Artificial Bee Colony Based Power System Stabilizer Design for a Turbo-Generator in a Single-Machine Power System

Transcription

1 Artificial Bee Colony Based Power System Stabilizer Design for a Turbo-Generator in a Single-Machine Power System H. Shayeghi H. A. Shayanfar A. Ghasemi Technical Eng. Department E.E.Department Center of Excellence for Power System Technical Eng. Department Automation and Operation University of Mohaghegh Ardabili Ardabil, Iran Iran University of Science and Technology, Tehran, Iran University of Mohaghegh Ardabili Ardabil, Iran hshayeghi@gmail.com, hashayanfar@yahoo.com, ghasemi.agm@gmail.com Abstract- This paper presents an Artificial Bee Colony (ABC algorithm for optimal tuning of the Power System Stabilizer (PSS in a Single-Machine Infinite- Bus (SMIB power system. The design problem of robustly tuning PSS parameters is formulated as an optimization problem according to the time domainbased objective function which is solved by the ABC technique that has strong ability to find the most optimistic results. To ensure performance and robustness of the proposed control strategy to stabilize low frequency oscillations The design process takes a wide range of operating conditions. The effectiveness of the proposed ABC based PSS is demonstrated on a SMIB power system through the nonlinear time domain simulation and some performance indices under different operating conditions in comparison with the particle swarm optimization based tuned stabilizer and conventional PSS. Results evaluation show that the proposed stabilizer achieves good robust performance for wide range of system operation conditions and is superior to the other PSSs. Moreover, the proposed control strategy has simple structure, easy to implement and tune which can be useful for the real world complex power system. Keywords: PSS Design, ABC Optimization, Low Frequency Oscillations, SMIB.. Introduction Stability of power systems is one of the most important aspects in electric system operation.this arises from the fact that the power system must maintain frequency and voltage levels at the noal values, under any disturbance, like a sudden increase in the load, loss of one generator or switching out of a transmission line during a fault []. 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.Once started, they would continue for a long period of time. In some cases, they continue to grow, causing system separation if no adequate damping is available. Moreover, low frequency oscillations present limitations on the power-transfer capability. To enhance system damping, the generators are equipped with Power System Stabilizer (PSS that provide supplementary feedback stabilizing signals in the excitation system. PSS augment the power system stability limit and extend the power-transfer capability by enhancing the system damping of low frequency oscillations associated with the electromechanical modes [2]. The lead compensator based stabilizers with fix parameters have practical applications and generally provide acceptable dynamic performance. However, the problem of PSS parameter tuning is a complex exercise. A number of 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]. Unfortunately, the conventional techniques are time consug as they are iterative and require heavy computation burden and slow convergence. In addition, the search process is susceptible to be trapped in local ima and the solution obtained may not be optimal [4]. Also, a set of controller parameters which stabilize the system under a certain operating condition may no longer yield satisfactory results when there is a drastic change in power system operating conditions and configurations [5]. 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 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 Tabu search, genetic algorithms, chaotic optimization algorithm, rule based bacteria foraging and Particle Swarm Optimization (PSO have * Correspanding Author. Address: hashayanfar@yahoo.com (H. A. Shayanfar

2 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 population-based 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, an Artificial Bee Colony (ABC algorithm is proposed for optimal tuning of PSS parameters to improve power system low frequency oscillations damping in this paper. The ABC algorithm is a typical swarm-based approach optimization, in which the search algorithm is inspired by the intelligent foraging behavior of a honey bee swarm process [2] and has emerged as a useful tool for the engineering optimization. It incorporates a flexible and wellbalanced mechanism to adapt to the global and local exploration and exploitation abilities within a short computation time. Hence, this method is efficient in handling large and complex search spaces [3]. The proposed method has been applied and tested on a weakly connected power system under wide range of operating conditions to show the effectiveness and robustness of the proposed ABC based tuned PSS and their ability to provide efficient damping of the low frequency oscillations.to show the superiority of the proposed design approach, the simulations results are compared with the PSO based designed and classical PSS under different operating conditions through some performance indices. The results evaluation show that the proposed method achieves good robust performance for wide range of load changes in the presence of large disturbance and is superior to the other stabilizers. 2. Power System Model A power system model consisting of a Single Machine connected to an Infinite Bus (SMIB through a circuit transmission line is used in the simulation studies. A schematic diagram for the model is shown in Fig.. The generator is equipped with excitation system and a power system stabilizer. All the relevant parameters are given in the Appendix. Efd AVR Control Input V t x e Fig.. SMIB power system The synchronous generator is represented by model., i.e. with field circuit and one equivalent damper winding on the q axis. The dynamic equations of the SMIB system considered can be summarized as [4, ]: S dsm ( 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.. Structure of the PSS The structure of PSS, to modulate the excitation voltage is shown in Fig. 2. The structure consists of 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 the 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 st st st W 3 stw st2 st4 Fig.2. Structure of power system stabilizer V S V S 3. ABC Algorithm Recently, Karaboga and Basturk [5] have described an artificial bee colony algorithm based on the foraging behavior of honey-bees for the numerical optimization problems. The algorithm simulates the intelligent foraging behavior of the honey bee swarms. It is a very simple, robust and population based stochastic optimization algorithm []. The imal model of forage selection in the honey bee swarms intelligence consists of three essential components: food sources, employed foragers and unemployed foragers, and two leading modes of the behavior, recruitment to a nectar source and abandonment of a source, are defined [7]. A food source value depends on many factors, such as its

