| Academic Open Internet Journal ISSN 1311-4360 |
Volume 21, 2007 |
Optimum Reactive Power Dispatch Using Genetic Algorithm
Author: * P.Subburaj, * Miss N.Sudha, * Mrs K.Rajeswari, * Dr.K.Ramar ** Dr.L.Ganesan
* National Engg College, K.R.Nagar, Kovilpatti, Tuticorin(Dist), Tamilnadu, India
** A.C College Of Engg And Techology, Karaikudi, Tamilnadu, India
Corresponding Author; P,Subburaj
Dept Of Electrical Engg
National Engg College
K.R Nagar,Kovilpatti
Tuticorin(Dist)Tamil Nadu,
India.
Abstract-Reactive Power Dispatch (RPD) is one of the important tasks in the operation and control of the power system. RPD problem can be formulated as a non-linear constrained optimization problem. This paper presents a Genetic Algorithm (GA) approach for solving the reactive power dispatch problem including the line flow constraint. Minimizations of real power loss with FACTS and without FACTS devices are the objectives of this reactive power optimization problem. The proposed algorithm has been applied to find the optimal reactive power control variables in IEEE 30 and IEEE 118-bus systems. The simulation results are promising and show the effectiveness and robustness of the proposed approach.
Keywords
Reactive Power Dispatch, FACTS devices, Genetic Algorithm, line loss.
I. INTRODUCTION
The purpose of Reactive Power Dispatch is mainly to improve the voltage profile in the system and to minimize the real power transmission loss while satisfying the unit and system constraints. This goal is achieved by proper adjustment of reactive power control variables like Generator bus voltage magnitudes (Vgi), transformer tap settings (ti), reactive power generation of the capacitor bank (Qci). To solve the RPD problem, a number of conventional optimization techniques [1-2] have been proposed. These include the Gradient method, Non-linear Programming (NLP), Quadratic Programming (QP), Linear programming (LP) and Interior point method. Though these techniques have been successfully applied for solving the reactive power dispatch problem, still some difficulties are associated with them. One of the difficulties is the multimodal characteristic of the problems to be handled. Also, due to the non-differential, non-linearity and non-convex nature of the RPD problem, majority of the techniques converge to a local optimum. Recently, Evolutionary Computation techniques like Genetic Algorithm (GA) [3], Evolutionary Programming (EP) [4] and Evolutionary Strategy [5] have been applied to solve the optimal dispatch problem. In this paper, GA based approach has been proposed to solve the RPD problem.
Genetic Algorithm [9, 10] is a general-purpose optimization algorithm based on the mechanics of natural selection and genetics. GA maintains a population of individuals that represent candidate solutions. Each individual is evaluated to give some measure of its fitness to the problem from the objective function. In each generation, a new population is formed by selecting the more fit individuals based on a particular selection strategy.
The introduction of Flexible AC Transmission System (FACTS) devices in a power system improves the stability, reduces cost of generation and also improves the loadability of the system. Optimal placement of multiple FACTS devices will naturally control the overall reactive power requirements. Due to high cost of FACTS devices, it is important to decide their optimal placement to meet the desired objective. GA based approach is suggested for optimal placement of the FACTS devices.
List of Symbols
Pi, Qi Real and Reactive Powers injected at bus i
Gij, Bij Mutual conductance and susceptance between
bus i and j
Gii, Bii Self-conductance and susceptance of bus i
Qgi Reactive power generation at bus i
Qci Reactive power generated by ith capacitor bank
tk Tap setting of transformer at branch k
Vi Voltage magnitude at bus i
qij Voltage angle difference between bus i and j
Sl Apparent power flow through the lth branch
gk Conductance of branch k
NB Total number of buses
NB-1 Total Number of buses excluding slack bus
NPQ Number of PQ buses
Ng Number of generator buses
Nc Number of capacitor banks
NT Number of tap-setting transformer branches
Nl Number of branches in the system
NTCSC Number of TCSC
XTCSC Reactance of TCSC
Xline Reactance of the transmission line
Xci Coefficient, which represents the degree of
Compensation by TCSC
II.MATHEMATICAL FORMULATION OF RPD PROBLEM
The objective of RPD is to identify the reactive power control variables, which minimizes the real power loss (Ploss) of the system. This is mathematically stated as follows:
Minimize F= [f1]
(1
The reactive power optimization problem is subjected to the following constraints.
