International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
Power loss minimization using cat swarm
optimization
P.Surya kumari1, Dr.P.Kantarao 2
PG student, Dept. of EEE, GMRIT, Rajam, Srikakulam, AP-532127, India1
Professor Dept. of EEE, GMRIT, Rajam,Srikakulam, AP-532127, India2
ABSTRACT
This paper presents an algorithm for solving the multi-objective reactive power dispatch problem in a power system. Model
analysis of the system is used for static voltage stability assessment. Loss minimization and maximization of voltage stability
margin are taken as objectives .Generator terminal voltages, reactive power generation of the capacitor banks and tap changing
transformer settings are taken as the optimization variables. The proposed approach employs cat swarm optimization (CSO)
algorithm for optimal settings of RPD control variables. The proposed approach is examined and tested on the standard IEEE 30bus test system with different objectives that reflect power loss minimization, voltage profile improvement, and voltage stability
enhancement. The results demonstrate the potential of the proposed approach and show its effectiveness and robustness to solve
the RPD .
Keywords: Reactive power dispatch , loss minimization, voltage stability enhancement, cat swarm optimization .
1. INTRODUCTION
One of the important operating requirements of a reliable power system is to maintain the voltage within the permissible
ranges to ensure a high quality of customer service. The optimal power flow (OPF) has been widely used for both the
operation and planning of a power system .Therefore, a typical OPF solution adjusting the appropriate control
variables[1], so that a specific objective in operating a power system network is Optimized(maximizing or minimizing)
with respect to the power system constraints, detected by electrical network.
The problem that has to be solved in a reactive power optimization is to determine the required reactive generation at
various locations so as to determine the required reactive generation at various locations so as to optimize the objective
function. Here the reactive power dispatch problem [2] involves best utilization of the existing generator bus voltage
magnitude, transformer tap setting and the output of reactive power sources so as to minimize the loss and to enhance the
voltage stability of the system.
Cat Swarm Optimization (CSO) is proposed in this paper .One of the more recent optimization algorithm based on swarm
intelligence is the Cat Swarm Optimization (CSO) algorithm[3]-[4]. The CSO algorithm was developed based on the
common behavior of cats. It has been found that cats spend most of their time resting and observing their environment
rather that running after things as this leads to excessive use of energy resources. To reflect these two important
behavioral characteristics of the cats, the algorithm is divided into two sub-modes and CSO refers to these behavioral
characteristics as ―seeking mode and ―tracing mode, which represent two different procedures in the algorithm.
Tracing mode models the behavior of the cats when running after a target while the seeking mode models the behavior of
the cats when resting and observing their environment.
The proposed algorithm identifies the optimal values of generation bus voltage magnitudes, transformer tap setting and
the output of the reactive power sources so as to minimize the transmission loss and to improve the voltage stability. The
effectiveness of the proposed approach is demonstrated through IEEE-30 bus system. The test results show the proposed
algorithm gives better results with less computational burden and is fairly consistent in reaching the near optimal
solution.
The performance of CSO algorithm was compared to that of different heuristic techniques .it is found that ,the
convergence speed of CSO is significantly better than that of DE[1],PSO[6]-[10], and evolutionary algorithms(EAs)[13][14].it is found that ,CSO is the best performing algorithm as it finds the lowest fitness value for the most of the problems
considered in that study.
