Neural Network Based Loading Margin Approximation for Static Voltage Stability in Power Systems

Transcription

1 Neural Network Based Loading Margin Approximation for Static Voltage Stability in Power Systems Arthit Sode-Yome, Member, IEEE, and Kwang Y. Lee, Fellow, IEEE Abstract Approximate loading margin methods have been developed using Artificial Neural Networks (NN) for static voltage stability in power systems. Artificial Neural Network is used to approximate the loading margin at particular generation direction and three different methodologies are used for finding NN training data sets. The proposed methods are validated and compared with actual loading margin and the Maximum Loading Margin methods in the modified IEEE 4-bus test system and Thailand power system. The methods will help system operators to approximate voltage stability margin or loading margin of the system in a simple way. Index Terms Loading margin, maximum loading margin method, voltage stability margin, neural networks, generation direction. B I. INTRODUCTION ECAUSE of several major power interruptions in recent years [, 2], voltage instability has been a major concern in power systems, especially in planning and operation. Voltage instability due to the lack of the ability to foresee the impact of contingencies is one of the main reasons for the worst North American power interruptions on August 4th, 23 [2]. Hence, many electric power utilities have been devoting a great deal of efforts in voltage stability assessment and the enhancement of stability margin. Major contributory factors to voltage instability are power system configuration, and generation and load patterns [, 3-6]. Generation pattern is easier to control by system operators compared to other factors, as long as there is enough margin left in the generators [4-5]. Conventionally, in typical voltage stability studies, all participating generators raise generation at the same rate or predefined rate. However, increasing generation this way may not lead to the highest voltage stability margin for the power system. Maximum Loading Margin (MLM) approach, which provides the maximum Loading Margin or static voltage stability margin, is proposed in reference [5]. An approximate This work was supported by Siam University, Bangkok, Thailand. A. Sode-Yome is with Siam University, Bangkok, Thailand ( arthit@ieee.org). K. Y. Lee is with Department of Electrical & Computer Engineering, Baylor University, Waco, TX , USA ( Kwang_Y_Lee@baylor.edu). and simple model representing the relationship between the generation direction (GD) and the loading margin (LM) is used to obtain the maximum loading-margin point. Although, MLM method can provide maximum LM in the GD space, it approximate LM based on curve fitting methods. Alternatively, one may be interested in approximating the LM directly from known LM and GD. In addition, utilities may be interested in modifying the Energy Management System (EMS) software in a simple way and/or separately from the routine real-time process. This can be done, for example, by using a heuristic approach such as Artificial Neural Networks (NN) [7]. Based on the above observation, attention is drawn in this paper to propose a simple simulation approach that provides an approximation of LM in the generation direction space using Artificial Neural Networks. If the LMs at various generation directions are trained using Neural Networks, operator can approximate LM of the system at a particular generation direction in an easy and simple way. It may be useful in the real-time EMS at the load dispatching center or the System Operator. The rest of the paper is organized as follows: Section II presents existing Generation Direction methods. New simulation approaches are proposed in Section III. Numerical results are presented in Sections IV. Finally, in Section V, major contributions and conclusions are given. II. GENERATION DIRECTION Generation pattern or direction is defined as the portions of generation increase in each participating generator to serve the desired load increase and losses in the system. Let K Gi be the factor for active power increase at generator i and P Gi,o be the generation at the base case, then, the generation P Gi at a higher loading point can be written as ( ) P = P + K () Gi Gi, o Gi where i =, 2, n, for all participating generators. The factor K Gi can be viewed as the generation direction (GD i ) and is very crucial for voltage stability. Generation direction can be worked out by finding the slope of generation increase for individual generator. Existing methods to identify GDs in voltage stability study are summarized below //$26. 2 IEEE

