PSS Design for a Single-Machine Power System Using Honey Bee Mating Optimization

Transcription

1 PSS Design for a Single-Machine Power System Using Honey Bee Mating Optimization H. Shayeghi H. A. Shayanfar E.E.Department Technical Eng. Department Center of Excellence for Power System Automation and Operation University of Mohaghegh Ardabili Iran University of Science and Technology, Tehran, Ardabil, Iran Iran A. Akbarimajd A. Ghasemi Technical Eng. Department Technical Eng. Department University of Mohaghegh Ardabili University of Mohaghegh Ardabili Ardabil, Iran Ardabil, Iran hshayeghi@gmail.com, hashayanfar@yahoo.com, akbarymajd@yahoo.com, ghasemi.agm@gmail.com Abstract- A Honey Bee Mating Optimization (HBMO) technique is proposed for the optimal tuning of the Power System Stabilizer (PSS) in this paper. The design problem of robustly selecting PSS parameters is formulated as an optimization problem according to the time domain-based objective function which is solved by the HBMO technique that has a strong ability to find the most optimistic results. To achieve desired level of robust performance and improve power system low frequency oscillations damping, The design process takes a wide range of operating conditions. The effectiveness of the proposed HBMO based PSS is demonstrated on a Single-Machine Infinite-Bus (SMIB) power system through the nonlinear time domain simulation and some performance indices under different operating conditions in comparison with the genetic algorithm based tuned stabilizer and conventional PSS. Results evaluation show that the designed HBMO based PSS has an excellent capability in damping power system low frequency oscillations and enhance greatly the dynamic stability of the power systems. Keywords: PSS Design, HBMO, Low Frequency Oscillations, SMIB.. Introduction Nowdays, many power-generating plants were equipped with continuously acting Automatic Voltage Regulators (AVRs). As the number of power plants with AVRs grew, it became apparent that the high performance of these voltage regulators had a destabilizing effect on the power system. On the other hand, by the development of interconnection of large electric power systems, there have been spontaneous system oscillations at very low frequencies in order of.2-3. Hz. In some cases, they continue to grow and presented a limitation on the amount of the power to be transmitted within the system, if no adequate damping is available []. Power System Stabilizers (PSSs) are auxiliary control devices on synchronous generators, used in conjunction with their excitation systems to provide control signals toward enhancing the system damping of low frequency oscillations associated with the electromechanical modes and extend power transfer limits; thus maintaining reliable operation of the power system [2]. The conventional lead-lag compensator based stabilizers is still widely used for practical applications and generally provide acceptable dynamic performance. This is because it performs well for a wide class of process. Also, they give robust performance for a wide range of operating conditions and easy to implement. However, the problem of PSS parameter tuning is a complex exercise. A number of the conventional techniques have been reported in the literature pertaining to design PSS namely: the eigenvalue assignment, mathematical programg, gradient procedure for optimization and also the modern control theory [2-5]. The main problem encountered in the conventional PSS design is that the power system constantly experience changes in the operating conditions due to variation in generation and load patterns, as well as change in transmission network. Thus, the investigations carried out using these approaches reveal that it exhibits poor dynamics performance, especially in the presence of the other destabilizing effects such as parameter variations and nonlinearities. A more reasonable design of the PSS is based on the gain scheduling and adaptive control theory as it takes into consideration the nonlinear and stochastic characteristics of the power systems [-7]. 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 * Correspanding Author. Address: hashayanfar@yahoo.com (H. A. Shayanfar)

