A Generalized Neuron Based PSS in A Multi- Machine Power System

Transcription

1 Dayalbagh Educational Institute From the SelectedWorks of D. K. Chaturvedi Dr. September, 2004 A Generalized Neuron Based PSS in A Multi- Machine Power System D. K. Chaturvedi, Dayalbagh Educational Institute O. P. Malik P. K. Kalra Available at:

2 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER Performance of a Generalized Neuron-Based PSS in a Multimachine Power System D. K. Chaturvedi, O. P. Malik, Life Fellow, IEEE, and P. K. Kalra Abstract An artificial neural network can work as an intelligent controller for nonlinear dynamic systems through learning, as it can easily accommodate the nonlinearities and time dependencies. In dealing with complex problems, most common neural networks have some drawbacks of large training time, large number of neurons and hidden layers. These drawbacks can be overcome by a nonlinear controller based on a generalized neuron (GN) which retains the quick response of neural net. Results of studies with a GN-based power system stabilizer on a five-machine power system show that it can provide good damping over a wide operating range and significantly improve the dynamic performance of the system. Index Terms Generalized neuron (GN), low-frequency oscillation, neural network, neuro-pss, power system stabilizer (PSS). 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 commonly used PSS (CPSS) was first proposed in the 1950 s 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 April 2, Paper no. TEC This work was supported by the Department of Science and Technology, Government of India, New Delhi, under the BOYSCAST fellowship scheme. D. K. Chaturvedi is with the Faculty of Engineering, Dayalbagh Educational Institute, Dayalbagh, Agra , India and also with the University of Calgary, Calgary, AB T3G 1VF, Canada ( dkc_foe@rediffmail.com; chaturve@ucalgary.ca ). O. P. Malik is with 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, Uttar Pradesh , India ( kalra@iitk.ac.in). Digital Object Identifier /TEC 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 on-line 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, does not raise any 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 on-line 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. An 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. DEVELOPMENT OF A GENERALIZED 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 (Fig. 1) has summation as the aggregation function with sigmoidal, radial basis, tangent hyperbolic, or linear limiters as the thresholding function. 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 that uses the fuzzy compensatory operators [18] that are partly sum and partly product to take into account the vagueness involved /04$ IEEE

3 626 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004 Fig. 1. Simple neuron model. 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, as shown in Fig. 2. The neuron has both and aggregation functions. The aggregation function has been used with the sigmoidal characteristic function (f1) while the aggregation function has been used with the Gaussian function (f2) as a characteristic function. The output of the part with a Sigmoidal characteristic function of the GN is and is the gain scale factor of. The output of the part with Gaussian characteristic function of the GN is and is the gain scale factor of. The final output of the neuron is a function of the two outputs and with the weights W and, respectively, and can be written in mathematical form as The GN model gives only one output. If a system requires more than one output, one GN is used for each output. 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. (1) (2) (3) Fig. 2. GN model. 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 multilayer 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 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 simplificity, 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 function for the proposed GN, but other functions like straight line, sine, cosine, etc. can also be used. A 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) Calculate the output of GN as given in (1) (3). Step 2) 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 a 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 th set of inputs (4) Then, the sum-squared error for convergence of all the patterns is (5) 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 (6)

4 CHATURVEDI et al.: PERFORMANCE OF A GN-BASED PSS IN A MULTIMACHINE POWER SYSTEM 627 b) Weights associated with the inputs of the part of the GN are (7) c) Weights associated with the input of the -part of the GN are (8) Fig. 3. Block diagram of GNN-based PSS. is the momentum factor for better convergence and is the learning rate. The Range of these factors is from 0 to 1 and is determined by experience. III. 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. IV. GNPSS 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 an infinite bus through a double circuit transmission line. Parameters of the dynamic model of the synchronous machine infinite bus system are given in the Appendix. Training of an ANN is a major exercise, because it depends on various factors such as the availability of sufficient and accurate training data, suitable training algorithm, number of neurons in the ANN, number of ANN layers, and so on. The GN with only one neuron is able to cope with the problem complexity, as the selection of the number of neurons and layers is not required. Performance 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 ANN 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, 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 (9) The output of the GN is the control signal u(t), which is a function of the deviation in angular speed and past control signals. Training data for the GN is collected from the system controlled by the tuned CPSS. The GN is trained off-line over a wide working range of the generator operating conditions i.e., output ranging from 0.1 to 1.0 pu and the power factor ranging from 0.7 lag to 0.8 lead. Similarly, a variety of disturbances are 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. V. SIMULATION RESULTS A number of simulation studies were performed to study the performance of the GNPSS on a single-machine infinite bus environment initially [21]. The GNPSS has also been implemented and its performance tested on a single-machine infinite bus system. The results are presented in [22]. In this environment, there is no multimode oscillation. To verify the damping ability of the GNPSS, the performance of the GNPSS is also investigated in a multimachine power system environment. A. Single-Machine Inifinite Bus System 1) CPSS Parameter Tuning: With the generator operating at pu and pu 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. 2) Performance Under Three-Phase to Ground Fault: The results have been compared for the GNPSS and conventional PSS for 100-ms three-phase to ground fault at generator bus under different operating conditions. The results are shown in Fig. 4 for deviation in angular speed at pu, pu lag, and pu, pu lead. Because CPSS has been tuned for pu, pu lag, performance at this operating condition as shown in Fig. 4 is practically the same for both the GNPSS and the CPSS. 3) Performance With Reference Operating Point Changes: The GNPSS performance is studied for a sudden change in the governor reference by 20% to its initial value. The results given in Fig. 5 show that the angular speed deviations are damped quickly with the GNPSS.