2 2 A. Conventional Approach Conventionally, the generation for a system is increased by a fixed pre-specified percentage in the planning stage, e.g., according to the spinning reserve [, 4]. The power generation of generator i after the load increase can be written as and ( ) P = P + K = P +Δ P (2) Gi Gi, o Gi Gi, o Gi Δ PGi =Δ PD +ΔP (3) loss where P Gi : the power generation of generator i, P Gi,o : the generation of generator i at base load, ΔP Gi : the increase of power generation at generator i, ΔP D : the total load increase, ΔP Loss : the total loss increase, : the number of generators. B. Optimal Power Flow Approach Traditional Optimal Power Flow (OPF) can be formulated to include voltage stability criteria as follows [8]: Minimize subject to C P a P b P c (4) 2 ( Gi ) = ( Gi Gi + Gi Gi + Gi ) n ( λ), ( δ δ ) P + P U U G cos + B sin = (5) Gi Di o i j ij ij ij ij j= n Gi ( λ) Di, o i j ( ij δij ij δij ) j= Q + Q U U G sin B cos = (6) P P P Gi min Gi Gi max U U U i min i i max S = P + Q S (9) 2 2 ij ij ij ij,max where C : total operating cost of the system, a Gi, b Gi, c Gi : cost coefficients of generator i, λ : load incremental parameter or loading factor (L.F.), P Gi, Q Gi : real and reactive power generation at bus i, P Di,o, Q Di,o : real and reactive power demand at bus i at base load, n : number of buses in the system, P Gi min, P Gi max : lower and upper power limits of generator i, U i min, U i max : lower and upper limits of voltage magnitude at bus i, P ij, Q ij,, S ij : real, reactive and apparent power in line ij, S ij, max : the MVA (Thermal) limit of line ij. Generation direction, in this approach, can be worked out by subtracting the new dispatch from the old dispatch for (7) (8) individual generators. C. Cost Participation Factor Approach Cost participation factor is viewed as the easiest method to identify amount of power generation with economic load dispatch consideration. It is calculated based on generators incremental cost [8]: Gi '' ( / Ci ) '' ( / C j ) Δ P = ΔP j= D () where C i : the cost function of generator i, C i : the second derivative of the cost function i, ΔP Gi : the increase in power generation for generator i, ΔP D : the total load increase. Among the existing methods, very few of them can provide the highest LM of the system. Hence, in the following section, the MLM method is presented to maximize the LM by searching in the generation direction space. D. Maximum Loading Margin Method The MLM method identifies a vector of the GDs of generators that gives maximum LM by approximating the surface of the LM as a function of the generation directions. If one can approximate the LM surface as a function of all generation direction variables (K Gi ), optimization technique can be used to provide the highest LM point. Mathematically, the method can be formulated by maximizing LM surface subject to GD constraints as follows [5]: Maximize LM = B + B K subject to n p i, p Gi () p= KGi = (2) i= K Gi (3) where K Gi is the generation direction for generator i, B i,p are the coefficients terms, B o is a constant term, p is the power term, and n is the number of terms of the polynomial approximation. If generation is increased according to this direction, the system will have the maximum loading margin. The MLM method provides a good approximation of the GD, which would give the maximum LM for a given case. Since LM surface may have multiple local maxima, as it can be approximated by polynomial equations, MLM method may be required to find the global maximum. E. Other Existing Methods Linear and quadratic estimates of the LM with respect to system parameters, including power generation, are computed by using sensitivity method to locally predict the new location of the maximum loading margin points [9].

3 3 From the existing methods, only MLM method can provide maximum loading margin in the generation direction space. This method requires an approximate LM surface equation based on the two-dimensional LM curves in each generation direction. This may be useful when one would like to find the maximum LM point based on an optimization technique. At the load dispatching center or the System Operator, however, one may be interested in finding the LM of the system in a simple way when generation directions are considered. Instead of finding LM directly from the equation, one may use heuristic methods such as Artificial Neural Networks to approximate the LM surface. This may be helpful for an operator at dispatching center to modify the EMS software. In the following, new LM approximation methods are proposed based on the actual LM, MLM method and Neural Networks. For ALM-NN method, the complete PV curve is plotted to obtain the LM of the particular generation direction. The process is then repeated until enough training data are obtained. For MLM-NN, the LM surface is approximated for all possible GDs using MLM method. The LM surface is used as a training data set in NN process by introducing GDs as inputs and LM as an