2 can not only provide good damping over a wide operating range but more importantly, it can also solve the coordination problem among the stabilizers. Many random heuristic methods, such as like Tabu search, genetic algorithms, chaotic optimization algorithm, rule based bacteria foraging and Particle Sswarm Optimization (PSO) have recently received much interest for achieving high efficiency and search global optimal solution in the problem space and they have been applied to the problem of PSS design [8-]. These evolutionary based methods are heuristic populationbased search procedures that incorporate random variation and selection operators. Although, these methods seem to be good approaches for the solution of the PSS parameter optimization problem, however, when the system has a highly epistatic objective function (i.e. where parameters being optimized are highly correlated), and number of parameters to be optimized is large, then they have degraded effectiveness to obtain the global optimum solution. In order to overcome these drawbacks, a Honey Bee Mating Optimization (HBMO) technique is proposed for the optimal tune of the PSS parameters to improve power system low frequency oscillations damping in this paper. The HBMO algorithm is a typical swarmbased approach to optimization, in which the search algorithm is inspired by the honey-bee mating process [2] and has emerged as a useful tool for the engineering optimization. It is a hybrid evolutionary algorithm which is comprised of GA, SA, local search, and some innovations for its self-adaptation. Unlike the other heuristic techniques, The HBMO algorithm has a flexible and well-balanced mechanism to enhance the global and local exploration abilities [3]. In this study, the problem of robust PSS design is formulated as an optimization problem and HBMO technique is used to solve it. A performance index is defined based on the system dynamics after an impulse disturbance alternately occurs in the system and used to form the objective function of the design problem. The proposed HBMO based designed PSS has been applied and tested on a weakly connected power system under wide range of operating conditions to illustrate their ability to provide efficient damping of low frequency oscillations. To show the superiority of the proposed design approach, the simulations results are compared with the GA based designed and classical PSS under different operating conditions through some performance indices. The results evaluation shows that the proposed method achieves good robust performance for wide range of load changes in the presence of very highly disturbance and is superior to the other stabilizers. 2. Power System Model For the stability analysis of power system, adequate mathematical models describing the system are needed. The models must be computationally efficient and be able to represent the essential dynamics of the power system. The stability analysis of the system is generally attempted using mathematical models involving a set of nonlinear differential equations. A schematic diagram for the test system is shown in Fig.. The generator is equipped with the excitation system and a power system stabilizer. System data are given in the Appendix. Fig.. SMIB power system The synchronous generator is represented by model., i.e. with field circuit and one equivalent damper winding on q axis. The nonlinear dynamic equations of the SMIB system considered can be summarized as [4, ]. S ds m ( DSm Tm Te ) dt 2H E q ( E fd ( xd x d ) id E q ) T E e fd B do ( k T A q q m A ( v d ref v V )) E q t d q s fd ) () T E i ( x x ) i i (2) 2.. PSS Model The structure of the PSS, to modulate the excitation voltage is shown in Fig.2. The structure consists a gain block with gain K, a signal washout block and two-stage phase compensation blocks. The input signal of the proposed method is the speed deviation (Δω) and the output is the stabilizing signal V S which is added to the reference excitation system voltage. The signal washout block serves as a high-pass filter, with the time constant T W, high enough to allow signals associated with oscillations in input signal to pass unchanged. From the viewpoint of the washout function, the value of T W is not critical and may be in the range of to 2 seconds []. The phase compensation block (time constants T, T 2 and T 3, T 4 ) provides the appropriate phase-lead characteristics to compensate for the phase lag between input and the output signals. K E fd AVR Control Input V t st st st W 3 stw st2 st4 V S Fig.2. Structure of power system stabilizer x e V S

