Reactive Power Optimization

8/10/2019 Reactive Power Optimization

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Seminar report on

Reactive Power Optimization of Power System

based on Improved Particle Swarm Optimization

DEPARTMENT OF

Electrical and Electronic Engineering

NIT - WARANGAL

Submitted by:

D S. NARESH

(ROLL NO: 142609)

Under the guidance ofAsst .Prof. Y. CHANDRA SHEKAR


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ABSTRACT

Reactive power optimization is a nonlinear, multivariable, multi-constrained programming

problem, which makes the optimization process complicated. In this paper, based on the

characteristics of reactive power optimization, a mathematical model of reactive power

optimization, including comprehensive consideration of the practical constraints and reactive

power regulation means for optimization, is established. Also particle swarm optimization (PSO)

has been studied, and the method based on improved particle swarm optimization for reactive

power is going to be taken in this paper. Optimization for the IEEE 14-bus system proves that

the improved PSO algorithm used in this paper for reactive power optimization is effective. The

algorithm is simple, convergent and of high quality for optimization, and thus suitable forsolving reactive power optimization problems, with some application prospect.


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INTRODUCTION

The purpose of Power system reactive power optimization is to find the reasonable reactive

compensation points and best compensation methods with the demand of reactive load power

system, which makes the power system safe and economic. The traditional reactive power

optimization methods include linear programming, Newton method, interior-point method ,

etc. In recent years, artificial intelligence such as genetic algorithm, particle swarm algorithm ,

ant algorithm realizes the algorithm from different approaches, and every one of them have

their own advantages, but also have defects. Particle Swarm Optimization (PSO) is a random

search algorithm, which is based on learning the accumulated experience of particulate

individuals and excellent information of groups to search the optimal regions of the space. PSO

algorithm considers control variables as its own properties. It is very convenient to process

optimization problem with continuous variables and discrete variables. Using PSO for power

system reactive power optimization is a very effective method. But PSO algorithm

convergences too fast and is easy to access to local convergence, which causes the accuracy of

convergence is not high. Based on the basic particle swarm algorithm, this paper made some

expansion and correction, including a reasonable inertia weight, shrinkage factor, crossover and

mutation and neighborhood model, and the improved particle swarm algorithm is easier to

jump out of local optimal solution than the basic particle swarm algorithm, thus converge to a

better solution, and improves the accuracy of convergence. Reactive power optimization test

through IEEE14 bus system shows that this algorithm is feasible to solve power system reactive

power optimization allocation problem.


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II. MATHEMATICAL MODEL OF POWER SYSTEM REACTIVE POWER

OPTIMIZATION.

A. Objective function:

To satisfy the demand of modern power grid, and better achieve the cost savings purpose, this

paper consider the satisfaction, system network loss and investment cost as the objective

function, the mathematical description is as follow:

Where, C is investment costs, are the coefficient for investment costs, system

network loss and satisfaction weight. In this paper we choose =1==20. PL is system

network loss, Nt, Nb are the number of On-load adjustable transformer and number of nodes

except slack bus. Svi is voltage satisfaction of on-load adjustable transformer near the load side;

Sqi is reactive power satisfaction of all nodes except slack bus. Their meanings are as follows:

B. Equality constraints:

Equality constraints include the active and reactive power balance constraint of each node:


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N is node number, PGi, PLi are generator active power output and active power of load at node

i. QGi, QLi, Qci are generator reactive power input, load reactive power and capacity of

capacitive reactive compensation device at node i.

C. Inequality constraints:

Inequality constraints can be divided into control variables constraints and state variables

constraints. The control variables include number of transformer taps and parallel capacitor

compensation capacity. The control variables constraints are as follows:

The state variables include reactive power of the generators, voltage of load bus and branch

reactive power, etc. The state variable constraints are as follows:


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III. BASIC PARTICLE SWARM ALGORITHM

Particle swarm optimization(PSO) method is an iterative optimization algorithm. The

particles need to update two extremes in each round of iteration, one is the individual extreme

which is the accumulation of their own experience of the individual, and the other one is theglobal extreme which is the accumulation of the group experience. The basic PSO algorithm can

be described as follows:

where i is the number of particles, j is the dimensional number of particles, t is the number of

iteration, c1 and c2 are the accelerating factors, they are usually between 0 to 2, r1 and r2 are

the independent random variables in the range *0,1+, xi=(xi1, xi2,, xin) is the current position

of the i particle, vi=(vi1, vi2,, vin) is the current velocity of the i particle, pi=(pi1, pi2,, pin) is

the best position that the i particle has passed in the movement , and pg=(pg1, pg2,, pgn) is

the best position that all the particles have passed in the movement. By analyzing the basic PSO

algorithm in (5) and (6), we can see the factors c1 and c2 make the particles move to the

direction toward the individual and global optimal position.

IV. IMPROVEMENT OF BASIC PARTICLE SWARM ALGORITHM

PSO algorithm convergence fast, but it has some shortcomings such as easy accessing to local

convergence and low convergence precision. This is because in the optimal process, all particles

consider the optimal particle as the goal, then search toward the same direction, which lead to

lose the ability to explore unknown area. Therefore, basic particle swarm algorithm need to

make some expansion and modification. The main improvement measures are as follows:

A.