2. PROBLEM FORMULATION
2.1 Nomenclature :
Ploss Network real power loss
Pi , Qi Real and reactive powers injected into network at bus i
Volume 2, Issue 9, September 2013
Page 174
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
Gij , Bij Mutual conductance and susceptance between bus i and bus j
Gii , Bii Self- conductance and susceptance of bus i
Qgi Reactive power generation at bus i
Qci Reactive power generated by i th capacitor bank
t k Tap setting of transformer at branch k
Vi Voltage magnitude at bus i
V j Voltage magnitude at bus j
 ij Voltage angle difference between bus i and bus j
S l Apparent power flow through the l th branch
g k Conductance of branch k
N B Total number of buses
N B 1 Total number of buses excluding slack bus
N PQ Number of PQ buses
N g Number of generator buses
N C Number of capacitor banks
N T Number of tap-setting transformer branches
N l Number of branches in the system
 i Voltage phase angle of i th generator bus
The RPD problem aims at minimizing the real power loss in a power system while satisfying the unit and system
constraints. This goal is achieved by proper adjustment of reactive power variables like generator voltage magnitudes
(V ), reactive power generation of capacitor banks (Q ) and transformer tap settings (t ). The optimal reactive power
gi
ci
k
dispatch problem is formulated as an optimization problem in which a specific objective function is minimized while
satisfying a number of Equality and inequality [11]-[14].
2.2 Real power losses:
This is mathematically stated as
Ploss 
Minimize
g v
k
i
2
vj 2 2vivjcosij 
(1)
kNl
k  i , j 
The real power loss given by (1) is a non-linear function of bus voltages and phase angles which are a function of control
variables. The minimization problem is subjected to the following equality and inequality constraints.
2.3 Equality Constraints
These constrains represents the typical load flow equations
NB
PiVi Vj  Gijcosij  Bijsinij 0,iNB1
(2)
j 1
NB
Qi Vi  Vj Gijsinij Bijcosij 0,iNPQ
j 1


(3)
2.4 Inequality Constraints
These constraints represent the system operating constraints. Generator bus voltages (Vgi), reactive power generated by
the capacitor (Qci), transformer tap setting (t k), 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.
Volume 2, Issue 9, September 2013
Page 175
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
These constraints are formulated as
i) voltage limits
V i min V i V i max ;iN B
(4)
ii) Generator reactive power capability limit
Q gi min Q gi Q gi max ;iN g
(5)
iii) Capacitor reactive power generation limit
(6)
Qci min Qci Qci max ;iNc
iv) Transformer tap setting limit
t k min  t k  t k max ;k  N T
(7)
v) Transmission line flow limit
S l S
l
max
;l  N
(8)
l
vi) Voltage stability constraint
L max  L min
(9)
The voltage stability index given in Equation (9) is evaluated as follows, First, the L-indices [19] of all the load buses
in the system are computed using the expression(10):
Ng
L j 1Fji
i 1
Vi
( ji  i  j )
Vj
The values of F ji are obtained from the matrix F
Where, FLG [YLL ] 1 [YLG ]
(10)
LG,
(11)
max
The maximum of the L indices (L ) gives the proximity of the system to voltage collapse. The bus with the highest L
index value will be the most vulnerable bus in the system which need critical reactive power support.
3. Cat swarm optimization
3.1 Overview
CSO algorithm[2] is divided into two sub models based on two of major behavioural of traits of cats. These are termed
as “Seeking mode” and “Tracing mode”.
Seeking mode has four essential factors .Such as SMP,SRD,CDC,SPC Which are designed as follows .
 Seeking Memory pool (SMP):- It is used to define the size of Seeking memory of each cat, indication any points sort
by cat.
 Seeking Rang of Selected Dimensions (SRD):- It is used to declare mutative ration for selected dimensions. While in
seeking mode; if a dimension is selected for mutation, the difference between old and new ones may not be out of range
,the range defines by SRD.
 Counts of Dimensions to Change (CDC):- It is used tell how many dimensions to will be varied. All these factors play
an important roles in seeking mode.
 Self Position Consideration (SPC):- It is a Boolean valued variable, and indicates whether the point at which the cat
is already standing will be one of the candidate point to move to.SPC cannot influence SMP.
3.2. Seeking Mode: Resting and Observing
The seeking mode of the CSO algorithm models the behaviour of the cats during the period of resting but staying alertobserving its environment for its next move .
The seeking mode of the CSO algorithm can be described as follows
Volume 2, Issue 9, September 2013
Page 176
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
Step 1:-Make j copies of the present position of each catk , where j=SMP. if the value of SPC is true. let
j=(SMP=1),then retain present position as one of the candidates.