output. For MLM-NN2, the single dimensional equations are used to train the NN. The LM surface is approximated using NN. After the NN is trained to find the appropriate weights and other NN parameters, one can use the trained NN to approximate the LM at any GDs of interest. The proposed method is validated in the test system and the results are shown in the following sections. III. PROPOSED METHODOLOGIES The simulation method is presented in two steps: Step I Obtaining Training Data Set and Step II Approximation of LM Using NN. Step : Obtaining Training Data Set Three methodologies for finding training data set, namely Actual LM Method with NN (ALM-NN), Maximum LM Method with NN (MLM-NN) and Maximum LM Method with NN 2 (MLM-NN2), are proposed. The methodologies are described as follows: Actual LM Method with NN (ALM-NN): The actual loading margins and corresponding generation directions can be found from exhaustive simulation using any voltage stability software to calculate loading margin of the power system for a given generation direction [5]. The actual LM and corresponding GD are used as a training data set. Maximum LM Method with NN (MLM-NN): The relationship of LM with respect to GD of each generator is found from a single dimensional space when only one generator except the swing bus is considered. The LM surface is approximated for multidimensional case based on the separability condition and the MLM method presented in Section II.D. Maximum LM Method with NN 2 (MLM-NN2): The relationship of LM with respect to GD of each generator is found from a single dimensional space when only one generator except the swing bus is considered. Each single dimensional equation is then used to train NN in Step 2. LM surface is found from the NN approximation. Step 2: Approximation of LM Using NN After LM and all possible GDs are found, the training data set is then used to train the NN. From the NN, the approximate LM can be found from any GD value. Fig. summarizes the process of the proposed approximate LM methods. In the beginning, generation direction is first set for the Continuation Power Flow (CPF) process. Then the training data set is found from any voltage stability software. Fig.. LM approximation using artificial neural networks. IV. NUMERICAL RESULT Two test systems in reference [5] are used to validate the proposed simulation technique. The modified IEEE 4-bus test system is used first to validate the proposed method, and then the methodology is applied to a practical system, namely the Thailand Power System. Details of test systems can be found in reference [5]. Results presented in the paper were produced with the help of UWPFLOW [] and another Neural Network Software. The UWPFLOW is a research tool for power flow that can be used to calculate loading margin of the power system for a given load and generation direction. In the following section,

4 4 simulation results are presented. The size of generation direction (GD) space is in proportion to the number of dispatchable generators considered in the study. To limit the number of generators in this study, a total of four generators are used for the IEEE 4-bus test system. In order to compare the result with the reference [5], the same cases in [5] are used in this paper. In the beginning, twogenerator cases are examined, then three- and four-generator cases are investigated to demonstrate the practical usefulness and to validate the proposed approach. After that, the proposed technique is validated in the Thailand Power System. The generation set points of generators at buses, 2, 6 and 8 are 5, 77.94, 4 and 4 MW, respectively, at the base load of 259 MW for IEEE 4-bus test system. The base case of Thailand power system is the operating condition at the maximum demand on March 3, 24. Three methodologies are validated in each case: two-, three-, four-generator cases as well as Thailand power system case in the following subsections. A. Two-Generator Cases In the case of two generators, three cases having generators at buses and 2 (G2), buses and 6 (G6), and buses and 8 (G8) are studied. In each case, bus is considered as a swing bus, which delivers the balance of the power. LM and corresponding GD are compared for Actual LM, MLM and ALM-NN methods in Fig. 2. The maximum LM is occurred and the corresponding GD are summarized in Table I for each case. The actual LM is found with the help of UWPLOW program based on the methodology presented in Section II. From Fig. 2 and Table I, it can be seen that the maximum LM and GDs are occurring almost at the same location for all cases. MLM-NN and MLM-NN2 are not considered in these cases as the MLM is based on multi-dimensional space. Loading Margin [p.u.] Actual LM for G-2 Actual LM for G-6.6 Actual LM for G-8 MLM ALM-NN GD of gen at buses 2, 6 or 8 [p.u.] Fig. 2. LMs in the two-generator