Inertia weight:To improve the convergence performance of PSO algorithm, Shi and Eberbart

introduced inertia weight in speed evolution equation:


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where w is called inertia weight. Inertial weight makes particles have the ability to

explore the unknown area. Choosing inertia weight reasonably can balance the global

and local search; improve the PSO algorithm search efficiency and convergence

accuracy. Specific improvement measures are as follows:

wmax and wmin are the maximum and minimum of w, which generally take 0.9 and 0.4.

itermax is the maximum iterating times. k is the current iteration.

B. Shrinkage factor:

In 1999 Clerc put forward the concept of shrinkage factor. This method can ensure thealgorithm convergence through the reasonable choice of w, c1 and c2. After introducing

the shrinkage factor, the velocity evolution equation of particle is as follow:

among them, the shrinkage factor is:

Research has shown that introducing the shrinkage factor to control particle velocity

evolution equation usually has better convergence.

C. Crossover and mutation:

Referring to the crossover technology in genetic algorithm, the particles of PSO

algorithm can be crossed. The crossover probability of particles is set by users,

according to which an amount of father generations are elected at each iteration

process. Let particles of the father generation do random cross, then the progeny

particles generated replaced the particles in father generation. In PSO algorithm, every

father generation particles have their own speed value and position. In the father


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generation group, we choose particle (a) and particle (b) randomly to do crossover

operation and the formulas are:

where r is a random variables in the range [0,1].

The method to introduce mutation operator is: a variable exotic is generated in the global

scope according to mutation rates, except for the global optimal particle. Then mutation

processing is done on particle c which is randomly generated from variation domain. The

formulas are:

where r is a random variables in the range [0,1]. xmaxxmin are the upper limit and lower

limit of the search space.

When crossover and mutation operators are introduced, not only the particle swarm's local

search ability strengthens, while also the global search ability strengthens. Of course, all these

process sacrifice the search speed.

D. Neighborhood model:

In an individual social cognitive system, apart from their own experience and excellent

information absorbed from the whole society, an individual generally learns from their best

neighborhood. Based on this idea, the neighborhood mode of PSO algorithm is introduced

which improves the social cognitive system of PSO algorithm.


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PSO based on fitness/distance (FDR - PSO) is one algorithm of this kind. Its speed evolution

equation is:

where c3 is an accelerating constant, r3 is a random number in the range [0,1], pnj is the

position vector of the best individual in domain.

There are two principles to choose the neighborhood particle, first is that it must be adjacent

with the individuals to be updated, and second is that its fitness must be higher than other

adjacent individuals.

V. REACTIVE POWER OPTIMIZATION USING IMPROVED PARTICLE

SWARM ALGORITHM:

The main steps of the reactive power optimization of power system based on improved PSO

algorithm in this paper are as follows:

Step 1: Enter the original parameters. Original parameters include not only the line parameters,the generator output and load, the upper and lower limits of the control variables and the

bound range of state variables, but also the population size of the particle swarm, the

maximum number of iterations, accelerated constants, and so on.

Step 2: Initialize the population. Let each group values of the control variables as an individual

particle swarm, in the form of integer encoding, to generate the initial population randomly in

the context of the global searching.

Step 3: Flow calculation. Decode every individual of the particle swarm. Correct the system

parameters for the flow calculation according to the decoded data. Finally get the powersystem operation parameters, in order to facilitate the calculation of the objective function.

Step 4: Calculate the objective function value. According to the objective function in step (3),

calculate the fitness of each particle, and determine whether it meets the bus voltage and

generator reactive power and other constraints. Use punitive measures in the case of the more

limited.


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Step 5: Record the optimal solutions of each individual particle and the global optimal solution

of particle swarm. For each particle, compare the current fitness of the individual to the optimal

solution. If the current fitness is better than the optimal solution, then select the current fitness

value as the optimal solution of individual particles; otherwise, the optimal solution of the

individual unchanged. After recording the individual optimal solution, select the optimalsolution of the individual optimal solutions as the global optimal solution.

Step 6: Fix the location and velocity of each particle. Calculate the current flight speed of each

particle. Fix the position of each particle.

Step 7: Crossover and mutation. Do crossover and mutation on the particles to produce the

next generation of particles.

Step 8: Determine whether it is under terminating condition. If the number of iterations at this

time is less than the maximum number of iterations, t= t+1, and go to Step (3); or end the

iteration, go to Step (9).

Step 9: Output the optimal solution. Optimal solution includes not only the control strategy of

the control variables, each node but also the data of state variables, such as the system voltage

of every node, system power loss and generator reactive power output, and so on.

VI. EXAMPLE:

In order to validate that the improved PSO algorithm can solve power system reactive power

optimization allocation problems, in this paper reactive power optimization test is done with

the IEEE14 bus system. (See in Figure) This System includes five generator (bus 10, bus11,

bus12, bus13 and bus14, while bus14 is the slack bus and others are PV bus), 11 load bus and

20 branch, including 3 branches contain On-load adjustable transformer (branch 10-5, branch 7-

4 and branch 9-4, corresponding to transformer T1, T2 and T3).

In this test, we set the population size of particle swarm to be 40, and the number of Iterations

is 60. Using pruning technology, it is convenient to determine that reactive power

compensation devices are needed at bus 1, 3, 6 and 8.

All the expenses involved are shown in TABLE. The calculation results are shown in TABLE

and TABLE


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Every bus voltages are optimized to close ideal value 1.0, and the network loss reduces, this

proves that the method proposed in this paper can improve the grid voltage quality.


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CONCLUSIONS:

This algorithm is simple, convergent and of high quality for optimization, and thus

suitable for solving reactive power optimization problems.

Using PSO for power system reactive power optimization is a very effective method.


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Reactive Power Optimization