Optimal Placement and Sizing of FACTS Devices for Loadability Enhancement in Deregulated Power Systems

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1 Optimal Placement and Sizing of FACTS Devices for Enhancement in Deregulated Power Systems Mahmoud Mohammadi, Dr.Alireza Rezazadeh, Dr.Mostafa Sedighizadeh Beheshti University Beheshti University, Evin, Tehran IRAN Abstract : This paper presents the use of Flexible AC Transmission Systems (FACTS for improving loadability of the system in deregulated electric power system.the optimallocation and parameter settingsof two types of FACTS devices have been investigated in this study. The Static Synchronous Series Compensator (SSSC and Thyristor Controlled Series Compensation (TCSC as two FACTS devices are considered in this paper. FACTS devicesare applied to maximize the system loadability subjectto the transmission line capacity limits. Harmony Search Algorithm (HSA as a novel heuristic algorithm is applied to find the proper size and location of FACTS devices.the results of the HSA are compared with those obtained using the Particle Swarm Optimization (PSO as the method of optimization to show the effectiveness of the proposed method in finding the best location and size of these devices. The proposed approach istested on IEEE 14- bus test systems. The results show that the optimal location and proper parameters selection of the FACTS devices effectively enhance thepower transmission system loadability. Keywords: Power System, Unified, Static Synchronous Series Compensator (SSSC, Thyristor Controlled Series Compensation (TCSC, Harmony Search Algorithm, Particle Swarm Optimization, 1. Introduction Restructuring in electric power industry has led to exhaustive usage of transmission systems. In deregulated electricity market, transmission systems are often operated near their rated capacity. The competition in electricity market has also lead to an increased volume of electricity trade. This situation leads to an unexpected need of power transfer through some transmission lines [1].One way to overcome this problem is to building new transmission lines. Therefore, the power networks should be expanded further to achieve a high operational efficiency and network security. In this situation, one of the possible alternatives is the Flexible AC Transmission System (FACTS technologies. The development of FACTS devices based on the progressive semiconductor technology opens up new opportunities for controlling the power flow of the transmission lines and extending the loadability of the available transmission system. FACTS devices can control the line reactance, bus voltage and line active and reactive power flows. Therefore FACTS devices are used to increase the capacity over existing transmission lines by proper power flow control over designed corridors and to provide voltage support in the network []. The SSSC and TCSCarefrom the family members of FACTS devices for load flow control. Many methods have been studied in the literature to model different FACTS devices in the load-flow studies [3-4]. In this paper static model of SSSC and TCSC is used. Different methods have been proposed for optimal placement and proper parameter setting of FACTS deviceswith several objective functions in the literature. In [5]optimal implementation of FACTS devices is discussed for relieving congested lines of the system. Reference [6] proposed theuse of TCSC and SVC to maximize ATC. Since incorporating FACTS devices in the Optimal Power Flow (OPF optimization is a very complicated problem different heuristic algorithms have been proposed to solve such a problem.genetic Algorithm (GA is proposed in ISBN:

2 [7]for optimal choice and allocation of FACTS devices in deregulated electricity market.in [8] in order to take into account the financial issue related to application of FACTS devices a proposal for investment recovery of these devices is proposed. Harmony Search Algorithm (HSA as a heuristic method is conceptualized using the musical process of searching for a perfect state of harmony [9].Compared to the earlier meta-heuristic optimization algorithms, HSA imposes fewer mathematical requirements that can be easily adopted for various types of engineering optimization problems [10]. References[11-1] demonstrate the potential of HSA in solving complex power system problems. Particle swarm optimization (PSO is another heuristic optimization algorithm that has been widely used in different locating problems in deregulated power system. It is a stochastic global optimization approach and its main strength is in its simplicity and fast convergence [13-14]. This paper introduces a new method for solving the complicated problem of optimal location and parameter setting of the FACTS devices.objective of the optimization problem is to maximize the loadability of the transmission system. The results of simulations carried out on the IEEE 14-bus test system are presented.the results of placing algorithm are also obtained using PSO algorithm. These results are compared to those obtained by HSA to show the ability of HSA to solve this optimization problem. The rest of paper is organized as follows. The static models of SSSC and TCSCare described in section. Section 3 explains the Harmony Search Algorithm. Proposed method is presented in section 4. The simulation results are presented and discussed in section 5. The conclusion is drawn in Section 6.. SSSC and TCSC Modeling and Formulation.1. SSSC Modeling The SSSC is composed of voltage source converter, diodes, a dc link capacitor, and controller connected to transmission line via a coupling transformer [15]. The SSSC can be easily modeled as a special case from UPFC when there is no control for voltage. Fig.1 depicts the equivalent circuit model of SSSC. This model was used in deriving the steady-state model for load flow and static analysis [16] which makes it proper for our study. Auxiliary bus between the existing buses of the system is a reference point of the power flow direction. The SSSC control parameters (voltage source magnitude and angle limits are as follows: Min Max VSC VSC V SC (1 0 ϕsc π Therefore in this paper, for load flow analysis and ATC enhancement, SSSC variables V SC and, are needed to be optimized. ϕ SC Fig. 1.SSSC static model. ( and (3 represent the derivation of the power flow equations of SSSC from bus n to bus l. Pnl = ( Vn + VSC gnl + VV n SC gnlcos( ϕsc δnl VV n SC( gnl cosϕsc + bnl sin ϕsc ( VV n l ( gnl cosδnl + bnl sin δnl Q = VV ( g sin( ϕ δ + b cos( ϕ δ nl n SC nl SC nl nl SC nl Vnbij VV n l( gnl sinδnl bnl cos δnl Pln = Vn gnl VV l SC ( gnlcosϕsc bnl sin ϕsc VV n l ( gnl cosδnl bnl sin δnl Qln = Vl bnl VV l SC ( gnl sinϕsc bnl cos ϕsc + VV( g sinδ + b cos δ n l nl nl nl nl According to the above relationships, the power injection model of network line with SSSC is implemented in the optimization problem... TCSC Modeling In this section TCSC static model and it's formulation in optimal power flow problem is presented. In static application of the TCSC it is usually modeled as a series reactance [17]. TCSC reactance limits are assumed to be: (3 ISBN:

3 0.7x x 0.7x (4 l c l Where, xc is the TCSC reactance and x l is reactance of the transmission line in which TCSC is located. 3. Harmony Search Algorithm HS is new heuristic optimization technique like Genetic Algorithm, Ant colony search algorithm, Tabu search but HS is more powerful than others [9], by its ability ti deal with discrete and continuous mathematic problem HS procedures, as shoen fig. HM=[ Where [ ] is changed by number of parameter. [ ] is harmony memory size (HMS. Step 3 :Improvise new harmony Improvise new from harmony memory consider rated (HMCR and pith adjust rated (PAR. Step 3.1 : harmony consider rated (HMCR ε w.p.hmcr (8 w.p.(1-hmcr Where is new value of HMCR is probability of choosing w.p. means with probability ε is member of step 3.: Pitch adjust rate(par PAR for (9 Where PAR is probability to shift *rand *bw (10 Where bw is range of rand is random number during 0-1 Fig.. HS process HS procedure can be described as follows ; Step 1 : Identify objective function and Equality & Inequality constraints by using eq.(5 (7 Minimize f(x (5 Subject to x i X, i= 1,... N (6 i Constraint g(x 0, h(x=0 (7 Where f(x is the objective function is the feasible set is the random using parameter. g(x is the inequality constraint. h(x is the equality constraint. Step : Initialize harmony memory (HM In this step, randomly choose the initial the value of from parameters and fill them in HM matrix eq. (5 in this step, random choose the value of.if the value of is the range of it have probability HMCR. If out of condition probability of is 1- HMCR and then will check PAR if PAR of is carry on the condition eq. (9, shift by eq.(10. Step 4 :In this stage, if the new harmony vector is better than the worst harmony vector in the HM in terms of the objective function value, the existing worst harmony is replaced by the new harmony. The HM is then sorted by the objective function value. PROPOSED ALGORITHM The objective of power systems operation and planning in deregulated power markets is to maximize the social welfare. In this paper, we use FACTS devices in order to maximize the system loadability and defer the upgrade investments of the network. Because of the high costs of investment offacts devices, there is considerable risk in their application; thereforethe best location and proper parameter settingis very important. The proposed algorithm is explained in two subsections. The first one discusses the objective ISBN:

4 function that should be maximized considering line flow limits, voltage limits and reactive power constraints. The second subsection presents the implementation of the HSA to maximize the loadability as an optimization problem Objective Function To achieve the best utilization of the existing transmission systems, FACTS device should be installed in such a place to maximize the system loadability as much as possible while have minimum installation cost of these devices and satisfy the thermal limits of the transmission lines and the bus voltage limits in the network [18]. The objective function in this study is defined as maximization of loadability while to consider the voltage magnitude and transmission line limits,penalty factors are also involved in the objective function to accommodate these limits: Objective Function = F F (11 F F T V N L = F (1 i = 1 N B n= 1 T, i = F (13 V, n T Where, is the increased loadability of the system after implementation of FACTS devices in the system. FTi, and FV, nrepresent proposed penalty functions for each line and each bus thatare shown in Figs.3 and 4, respectively. Fig.3. Proposed penalty function for transmission lines limit Fig. 4. Proposed voltage penalty function V 3.. Implementation of Harmony Search Algorithm The objective of power systems operation and planning in the deregulated markets is to maximize the social welfare through minimizing investment costs on transmission network. Fig. 5 shows proposed optimization procedure based on HSA. In this procedure after initializing optimization problem and algorithm parameters, Harmony Memory (HM is initialized. All transmission lines of the system are considered as a potential location for placement of UPFC. After initializing HM, OPF is performed for the new system with FACTS devices. Based upon results of OPF, loadability of the system is calculated for each harmony vector. Then using (11 the objective function value for each harmony vector that is a potential solution is calculated. Next, a new harmony is improvised from the HM. After these processes, based on the calculated objective function of harmony vectors, HM will be updated. Finally, the termination criterion is checked. Termination criterion is assumed to be the number of iterations in this paper. The same procedure is used for applying the PSO algorithm to this optimization problem. 4. Case Study The proposed method is applied to the IEEE 14- bus test systems [19] for investigating the performance the proposed methods. HSA and PSO parameters are presented in Table 1. IEEE 14-bus test system comprises 5 generators and 11 loads and 0 transmission lines. The data for the generators in and load profile can be found in [19]. Loads and Units data are available in Tables 1 and of Appendix, respectively. TABLE 1 HS AND PSO ALGORITHMS PARAMETERS HS PARAMETERS NO. OF UPFC HMS HMCR PAR ITER MAX PSO PARAMETERS NO. OF UPFC SWARM SIZE C1 C W1 W ITER MAX ISBN:

5 Fig. 5.Proposed optimization method procedure ISBN:

6 TABLE HSA AND PSO RESULTS OF UPFC PARAMETERS AND SELECTED BRANCHES SSSC LOCATING HAS No. of SSSC Branch # From To VT ( pu φ T ( Rad % % PSO No. of SSSC Branch # From To VT ( pu φ T ( Rad % % % 76% 76% 63% 67% 76% 5. Simulation Results Table and 3 show the best lines for placement as well as the optimum parameter selection of SSSC and TCSC, respectively that are obtained from the HSA and PSO algorithms. From the simulation results presented in Table by applying both algorithms and considering the best results for SSSC application from both methods, it can be seen to increase the system loadability up to 31%, one SSSC is required and for increasing the system loadability between (31% - 61%, two SSSCs are required. While for an increasing of system loadability between (61%- 65%, at least three SSSCs are needed. For increasing the system loadability between (65% - 76%, four SSSCs are required and with more than four SSSC the loadability of the system will not increase further. Based upon the results presented in Table 3 by applying both techniques and considering the best results for TCSC application, it can be observed to increase the system loadability up to 11%, one TCSC is required and for increasing the system loadability between (11% - 15%, two TCSCs are required. While for an increasing of system loadability between (15%-1%, at least three TCSCs are needed. For increasing the system loadability between (1% - 3%, four TCSCs are required and for an increasing of system loadability between (3%-7%, at least five TCSCs are needed. ISBN:

7 TABLE 3 HSA AND PSO RESULTS OF UPFC PARAMETERS AND SELECTED BRANCHES TCSC LOCATING HAS No. of TCSC Branch # From To x c % % PSO No. of TCSC Branch # From To x c % % % 3% 7% 13% 17% 17% 5.1. Discussion Based upon the results from the both algorithms the optimal locating and parameter setting of the FACTS devices can increase the loadability of the system effectively. It will lead to upgrade investment deferral and can decrease the planning costs. It was observed from the results that the HSA has advantages in finding the best solution over the PSO algorithm in this specific optimization problem. To compare the HS and PSO algorithms Table 4 is presented. Tables and 3 are narrowed down in Table IV, where improvements in loadability of the network due to installation of the SSSC and TCSC using HS and PSO algorithms are compared. Comparing the results of these two algorithms it can be seen that the HS algorithm is more efficient in finding the proper location and optimal parameter setting of FACTS devices. This advantage is more highlighted in the TCSC implementation. ISBN:

8 TABLE 4 COMPARISON OF THE LOADABILITY OF THE RESULTS OF HSA AND PSO SSSC APPLICATION FACTS DEVICE NO OF SSSC HSA PSO SSSC TCSC APPLICATION FACTS DEVICE NO OF TCSC HSA PSO TCSC Table 4 is depicted in Fig. 5. It can be observed from the result presented both in Table 4 and Fig. 5 that SSSC is a more capable device in enhancing the loadability of the system. The prominence of the SSSC over TCSC is such that even with one SSSC the loadability is more increased that with five TCSC SSSC HSA SSSC PSO TCSC HSA TCSC PSO No of FACTS Devices Fig. 6. Enhancement of due to application of FACTS devices However, since the installation cost of the TCSC is much lower than SSSC its application might be more cost effective than the application of the TCSC. The desired level of enhancement in loadability of the system and the value that it bring to the system versus the cost associated with the FACTS device implementation determine which FACTS device is more proper for the system, that is out of the scope of this study. 6. Conclusion Implementation of FACTS devices to enhance the loadability of the system to improve the system security and defer the upgrade investment costs of transmission expansion planning has been proposed in this paper. The HSA and PSO algorithms were applied to find the best branch and proper parameter setting. The IEEE 14-bus test system was used to demonstrate the effectiveness of the proposed algorithms. The results show significant improvement in network loadability by optimal implementation of UPFC. The results also demonstrate the advantage of HSA over PSO algorithm in finding the optimal location and size of FACTS devices.appendix TABLE 1 LOAD DATA FOR IEEE 14-BUS TEST SYSTEM Bus No Pd Qd Bus No Pd Qd TABLE GENERATING UNITS DATA FOR IEEE 14-BUS TEST SYSTEM Bus # a ($/(MWh b ($/MWh c ($/h max p g (MW min p g (MW References [1] H. Hashemzadeh, S. H. Hosseini, Locating Series FACTS Devices Using Line Outage Sensitivity Factors and Particle Swarm Optimization for Congestion Management, IEEE General Meeting., 009. [] H. Hashemzadeh, M. Ehsan, Locating and Parameters Setting of Unified Power Flow Controller for Congestion management and Improving the Voltage Profile. Asia- Pacific Power and Energy Eng. Conf., Mar [3] X. P. Zhang, Advanced modeling of the multi control functional static synchronous series compensator (SSSC in Newton power flow, IEEE Trans. Power Syst., Vol. 18, no. 4, pp , 003. [4] Y. Zhang, and Y. Zhang, A novel power injection model of embedded SSSC With multi-control modes for power flow analysis inclusive of practical Constraints, Electric Power Syst. Res. Vol. 76, pp , 006. [5] S. N. Singh and A. K. David, Optimal location of FACTS devices for congestion management, Electr. Power Syst. Res., vol. 58, pp , June 001. [6] G. M. Rao1, P. V. Ramarao, and T. J. kumar, Optimal location of TCSC and SVC for enhancement of ATC in a de-regulated environment using RGA, IEEE Int. Conf. on ISBN:

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