3 3. HBMO A honey-bee colony typically consists of a single egg laying long-lived queen, several thousand drones (depending on the season), workers and a large family of bees living in one bee-hive [5]. Each bee undertakes sequences of actions which unfold according to genetic, ecological and social condition of the colony. A mating flight starts with a dance performed by the queen who then starts a mating flight during which the drones follow the queen and mate with her in the air. After the mating process, the drones die. In each mating, sperm reaches the spermatheca and accumulates there to form the genetic pool of the colony. Each time a queen lays fertilized eggs, she randomly retrieves a mixture of the sperm accumulated in the spermatheca to fertilize the egg and this task can only be done by the queen [2-3]. The HBMO algorithm combines different phases of the marriage process of the honey bee. It starts with random generation of a set of initial solutions. Based on their fitness, randomly generated solutions are then ranked. The fittest solution is named queen, whereas the remaining solutions are categorized as drones (i.e., trial solutions). In order to form the hive and start mating process, the queen, drones and workers (predefined heuristic functions) should be defined. Each queen is characterized with a genotype, speed, energy and a spermatheca with defined capacity. In the next step, drones must be noated to mate with the queen probabilistically during the mating flight. At the start of the flight, the queen is initialized with some energy content and returns to her nest when the energy is within some threshold of either near zero or when the spermatheca is full. The mating flight may be considered as a set of transitions in a state-space (the environment). An annealing function is used to describe the probability of a Drone (D) that successfully mates with the Queen (Q) as follows [2]: ( f ) S ( t ) p rob ( Q, D ) e (3) Where, (f) is the absolute difference of the fitness of D and the fitness of Q and the s(t) is the speed of queen at time t. The fitness of the resulting chromosomes of drone, queen or brood is detered by evaluating the value of the objective function. After each transition in space, the queen s speed and energy decays is given by: S ( t ) S ( t ) (4) E ( t ) E ( t ) (5) Where, α(t) is the speed reduction factor and γ is the amount of energy reduction after each transition (α, γ [,] ). In order to develop the algorithm, the capability of workers is restrained in brood care and thus, each worker may be regarded as a heuristic that acts to improve and/or take care of a set of broods. The rate of improvement in the brood s genotype, defines the heuristic fitness value. The fitness of the resulting genotype is detered by evaluating the value of the objective function of the brood genotype and/or its normalized value. It is important to note that a brood has only one genotype []. In general, the whole process of HBMO algorithm as can be summarized at the five main steps as follows: i) Generate the initial drone sets and queen: The algorithm starts with the mating flight, where a queen (best solution) selects drones probabilistically to form the spermatheca (list of drones). A drone then selected from the list randomly for the creation of the broods. ii) Flight matting: This steps do the flight matting of queen Q. The best drone D k with the largest prob(q, D) among the drone set D is selected the object of matting for the queen Q. After the flight matting the queen s speed and energy decay is reduced by Eq. (4). The flight matting is continues until the speed s(t) is less than a threshold d or the number of sperms of the queen s spermatheca is less than the one threshold. iii) Breeding process: In this step, a population of broods is generated based on the matting between the queen and the drones stored in the queen s spermatheca. The breeding process can transfer the genes of drones and the queen to the j-th individual based on the Eq. (). child parent ( parent 2 parent) () Where, is the decreasing factor (β [,]). iv) Adaptation of worker s fitness: The population of broods is improved by applying the mutation operators as follows: k k k Brood i Brood i ( ) Brood i (7) [,], The is randomly generated and is predefined. The best brood (brood best ) with imum objective function value is selected as the candidate queen. If the objective function of the brood best is superior to the queen, the queen replace with brood best. v) Check the teration criteria: If the teration criteria satisfied finish the algorithm, else generate new drones set and go to step 2. The algorithm continues with three user-defined parameters and one predefined parameter. The predefined parameter is the number of Workers (W), representing the number of heuristics encoded in the program [2, 5]. The user-defined parameters are number of queens, the queen s spermatheca size representing the imum number of mating per queen in a single mating flight and the number of broods that will be born by all queens. The speed of each queen at the start of each mating flight initialized randomly. Since this algorithm is combination of simulated