EQUALITY CONSTRAINTS
These constraints represent load flow equation such as
(2)
(3)
INEQUALITY CONSTRAINTS
These constraints represent the system operating constraints. Generator bus voltages (Vgi), reactive power generated by the capacitor (Qci), transformer tap setting (tk), are control variables and they are self restricted. Load bus voltages (Vload) reactive power generation of generator (Qgi) and line flow limit (Sl) are state variables, whose limits are satisfied by adding a penalty terms in the objective function. These constraints are formulated as
(i) Voltage limits
(4)
(ii) Generator reactive power capability limit
(5)
(iii) Capacitor reactive power generation limit
(6)
(iv) Transformer tap setting limit
(7)
(v) Transmission line flow limit
(8)
FACTS Devices
As power transfer grows, the power system can become increasingly more difficult to operate, and the system becomes more insecure with unscheduled power flows and higher losses. The rapid development of self-commutated semiconductor devices, have made it possible to design power electronic equipments. These equipments are well known as Flexible AC Transmission systems (FACTS) devices [7]. Thyristor Controlled Series Compensator (TCSC) is a capacitive reactance compensator, which consists of a series capacitor bank shunted by a thyristor-switched reactor to provide a stepwise control of series capacitive reactance.
Fig 1. TCSC Module
The TCSC may have one of the two possible characteristics: capacitive or inductive, respectively to decrease or increase the reactance of the line Xline. The rating of TCSC is depending on the reactance of the transmission line where the TCSC is located:
Xmin = -0.5 Xmax = 0.5
IV. OVERVIEW OF GENETIC ALGORITHM
Some members of new population undergo genetic operations to form new solutions. The three commonly used operations are reproduction, crossover and mutation. This section briefly describes the various components of GA.
Reproduction
The reproduction operator is a probabilistic selection in which strings are selected so as to produce offspring based on their fitness value. There are number of selection methods such as fitness proportionate selection, ranking and tournament selection. Tournament selection is used in this work. In tournament selection, ‘n’ individuals are selected randomly from the population, and the best of the ‘n’ is inserted into the new population for further genetic processing. This procedure is repeated until the mating pool is filled.
Crossover operation
The crossover operator is mainly responsible for the global search property of the GA. The operator basically combines substructures of two parent chromosomes to produce new structures, with the chosen probability (Pc). Crossover can occur at single position (single crossover) or at a number of different positions (multiple crossover). In RPD problem, two point crossover is used in which two crossover sites are randomly chosen and offspring’s are produced by swapping the bits after the chosen crossover sites.
Mutation
The final genetic operator in the algorithm is mutation. The mutation operator is used to inject new genetic materials into the population. Bitwise mutation is performed here which switches a few randomly chosen bits from 1 to 0 (or) 0 to 1 with a small probability (Pm). After mutation, the new generation is complete and the procedure begins again with the fitness evaluation of the population.
Genetic Algorithm implementation for RPD problem
When applying GA’s to solve a particular optimization problem, two main issues must be addressed.
(i) Representation of the decision variables
(ii) Formation of the fitness function
These issues are explained in the subsequent section.
Population Representation
In the RPD problem, the elements of the solution consist of the control variables namely, Generator bus voltage (Vgi), reactive power generated by the capacitor (QCi), and transformer tap settings (tk). These variables are represented as binary strings in the GA population. The length of the binary strings is based on their actual value to obtain accurate solution. The binary strings are randomly generated as shown below.
10001 10111 ...... 11111 110 110
....... 001
11011 11011 ..... 11000
Fitness Function
In the RPD problem, the objective is to minimize the total real power loss while satisfying the constraints (2) to (8). For each individual, the equality constraints are satisfied by running Newton-Raphson algorithm and the constraints on the state variables are taken into consideration by adding penalty function to the objective function. With the inclusion of the penalty factors, the new objective function then becomes,
(9)
Where,
Generally, GA searches for a solution with maximum fitness function value. Hence, the minimization objective function given in (9) is transformed into a fitness function (f) to be maximized as,
V.SIMULATION RESULTS
In order to demonstrate the effectiveness and robustness of the proposed technique, minimization of real power loss under two conditions, without and with FACTS devices were considered. The validity of the proposed Genetic Algorithm technique is demonstrated on IEEE 30 and IEEE 118-bus systems.
CASE1: IEEE 30-BUS SYSTEM
The IEEE 30-bus system has 6 generator buses, 24 load buses and 41 transmission lines of which four branches are with the tap setting transformers. The real power settings are taken from [1]. The lower voltage magnitude limits at all buses are 0.95 p.u. and the upper limits are 1.1 for all the PV buses and 1.05 p.u. for all the PQ buses and the reference bus. The lower and upper limits of the transformer tappings are 0.9 and 1.1 p.u. respectively. The capacitor bank rating is set as 0-20 MVAR. The optimal settings of GA control parameters are given below:
Maximum generation : 60
Population size : 30
Crossover Probability (Pc) : 0.7
Mutation Probability (Pm) : 0.01
Minimization of Real Power Loss (Ploss)
The proposed algorithm is applied for loss minimization in the base condition i) without considering FACTS devices, ii) with the inclusion of FACTS devices. Without FACTS devices, the algorithm
