2013 International Conference on Power, Energy and Control (ICPEC)
Optimal Location of TCSC in Transmission Lines using Contingency Severity Index and Performance Index Methods for Single Contingency using PSO Shivashankar.S, Member IEEE Asst.Professor, Dept. of EEE Saveetha School of Engineering, Saveetha University
[email protected] Abstract -During line contingencies, overloads in transmission lines occur, which can destabilize the system. These line overloads can be minimized by placing Thyristor Controlled Series Capacitor (TCSC) with appropriate setting. In this paper, possible single contingencies are created in transmission lines and the effects are calculated in terms of Contingency Severity Index (CSI) and Performance Index (PI) methods. The calculated values from both the methods are ranked in ascending order. The top ranked lines are more severely affected, which is also the correct location for placement of TCSC. TCSC’s are placed in top three lines taken from CSI and PI methods, and their effects in minimizing the overloads and objective function is noticed. A comparative study is done on the effects of TCSC placement by two ranking methods. The results are calculated for a sample IEEE 6 and a practical30 Bus Indian system. The optimal setting of TCSC is done by Particle Swarm Optimization (PSO) Technique. Keywords:-Contingency Severity Index (CSI), Performance Index (PI), Thyristor Controlled Series Capacitor (TCSC), Particle Swarm Optimization (PSO), Severity of Overload (SOL).
devices which can be installed in a power system network [2], [5]. In this work, we analyse a power system network, where all possible single contingency is done on transmission lines, and line overloads is noticed. The lines are ranked from two ranking methods namely CSI and PI method. The line which is ranked the most is the best pick for placing TCSC. TCSC’s are placed in transmission lines and their effects in minimising the overload and objective function is noticed and a comparative study is done to show the superiority of one ranking method over another.
I.INTRODUCTION
The participation matrix U : This is an (m x n) binary matrix, whose entries are “1” or “0” depending upon whether or not the corresponding branch is overloaded, where n is the total number of branches of interest, and m is the total number of single and multiple contingencies.
In today’s scenario there is always a steady increase in demand of electricity. Due to complex interconnections in a power system network, it is increasingly difficult to analyze the flow of power in transmission lines. Researchers are very intense towards studying the stability of system for different contingency conditions[1]. FACTS are thyristor controlled power electronic device which are installed in power system network, control parameters like series impedance, shunt impedance, current, voltage, phase angle. In particular, the power transfer capability of the transmission lines can be enhanced by installing FACTS devices in it. TCSC (Thyristor Controlled Series Capacitor), SVC (Static Var Compensator), STATCOM (Static Compensator), UPFC (Unified Power Flow Controller) are few notable FACTS
II.PROBLEM FORMULATION A. Optimal location of TCSC: CSI method[3]: CSI
(1)
Where,
The ratio matrix W: This is an (m x n) matrix of normalized excess (overload) branch flows. It’s (i, j)th element, wij is the normalized excess power flow (with respect to the base case flow) through branch “j” during contingency “i” and is given by : , ,
−1
(2)
Where, Pij, cont - Power flow through branch “j” during ontingency “i” Poi, Base, - Base case power flow through branch “j”.
978-1-4673-6030-2/13/$31.00 ©2013 IEEE 135
2013 International Conference on Power, Energy and Control (ICPEC) The Contingency probability array P:This is an (m x 1) array of branch outage probabilities. The probability of branch outage is calculated based on the historical data about the faults occurring along that particular branch in a specified duration of time. It will have the following form: (3) Pmx1=[p1p2….pm]T Where, Pi - Probability of occurrence for contingency “i” and is taken as 0.02. m - The number of contingencies PI method [4]: ∑ / (4) Where, Pi = Active power flow in line i, Pimax = Maximum active power flow in line i, n is the specified exponent, L is the total number of transmission lines in the system. B. Optimal setting of TCSC: For finding the optimal setting of TCSC, Particle Swarm Optimization (PSO) technique is used to solve the above problem.The objective Function for the work is to minimize Severity of Overload (SOL), and total system overloads. Objective Function = {Minimize SOL and Total Number of system overloads} The formulation of severity of overload (SOL) is given below, SOL
(5)
Where, m – Number of single contingency considered n – Number of lines – weight factor = 1 ạk – Real power transfer on branch k. Pk Pkmax – maximum real power transfer on branch k
every particle in the swarm is calculated using equation (7) and (8) to produce new swarm of particles [6]. +1
+1
∗
+
+ 2∗
2 *
+
+1
∗
−
* −
(7) (8)
Where,
– Velocity of particle I at kth iteration. + 1 – Velocity of particle I at (k+1)th iteration W - The inertia weight = 0.786 C1=C2 =2 – Weighting factor - Current position of particle at kth iteration + 1 - Current position of particle at (k+1)th iteration - Personal best of particle i Pbesti - Global best of the swarm i Gbesti
IV.RESULTS AND DISCUSSION Simulation is done in MATLAB R2007b, following are the results and relative study of CSI method and PI method for placement of TCSC in transmission lines for possible single contingency. The comparative study between PI and CSI method is done for following sample cases, (a) 6 Bus system: (i) CSI ranking and TCSC placement in transmission lines: Table 1: CSI ranking of transmission lines
Rank
Line Number
CSI value
Number of times overloaded
1
5-6
0.224
1
2 3 4
3-5 2-5 1-2
0.0433 0.0406 0.0404
5 4 3
5
2-6
0.0357
4
6
1-4
0.0254
3
III. PARTICLE SWARM OPTIMIZATION (PSO)
7
2-4
0.0211
1
PSO an optimization technique where initial population is created and every particle in the swarm is solved for the objective function. For each iteration there is Pbest (personal best) value for each particle in the swarm and a Gbest (global best), the best valueattained up to now by any particle in the swarm. With the help of personal and global best values, the velocity and new position of
8
1-5
0.0170
2
9
3-6
0.0079
1
The optimal setting of TCSC should satisfy its constraint, (6) -0.5XL