cases. B. Three- Generator Cases Three cases of generator locations are considered: generators are located at buses, 2 and 6 (Case G26); at buses, 2 and 8 (Case G28); and at buses, 6 and 8 (Case G68). The maximum LM and corresponding GD of each case are shown in Table II. From Table II, the maximum LM of G26, G28 and G68 cases are.655,.286 and.686, respectively, as shown in Actual LM cases. The maximum LM and GDs for Actual LM and ALM-NN cases are occurring almost at the same location since the ALM-NN approximates the surface from the Actual LM. Similarly, MLM and MLM- NN cases provides similar LM surface. The approximate LM solutions for ALM-NN and MLM-NN are very close to the actual LM value and the approximate LM from the MLM method. It can be seen that neural networks can capture nonlinearity of LM surface. MLM-NN2, on the other hand, gives the solution away from the actual LM for the case G26. This depends upon how to choose the NN parameters, such as number of hidden layers, number of neurons, etc., in the training process. MLM-NN2 train the NN from the single dimensional plot to approximate the LM surface in multidimension thus error may has occurred. This problem can be solved, for example, by introducing more training data. LM and corresponding GD for G26 case are compared in three dimensional plots for the proposed methodologies as seen in Figs From the Figs 3-5, it can be seen that the LM surface of actual LM, ALM-NN and MLM-NN are almost the same. The MLM-NN2, as seen in Fig. 6, on the other hand, is little different from the Actual LM as it depends upon the training parameters of NN. However, it may be acceptable if only shape of LM surface is considered. The surface may be similar to the actual LM surface if more training data inside the boundary are used. Figs. 7 and 8 show approximate LM surfaces using MLM- NN for the cases G28 and G68, respectively. The surfaces are very similar to the actual LM surfaces, which can be seen in reference []. TABLE I. GDS AND LM FOR TWO -GENERATOR CASES. Cases Actual LM/MLM/ALM-NN LM (p.u.) GDs G2.286/.286/.367 (,) for all G6.686/.686/.6672 (.6,.4) for all G8.9246/.9246/ (.9,.)/(.9,.)/(,) TABLE II. GDS AND LMS FOR THREE -GENERATOR CASES Cases Methods GD LM (p.u.) G26 Actual LM (,.7,.3).655 ALM-NN (,.7,.3) MLM (,.7,.3).655 MLM-NN (,.7,.3).465 MLM-NN2 (,.5,.5).936 G28 Actual LM (,, ).286 ALM-NN (.,.9, ) MLM (,, ).286 MLM-NN (,.9,.).38 MLM-NN2 (.,.9, ).387 G68 Actual LM (.6,.4, ).686 ALM-NN (.6,.4, ).7835 MLM (.5,.4,.).676 MLM-NN (.5,.4,.) MLM-NN2 (.6,.4, ).66374

5 Fig. 3. Actual LMs in case G Gen. Direction of Pgen2 [p.u.] Fig. 7. Approximate LMs in case G28 using MLM-NN Gen. Direction of Pgen8 [p.u.] Fig. 4. Approximate LMs in case G26 using ALM-NN Fig. 5. Approximate LMs in case G26 using MLM-NN Gen. Direction of Pgen at Bus 6 [p.u.] Gen. Direction of Pgen at Bus 8 [p.u.] Fig. 8. Approximate LMs in case G68 using MLM-NN. C. Four-Generator Case The same idea of the proposed methodologies can be applied to the case of four generators, located at buses, 2, 6 and 8. The maximum LMs are compared for all cases and methodologies in Table III. From the table, ALM-NN and MLM-NN provide the solution close to the actual LM and the MLM method. MLM-NN2 gives different solution. One may tune the NN parameter to get the closer solution. However, it may take much more times and may not be practical in some cases. In the following subsection, only MLM-NN is applied to a practical power system, Thailand power system. TABLE III. GD AND LMS FOR FOUR -GENERATOR CASE Fig. 6. Approximate LMs in case G26 using MLM-NN Methods GD at buses, 2, 6, 8 LM (p.u.) Actual LM (,.7,.3, ).655 ALM-NN (,.7,.3, ) MLM (,.6,.3,.).494 MLM-NN (,.7,.3, ).5865 MLM-NN2 (.6,,.4, ).878 D. Thailand Power System To validate the proposed technique in a practical power system, Conventional Method 2 [5], MLM method and MLM- NN are compared. Details of the Thailand Power System can be found from reference [5]. The GDs and LMs using the

6 6 proposed approaches for Thailand power system are given in Table IV. From the table, the MLM-NN provides the solution close to the Actual LM and the MLM methods since it trains the network from the MLM method. The difference may be due to the flat LM surface of Thailand power system since the generation is far away from the load area and at the weakest bus of the system. Multilayer perceptron with activation functions and backpropagation are used in this paper to capture the nonlinearity of the training data. There are -276 training data used in the training process. The result is obtained from the best solution of training results that provide the minimum training error. Number of neurons and types of activation function are obtained from the best solution using NN software. The training times are only few minutes and testing time for each case is less