Step 2:- For each copy according to CDC add or subtract SRD percent values and replace the old ones.
Step 3:-Calculate the fitness values (FS) of all candidate points.
Step 4:-If all the FS[3] are not exactly equal calculate the selecting probability(12) of each candidate point .otherwise
set all the selecting probability of each candidate point to 1.
Pi 
FS i  FS b
FS max  FS min
, where 0 i  j
(12)
If the global of the fitness is to find the minimum solution .FSb=FSmax , otherwise FSb=FSmin.
Step 5:- Randomly pick the point to move to form the candidate points, and replace the position of catk .
3.3.Tracing Mode.:- Running after a target
Step1:- update the velocities for every dimension (Vid) according to eq (13)
Step 2:- check if the velocities are in the range of maximum velocity is over-range, it is set equal to the equal.
Step 3:- update the position of catk according to eq (14)
(13)
Vid W *Vid C*r* Pgd  Xid 
Where ,W is inertia weight ,Pgd is position of cat, who has the best fitness value. Xid is the position of catk, C is constant
r is a random value in the range of [0,1].
Xid Xid Vid
(14)
3.3 CSO flow chart
Fig 1.CSO flow chart
4.Results
The proposed CSO algorithm has been tested on the standard IEEE 6-generator,30-bus test system shown in fig.1 The
IEEE-30 bus system has 6 generator buses,24 load buses and 41 transmission lines of which 4 branches are (6-9),(610),(4-12) and(28-27) are with the tap setting transformers .This system has 19-control variables as follows :6-genetor
voltage magnitudes,4-tap transformer setting and 9-switchable VAR .System description is given in Table 1.
Volume 2, Issue 9, September 2013
Page 177
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
Fig2: Single line diagram of IEEE-30 bus test system
Table1: System description of IEEE 30 bus test system
Variable
30-bus system
S. No
1
Buses
30
2
Branches
41
3
Qsvc
9
4
Generators
6
5
Tap–changing transformers
4
Variable limits of control variables are given in Table2
Table 2: Control variable limits
S.No
Control variable limits
Limits
1
Generator voltage (Vg)
(0.95-1.1) p.u.
2
Tap setting(tk)
(0.95 -1.1)p.u.
3
MVAR by static compensators (Qsvc)
(0.0-5.0) p.u
RPD with loss minimization objective . Here the CSO algorithm was applied to identify the optimal control variables of
the system under base-load condition, with loss minimization and without considering the voltage stability of the system.
It was run with different control parameter settings and the minimization solution was obtained with the following
parameter setting s are shown in Table3
Table3: CSO Parameters for best results of optimal power flow for IEEE 30-bus system
S.No
Parameters
Values
1
Populations
170
2
Iterations
180
3
Copies
30
The minimum and maximum limits for the control variables along with the initial settings Table 4 :The optimal values of
the control variables along with the minimum loss obtained are given in Table 5.Corresponding to this control variable
Volume 2, Issue 9, September 2013
Page 178
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
setting, it was found that there are no limit violations in any of the state variables. The minimum loss obtained by the
proposed method is less than the values presented in the other papers. It is tabulated in the Table 5
Table 4 :The minimum and maximum limits for the control variables along with the initial settings
Table 5:Optimal settings of control variables for CSO
Volume 2, Issue 9, September 2013
Page 179
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
Fig 3. Power loss variation with no of iteration
Fig 4. fitness variation with no of iterations
Fig 3,4 shows the graph between power loss and fitness variations with respective to no iterations
Table 6: Comparison of Power Losses for different methods
Method
Minimum Power loss(pu)
Evolutionary programming[10]
5.0159
DE[1]
0.0485
Proposed algorithm
0.0478
5.Conclusions
In this paper ,CSO optimization algorithm has been proposed ,developed and successfully applied to solve reactive power
dispatch problem .The RPD has been formulated as a constrained optimization problem where several objective functions
have been considered to minimize the power losses, to improve the voltage profile ,and to enhance the voltage stability.
