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TJPRC: International Journal of Power Systems & Microelectronics (TJPRC: IJPSM) Vol. 2, Issue 1, Jun 2016, 39-50 © TJPRC Pvt. Ltd. OPTIMAL PLACEMENT OF TCSC FOR REACTIVE POWER RESERVE MANAGEMENT WITH REACTIVE POWER LOSS MINIMIZATION USING HYBRID PSOGSA L. N. MRUNALINI DEVI1 & A. SURYA PRAKASH RAO2 1 2 Research Scholar, Department of E .E. E, Sir C. R. REDDY College of Engineering, Andhra Pradesh, India Sr.Assistant Professor, Department of E.E.E, Sir C. R. REDDY College of Engineering, Andhra Pradesh, India ABSTRACT This paper presents a novel heuristic optimization method inspired by law of gravity to reduce the reactive power losses in the system by incorporating series compensating FACTS device, TCSC using a hybrid method based on particle swarm optimization (PSO) and gravitational search algorithm (GSA).This algorithm named as hybrid PSOGSA combines the social thinking feature in PSO with the local search capability of GSA. A power system during disturbances is at a risk of voltage instability due to insufficient reactive power reserve. The optimal placement and parameter setting of multiple TCSCs with proposed algorithm ensures reactive power reserve management which is the suboptimal solution of reactive power loss convergence, robustness and most significantly its optimal search behavior. The effectiveness of the proposed work is tested for IEEE 30 bus test system. It is observed that the proposed algorithm can be applied to larger systems and do not suffer with computational difficulties. KEYWORDS: Facts Devices, Hybrid PSOGSA, TCSC, Reactive Power Reserve and Reactive Power Loss Original Article minimization. Experimental results justify the superiority of the approach over PSO and GSA techniques in terms of its fast Received: Jan 07, 2016; Accepted: Jan 10, 2016; Published: Jan 18, 2016; Paper Id.: TJPRC: IJPSMJUN20164 INTRODUCTION The reactive power demand of a power system increases dramatically whenever the system is overloaded or subjected to sudden disturbances or contingencies. If the sufficient amount of reactive power is not supplied to the system then there will be a drop across terminal bus voltages and has been found responsible for system block outs in many countries across the world [1].Hence, adequate reactive power reserves are must for the system to overcome voltage instability problem. In a deregulated power system environment, the optimum bidders are chosen based on real power cost Characteristics, so it results in reactive power shortage and hence loss of voltage stability of the system. The reactive power reserves of a power system at generators can be improved by reducing the reactive power losses of the system. As the losses in the system are reduced the reactive power conserved can act as reserve capacity of the generators. Voltage profile improvement alone cannot ensure the voltage stability. The authors [2-3] discuss methods to access voltage stability of a power system to find the possible ways to improve the voltage stability. The amount of reactive power reserves at the generating stations is found to be the measure of degree of voltage stability and it www.tjprc.org [email protected] 40 L. N. Mrunalini Devi & A. Surya Prakash Rao stressed the importance of reactive power management from generators point of view which so far paid less attention rather than the load’s perspective. In [4] T. Manezes et al. proposes a strategy to improve voltage stability by dynamic var sources scheduling. In [5] a methodology to reschedule the reactive power injection from generators and synchronous condensers with the aim of improving the voltage stability margin is proposed. An alternative approach for optimal reactive power dispatch based on iterative techniques is considered in [7-8]. H. Yoahida et al. has adopted easy to implement search algorithm PSO for reactive power and voltage control. Reactive power reserve management rather than reactive power scheduling is proposed to enhance voltage stability (Feng Dong et al. 2005). The difficulty in controlling the modern power systems due to increased power flows is resolved by the advent of fast acting, self commutated power electronics converters well known as FACTS Controllers introduced by Hingorani [12].which are useful in taking fast control actions to ensure security of power systems. Thyristor controlled series capacitor (TCSC) is a series compensating FACTS device inserted in transmission lines to vary its reactance and thereby reduces the reactive power losses