3 proximity to the nest, richness or concentration of energy and the ease of extracting this energy. The employed foragers are associated with particular food sources, which they are currently exploiting or are employed. They carry with them information about these food sources and share this information with a certain probability. There are two types of unemployed foragers, scouts and onlookers. Scouts search the environment surrounding the nest for new food sources, and onlookers wait in the nest and find a food source through the information shared by employed foragers. In the ABC algorithm, the colony of artificial bees contains of three groups of bees: employed bees, onlookers and scouts. The food source represents a possible solution of the optimization problem and the nectar amount of a food source corresponds to the quality (fitness of the associated solution. Every food source has only one employed bee. Thus, the number of employed bees or the onlooker bees is equal to the number of food sources (solutions. An onlooker bee chooses a food source depending on the probability value associated with that food source, p i, calculated by the following expression: p i fit i (3 SN fit n n Where fit i is the fitness value of the solution i evaluated by its employed bee, which is proportional to the nectar amount of the food source in the position i and SN is the number of food sources which is equal to the number of employed bees (BN. In this way, the employed bees exchange their information with the onlookers. In order to produce a candidate food position from the old one, the ABC uses the following expression: v x ( x x kj (4 Where, k,2,..., BN and j,2,..., D are randomly chosen indexes. Although k is detered randomly, it has to be different from i. is a random number between [, ]. It controls the production of a neighbour food source position around x and the modification represents the comparison of the neighbor food positions visually by the bees. Equation (4 shows that as the difference between the parameters of the x and x kj decreases, the perturbation on the position x decreases, too. Thus, as the search approaches to the optimum solution in the search space, the step length is adaptively reduced. The food source whose nectar is abandoned by the bees is replaced with a new food source by the scouts. In the ABC algorithm this is simulated by randomly producing a position and replacing it with the abandoned one. If a position cannot be improved further through a predetered number of cycles called limit then, that food source is assumed to be abandoned. After each candidate source position v is produced and then, evaluated by the artificial bee, its performance is compared with that of x. If the new food has equal or better nectar than the old source, it is replaced with the old one in the memory. Otherwise, the old one is retained. In other words, a greedy selection mechanism is employed as the selection operation between the old and the current food sources. The main steps of the algorithm are given by [2, 7]: i Initialize the population of solutions and evaluate them. ii Produce new solutions for the employed bees, evaluate them and apply the greedy selection mechanism. iii Calculate the probabilities of the current sources with which they are preferred by the onlookers. iv Assign onlooker bees to the employed bees according to probabilities, produce new solutions and apply the greedy selection mechanism. v Stop the exploitation process of the sources abandoned by bees and send the scouts in the search area for discovering new food sources, randomly. vi Memorize the best food source found so far. vii If the teration condition is not satisfied, go to step 2, otherwise stop the algorithm. It is clear from the above explanation that there are three control parameters used in the basic ABC: The number of the food sources which is equal to the number of employed or onlooker bees (SN, the value of limit and the Maximum Cycle Number (MCN. 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 follows: J NP i t tsim t 2 2 t ( dt (5 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

4 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 ABC algorithm 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. (5, 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 ABC and PSO algorithms are given in Table 2. The Classical PSS (CPSS is designed using the tuning guidelines given in [4] for the noal operating point. Fig. 3 shows the imum fitness functions evaluating process. Table. Operation conditions Case No. P Q x e H Case (Base Case Case Case Case Case Case Case Case Case Case Cost Function Fig. 3: Fitness convergence, Dashed (PSO and Solid (ABC. Method ABC PSO CPSS Iteration Table 2. Optimal PSS parameters K pss T T T T Simulation Results The behavior of the proposed ABC based designed PSS (ABCPSS under transient conditions is verified by applying disturbance and fault clearing sequence under different operating conditions. In comparison with the PSO based tuned PSS (PSOPSS and classical PSS. The disturbances are given at t = sec. System responses in the form of slip (S m are plotted. Fig. 4 shows the system response at the lagging power factor operating conditions with weak transmission system by applying a step change of. pu in input mechanical torque. It can be seen that the system with CPSS is highly oscillatory. ABC and PSO based tuned stabilizers are able to damp the oscillations reasonably well and stabilize the system at all of the operating conditions. Fig. 5 depicts the responses of the 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 ABCPSS shows its superiority over PSOPSS and CPSS. Fig. refers to a three-phase to ground fault for ms at generator teral. It can be seen that the proposed PSS has good performance in damping low frequency oscillations and stabilizes the system quickly. Moreover, the system performance analysis under different operating conditions and disturbances show that the ABC based tuned PSS is superior to the PSO and the classical based methods designed stabilizer. x -4 (a x -4 (b x -4 (c Fig. 4. T m=. (p.u., X e=.3; CPSS (Dotted, PSOPSS (Dashed and ABCPSS (Solid a P=.8, Q=.4 b P=.5, Q=. c P=., Q=