than second. Compared to reference [], MLM-NN2 and the validation of the approximate LM methods in three-, four-generator and practical power system cases are proposed. TABLE IV. GDS AND LMS FOR THE THAILAND POWER SYSTEM Methods GD (RB, MM, BPK, SB, WN) LM (p.u.) Conv. Meth.2 [5] (.34,.33,.33,, ).6 Actual LM (,.3,.7,, ).34 MLM Method (,.3,.7,, ).34 MLM-NN (.2,.,.7,, ).3687 From the simulation results, it may be concluded that ALM- NN are suitable when the actual LM surface is known. MLM- NN, on the other hand, may be appropriate when LM surface approximation is required. MLM-NN2 provides good information of the shape of LM surface. The proposed methodology may be applied to EMS system at load dispatch center or System Operator by considering different scenarios of the system in order to assist the operator to increase the LM of the system by dispatching generation in appropriate locations. V. CONCLUSION This paper proposes new methods for approximating loading margin or voltage stability margin of the system using Artificial Neural Networks. Loading margins in generation direction space are used to train neural networks. The proposed methods are validated and compared with Actual LM and MLM methods in the multiple-generator cases in the modified IEEE 4-bus test system and the Thailand Power System. The numerical test shows that the proposed method is able to find the appropriate LMs. It can be used in the EMS system to help System Operator to approximate voltage stability margin based on generation directions in a simple way. REFERENCES [] IEEE/PES Power System Stability Subcommittee, Voltage Stability Assessment: Concepts, Practices and Tools, special publication, final draft, Aug. 23. [2] Blackout of 23: Description and Responses, Available: [3] B. H. Lee and K. Y. Lee, "Dynamic and static voltage stability enhancement of power systems," IEEE Transactions on Power Systems, Vol. 8, No., pp , 993. [4] A. Sode-Yome and N. Mithulananthan, Comparison of shunt capacitor, SVC and STATCOM in static voltage stability margin enhancement, International Journal of Electrical Engineering Education, Vol. 4, No. 3. pp.58-7, 24. [5] A. Sode-Yome, N. Mithulananthan, and K. Y. Lee, A maximum loading margin method for static voltage stability in power systems, IEEE Trans. Power Syst., Vol. 2, pp , 26. [6] C. A. Canizares, A. C. Z. De Souza, and V. H. Quintana, Comparison of performance indices for detection of proximity to voltage collapse, IEEE Trans. Power Syst., Vol., No. 3, pp , Aug [7] S. Samarasinghe, Neural Networks for Applied Sciences and Engineering, Auerbach Publications, Tylors and Francis Group, New York, 27. [8] A. Sode-Yome and N. Mithulananthan, Generation direction based on optimization technique for power system static voltage stability, Australasian Universities Power Engineering Conference, Hobart, Australia, Sep , 25. [9] S. Green, I. Dobson and F. L. Alvarado, Sensitivity of loading margin to voltage collapse with respect to arbitrary parameters, IEEE Trans. Power Syst., Vol. 2, No., pp , Feb [] C. A. Cañizares, et al., UWPFLOW: Continuation and Direct Methods to Locate Fold Bifurcations in AC/DC/FACTS Power Systems, University of Waterloo, available at June. 29. [] A. Sode-Yome and K. Y. Lee, Approximate loading margin methods using artificial neural networks in power systems, International Conference on Intelligent System Application to Power System, Curitiba, Brazil, Nov. 29. Arthit Sode-Yome (M 4) received the B.Eng degree in Electrical Engineering from Prince of Songkla University, Thailand, in 993, M.S. degree in Electrical Engineering from the Pennsylvania State University, USA, in 996 and Doctoral Degree in Energy from Asian Institute of Technology, Thailand, in 25. Dr. Arthit has worked at Electricity Generating Authority of Thailand since 994. He is a lecturer at Department of Electrical Engineering, Siam University, Thailand. His main research interests are voltage stability, FACTS, neural networks, optimization techniques and HVDC. Kwang Y. Lee (F ) received his B.S. degree in Electrical Engineering from Seoul National University, Korea, in 964, M.S. degree in Electrical Engineering from North Dakota State University, Fargo, in 968, and Ph.D. degree in System Science from Michigan State University, East Lansing, in 97. He has been on the faculties of Michigan State, Oregon State, Houston, the Pennsylvania State University, and Baylor University, where he is currently Professor and Chair of Electrical and Computer Engineering and Director of Power and Energy Systems Laboratory. His interests are power systems control, operation and planning, and intelligent systems applications to power plants and power systems control. Dr. Lee is a Fellow of IEEE, Editor of IEEE Transactions on Energy Conversion, and former Associate Editor of IEEE Transactions on Neural Networks.