and increases transmission capacity of the system. As other FACTS devices, TCSC is also a costly device and hence it is important to place it at optimal location and to find optimal size. In recent times, many heuristic and hybrid approaches such as genetic algorithm (GA), particle swarm Optimization (PSO), differential evolution (DE), GA-PSO and DE-PSO have been proved effective in optimally locating FACTS devices. A new population based hybrid algorithm PSOGSA is implemented to optimally locate TCSC with an aim to minimize reactive power losses of the system. The PSOGSA algorithm incorporates some features of particle swarm optimization algorithm into gravitational search algorithm i.e. exploitation ability of PSO with ability of exploration in GSA to unify their strength. PROBLEM FORMULATION • Reactive Reserves The different reactive power sources of a power system are synchronous generators and shunt capacitors. During a disturbance the real power demand does not change considerably but reactive power demand increases dramatically. This is due to increased voltage decay with increasing line losses and reduced reactive power generation from line charging effects Sufficient reactive power reserves should be made available to supply the increased reactive power demand and hence improve the voltage stability limit. The reactive power reserve can be improved by reducing the reactive power losses in the system. The reactive power reserve of a generator is the ability of the generator to support bus voltages under increased load condition or system disturbances. www.tjprc.org [email protected] Optimal Placement of TCSC for Reactive Power Reserve Management with Reactive Power Loss Minimization Using Hybrid PSOGSA • 41 Modeling of TCSC TCSC (Thyristor controlled series capacitor) is a series compensation FACTS device which consists of a series capacitor bank shunted by thyristor controlled reactor. The basic idea behind power flow control with the TCSC is to decrease or increase the overall lines effective series transmission impedance, by adding a capacitive or inductive reactance correspondingly. Figure 1: TCSC as a Variable Reactance Incorporated in the System The TCSC is modeled as variable reactance, where the equivalent reactance of line Xij is defined as = + (1) Where, = ∗ (2) −0.8' ≤ ≤ 0.2' (3) = !"! Where, Xline is the transmission line reactance, and XTCSC is the TCSC reactance. The level of the applied compensation of the TCSC usually varies between 20% inductive and 80% capacitive. • Objective Function The goal of reactive power planning is to minimize the reactive power losses of the system there by minimizing the reactive power generated by optimally placing TCSC. Hence, the objective function can be mathematically expressed as * = +(,'-.. + /0 1'2 + /3 ,'2 ) (4) Where, 7 8 ,'-.. = ∑9:0 ,6'-.. 1'2 = ,'2 = >[email protected] ∑ABC <= D<=8EF <=GHI D<=GEJ > M L DL 8EF ∑ABC = = GHI DL GEJ L= = (5) (6) (7) Where,16'2 ,6'2 are defined as www.tjprc.org [email protected] 42 L. N. Mrunalini Devi & A. Surya Prakash Rao 16'2 = O 16PQR 16 > 16PQR U 16P 16 < 16P ,PQR ,6 > ,6PQR U ,6'2 = O 6P ,6 ,6 < ,6P Equation (5) is the expression for total reactive power loss of the system and NL represents total number of transmission lines in the system.The second and third terms in the ojective function are normalized violations of load bus voltages and generator reactive power outputs. NPQ and NG are number of load buses and generator buses respectively./0 /3 are penality coefficients set to 10. The objective function is subjected to both equality and inequality constraints. constraint 1: Real power balance equation 7 Y 1 1Z [Z ( ) cos_`Z + Z − a = 0 VW − VX − ∑Z:0 (8) Constraint 2: Reactive power balance equation 7 Y ,W − ,X − ∑Z:0 1 1Z [Z ( ) sin_`Z + Z − a = 0 (9) Constraint 3: Reactance limits of TCSC P PQR ≤ ≤ (10) HYBRID PSOGSA PSOGSA is formulated by S. Mirjalili et al. [17]. The basic concept behind the hybridization is to combine the ability of social thinking (gbest) in PSO using the local search capability of GSA. The proposed algorithm considers N agents in the system. The algorithm starts with randomly defining all agents in search space. It considers agents as objects and the position of ith agent is given by = (e0 , … . , eh , … . e ) i=1, 2….N (11) Where, Xi is the position in the dth dimension of the ith agent. In this problem each agent is defined as a vector containing the line number and the size of TCSC in terms of reactance. Hence the dimensionality of the problem is two. Agent: [@ Φ] Where @: is the TCSC line location number. Φ: is the TCSC size. The gravitational forces from agent j on agent i at a specific time t is defined as *Zh () = i() www.tjprc.org PE (j)×Pl (j) mEl (j)n∈ peZh () − eh ()q (12) [email protected] Optimal Placement of TCSC for Reactive Power Reserve Management with Reactive Power Loss Minimization Using Hybrid PSOGSA 43 Where, Mi (t) and Mj(t) are masses of objects i and j,G(t) is the gravitational constant at time t, Rij(t) is the Euclidean distance between i and j, ε is a small constant Gravitational constant G(t) is initialized randomly in the beginning and is reduced with time to control the search accuracy. i() = ir × exp p−v × jw 2QRjw q (13) It means G is the function of time t and initial value G0, where G0 is the initial value of gravitational constant, α is the user specified descending coefficient, iter is the current iteration, and maxiter is maximum number of iterations. Let the total force acting on agent i in the dimension d is calculated as h *h () = ∑7 Z:0,Zx Z *Z () (14) The acceleration of ith agent at iteration t having d dimension is given according to the law of motion i.e., the acceleration of an agent is proportional to the resultant force and inverse of its mass, so the acceleration of all agents should be calculated as h () = yEz (j) PE (j) (15) The velocity of the agents is given as 1h ( + 1) = { × 1h () + 0′ × × h () + × × p| − eh ()q (16) Where, vid is the velocity of agent i at iteration t in dimension d, cj1 is a weighting factor, w is a weighting function, gbest is the best solution found so far. At each, iteration the position of an agent is updated as h () = h () + 1h ( + 1) (17) Where, vid (t+1) is the velocity of next agent and xid is the position of ith agent in dth dimension at iteration t. The value of masses of agents are calculated by comparison of fitness () = }~wwjj..E (j)Dr.∗-w.j(j) .j(j)D-w.j(j) ()∗ M (t) = ∑ BC () (18) (19) Where, current-fitnessi(t) is the fitness value of the agent i at any time t, and best (t) and worst (t) are the minimum and maximum fitness value of all agents. The agents exploring in the search space are attracted towards other agents by means of gravity force. The heavier mass represents a good solution. Here gbest help them in finding the optima around a good solution. The optimal solution is found by using the exploitation ability of PSO. Global search and local search balance is accomplished by adjusting the values C1 and C2. www.tjprc.org [email protected] 44 • L. N. Mrunalini Devi & A. Surya Prakash Rao Flow Chart of PSOGSA Figure 2: Flow chart of hybrid PSOGSA CASE STUDIES The optimal reactive power reserve management is formulated with primary objective of minimization minimi of reactive power losses. The search space is bounded by violation limits to avoid unfeasible solutions. The objective ective function (4) with reactive power losses along with equality and inequality constraints is solved by proposed algorithm to locate TCSC in most suitable line. The system (Figure 3) represents IEEE 30 bus test system it has 6 generator buses, 24 load buses and 41 branches. Figure 3: IEEE 30 Bus Test Systems For a TCSC to be placed in the line, the lines with tap changing transformers are not considered. Each time when the particle’s new position includes a line with tap setting transformer, the position is changed to the geographically closest line (line without transformer). In order to limit the sizes of the TCSC units, the restrictions on level of compensation is applied to the particles using Equation (3) so that the power ower flows flow does not diverge giving worst solutions. www.tjprc.org [email protected] Optimal Placement of TCSC for or Reactive Power Reserve Management with Reactive Power Loss Minimization Using Hybrid PSOGSA P 45 The he reduction in reactive power loss by implementation of the proposed algorithm with one, two and three TCSC devices is tabulated as in Table 1. Table 1: Simulation Results of Reactive Power Loss Optimal Location of TCSCs (Line Number) IEEE 30 BUS SYSTEM Without TCSC With 1 TCSC With 2 TCSCs With 3 TCSCs Line Reactance With Out With TCSC TCSC Q LOSS (MVAR) % Loss Reducti on - - - 22.2444 - 5 0.1983 0.09915 14.4833 34.89 5,1 0.0575 0.0287 6.296 71.7 5,1,2 0.1852 0.0926 1.2919 94.1922 TCSC device is installed on different branches one by one based on the proposed algorithm and further the model has been applied to multiple TCSC devices. The optimal location of single TCSC at which the value of objective function is minimum, can be found as line