5 x -4 (a x -3 (b x -4 (c Fig. 5. T m=. (p.u., X e=.; CPSS (Dotted, PSOPSS (Dashed and ABCPSS (Solid a P=.8, Q=.4 b P=.5, Q=. c P=., Q= x -3 (a x -3 (b x (c x -3 (d Fig.. 3-φ to ground fault ms, CPSS (Dotted, PSOPSS (Dashed and ABCPSS (Solid X e=.3: a P=.8, Q=.4 b P=., Q=.5 X e=.: c P=.8, Q=. d P=.8, Q=.2 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 [8]: FD OS US T s [(5 (8. ] (7 ITAE t dt 8 (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 the these indices are, the better the system response in terms of the time-domain characteristics. Numerical results of performance robustness for all cases as given in Table by applying a step change of. pu in input mechanical torque at t = sec are listed in Table 3. Case No Table 3. Performance indices ABCPSS PSOPSS ITAE FD ITAE FD CPSS ITAE FD

6 It can be seen that the values of these system performance characteristics with the proposed ABC based tuned PSSs are much smaller compared to that of PSO 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 ABC based tuned PSS.. Conclusions In this paper, ABC optimization technique is proposed for power system stabilizer design in a SMIB power system. To design PSS problem, a nonlinear simulation-based objective function is developed to increase the system damping and then the ABC technique is implemented to search for the optimal stabilizer parameters. The proposed ABC algorithm is easy to implement without additional computational complexity. Thereby, experiments of this algorithm gives quite promising results. The ability to jump out the local optima, the convergence precision and speed are remarkably enhanced and thus the high precision and efficiency are achieved. The effectiveness of the proposed stabilizer, for power system stability improvement, is demonstrated by a weakly connected example power system subjected to severe disturbance. The dynamic performance of the ABC based tuned PSS has also been compared with the PSO and classical methods based designed PSS to show its superiority. The nonlinear simulation results under wide range of operating conditions show the effectiveness and robustness of the ABC based PSS ability to provide efficient damping of low frequency oscillations and its superiority to the other methods. The system performance characteristics in terms of ITAE and FD indices reveal that the proposed stabilizers demonstrates that the overshoot, undershoot, settling time and speed deviations of the machine are greatly reduced under severe disturbance conditions. 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. 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] D. Karaboga, B. Akay, A comparative study of artificial bee colony algorithm, Applied Mathematics and Computation, Vol. 24, pp. 8-32, 29. [3] C. Zhang, D. Ouyang, J. Ning, An artificial bee colony approach for clustering, Expert Systems with Applications, Vol. 37, pp , 2. [4] K. R. Padiyar, Power System Dynamics- Stability and Control, Second edition, BS Publications, Hyderabad, India, 28. [5] D. Karaboga, B. Basturk A powerful and efficient algorithm for numerical function optimization: Artificial Bee Colony (ABC algorithm, Journal of Global Optimization, Vol. 37, pp , 27. [] S. N. Omkar, J. Senthilnath, R. Khandelwal, G. N. Naik, S. Gopalakrishnan, Artificial Bee Colony (ABC for multi-objective design optimization of composite structures, Applied Soft Computing, Article in press (2. [7] C. Zhang, D. Ouyang, J. Ning, An artificial bee colony approach for clustering, Expert Systems with Applications, Vol. 37, pp , 2. [8] H. Shayeghi, A. Jalili, H. A. Shayanfar, Multi-stage fuzzy load frequency control using PSO, Energy Conversion and Management, Vol. 49, pp , 28.

7 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, one in Power Systems Analysis, one in MATALAB, one in Electric Circuits, one in Electric DC Machines, one in Electric Installations (all in Persian language. Also, he is co-authored of a book chapter- A Review on Load Frequency Control Strategies in the book Complex Behaviour of the Distributed Generation System: Intelligent Management of the Renewable Energy Resources for assuring the DG System Power Quality and a Sustainable Development. 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.and IEEE. 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 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. 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. 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