4 annealing, genetic operator and swarm intelligence, it is very interesting optimization algorithm that used in the optimization problems of reservoir operation. 4. Problem Formulation In case of the above lead-lag structured PSS, the washout time constants is usually specified. In the present study, washout time constant T W = sec is used. The controller gain K and the time constants T, T 2, T 3 and T 4 are to be detered. It is worth mentioning that the PSS is designed to imize the power system oscillations after a large disturbance so as to improve the power system stability. These oscillations are reflected in the deviations in power angle, rotor speed and line power. Minimization of any one or all of the above deviations could be chosen as the objective. In this study, an Integral Square Time of Square Error (ISTSE) of the speed deviations is taken as the objective function expressed as: J NP t tsim t i 2 2 t ( ) dt (8) Where, Δω denotes the rotor speed deviation for a set of PSS parameters, t sim is the time range of the simulation and NP is the total number of operating points for which the optimization is carried out. It is aimed to imize this objective function in order to improve the system response in terms of the settling time and overshoots under different operating condition. The design problem can be formulated as the following constrained optimization problem, where the constraints are the controller parameters bounds [9, ]: Minimize J Subject to: K K K T T T T2 T2 T2 T3 T3 T3 T4 T4 T4 Typical ranges of the optimized parameters are [.-5] for K and [.-] for T, T 2, T 3 and T 4. The proposed approach employs HBMO to solve this optimization problem and search for an optimal or near optimal set of PSS parameters. The optimization of the PSS parameters is carried out by evaluating the objective cost function as given in Eq. (8), which considers a multiple of operating conditions are given in Table. The operating conditions are considered for wide range of output power at different power factors. Results of the PSS parameter set values based on the objective function J, by applying a three phase-toground fault for ms at generator teral at t= sec using the proposed HBMO and GA algorithms are given in Table 2. The Classical PSS (CPSS) is design using the tuning guidelines given in [4] for the noal operating point. Fig. 3 shows the imum fitness functions evaluating process. (9) Cost Table. Operation conditions Case No. P Q x e H Case (Base case) Case Case Case Case Case Case Case Case Case Iteratio Fig. 3: Fitness convergence, Dashed (GA) and Solid (HBMO). Table 2. Optimal PSS parameters Algorithm K T T 2 T 3 T 4 Classic GA HBMO Simulation Results The behavior of the proposed HBMO based designed PSS (HBMOPSS) under transient conditions is verified by applying disturbance and fault clearing sequence under different operating conditions. In comparison with the GA based tuned PSS (GAPSS) and classical PSS. The disturbances are given at t = sec. System responses in the form of slip (S m ) are plotted. The following types of disturbances have been considered. Scenario : A step change of. pu in the input mechanical torque. Scenario 2: A three phase-to-ground fault for ms at the generator teral. Figure 4 shows the system response at the lagging power factor operating conditions with weak transmission system for scenario. It can be seen that the system with CPSS is highly oscillatory. HBMO and GA based tuned stabilizers are able to damp the oscillations reasonably well and stabilize the system at all operating conditions. Figure 5 depicts the responses of same operating conditions but, with strong transmission system. System is more stable in this case, following any disturbance. Both PSSs improve its dynamic stability considerably and HBMOPSS shows its superiority over GAPSS and CPSS. Figure refers to a three-phase to ground fault at the generator teral. Figure 7 depicts the system response in scenario with inertia H'= H/4. It can be seen that the proposed HBMO based PSS has good performance in damping low frequency oscillations and stabilizes the system quickly.

5 Moreover, it is superior to the GA and classical based methods tuned stabilizer. Speed Division -2 x -4 ( b) (c) -2 x Fig. 4. T m=. (p.u.) under X e=.3; CPSS (Dotted), PSOPSS (Dashed) and HBMOPSS (Solid) a) P=.8, Q=.4 b) P=.5, Q=. c) P=., Q=.5-2 x -4-4 x ( b) (c) x -3 x Fig. 5. T m=. (p.u.) under X e=.; CPSS (Dotted), GAPSS (Dashed) and HBMOPSS (Solid) a) P=.8, Q=.4 b) P=.5, Q=. c) P=., Q=.5 x -3 (b) Fig.. 3-φ to ground fault ms for X e=.3, CPSS (Dotted), GAPSS (Dashed) and HBMOPSS (Solid) : a) P=.8, Q=.4 b) P=., Q=.5 x -3 x -3 (b) Fig. 7. T m=. (p.u.) under X e=., CPSS (Dotted), GAPSS (Dashed) and HBMOPSS (Solid) : a) P=., Q=.5 b) P=., Q=.

