Download International Electrical Engineering Journal (IEEJ) Vol. 5(2014) No.12, pp. 1696-1702

International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
Imperialistic Competitive Algorithm (ICA)
for Solving Optimal VAR Dispatch
Problem
1
K.R.VADIVELU and 2G.V MARUTHESWAR
1
[email protected],[email protected]
Abstract: This paper presents an application of Fast
Voltage Stability Index (FVSI) to Imperialistic
Competitive Algorithm (ICA) for solving reactive power
dispatch problem in a power system. Generator terminal
voltages, reactive power generation of the capacitor
banks and tap changing transformer setting are taken as
the optimization variables. Imperialistic Competitive
Algorithm (ICA), is presented in this paper for solving
global unconstrained optimization problem. In order to
evaluate the proposed algorithm, it has been tested on
IEEE 30 bus system and the performance of the algorithm
is compared with gravitational search algorithm (GSA).
Results show that (ICA) is more efficient than others for
solution of single-objective Optimal VAr problem.
Key Words: Imperialistic Competitive Algorithm (ICA), swarm
intelligence, optimal reactive power, transmission loss
1. INTRODUCTION
Optimal reactive power dispatch problem is one of the
important problems in power systems. Major point is
operating the system unconfident mode and also to get better
the economy of the system. The sources of the reactive power
are the generators, synchronous condensers, capacitors, static
compensators and tap changing transformers. Here the
reactive power dispatch problem involve best use of the
accessible generator bus voltage magnitudes, transformer tap
setting and the output of reactive power sources so as to
reduce the loss and to improve the voltage stability of the
system. Various mathematical techniques have been utilize to
solve this optimal reactive power dispatch problem like the
gradient method [1], [2], Newton method [3] and linear
programming [4]-[7]. They include Interior Point Methods
(IMPs) [8], [9] and [10], Newton-based Nonlinear
Programming method [11] and Successive Linear
Programming (SLP) [12].The gradient and Newton methods
failed to handle inequality constraints. CPF was incorporated
successfully in [13]. The traditional solutions to the problem
of OPF are highly sensitive to starting points and therefore
they usually result in monotonic solution. In order to conquer
this problem, evolutionary algorithm is used. Genetic
algorithms are an example for evolutionary algorithms that
assess complex scenarios and provide solution that will be
more precise when compared with conventional solutions
[14], [15]. To the problem of OPF Particle Swarm
Optimization (PSO) has been applied in [10] that worked out
food searching behavior of animals of birds. They also
computed the best positional locally and globally at any given
point of time in order to find out the best options for
searching. This paper heart on building a new evolutionary
algorithm for solving OPF-CPF problem. The algorithm is
named as “Imperialistic Competition Algorithm”. This
algorithm is used to show the real power loss minimization
and maximization of VSL of the power distribution systems.
ICA has been applied earlier in power distribution systems for
harmonic estimation problem [16]. The forging behavior of E.
coli (bacteria) has been used in [14].ICA has been around for
few years. Recently it was explored in [17] and later used for
harmonic estimation problem in power distribution systems as
discussed in [14]. Foraging behavior of E.coli is used to build
the algorithm. These bacteria live in human intestine. Many
variables are simultaneously optimized.. The outcome result
revealed that the proposed method has power and can be used
in solving real world problems pertaining to extremely
nonlinear epistemic. Optimization of the said variables for
real power loss minimization and VSL maximization.In this
paper, maximum loadabilty is estimated through voltage
stability analysis. Voltage stability analysis is conducted
using the Fast Voltage stability index (FVSI) [18,19]. The
reactive power at a particular bus is augmented until it reach
the unsteadiness point at bifurcation. At the instability point,
the connected load at the particular bus is resolute as the
maximum load-ability. The maximum load-ability for each
load bus will be sorted in rising order with the smallest value
being ranked highest. The highest rank, imply the weak bus in
the system that has the lowest sustainable load. The proposed
come up to has been used in the RPP problems for the IEEE
30-bus system [3] which consists of six generator buses, 21
load buses and 41 branches of which four branches, (6,9),
(6,10), (4,12) and (28,27) are under load tap-setting
transformer branches. The reactive power source installation
buses are buses 30, 26, 29 and 25 which are identified based
on the FVSI technique. There are totally 14 control variables
2. PROBLEM FORMULATION
1696
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
i  N PQ
The objective function in RPP problem comprises two terms
j  Nl
[20]. The first expression represent the total cost of energy
loss as follows:
(5)
iii) Reactive Power source Installation Restriction
WC  h d1Ploss ,1
QCi
(1)
min
 QCi  QCi
i  NC
max
iv) Reactive Power source Generation Restriction
1 N1
Where, Ploss ,1 is the network real power loss during the
period of load level 1. The Ploss ,1 can be expressed in the

