Optimal Location and Parameter Setting of UPFC based on PSO for Enhancing Power System Security under Single Contingencies

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1 Optimal Location and Parameter Setting of UPFC based on PSO for Enhancing Power System Security under Single Contingencies 1 Nedunuri Vineela, 2 Chunduri Rambabu 1 Sri Vasavi Engineering College, Tadepalligudem, Andhra Pradesh, India Abstract Secure operation of power system has become an important and critical issue in now a day s large, complex, and load demand-increasing power systems. Unified Power Flow Controller (UPFC) is one of the most effective Flexible AC Transmission Systems (FACTS) devices for enhancing power system security. The performance of UPFC can be improved to some extent and its highly depends upon the location and the parameters setting of this device in the system. This paper presents an approach to find the optimal location and optimal parameters setting of UPFC for enhancing power system security under single contingencies. In this paper firstly we performed contingency analysis and ranking process to determine the severest contingencies. These contingencies are considered as line overloads and bus voltage violations taken as a performance index. Secondly, we apply Particle Swarm Optimization (PSO) techniques to find out the optimal location and the optimal parameter setting of UPFC corresponding to different contingencies scenarios. Proposed algorithm is tested on IEEE 30-bus power system for getting optimal location and UPFC parameters. UPFC in such location significantly enhances the power system security by eliminating or minimizing the overloaded lines and the bus voltage violations. Keywords Contingency Analysis, Power Flow, Unified Power Flow Controller (UPFC), Particle Swarm Optimization (PSO) I. INTRODUCTION Modern electric power systems are large-scale and highly complex interconnected transmission systems, which in turn make the system more vulnerable to security problems. Commonly, Power systems are planned and operated based on the N-1 security criterion, which implies that the system should remain secure under all important first contingencies. One solution to cope with this problem is to design the system to meet the N-1 security criterion which is somewhat conservative and costly. An alternative solution to improve the security of power system is the Flexible AC Transmission Systems (FACTS) devices which is a concept proposed by N.G. Hingorani [1]. Flexible AC Transmission System (FACTS) devices is a new integrated concept based on power electronic switching converters and dynamic controllers to enhance the system utilization and power transfer capacity as well as stability, security, reliability and power quality of AC system interconnections. Unified Power Flow Controller (UPFC) is a versatile FACTS s device which can independently or simultaneously control the active power, the reactive power, and the bus voltage to which it is connected [2].However, to achieve such functionality, it is important to determine the optimal location of this device to be installed in power system with appropriate parameters setting. Since UPFC can be installed in different locations, its effectiveness will be different. Therefore, we will face the problem of where we should install the UPFC. For this reason, some performance indices must be satisfied. The following factors can be considered in the selection of the optimal installation and the optimal parameters setting of UPFC: The topology of the system, the stability margin improvement, the power transmission capacity increasing, and the power blackout prevention. Therefore, conventional power flow algorithm Therefore, conventional power flow algorithm [3] should incorporate with UPFC considering one or all of the above mentioned factors. New algorithms have been developed for optimal power flow incorporating with UPFC device as well as for its optimal placement. An evolutionary programming approach to determine the optimal allocation of multi-type FACTS devices [5] and [6], a particle swarm technique for optimal location of FACTS devices [7] and [8]. For the security analysis is performed to develop various control strategies to guarantee the avoidance and survival of emergency condition and operate the system at lowest cost. Also a lot of work has been done in the contingency analysis area. Different contingency selection methods can be found in [9] - [12]. Operation scheme of FACTS devices to enhance the power system steady-state security level considering a line contingency analysis suggested in [13]. This paper deals with the application of Particle Swarm Optimization (PSO) to find out the optimal location and the optimal parameters setting of UPFC device under single contingencies to eliminate or minimize the overloaded lines and bus voltage violations. 6

