IRJET- Particle Swarm Optimization based Reactive Power Optimization of Utility Grid with Wind Generation

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 07 Issue: 01 | Jan 2020 www.irjet.net p-ISSN: 2395-0072
© 2020, IRJET | Impact Factor value: 7.34 | ISO 9001:2008 Certified Journal | Page 1117
Particle Swarm Optimization based Reactive Power Optimization of
Utility Grid with Wind Generation
Hailu Tibebe Mengistu1, Melese Loha Anjulo2
1Chief Electromechanical Engineer, BGI, Hawassa, Ethiopia
2Senior Electrical Engineer, SNNPRS Industrial Parks Development Corporation, Hawassa, Ethiopia
-------------------------------------------------------------------***----------------------------------------------------------------------
Abstract-Reactive power is important function of
regulating voltage. In developing countries like Ethiopia,
the electric utility company should optimize the reactive
power for the transmission/distribution system to improve
the active power loss of the distribution/transmission
system. This paper presents a method to minimize the
active power loss in a practical power system and
determines the best location placement of a new installed
wind generation with aim of loss reduction and voltage
profile improvement. Reactive power optimization
problem is nonlinear and has both equality and inequality
constraints. A southern region 21-bus power network
system is used for testing the developed algorithm. A
mathematical model of reactive power optimization was
established based on the constraint conditions. The results
have been validated using MATLAB programming. After
completing the reactive power optimization based on the
particle swarm algorithm with wind generation, the active
power network loss value of the system was reduced by
18.43%. Particle swarm optimization algorithm and Mat-
power 3.2 toolbox are used to solve the reactive power
optimization problem
Keywords: Particle Swarm, Optimization, Reactive
Power, Utility, Mat-power 3.2 and MATLAB
1. Introduction
Particle swarm optimization, PSO is a fast, simple and
efficient population-based optimization method. Each
particle updates its position based upon its own best
position, global best position among particles and its
previous velocity vector according to the following
equations [1]:
(1)
(2)
Where,
1k
iv 
: The velocity of th
i particle at ( 1)th
k  iteration
w : Inertia weight of the particle [0.2, 1]
k
iv : The velocity of th
i particle at th
k iteration [-
0.003, 0.003]
1, 2c c : Positive acceleration constants having values
between [2.1, 2]
1 2,r r : Randomly generated numbers between [0, 1]
ibestp : The best position of the
th
i particle obtained
based upon its own experience
bestg : Global best position of the particle in the
population
1k
ix 
: The position of
th
i particle at ( 1)th
k  iteration
k
ix : The position of
th
i particle at
th
k iteration
 : Constriction factor [0.729]. It may help insure
convergence.
Suitable selection of inertia weight w provides good
balance between global and local explorations.
- (3)
Where, maxw is the value of inertia weight at the
beginning of iterations, minw is the value of inertia
weight at the end of iterations, iter is the current
iteration number and maxiter is the maximum number of
iterations.
1.1. PSO Parameters Selection
The selection of the PSO parameters for general problem
is listed in table-1. Programmers may change some of
these parameters based on different problems.