Ploss   gk Vi  V j  2VV
i j cos ij
2

min
 Qgi  Qgi
i  Ng
max
v) Bus Voltage Restriction
Vi
following equation in the duration dl:
2
Qgi
min
 Vi  Vi
i  Ng
max
vi)Transformer Tap Setting Restriction
(2)
Tk
min
 Tk  Tk
max
i  NT
k  NE
Where, reactive power flow equations are considered as
k   i, j 
equality constraints; VAR source installment restrictions,
reactive power generation restrictions, transformer tap-setting
The second term represents the cost of VAR source
restrictions and bus voltage restrictions are used as inequality
installments which has two components, namely, fixed
constraints.
installment cost and purchase cost:
IC    ei  CCi QCi

QCi
min
Can be less than zero and if Qci is selected
as a negative value, say in the light load period, variable
(3)
inductive reactance should be installed at bus i. The
i  NC
transformer tap setting Tk, generator bus voltages Vg and VAR
The objective function, therefore, can be expressed as
source installments QC are control variables so they are
self-restricted. The load bus voltages Vload and reactive power
follows:
generations Qg are state variables which are restricted by
Min fc = IC + WC ,
(4)
Subjected to
adding them as the quadratic penalty terms to the objective
function. Equation (4) is therefore changed to the following
Min
i) Real Power balance equation
0=Pi  Vi V j  Gij cos ij  Bij sin ij 
i  N B l
j  Nl
ii) Reactive Power balance equation
0=Qi  Vi V j  Gij sin ij  Bij cos ij 

FC  FC   Vi Vi  Vi
i  NQg lim
    Q
lim 2
Qgi
i  NV lim
gi
 Qgi

lim 2
(6)
Subjected to
0=Pi  Vi V j  Gij cos ij  Bij sin ij 
i  N B l
1697
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
j  Nl

R
R2 


2
V2  
 cos   V1V2   X 
 Q2  0
X 
 X sin 


0=Qi  Vi V j  Gij sin ij  Bij cosij 
i  N PQ
(7)
Setting the discriminate of the equation to be greater than or
j  Nl
equal to zero yields
Where, λvi and λQgi are the penalty factors which can be
increased in the optimization procedure;
and
are
defined in the following equations:

R
 X sin   cos 


2

R2 
 
 Q2  0
 V1   4  X 
X 
 

(8)
Vi
if Vi Vi
  max
max
if Vi Vi
Vi
min
Vi
lim
rearrange (8), we obtain
min
4Z 2Q2 X
(V1 ) 2  R sin   cos  
2
1
(9)
Since δ is normally very small, then
Qgi
lim
min
min
min