2 The rest of this paper is organized as follows: In section II, we describe the FACTS device UPFC. In section III, we describe the contingency analysis and ranking procedure as well as the objective function which we adopt in this work. In section IV, we describe our implementation of PSO algorithm according to the optimization objective. Section V presents the simulation results from implementing PSO algorithm in the MATLAB environment. In this section, we discuss an IEEE 30-bus system. Finally, in section VI, we conclude the main results and achievements that we have obtained in this paper. II. FACTS DEVICES Flexible AC transmission system (FACTS) gives solution to the problems and limitations which are introduced in power system with the introduction of power electronics based control for reactive power. Various issues associated with the use of FACTS devices are proper location, appropriate size and setting, cost, modelling and controller inter-actions. This paper deals with the optimal setting aspects of FACTS device such as UPFC, especially to manage congestion in the electricity markets. A. Unified Power Flow Controller(UPFC) Unified Power Flow Controller (UPFC) is considered as a powerful device of the Flexible Alternating Current Transmission Systems (FACTS) family, where it has both a shunt and a series controller inside its frame. Therefore UPFC has the ability to do both of Static VAR Compensator (SVC) and Static Synchronous Series Compensator (SSSC) performance simultaneously. UPFC Modeling for Power Flow The equivalent circuit of an UPFC, shown in Figure 1 is attached with power system equations, and programmed in Matlab for results output. It consists of two synchronous voltage sources (SVS), which are Simultaneous coordinated together to achieve the required performance mode [14]. The UPFC voltage sources are: Where = (1) = (2) Vvr the magnitude of the shunt SVS voltage vr the value of the shunt SVS angle Vcr the magnitude of the series SVS voltage dcr the value of the series angle The active and reactive power equation for bus k and m can be combined with (1) and (2) to get: Where (5) (6) (3) (4) V k and Vm the voltage magnitudes at bus k and bus m θ k and θ m the voltage magnitudes at bus k and bus m. P cr and Q cr the series SVS active and reactive powers P vr and Q vr the shunt SVS active and reactive powers G mm, G kk, G km, G mk the conductance elements, related to lines between buses k and m B mm, B kk, B km, B mk the susbtance elements, related to lines between buses k and m and G vr,b vr,g cr, B cr the susbtances and conductances for shunt and series SVS. The above equations are added to the problem constraints, which are equality constraints as the active and reactive power balance equations at each bus in the network. Also the inequality constraints as the generation power limits, bus voltage limits, power line limits and UPFC parameters constraint are included. III. PROBLEM FOMULATION Fig 1 UPFC Equivalent circuit A. Contingency Analysis Procedure A contingency is considered to be the outage of a 7

3 generator, a transformer or a line. With increasing trends of interconnection of power system these contingencies affects other power system. Hence consideration of these contingencies has been vital. The system may become unstable and enters an insecure state when a contingency event is occurred. Contingency analysis is one of the most important functions performed in power systems to establish appropriate preventive and / or corrective actions for each contingency. Contingency analysis procedure consists of line contingency analysis, contingency selection, detection of overloaded lines and bus voltage violations, and ranking of the severest contingencies cases. The best possible method for contingency analysis is Newton Raphson method. The contingencies are selected by calculating a kind of severity indices known as Performance Index (PI). In this paper we focus only on the single contingencies result from line outage (N-1 Contingency). For each line outage contingency in the system, we list the all overloaded lines and the buses which have voltage violations, and then the lines are ranked according to the severity of the contingency, in other words, according to the number of the thermal and voltage violations limits. Then the most critical contingencies are determined. After determining the most critical contingencies scenarios, PSO techniques are applied to find the optimal location and parameters setting of UPFC. Installing UPFC in such optimal location with such optimal parameters will eliminate or minimize the overloaded lines and the bus voltage violations under these critical contingencies according to the objective function described in B. B. Objective Function The OPF problem is to optimize the steady state performance of a power system interms of one or more objective functions while satisfying several equality and inequality constraints. The objectives considered here are minimization of fuel cost and for enhancing the system security level, UPFC should be located in order to eliminate or minimize the line overloads and to prevent bus voltages violations. This is achieved by rescheduling of real power generation, generator voltage magnitude, reactive power generation of capacitor bank and transformer tap setting. Power flow equations are the equality constraints of the problems, while the inequality constraints include the limits on real and reactive power generation, bus voltage magnitudes, transformer tap positions and line flows. The expression representing the objective functions and the constraints are given below: Objective function 1: Fuel cost of generating units parameters setting of the UPFC in the power network to eliminate or minimize the overloaded lines and the bus voltage violations under the most critical single contingencies, the following performance index is selected: Subject to: Min F 2 (8) g ( x, u) 0 (9) h ( x, u) 0 (10) Where: F 2 minimized; represents the objective function to be g (x, u) represents the equality constraints corresponding to active and reactive power balance equations; h(x,u) represents the inequality constraints corresponding to UPFC parameter bounds limits, active and reactive power generation limits, bus voltage limits, and phase angles limits; x represents the state vector of the power system consisting of voltage magnitude and phase angles; and u represents the vector of control variables to be optimized(i.e., location of UPFC and its parameters setting: V cr and V vr ). For enhancing the system security level, we considered the following technical objective function []: Where: (11) and represent the current apparent power in lineland the apparent power rate of line l, respectively; represents the voltage magnitude at busm; represents the bus m nominal voltage; and represent two weights and are determined in order to have the same index value for 10% voltage difference and for 100% branch loading; q and r represent two coefficients are used to penalize more or less overloads and voltage variations, respectively (for the presented study, they are considered to be equal to 2); and ntl and nb represent the number of lines and the number of buses in the system. (7) 1. Equality constraints In power system with n buses, at each bus i, the sum of Objective function 2: The main objective of this work total injected real and reactive power must be equal to is to determine the optimal location and the optimal 8

