reactive power optimization
TRANSCRIPT
-
8/10/2019 Reactive Power Optimization
1/15
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
-
8/10/2019 Reactive Power Optimization
2/15
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.
-
8/10/2019 Reactive Power Optimization
3/15
-
8/10/2019 Reactive Power Optimization
4/15
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.
-
8/10/2019 Reactive Power Optimization
5/15
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:
-
8/10/2019 Reactive Power Optimization
6/15
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:
-
8/10/2019 Reactive Power Optimization
7/15
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:
-
8/10/2019 Reactive Power Optimization
8/15
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
-
8/10/2019 Reactive Power Optimization
9/15
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.
-
8/10/2019 Reactive Power Optimization
10/15
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.
-
8/10/2019 Reactive Power Optimization
11/15
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
-
8/10/2019 Reactive Power Optimization
12/15
-
8/10/2019 Reactive Power Optimization
13/15
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.
-
8/10/2019 Reactive Power Optimization
14/15
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.
-
8/10/2019 Reactive Power Optimization
15/15