number 5. That means locating a TCSC in this line gives best optimum value for the objective function. When only one TCSC is incorporated, the reactive power loss reduction is from 22.244 MVAR to 14.4833 MVAR, which is about 34%. For two TCSCs the reduction is i about 71% and for three TCSCs it is 94% which shows maximum improvement. The he total reactive power loss in the system with and without installation installation of TCSCs is illustrated in Figure 4. Figure igure 4: Reduction in Total Qloss with PSOGSA The reactive power generation, before and after positioning of TCSC, from all 6 generator buses and 2 SVC buses (bus10 and bus 24) are tabulated in Table II. Table 2: 2 Reactive Power Generation at Different Buses Given bus No 1 2 www.tjprc.org Q gen Without TCSC in MVAR -17.021 48.822 Q gen With 1 TCSC in MVAR Q gen With 2 TCSC in MVAR Q gen With 3 TCSC in MVAR -17.967 41.001 -20.192 27.296 -11.917 16.371 [email protected] 46 L. N. Mrunalini Devi & A. Surya Prakash Rao 5 8 10 11 13 24 35.975 30.975 19 16.119 10.432 4.3 Total Q g (MVAR) 148.4442 Table 2: Contd., 38.401 35.856 29.709 38.029 19 19 15.961 16.804 10.279 11.402 4.3 4.3 140.6831 132.4960 34.735 37.085 19 16.740 11.178 4.3 127.4920 SVC buses (10 and 24) are not considered for minimization of reactive power generation and therefore there is no change in Qgen at those buses. Therefore the candidate buses considered for reactive power generation reduction are only the generator buses of 1, 2,5,8,11 &13. The effective reactance of the line is reduced with TCSC in the system. When three TCSCs are used, reactive power generation is reduced from 148.442 MVAR to 127.492 MVAR (about 14%).That is the reactive power reserve is increased by 14%, making the system more voltage secured in terms of additional capability of generators to generate more reactive power during disturbance or contingency. Figure 5: Reduction in Total Qgen with PSOGSA The total otal reactive power generation (Qgen) from all the generator buses is shown in Figure 5. It is observed from the plot that the reduction in Qgen is encouraging and the reactive power reserve of the system is improved. In addition to the principle objective of reactive power reserve management, the three TCSC T locations (lines 5, 1 and 2) which are major power transmitting channels in the IEEE 30 bus test system are expected to be with increased power handling capacity as the effective reactance of the line is reduced. Comparative Analysis The effectiveness of the proposed algorithm is proved by comparing the simulation results of PSOGSA with that of PSO and GSA and results for IEEE 30 bus test system are tabulated as follows. www.tjprc.org [email protected] Optimal Placement of TCSC for Reactive Power Reserve Management with Reactive Power Loss Minimization Using Hybrid PSOGSA 47 Table 3: Comparison of Reactive Power Losses Parameters PSO With 1 TCSC Step by With 2 Step TCSCs Placement With 3 TCSCs Simultaneous Placement of three TCSCs Qloss (MVAR) GSA PSOGSA 14.6724 14.4833 14.4833 6.4582 6.2960 6.2960 1.421 1.4061 1.292 9.1018 6.2592 6.1095 Multiple TCSCs can be optimally placed in the system either simultaneously or step by step. The reactive power losses in both the cases is shown in Figure 6 Figure 6: Reduction in Qloss with Three TCSCs From the figure it is observed that step by step placement gives better results compared to simultaneous placement and it also shows that in both the cases PSOGSA gives the improved performance over the other two methods. In case of step by step placement the reactive power loss minimization using PSOGSA is about 94% where as for PSO and GSA it is 93.60% and 93.68% respectively. Hence, the percentage of loss minimization is more with hybrid PSOGSA. The total reactive power generation of the system, computed using all three methods is tabulated as follows Table 4: Comparison of Simulation Results Qgen(MVAR) Parameters With 1 TCSC With 2 TCSCs With 3 TCSCs PSO GSA PSOGSA 140.8724 140.6831 140.6831 132.6582 132.4960 132.4960 127.6210 127.6061 127.4920 The total reactive power reserve of the system improves with reduction in reactive power generation and it is more in the case of PSOGSA. Hence, from the results it is evident that step by step placement of multiple TCSCs with PSOGSA gives optimum results. www.tjprc.org [email protected] 48 L. N. Mrunalini Devi & A. Surya Prakash Rao Figure 7: Convergence Characteristics with Single TCSC Figure 8: Convergence Characteristics with Two TCSCs Figure 9: Convergence Characteristics with Three TCSCs The convergence