4 zero. The specified power is equal to the difference between the power generation and the load. These constraints are mathematically represented as: (12) (13) Where and are the real and reactive power outputs injected at bus- i respectively, the load demands at the same bus is represented by and, and elements of the bus admittance matrix are represented by and. 1. Inequality constraints The inequality constraints reflect the limits on physical device in the power system as well as the limits created to ensure security. The inequality constraints which are generally considered are upper and lower bus voltage limits, maximum line loading limits and limits on tap settings. These constraints are mathematically represented as: 1) Generators real and reactive power outputs i=1 NG (14) i=1 NG () 2) Voltage magnitudes at each bus in the network 3) Transformer tap settings i=1 NL (16) i=1 NT (17) 4) Reactive power injections due to capacitor banks 5) Transmission lines loading i=1, nl (19) 6) Voltage stability index i=1 CS (18) i=1 NL (20) 7) UPFC constraints: Reactance constraint of UPFC X UPFCi min = Minimum reactance of UPFC at line i X UPFCi max = Maximum reactance of UPFC at line i = number of UPFCs IV. METHODOLOGY FOR OPTIMAL LOCATION OF UPFC A. Particle Swarm Optimization Technique Particle Swarm Optimization (PSO) is a stochastic global optimization approach and its main strength is in its simplicity and fast convergence rates [16]- [18]Particle Swarm Optimization (PSO), which has gained rapid popularity as an efficient optimization technique, is relatively a recent heuristic introduced by Eberhart and Kennedy [19]. It is based on the analogy of swarm of birds and school of fish. In PSO, each individual called particle makes his decision using his own experience together with other individuals experience. PSO has a flexible and well- balanced mechanism to enhance and adapt the global and local exploration and exploitation abilities within a short calculation time. The main advantages of PSO algorithm are summarized as: simple concept, easy implementation, robustness to control parameters, and computational efficiency when compared with mathematical algorithm and other heuristic optimization techniques [20]. Each particle in PSO flies in the D-dimensional problem space with a velocity dynamically adjusted according to the flying experiences of its own and other particles. The location of the ith particle is represented as X i = [x i1, x i2,., x id ], where, x id [l d, u d ], d [1, D]. l d and u d, are the lower and upper bounds for dth dimension, respectively.in every iteration each particle is updated by following two best values. The first one is the best solution (fitness value) it has achieved so far. This value is called Pbest and represented as P i = [P i1, P i2,., P id ]. Another best value that is tracked by the particle swarm optimizer is the best value obtained so far by any particle in the population. This best value is the global best called Gbest. The velocity of ith particle is represented as V i = [v i1, v i2,., v id ] and is clamped to a maximum velocity V max = [v max1, v max2,., v maxd ] which is specified by the user. After finding the best values the particles update its velocity and position with the following equation: (22) X id (n+1) = X id (n) + V id (n+1) i=1, 2, m, d=1,2,.., D (23) X UPFCi min X UPFCi max i=1, 2 (21) Where: Where X UPFC = Reactance of UPFC at line i 9

5 c 1 and c 2 are two positive constants called cognitive and social parameters respectively, m is the size of the swarm, D is the number of members in a particle, incorporated together for the simulation purposes. The proposed PSO based approach was applied to the IEEE 30-bus test system (shown in Fig.3) for power system security enhancement, under normal and contingency states. r 1 and r 2, are random numbers, uniformly distributed in[0,1], n is the pointer of iterations (generations), and w is the inertia weight, which provides a balance between global and local explorations and thus requiring less iteration on average to find a sufficiently optimal solution. It is specified by equation (24) Where: W max is the initial weight, W min is the final weight, iter is the current iteration number, and iter max is the maximum iteration number (generations). B. PSO Flow chart Fig. 3. IEEE 30-bus system Note: Old Bus Numbers : 3, 4, 6 Modified New Bus Numbers : 8, 11, 13 B. Results In this paper, the optimal location and the optimal parameters setting of UPFC device in the network were optimized to eliminate or minimize the line overloads and the bus voltage violations under single contingencies. Active and reactive power generation, generator voltages, shunt compensators and transformer tap settings are considered as control variables. Therefore, the UPFC is modeled for the purpose of fundamental steady-state analysis as a coordination of two synchronous voltage sources, V cr and V vr, respectively [21]. For PSO based algorithm the parameters utilized in this simulation are given in table I. Fig. 2. Flow chart for PSO V. SIMULATION RESULTS TABLE I : PARAMETER VALUES FOR PSO Parameters of PSO c1 and c Number of generations 100 Population size 20 The program was written in MATLAB and executed on PC with Core2due processor. The results of simulation are given below: i) PSO -OPF for IEEE 30-bus system A. Test System Matlab Codes for PSO and a modified power flow algorithm to include UPFC were developed and The optimal values of control variables from the algorithm are given in the Table II Table II : Optimal setting of control variables 10