if Q gi
Qgi
Qgi
  max
max
max
if Q gi
Qgi

Qgi
=0,
=0,
=X
(10)
Taking the symbols ‘i’ as the sending bus and ‘j’ as the
receiving bus, FVSI can be defined by
3. FVSI FORMULATION
=
The FVSI is resulting from the voltage quadratic equation at
(11)
the receiving bus on a two- bus system [19]. The two-bus
.
representation
3.1. RANKING OF CRITICAL BUSES BASED ON
is
illustrated
in
Figure.1.
MAXIMUM LOADABILITY
The basic concept behind this technique is use of Line
V1
∟
0
B
u
s
1
Bus 2
V2
∟δ
P1 ,Q1,S1
P2,
Q2,
S2
Stability Index for indicating the voltage stability condition
formulated based on line termed as Fast Voltage Stability
Index in order to determine the maximum load-ability in a
power system. Maximum load-ability is estimated through
Voltage stability analysis. The margin measured from base
case solution to the maximum convergence point in the load
R+
jX
flow determines the maximum load-ability at a particular bus
Fig. 1two-bus power system model
From the figure, the voltage quadratic equation at the
receiving bus is written as
in the system. Voltage stability is conduct by using line
stability index indicate by FVSI to indicate the stressfulness
of a line in a transmission system.
The reactive power at a particular load bus is increased until it
reaches the instability point at bifurcation. At the instability
1698
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
point, the connected load at the particular bus is determined as
maximum load-ability of a particular bus which beyond this
converges and optimized the said parameter in power
distribution systems. The ICA applied to this project has the
steps given in listing 1
limit system infringement will be experienced. The individual
maximum load-ability obtained from the load bus will be
sorted in climbing order with the smallest value being ranked
highest. The highest rank implies the weak bus in the system
that has the lowest sustainable load. The bus which ranked
lowest is the most secure bus in the system.
3.2. DETERMINING THE MAXIMUM OADABILITY
FOR WEAK BUS
IDENTIFICATION
The following steps are implemented.
Step 1:
Run the power flow program for the base case.
Step 2:
Assess the FVSI value for every line in the system.
Step 3:
Slowly increase the reactive power loading by 0.01pu at a
chosen Load Bus until the load flow solution fails to give
results for the Maximum Computable FVSI.
Step 4:
Take out the stability index that has the highest value.
Step 5:
Choose another load bus and repeat steps 3 and 4.
Step 6:
Extract the maximum reactive power loading for the
maximum Computable FVSI for every load bus. The
Algorithm: Imperialistic competitive Algorithm
Inputs: Transformer tap positions,VAr compensators,
Penalty factors
Outputs: Optimized Voltage magnitude and Real Power
Loss
Step 1
Initialization of variables
Repeat
Input variables and penalty factors to ICA base line
algorithm
Compute objective function for real power loss
Optimize real power loss
Until Voltage magnitude is completely optimized
list 1 –steps to optimize real power loss and Voltage
magnitude can be seen in list 1 ,the algorithm runs in two part
loops.The first part loop optimizes the real power loss.It does
mean that it reduces real power loss while the second part
loop focuses on rising the Voltage magnitude.The more in
Voltage magnitude,the more steady the transmission system
should be.The underlying algorithm is ICS that has been
adopted from [18]
maximum reactive power Loading is referred to as the
Step 7:
maximum load-ability of a particular bus.
5. NUMERICAL RESULTS
Sort the maximum load-ability obtained from step 6 in
