgary, Calgary, AB, Canada, where he has been since He has performed research work in collaboration with teams from Russia, Ukraine, China, and India. In addition to his research and teaching, he has served in many additional capacities at the University of Calgary including Associate Dean of Academics/Student Affairs and Acting Dean of the Faculty of Engineering. P. K. Kalra graduated in electrical engineering from Dayalbagh Educational Institute, Agra, India. Currently, he is a Professor at the Indian Institute of Technology, Kanpur, India.