6 Objective function-1 Objective function-2 International Journal of Advance Electrical and Electronics Engineering (IJAEEE) Control variables Objective -1 Objective- 2 P G P G P G P G P G P G Q G Q G Q G Q G Q G Q G V V V V V V T T T T Q sh Q sh Q sh Q sh Q sh Q sh Q sh Q sh Q sh Cost Loss Time Tables II present the results for IEEE 30-bus test system. From Table II it is observed that all the state variables satisfy lower and upper limits Graph between Objective function-1 & iter Graphs between Objective function & iter no of. iterations Fig 4. Objective function -2 (security) From figures 3 & 4 shows the convergence characteristics of the two objective functions. It can be observed that the proposed PSO has the better convergence. Obtained results are compared with existing methods reported in literature is tabulated in table III. From this we can observe that the proposed PSO method including constraints is outperforming the other methods. ii) Method Table III Comparisons of Fuel Costs Fuel Cost ($/hr) EP[22] TS[22] TS/SA[22] ITS[22] IEP[22] SADE_ALM[23] MDE-OPF[24] Genetic Algorithm[25] Gradient method[26] PSO(proposed) PSO for contingency in IEEE 30- bus system no of. iterations Fig 3. Objective function -1 (cost) IEEE 30-bus system consists of six generators, thirty buses, thirty seven transmission lines and twenty loads as shown in Fig 2. Contingency analysis and ranking process is performed on this 30-bus system. There are 37 possible single contingencies. For each single line outage, we find the Number of Over Loaded Lines (NOLL) and the Number of Voltage Violation Buses (NVVB). Then we rank the lines according to the severity of the contingency. Performance Index PI= (NOLL +NVVB) as shown in Table IV. PI is zero for the remaining lines. 11

7 From Bus To Bus Overloaded lines Overloading % Voltage Violation Buses Overloaded lines Overloading % Voltage Violation Buses Optimal placement of UPFC Rank International Journal of Advance Electrical and Electronics Engineering (IJAEEE) Table IV Ranking of branches for IEEE 30-bus system Line Nu mbe r Fro m Bus Line To Bu s Number of Over Loaded Lines (NOLL) Number of Voltage Violation Buses (NVBB) Performa nce Index PI=(NOL L+ NVBB) Rank From Table IV, we can find that above lines are the severest contingencies scenarios in this system. In the case of one of this lines is outage, the most overloaded lines and bus voltage violations will be encountered. Therefore, to investigate the effectiveness of UPFC on the system under such cases, we apply PSO techniques to find the optimal location and the optimal parameters setting of UPFC which eliminate or minimize the overloaded lines and bus voltage violations. Voltage profile for IEEE 30-bus system by PSO technique when line 1-8 is outage is shown in Fig.5. Before placing UPFC in this system, there were 3 buses which have voltage violations, and after placing UPFC all of them are eliminated. These results are achieved by applying PSO technique. Fig.6 shows the percentage of loading in IEEE 30-bus system when line 1-8 is outage. Before placing UPFC in this system, there was 1 overloaded line and after placing UPFC that line was eliminated. Fig. 5. Voltage profile for IEEE 30-bus system when line 1-8 is outage by PSO Fig. 6. Percentage of line loading for IEEE 30-bus system when line 1-8 is outage by PSO Overloaded lines and bus voltage violations before and after placing UPFC in this system with optimal location and optimal parameters setting of UPFC obtained by applying PSO technique is as shown in Table V. Table V - Overloaded Lines and Bus Voltage Violations Before and after Placing UPFC for IEEE 30-Bus System with Optimal Location and Optimal Parameters Setting of UPFC by PSO Optimal setting of Before Placing UPFC After Placing UPFC UPFC

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9 Objective function International Journal of Advance Electrical and Electronics Engineering (IJAEEE) The minimization of the objective function achieved by PSO technique when line 2-5 is outage is as shown in Fig the system results in eliminating all of the overloaded lines. While all of the bus voltage violations are eliminated by placing UPFC in optimal location with optimal parameter settings achieved by applying PSO Graphs between objective function & iter VI. CONCLUSION no of. iterations Fig.7.Minimization of objective function by PSO technique for IEEE 30-bus system when line 2-5 is outage In this paper, the effectiveness of UPFC for enhancing the security of power systems under single contingencies has been investigated. Determination of the severest contingencies scenarios were done based on the contingency selection and ranking process. The most powerful evolutionary optimization technique namely: Particle Swarm Optimization is successfully applied to the problem of optimal location and parameters setting of UPFC. Maximization of power system security was considered as an optimization criterion. The simulations are carried out on IEEE-30 bus system. Finally, our results show that the UPFC can significantly improve the security of power systems under single contingencies From Table V, we find that despite of placing UPFC in 14

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