The validity of the proposed ica Algorithm technique has
been demonstrated in standard IEEE-30 bus system. The
test system has six generators at the buses 1, 2, 5, 8, 11 and
13 and four transformers with off-nominal tap ratio at lines
6-9, 6-10, 4-12, and 28-27 and the number of the optimized
control variables is 10 for this reactive power dispatch
problem. The minimum voltage magnitude limits at all
buses are 0.95pu. The maximum limit values for generator
buses are 1.1pu and 1.05pu for the remaining buses. The
minimum and maximum limits of the transformers tapping
are 0.9 and 1.1pu. The buses for possible VAR source
installation based on max load buses are 25, 26, 29 and 30..
The maximum loadability and FVSI values for the IEEE 30
bus system are given in Table I. The optimum control
parameter settings of the proposed ICA approach are given
in Table I. And Table II and Table III show the comparison of
power loss and voltage deviations. Form the simulation, the
most excellent value of active power loss is 4.31934. The
voltage deviations obtained from proposed ICA approach
respectively. As seen in figure 3, it is evident that the results
reveal the Vm at bus 20with respect to load at bus 20. The
results revealed that the proposed protocol is capable of
achieving its dual goal including the enhancement voltage
stability limit.Fig.4 gives the Bus voltage magnitude using
ascending order. The smallest maximum load-ability is
ranked the highest, implying the Weakest bus in the system.
4. IMPERIALISTIC COMPETITIVE ALGORITHM
(ICA).
The proposed algorithm is twofold in its functionality. It is
destined for minimization of real power loss and also
enhancing the voltage stability. The double purpose is serve
using a novel algorithm which is enthused by Evolutionary
Algorithms (EAs).EAs have been good candidate to solve real
world complex problems. Our algorithm is known as
Imperialist Competitive Algorithm. This algorithm was
originally conceived by Atashpaz-Gargari and Lucas
[18].The ICA algorithm has been exploited in this paper or
achieving its goals. As the ICA is one of the EAs, it is found
suitable for solving the optimization problems specified in
this paper. The algorithm has an iterative process that takes
care of optimizing two variables i.e., real power loss and
voltage stability limit. These two variables are considered
appropriately in the form of empires and colonies. By treating
them as part of objective functions, the algorithm finally
1699
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
ICA. The optimum control parameter settings of the
proposed ICA approach are given in Table I. And Table II
and Table III show the comparison of power loss and
voltage deviations. Form the simulation, the most excellent
value of active power loss is 4.31934. The voltage
deviations obtained from proposed ICA approach
respectively. As seen in figure 3, it is evident that the results
reveal the Vm at bus 20with respect to load at bus 20. The
results revealed that the proposed protocol is capable of
achieving its dual goal including the enhancement voltage
stability limit.Fig.4 gives the Bus voltage magnitude using
ICA.
Control
Variables
setting
Case 1:
Power
Loss
Case 2:
Voltage
Deviations
VG1
1.02
0.98
VG2
VG5
1.03
1.03
0.94
1.02
VG8
1.02
1.04
VG11
VG13
1.02
0.94
1.01
1.03
T6-9
T6-10
1.00
1.02
0.90
1.01
T4-12
T27-28
1.02
1.02
1.03
0.90
Power loss
(MW)
Voltage
deviations
4.429765
6.261549
0.723125
0.104678
TABLEI .III. COMPARISON OF THE RESULTS FOR
ACTIVE POWER LOSS
Figure 2.IEEE 30 bus system
TABLE.I.Bus Ranking and FVSI Values