characteristics of PSO, GSA and PSOGSA in each case are shown in the above figures. From the obtained convergence characteristics it is observed that the PSOGSA exhibits better convergence when compared with other two methods. www.tjprc.org [email protected] Optimal Placement of TCSC for Reactive Power Reserve Management with Reactive Power Loss Minimization Using Hybrid PSOGSA 49 CONCLUSIONS The problem of optimal placement of TCSC to minimize reactive power losses with the aim of reactive power reserve management for improved operation of power system is solved by using hybrid PSOGSA in this paper. The simulation results show that multiple TCSCs can be used for minimizing reactive power losses leaving sufficient amount of reactive power reserves at generator buses. The security margin increases with the number of TCSCs but there should be a limit on the number of devices due its cost constraint. The feasibility of the proposed method is verified by using IEEE 30 bus test system and the results are compared with PSO and GSA. From the simulation results, it is evident that the proposed algorithm has the ability to find the better solution with improved convergence characteristics and computational efficiency. Hence the proposed hybrid PSOGSA algorithm is proved to be a promising alternative approach to solve complex optimization problems in power systems. REFERENCES 1. C. W. Taylor, “Power System Voltage Stability”. New York: McGraw-Hill, 1994. 2. P. Kessel and H. Glavitsch, “Estimating the Voltage Stability of Power System,” IEEE Trans. Power delivery, Vol. PWRD-1, No. 3, pp. 346- 354, July 1986. 3. H. Wan, J. D. Mc Calley and V. Vittal, “Risk Base Voltage Security Assessment”,IEEE Transaction on Power Systems,Vol. 15, No. 4, Nov. 2000. 4. T. Menezes, L. C. da Silva, and V. F. da Costa, “Dynamic VAR sources scheduling for improving voltage stability margin,” IEEE Trans. Power Syst., vol. 18, 2003 5. S. Granville, “Optimal reactive dispatch through interior point methods,” IEEE Trans. Power Syst., vol. 9, no. 1, pp.136–146, Feb. 1994. 6. Lee, K. Y. and Yang, F. F.,“Optimal Reactive Power Planning Using Evolutionary Algorithms : A Comparative Study for Evolutionary Programming, Evolutionary Strategy, Genetic Algorithm and Linear Programming”, IEEE Transactions on power systems, Power-Delivery, vol. 10, pp.1471,1478, 1995. 7. C. W. Liu, C. S. Chang and J. A. Jiang, “Genetic algorithms as a Reactive Power Dispatching Aid for Voltage Security Enhancement”, Proc. Natl.Sci. Counc. ROC(A), Vol.25. 8. H. Yoshida, K.Kawata, Y.Fukuyama, S.Takayama and Y.Nakanishi, “A particle swarm optimization for reactive power and voltage control considering voltage security assessment,”IEEE Trans.on Power Systems, vol.15, pp. 1232-1239, 2000. 9. Feng Dong,et al, “Improving Voltage Stability by Reactive Power Reserve Management” IEEE transactions on Power Systems, Vol. 20,N0.1, pp.338-345, Feb 2005. 10. Noroozian M. Angquist L., Ghandhari M., Andersson G.“Improving Power System Dynamics by Series-Connected FACTS Devices”, IEEE Transactions on Power Delivery, vol. 12, No. 4, pp.1635-1641, 1997. 11. Wood A.J. and Wollenberg B.F. “Power Generation,Operation, and Control”, John Wiley and Sons, New York, 1996. 12. N G. Hingorani, L.Gyugyi, “Understanding FACTS:Concepts and Technology of Flexible AC Transmission Systems”, IEEE Press, New- York, 2000. 13. Preecha Preedavichit, Srivastava, S. C., “Optimal Reactive Power Dispatch Considering FACTS Devices”, Electric power system research, Vol. 46, 1998. www.tjprc.org [email protected] 50 L. N. Mrunalini Devi & A. Surya Prakash Rao 14. Paserba, N.Miller, E.Laesen and R.Piwko, “A Thyristor controlled series compensation model for power system stability analysis”,IEEE. 15. Ghamgeen I. Rashed “Optimal Location of TCSC in a Power System Based on Differential Evolution Algorithm Considering Transmission Loss Reduction”, Proceedings of the 8th World Congress on Intelligent Control and Automation June 21-25 2011, Taipei, Taiwan. 16. “Optimal Location and Initial Parameter Settings of Multiple TCSCs for Reactive Power Planning Using Genetic Algorithms”, Narayana Prasad Padhy IEEE conference 2004. 17. Mirjalili S, Mohd Hashim S Z, “A new Hybrid PSOGSA Algorithim for Function Optimization”, IEEE International Conference on Computer Information and application (ICCIA 2010), China , 2010, 374~ 377. 18. E. Acha, C. R. Fuerte-Esquivel, H. Ambriz-Perez, and C.Angeles-Camacho, “FACTS: Modelling and Simulation in Power Networks”, Chichester, U.K.: Wiley, 2004. www.tjprc.org [email protected]