5 628 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004 Fig. 5. Performance of GN-based PSS with 20% step change in Pref at P= 0:7 pu and Q=0:3 pu lag. Fig. 4. Performance of GNPSS and CPSS for a three-phase to ground fault. (a) P=0:9and Q=0:4lag. (b) P=0:5and Q=0:5lead. A step change of 5% to its initial value was applied to Vref at and lead. The variation in angular speed is shown in Fig. 6. Fig. 6. Results of PSSs at P=0:9and Q=0:4lead under a 5% step change in reference voltage. B. Multimachine System 1) Performance of GNPSS With Disturbance in Torque Reference: A five-machine power system without infinite bus, shown in Fig. 7, is used to study the performance of the previously trained GNPSS on a system with multimode oscillations. In this system, generators #1, #2, and #4 are much larger than generators #3 and #5. All five generators are equipped with governors, AVRs, and exciters. The whole system can be viewed as a combination of two areas connected through a tie transmission line between bus #6 and #7. Generators #1 and #4 form one area and generators #2, #3, and #5 form another area. Parameters of all generators, transmission lines, loads and operating conditions are given in the Appendix. Under normal operating conditions, each area serves its local load and is almost fully loaded with a small load flow over the tie line. Fig. 7. Schematic diagram of a five-machine power system. When a disturbance happens in the system, multimodal oscillations will arise because of the different inertias of the generators and the topology of the system.

6 CHATURVEDI et al.: PERFORMANCE OF A GN-BASED PSS IN A MULTIMACHINE POWER SYSTEM 629 Fig. 8. System response with GNPSS installed on generator #3 and a 60:1 pu step change in torque reference at G3. a) Simulation Studies With GNPSS Installed on One Generator: The GNPSS is trained for a single-machine infinite bus system and the same parameters (weights) are used for GNPSS with multimachine system. For five generating units in the system, only generator #3 is installed with the proposed GNPSS. The speed deviation of generator #3 is sampled at a fixed time interval (30 ms). The system responses are shown in Fig. 8 for the operating conditions given in the Appendix. It is observed that the proposed GNPSS on generator #3 can provide satisfactory damping to the local oscillation mode in. However, it has little influence on the inter-area oscillation between generator #1 and #2. This is because the rated capacity of generator #3 is much smaller that that of generators #1 and #2. Generator #3 does not have enough power to control the inter-area oscillation between generator #1 and #2. To compare the performance of the GNPSS and CPSS, a CPSS with the following transfer function is installed on generator #3: (10) Fig. 9. System response under change in Tref with only GNPSS and only CPSS installed on G1, G2, and G3. Parameters of the CPSS are tuned carefully so that the CPSS has almost the same performance as the GNPSS. The following parameters are set for the CPSS for all studies in the multimachine environment: b) GNPSS Installed on Three Generators: In the previous test, the results show that it is not enough to install one GNPSS to damp both local and inter-area modes of oscillation. Three GNPSSs are installed on generators #1, #2, and #3. A 10% step decrease in mechanical input torque reference of generator #3 is applied at 1 s and returns to its original level at 10 s. The simulation results of only GNPSSs and only CPSSs applied at generators #1, #2, and #3 are shown in Fig. 9. It is clear from