6 To demonstrate performance robustness of the proposed method, two performance indices: the Integral of the Time multiplied Absolute value of the Error (ITAE) and Figure of Demerit (FD) based on the system performance characteristics are defined as [7]: FD OS US T s [(5 ) (8 ). ] () IT A E t dt 8 () Where, Overshoot (OS), Undershoot (US) and settling time of rotor angle deviation of machine is considered for evaluation of the FD. It is worth mentioning that the lower the value of these indices are, the better the system response in terms of time-domain characteristics. Numerical results of performance robustness for all cases as given in Table for scenario and 2 are listed in Table 3 and 4, respectively. Table 3. Performance indices for scenario HBMOPSS GAPSS CPSS Case No ITAE FD ITAE FD ITAE FD Table 4. Performance indices for scenario 2 HBMOPSS GAPSS CPSS Case No ITAE FD ITAE FD ITAE FD It can be seen that the values of these system performance characteristics with the proposed HBMOPSS are much smaller compared to that GA and classical based designed PSS. This demonstrates that the overshoot, undershoot, settling time and speed deviations of machine is greatly reduced by applying the proposed HBMO based tuned PSS.. Conclusions This paper presents improvement of power systems low frequency oscillations using HBMO based designed PSS in a SMIB power system. The PSS design problem is converted into an optimization problem which is solved by a HBMO technique with the time domainbased objective function considering different operation conditions. The proposed HBMO algorithm combines the advantages of GA, SA, local search, and some innovations for its self-adaptation. It has stronger global search ability and more robust than GA and other heuristic methods. The effectiveness of the proposed stabilizer, for power system stability improvement, is demonstrated by a weakly connected example power system subjected to severe disturbance in comparison with GA and classical methods based designed PSS to show its superiority. The nonlinear simulation results under wide range of operating conditions show the robustness of the proposed method and their ability to provide efficient damping of low frequency oscillations. The system performance characteristics in terms of ITAE and FD indices reveal that using the proposed stabilizer the dynamic performance of the system such as overshoot, undershoot and settling time are greatly reduced under various severe disturbances. Appendix: System data Generator: R a =, x d = 2., x q =.9, x' d =.244, x' q =.244, f = 5 Hz, T' do =4.8, T' qo =.75, H=3.25, Transmission line: R=, x e =.3. Exciter: K A =5, T A =.5, E fd =7., E fd =-7.. References [] M. Anderson and A. A. Fouad, Power System Control and Stability, Ames, IA: Iowa State Univ. Press, 977. [2] P. Kundur, Power System Stability and Ccontrol, McGraw-Hill Inc., New York, 994. [3] Y. Hsu, C. Y. Hsu, Design of proportional integral power system stabilizer, IEEE Trans. on Power Systems, Vol., No. 2, pp. 4-53, 98. [4] P. Kundur, M. Klein, G. J. Rogers, M. S. Zywno, Application of power system stabilizers for enhancement of overall system stability, IEEE Trans. on Power Systems, 4-2, 989. [5] M. J. Gibbard, Robust design of fixed-parameter power system stabilizers over a wide range of operating conditions, IEEE Trans. on Power Systems, Vol., pp , 99. [] D. A. Pierre, A perspective on adaptive control of power systems, IEEE Trans. on Power Systems, Vol. 2, pp , 987. [7] Y. Zhang, G. P. Chen, O. P. Malik and G. S. Hope, An artificial neural network based adaptive power system stabilizer, IEEE Trans. on Energy Conversion, Vol. 8, No., pp. 7-77, 993. [8] Y. L. Abdel-Magid, M. A. Abido, Optimal multiobjective design of robust power system stabilizers using genetic algorithms, IEEE Trans.