Table 1: PSO Parameters Selection
Particle
size
20-50 works well for most of the
optimization problems.
However, as the dimension increase,
the number of the particle should also
increase according.
Particle size = 50
Dimension
of the
particles
Equals the number of control variables
= 8
Domains
of the
particles
Depends on the upper bound and
lower bound constraints
Accelerati
on factor
[C1=2.1, C2=2]
Stopping
criteria
 Iteration number = 200
 Difference between the
current best solution and the
previous best solution
 No improvement after a
certain number of iterations
Inertial
Weight
[Final Inertia weight = 0.2,Initial
Inertia weight = 1]
Constrictio
n Factor
[0.729].
1.2. Procedure for RPO using PSO for SNNPR 21-bus
Power Network
The main optimization steps of the PSO based reactive
power optimization are as follows:
(1) Define control variables (vg1, vg2, vg3, T1, T2,
T3, QC4 and QC13) within their permissible
range, define population size (=50), no of
iteration (=200), assume suitable values of PSO
parameters, input the data of 21 bus power
network system.
(2) Take iter=0
(3) Randomly generate the population of particles
and their velocities
(4) For each particle run NR load flow to find out
losses.
(5) Calculate the fitness function of each particle
using eq. (11)
(6) Find out “personal best (Pbest)” of all particles
and “global best(Gbest)” particle from their
fitnesses
(7) Iter=iter+1
(8) Calculate the velocity of each particle using eq.
(1) and adjust it if its limit gets violated
(9) Calculate the new position of each particle using
eq. (2)
(10) For each particle run NR load flow to
find out losses.
(11) Calculate the fitness function of each
particle using eq. (11)
(12) For each particle if current fitness(P) is
better than Pbest then Pbest=P
(13) Set best of Pbest as Gbest
(14) Go to step no. 7, until max. No of
iterations is completed.
(15) Coordinate of Gbest particle gives
optimized values of control variables and its fitness
gives minimized value of losses.
1.3 Active power loss minimization
The active power loss of the system equals the sum of
the real power loss on each branch, and it can be
described as:
Min F= Min(Ploss)
=∑ + - 2 (4)
Where,
N = number of branches,
Gij = the conductance of the branch between bus i and
bus j,
Vi = the voltage magnitude of bus i,
Vj = the voltage magnitude of bus j,
ɵij = the difference of phase angle between bus i and bus j
1.4 Constraint
To process Reactive power optimization problem has
both equality and inequality constraints.
I. Equality Constraint
The equality constraints are the power balance
equations, which can be defined by the equations below:
a. Real Power Constraint:
H1= - ∑ ( cos + sin =0 (5)
i
b. Reactive Power Constraint:
H2= - - ∑ ( =0 (6)

i
II. Inequality Constraint
The inequality constraints are the ranges of the voltage
magnitudes, tap positions of the transformers, and
reactive power injection.
a. Bus Voltage magnitude constraints:
V i-min ≤ V i ≤ V i-max (7)
b. Generator bus reactive power constraints:
Q Gi-min ≤ Q Gi ≤ Q Gi-max (8)
c. Transformer Tap position constraints:
T i-min ≤ T i ≤ T i-max (9)
d. Reactive power source capacity constraints:
Q ci-min ≤ Q ci ≤ Q ci-max (10)
Where,
N = number of branches,
Gij = branch conductance between bus i and bus j,
Vi = voltage magnitude of bus i,
Vj = voltage magnitude of bus j,
ɵij = phase angle difference between bus i and bus j
PGi = active power generation at bus i
PDi = active power demand at bus i
QGi = reactive power generation at bus i
QDi = reactive power demand at bus i
Qci = reactive power source i installation
III. Exterior Penalty Function (EPF) Method
Reactive power optimization problem is a constrained
problem. In optimization, the constrained problems are
usually converted into unconstrained problems for
convenience. One of the commonly used methods to
convert the constrained problem is adding exterior
penalty function terms to the objective function. Penalty
function is used to handle inequality constrains. So, the
amplified objective function (fitness function) would be
as eq. (11).
(11)
Where,
( )
rh is the penalty multiplier for the equality constraint.
rg is the penalty multiplier for the inequality constraint.
F is called the augmented function.
The equality constraint in this thesis will be
automatically fulfilled by using MATPOWER 3.2 toolbox,
so only inequality constraints need to be concerned.
Therefore, the final objective function could be described
as [2]:
∑ ∑ (
∑ ( (12)
Where,
{
(13)
{
(14)
{
(15)
In Exterior Penalty Function, if all the control variables
are within the limits, the penalty function would be zero.
On the opposing, if the control variables go outside the
limits, then the penalty function would be added to the
objective function to penalize the violation. In reactive
power optimization, if the control variables go above the
voltage limit, major damages to the power systems
would occur. So, the voltage magnitudes, tap positions,
and reactive power injection have to be sensibly
examined.
2. SNNPR 21-Bus Power Network
To prove the effectiveness of the developed PSO based
algorithm for reactive power optimization, a practical
21-bus distribution test system is used as shown in
figure-1.
The voltage levels of the test system are 400KV, 230 kV,
132 kV and 66 kV. The Southern Region 21-Bus network
system has three generators at bus numbers 1, 2 and 3.
The first PV one is at bus 1; the second PV is at bus 2; the
3rdgenerator is at Bus 3(slack bus).This system includes
of 21 transmission lines, three tap-ratio transformers in
lines between bus numbers 1-6, 17-18 and 18-20. In
addition, bus numbers 4 and 13 has been selected as
shunt VAR compensation buses. The lower limits voltage