Rank
1
2
3
4
5
6
7
8
9
10
Bus
30
26
29
25
15
27
10
24
14
18
Qmax(p.u)
0.26
0.29
0.33
0.47
0.50
0.57
0.60
0.62
0.75
0.77
FVSI
0.9786
0.9649
0.9946
0.9760
0.9708
0.9856
0.9837
0.9748
0.9764
0.9876
Control
Variabl
es
Setting
ICA
GSA
[21]
Multi
Objectiv
e
Ea [22]
As Single
Objective
[22]
1.049
Individ
ual
Optimi
zations
[22]
1.050
VG1
1.03
1.050
1.045
VG2
1.03
1.024
1.041
1.045
1.042
VG5
1.03
1.025
1.018
1.024
1.020
VG8
1.02
1.02
1.017
1.025
1.022
VG11
1.02
1.03
1.084
1.073
1.057
VG13
0.94
0.98
1.079
1.088
1.061
T6-9
1.00
1.06
1.002
1.053
1.074
T6-10
1.02
1.08
0.951
0.921
0.931
T4-12
1.02
1.10
0.990
1.014
1.019
T27-28
1.02
1.03
0.940
0.964
0.966
Power
Loss
(Mw)
Voltage
Deviati
ons
4.31
4.61
5.1167
5.1168
5.1630
0.69
0.83
0.7438
0.6291
0.3142
TABLE II. OPTIMUM CONTROL PARAMETERS VALUES
TABLE IV. COMPARISON OF THE RESULTS FOR
1700
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
VOLTAGE DEVIATIONS
Voltage Profiles at all buses
Control
Variabl
es
Setting
IC
A
VG1
0.98
VG2
GSA
[21]
Multi
Objec
tive
EA
[22]
1.016
As Single
Objectiv
e
[22]
0.995
Individu
al
Optimiz
ations
[22]
1.009
0.94
0.950
1.006
1.012
1.021
VG5
1.02
1.043
1.021
1.018
1.021
VG8
1.04
1.021
0.998
1.003
1.002
VG11
1.01
1.100
1.066
1.061
1.025
VG13
1.03
1.062
1.051
1.034
1.030
T6-9
0.90
0.905
1.093
1.090
1.045
T6-10
1.01
1.035
0.904
0.907
0.909
T4-12
1.03
1.038
1.002
0.970
0.964
T27-28
0.90
0.925
0.941
0.943
0.941
Power
Loss
(Mw)
Voltage
Deviatio
ns
6.10
6.371
5.8889
5.6882
5.6474
0.09
0.106
0.1435
0.1442
0.1446
Voltage at respective buses
1.5
1.021
Table I and II shows the bus ranking and optimal control
parameter values. Table III shows the active power loss is less
using proposed ICA algorithm
comparing with GSA
.Table.IV, voltage magnitude is less than using ICA algorithm
comparing with GSA.
0
[2]
0.6
0.4
[3]
0.2
0.4
0.6
0.8
10
15
bus numbers
20
25
30
FVSI approach has been developed for solving the weak bus
leaning optimal VAr dispatch problem. Based on FVSI, the
locations of reactive power strategy for voltage control are
determined. The individual maximum load-ability obtained
from the load buses will be sorted in rising order with the
least value being ranked highest. The maximum rank implies
the weakest bus in the system with low sustainable load.
These are the possible locations for reactive power devices to
maintain stability of the system. The proposed approach has
been applied to optimal VAr power dispatch problem on the
IEEE 30- bus power system. The simulation results indicate
the effectiveness and robustness of the proposed algorithm to
solve optimal VAr power dispatch problem in test system.
The ICA approach has revealed best quality solution for the
different objective functions.
0.8
0.2
5
6. CONCLUSION
[1]
0
0
Figure. 4 Bus voltage profile using ICA
CPF Curve
Prediction-Correction Curve
1
0
0.5
REFERENCES
Vm at bus 20 w.r.t. load (p.u.) at 20
1.2
1
1
1.2
[4]
Fig. 3 – Results of experiments (voltage)
[5]
O. Alsac and B. Scott,(1974) “Optimal load flow with
steady state security,” IEEE Transaction on Power
Apparatus and Systems, vol. PAS-93, no. 3, pp. 745-751.
K. Y. Lee, Y. M. Paru, and J. L. Oritz,(1985) “A united
approach to optimal real and reactive power dispatch,”
IEEE Transactions on Power Apparatus and Systems, vol.
PAS-104, no. 5, pp. 1147-1153..
A. Monticelli, M. V. F. Pereira, and S. Granville,(1987)
“Security constrained optimal power flow with post
contingency corrective rescheduling,” IEEE Transactions
on Power Systems, vol. PWRS-2, no. 1, pp. 175-182.
N. Deeb and S. M. Shahidehpur,(1990) “Linear reactive