7 on Power Systems, Vol. 8, No. 3, pp , 23. [9] H. Shayeghi, H.A. Shayanfar, S. Jalilzadeh, A. Safari, Multi-machine power system stabilizers design using chaotic optimization algorithm, Energy Conversion and Management, Vol. 5, pp , 2. [] S. Mishra, M. Tripathy, J. Nanda, Multi-machine power system stabilizer design by rule based bacteria foraging, Electric Power Systems Research, Vol. 77 pp , 27. [] H. Shayeghi, H.A. Shayanfar, A. Safari, R. Aghmasheh, A robust PSSs design using PSO in a multi-machine environment, Energy Conversion and Management, Vol. 5, pp. 9-72, 2. [2] O. Bozorg Haddad, A. Afshar, M. A. Mariño, Honey-bees mating optimization (HBMO) algorithm: a new heuristic approach for water resources optimization, Water Resources Managament, Vol. 2, pp. -8, 2. [3] F. Mohammad, A. Babak, M. Ali, Application of honey-bee mating optimization algorithm on clustering, Applied Mathematics and Computations, Vol., 52-53, 27. [4] K. R. Padiyar, Power system dynamics- stability and control, Second edition, BS Publications, Hyderabad, India, 28. [5] B. Amiri, M. Fathian, Integration of self organizing feature maps and honey bee mating optimization algorithm for market segmentation, Journal of Theoretical and Applied Information Technology, pp. 7-8, 27. [] M. Fathian, B. Amiri, A honeybee-mating approach for cluster analysis, International Journal of Advance Manufacturing and Technology, Vol. 38, pp , 28. [7] H. Shayeghi, A. Jalili, H. A. Shayanfar, Multistage fuzzy load frequency control using PSO, Energy Conversion and Management, Vol. 49, pp , 28. Biographies Hossein Shayeghi received the B.S. and M.S.E. degrees in Electrical and Control Engineering in 99 and 998, respectively. He received his Ph. D. degree in Electrical Engineering from Iran University of Science and Technology, Tehran, Iran in 2. Currently, he is an Associate Professor in Technical Engineering Department of University of Mohaghegh Ardabili, Ardabil, Iran. His research interests are in the Application of Robust Control, Artificial Intelligence and Heuristic Optimization Methods to Power System Control Design, Operation and Planning and Power System Restructuring. He has authored five books in Electrical Engineering area (all in Persian language). He has published more than papers in International Journals and Conferences proceedings. He is a member of Iranian Association of Electrical and Electronic Engineers (IAEEE) and IEEE. Heidarali Shayanfar Received the B.S. and M.S.E. Degrees in Electrical Engineering in 973 and 979, respectively. He received his Ph. D. Degree in Electrical Engineering from Michigan State University, U.S.A., in 98. Currently, He is a Full Professor in Electrical Engineering Department of Iran University of Science and Technology, Tehran, Iran. His Research Interests are in the Area of Application of Artificial Intelligence to Power System Control Design, Dynamic Load Modeling, Power System Observability Studies, Voltage Collapse, Congestion Management in a Restructured Power System, Reliability Improvement in Distribution Systems and Reactive Pricing in Deregulated Power Systems. He has published more than 35 papers in International Journals and Conferences proceedings. He is a Member of the Iranian Association of Electrical and Electronic Engineers and IEEE. He has published more than 35 techincal papers in the International Journals and Conferences Proceedings. Adel Akbarimajd was born in 975 and received his B.S. degree in Control Engineering from Ferdousi University of Mashhad, Iran in 997 and M.S. degree in Control Systems from Tabriz University of Iran in 2. In 27, he spent six month in the Biorobotics Laboratory, EPFL, Switzerland as visiting researcher. He received his Ph.D. in AI and robotics from University of Tehran in 29. Later he moved to Department of Engineering at University of Mohaghegh Ardabili, where he currently is an assistant professor. His research interests include dynamical systems, control theory, system identification and computational intelligence. Ali Ghasemi Received the B.S. Degree in Electrical Engineering from Esfahan University of Technology, Esfan, Iran in 29. Currently, He is a M.S.E. student in Technical Eng. Department of the University of Mohaghegh Ardabili, Ardabil, Iran. His Areas of Interest in Research are the Application of Heuristic Optimization to Power System Control.