7 630 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 19, NO. 3, SEPTEMBER 2004 Fig. 10. System response with only GNPSS and only CPSS installed on G1, G2, G3 for three-phase to ground fault. the results that both modes of oscillations are damped out very effectively. 2) Three-Phase to Ground Fault: In this test, a three-phase to ground fault is applied at the middle of one transmission line between buses #3 and #6 at 1 s and the faulty line is removed 100 ms later. At 10 s, the faulty line is restored successfully. The GNPSSs are installed on generators #1, #2, and #3. The system responses are shown in Fig. 10. The results with CPSSs installed on the same generators are also shown in the same figures. From the system responses, it can be concluded that although the CPSS can damp the oscillations caused by such a large disturbance; the proposed GNPSS has much better performance. 3) Coordination Between GNPSS and CPSS: The advanced PSSs would not replace all CPSSs being operated in the system at the same time. Therefore, the effect of the GNPSS and CPSSs Fig. 11. System response with GNPSS at G1, G3 and CPSS on G2, G4, and G5 for 60:2 pu step change in torque reference. working together needs to be investigated. In this test, the proposed GNPSS is installed on generators #1 and #3 and CPSSs on generators #2, #4, and #5. The operating conditions are the same as given in the Appendix. A 0.2-pu step decrease in the mechanical input torque reference of generator #3 is applied at 1 s and returns to its original level at 10 s. The system responses with combination of GNPSS and CPSS are compared to system response with CPSS installed on all five machines as shown in Fig. 11. The results demonstrate that the two types of PSSs can work cooperatively to damp out the oscillations in the

8 CHATURVEDI et al.: PERFORMANCE OF A GN-BASED PSS IN A MULTIMACHINE POWER SYSTEM 631 governor, and CPSS used in the simulation studies of the singlemachine infinite bus system are given in [6]. B. Multimachine Power System 1) Generator parameters on a 100-MVA base. For small generators #3 and #5 '' '' ' For big generators #1, #2, and #4 '' ' Fig. 12. Schematic diagram of AVR and exciter model. TABLE I OPERATING CONDITIONS Time constant for all generators ' '' '' 2) Simplified IEEE standard type ST1A AVR and exciter model is shown in Fig. 12 and its parameters are system. The proposed GNPSS input signals are local signals. The GNPSS coordinates itself with the other PSSs based on the signals it receives. VI. CONCLUSION A GN can incorporate the nonlinearities involved in the system. It uses only one neuron and is trained using a back-propagation learning algorithm. Because it has a much smaller number of weights than the common multilayer 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 singlemachine infinite bus as well as a multimachine power system. Simulation studies described in the paper show that the performance of the GNPSS provides good performance over a wide range of operating conditions on single-machine infinite bus system The effectiveness of GNPSS to damp multimode oscillations in a five-machine power system provides satisfactory results if correctly installed and can cooperate with other GNPSSs or CPSSs. APPENDIX I A. Single-Machine Infinite Bus System The generating unit is modeled by seven first-order nonlinear differential equations. Parameters for generator, Exciter, AVR, for gen- 3) Governor Model: erator #1, #2, #4, and for generator #3 and #5. 4) Operating conditions are shown in Table I. 5) Load admittance (pu): REFERENCES [1] F. P. DeMello and T. F. Laskowski, Concepts of power system dynamic stability, IEEE Trans. Power App. Syst., vol. PAS-94, pp , [2] F. P. DeMello, L. N. Hannett, and J. M. Undrill, Practical approaches to supplementary stabilizing from accelerating power, IEEE Trans. Power App. Syst., vol. PAS-97, pp , [3] E. V. Larsen and D. A. Swann, Applying power system stabilizer, IEEE Trans. Power App. Syst., vol. PAS-100, pp , [4] K. S. Ohtsuka, S. Yokokama, H. Tanaka, and H. Doi, A multivariable optimal control system for a generator, IEEE Trans. Energy Conversion, vol. EC-1, pp , June [5] D. A. Pierre, A perspective on adaptive control of power systems, IEEE Trans. Power Syst., vol. PWRS-2, pp , May [6] Y. Zhang, G. P. Chen, O. P. Malik, and G. S. Hope, An artificial neural network based adaptive power system stabilizer, IEEE Trans. Energy Conversion, vol. 8, pp , June [7] E. Swidenbank, S. McLoone, D. Flym, G. W. Irwin, M. D. Brown, and B. W. Hogg, Neural network based control for synchronous generators, IEEE Trans. Energy Conversion, vol. 14, pp , Dec [8] M. A. Abido and Y. L. Abdel-Magid, Tuning of power systems stabilizers using fuzzy basis function networks, Elect. Mach. Power Syst., vol. 27, pp , [9] T. Hiyama and C. M. Lim, Application of fuzzy logic control scheme for stability enhancement of a power system, in Proc. IFAC Symp. Power Systems and Power Plant Control, Singapore, Aug

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