power optimization in a large power network using the
decomposition approach,” IEEE Transactions on Power
Systems, vol. 5, no. 2, pp. 428-435.
E. Hobson,(1980) “Network constrained reactive power
control using linear programming,” IEEE Transactions on
Power Systems, vol. PAS-99, no. 4, pp. 868-877.
1701
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem
International Electrical Engineering Journal (IEEJ)
Vol. 5(2014) No.12, pp. 1696-1702
ISSN 2078-2365
http://www.ieejournal.com/
[6]
[7]
[8]
[9]
[10]
]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
K. Y. Lee, Y. M. Park, and J. L. Oritz,(1984) “Fuel-Cost
optimization for both real and reactive power dispatches,”
IEE Proceedings C, vol. 131, no. 3, pp. 85-93.
M. K. Mangoli and K. Y. Lee,(1993) “Optimal real and
reactive power control using linear programming,” Electr.
Power Syst. Res., vol. 26, pp. 1-10.
J. L. Martinez Ramos, A. G. Exposito, and V.
Quintana,(2005)“Transmissionloss reduction by interior
point methods:implementation issues andpractical
experience,” Proc. Inst.Elect. Eng., Gen., Transm.,
Distrib.,vol. 152, no. 1, pp. 90–98,.
G. Torres and V. Quintana,(1998) “An interior point
method for nonlinear optimalpower flow using voltage
rectangular coordinates,” IEEE Trans.Power Syst., vol. 13,
no. 4, pp.1211–1218.
S. Granville,(1994) “Optimal power dispatch through
interior pont methods,”IEEE Trans. Power Syst., vol. 9, no.
4, pp. 1780–1787.
D. Sun et al.,(1984) “Optimal power flow by newton
approach,”IEEE Trans.Power App. Syst., vol. PAS-103,
no. 10, pp.2864–2875.
P. Ristanovic,(1996) “Successive linear programming
based OPF solution,”Optimal Power Flow: Solution
Techniques,Requirements and Challenges,IEEE Power
Eng. Soc., pp. 1–9.
F. Milano, C. A. Canizares, and A. J. Conejo,
(2005)“Sensitivitybased security-constrained OPF market
clearing model,”IEEE Trans. Power Syst.,vol. 20, no. 4, pp.
2051–2060.
M. Tripathy and S. Mishra,(2007) “Bacteria
Foraging-Based Solution to Optimize Both Real Power
Loss and Voltage Stability Limit”. IEEE Transactions on
Power Systems, Vol. 22, No. 1, February.
Esmaeil Atashpaz-Gargari, Caro Lucas, “Imperialist
Competitive Algorithm: An Algorithm for Optimization
Inspired by Imperialistic Competition”. CIPCE
S. Mishra(2005), “A hybrid least square-fuzzy bacteria
foraging strategy forharmonic estimation,” IEEE Trans.
Evol.Comput., vol. 9, no. 1, pp.61–73.
2005K. M. Passino, (2002)“Biomimicry of bacterial
foraging for distributed optimizationand control,” IEEE
Control Syst.Mag., vol. 22, no. 3, pp.52–67.
A.C.G. Melo, S. Granville, J.C.O. Mello, A.M. Oliveira,
C.R.R. Dornellas, and J.O. Soto, (1999) “Assessment of
maximum loadability in a probabilistic framework,” IEEE
Power Eng. Soc.Winter Meeting, vol. 1, pp. 263-268.
I. Musirin, T.K.AbdulRahman,(2002) “Estimating
Maximum Loadability for Weak Bus Identification using
FVSI”, IEEE Power Engineering Review, pp. 50-52.
L.L.Lai,(1997) “Application of Evolutionary Programming
to Reactive Power Planning comparison with nonlinear
programming approach”, IEEE Transactions on Power
Systems, Vol. 12, No.1, pp. 198 – 206
S. Duman, Y. Sonmez, U. Guvenc, and N.
Yorukeran,(2011) “Application of gravitational search
algorithm for optimal reactive power dispatch problem,”
IEEE Trans. on Power Systems, pp. 519-523.
and Systems Conf., pp. 1054-1057.
M. A. Abido and J. M. Bakhashwain,(2003) “A novel
multiobjective evolutionary algorithm for optimal reactive
power dispatch problem,” in Proc. Electronics, Circuits
1702
.Vadivelu and .Marutheswar,
Imperialistic competitive algorithm (ICA) for solving optimal var dispatch problem