magnitude of all buses is considered as 0.9 pu, while the
upper limit is considered as 1.1 pu for the generator
buses and 1.05 pu for the load buses.
Figure 1: SNNPR 21-Bus Power Network System
The initial operating conditions for the developed
method are given as follows for 100 MVA base. The total
load of the system is 360.20MW and 29MVAr.
MATPOWER toolbox is used to calculate the power flow
of practical 21-bus distribution system. Before
optimization, the total real and reactive power loss of the
entire system is 18.543MW and 23.14MVAr,
respectively.
3. SNNPR 21-Bus Power Network RPO with WGs
A comparison of the real power loss of base case,
optimization without new WG and optimization when
WG is installed on various buses of southern region 21-
bus distribution network is illustrated in figure-2.
Figure 2: Comparison of loss reduction
It can be seen that optimization with a new WG can
further reduce the active power loss than optimization
using PSO without WG. After integrating a new WG on
bus 14, the total active power loss can be reduced to
minimum 15.125 MW. The optimal placement of a new
WG is on bus 14.
Figure-3 shows the optimal loss reduction process of the
proposed method when a small wind turbine is installed
on bus 14. The particles start to converge after
conducting 90 iterations. Finally, the total power loss of
the system is 15.125 MW. The total CPU time is 210sec.
In the figure-3 below shows the graphical representation
of total active power loss with respect to total number of
iterations. After 90 iterations, no improvement is
displayed.
Figure 3: SNNPR 21-Bus Loss Reduction with WG
The results from table-2 show the optimal settings of
control variables to get minimum active power loss

when anew WG is installed on bus 14. The total active
power loss after optimization with a new WG is 15.125
MW.
Table 2-Optimal Results of Control Variables with WG
CONCLUSION
The combined technique of particle swarm optimization
algorithm with MATPOWER toolbox is applied to solve
reactive power optimization problem and to determine
the optimal placement of new installed WG in existing
system. The performance of the developed technique
was tested on the SNNPR 21-Bus power network and the
simulation results were compared without and with
integrating wind generation to the system. It can be
observed that reactive power optimization approach for
distribution system with a wind generation can further
reduce the active power loss than without wind
generation. The benefit of lower active power loss
obtained will provide better economic dispatch and
secure operation in power system. Before the reactive
power optimization, the reactive power in 21-Bus power
network is arbitrary distributed. When 2 MW wind
generations is installed into the system, the active power
loss was reduced from 18.543MW to 15.125MW which is
18.43 %. The optimization meaningfully decreased the
active power loss of the system. Results were attained
after conducting 90 iterations, which replicates the
excellent searching ability of particle swarm
optimization algorithm for solving nonlinear problems.
As the output of the wind generation increases, the
active power loss of the system could be decreased. The
Mat-power 3.2 toolbox is used to calculate the power
flow and manage the equality constraints in Particle
Swarm Optimization based reactive power optimization.
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Bus Control
Variables
Min Max With New
WG on Bus
14
1 VG1(p.u) 0.9 1.1 0.9399
2 VG2 0.9 1.1 1.0827
3 VG3 0.9 1.1 1.1206
14 VWG 0.9 1.1 0.98
1-6 T1 0.95 1.05 0.974
17-18 T2 0.95 1.05 1.0062
18-20 T3 0.95 1.05 1.0019
4 QC4(MVAr) 0 20 19.5529
13 QC13 0 10 6.4804
Active Power Loss (MW) 15.125

Bibliography
Received M.Sc., Power System and
Energy Engineering Department of
Electrical and computer Engineering,
Hawassa University, his primary
interest is in distributed generation.
Received M.Sc., Power System and
Energy Engineering Department of
Electrical and computer Engineering,
Hawassa University, his primary
interest is in hybrid renewable
energy system.

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