The proposed approach has been tested and examined on the standard IEEE 30-bus test system. the results demonstrate
the effectiveness and robustness of the proposed algorithm to solve RPD problem. This paper shows that such excellent
results with different objective functions shows that makes the proposed CSO optimization technique is good in dealing
with power system optimization problems.
References
[1] K. Vaisakh and P. K. Rao, “Differential Evolution based optimal reactive power dispatch for voltage stability
enhancement,” Journal of Theoretical and Applied Information Technology, pp. 700-709, 2008.
[2] P.Aruna Jeyanthy and Dr.D.Devaraj, “Optimal Reactive Power Dispatch for Voltage Stability enhancement using
real coded genetic algorithm”, International Journal of Computer and Electrical Engineering, Vol 2, No.4, Aug 2010,
1793-8163.
[3] S-C Chu, P-W Tsai and J-S. Pan. Cat Swarm optimization. Proceedings of the 9th Pacific Rim International
Conference on Artificial Intelligence, LNAI 4099, Guilin,(2006), pp. 854-858.
[4] J.-C. Hwang, J.-C. Chen and J.-S. Pan. CSO and PSO to Solve Optimal Contract Capacity for High Tension
Customers. Proceedings of 8th International Conference on Power Electronics and Drive Systems, PEDS-2009,
(2009), pp. 76-81.
[5] A.A.Abou El Ela,M.A. Abido,S.R.Spea,” Differential evolution algorithm for optimal reactive power dispatch,”
Journal of Electrical Power and Energy Systems Vol. 81,2011, pp 485-464.
[6] Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading
Effects”, IEEE Transactions on Power Systems, Issue 4,Vol. 22, pp.2030 – 2038, 2007.
[7] P.R.Sujin, Dr.T.Ruban Deva Prakash and M.Mary Linda . Particle Swarm Optimization Based Reactive Power
Optimization., Journal Of Computing, Volume 2, Issue 1, January 2010, Issn 2151-9617.
Volume 2, Issue 9, September 2013
Page 180
International Journal of Application or Innovation in Engineering & Management (IJAIEM)
Web Site: www.ijaiem.org Email: editor@ijaiem.org, editorijaiem@gmail.com
Volume 2, Issue 9, September 2013
ISSN 2319 - 4847
[8] B. Zhao, C.X. Guo and Y.J. Cao, “Improved particle swam optimization algorithm for OPF problems”, IEEE-PES
Power Systems Conference and Exposition, Vol. 1, pp.233 - 238, 10-13 October 2004.
[9] Nakhon Ratchasima . Power Loss Minimization Using Optimal Power Flow Based on Particle Swarm Optimization.,
U. Leeton University of Technology, THAILAND 30000.
[10] Granville, S. 1994.’Optimal Reactive Power Dispatch through Interior Point Methods’ IEEE Trans. on
PowerSystems Vol.9.No.1,pp.98-105.
[11] H. W. Dommel and W. F. Tinny, “Optimal power flow solutions,” IEEE trans. on power app & systems, 87 , 1968,
pp 1866-1876.
[12] Wu Q.H. and Ma J. T.(1995) ‘Power System Optimal Reactive Power Dispatch Using Evolutionary Programming’,
IEEE Trans on power system, Aug,Vol.10.No.3,pp.1243-1249.
[13] T.Jayabarathi, K.Jayaprakash, D.N.Jeyakumar, T.Raghunathan, “Evolutionary Programming Techniques For
Different Kinds Of Economic Dispatch Problems”, Electric Power Systems Research, Vol. 73, 2005, pp. 169-176.
[14] Rainer Storn, Kenneth Price, “Differential Evolution – A Simple and Efficient Adaptive Scheme for Global
Optimization Over Continuous Spaces” TR-95-012, March 1995.
[15] Dervis Karaboga, Selcuk Okdem, “A Simple and Global Optimization Algorithm For Engineering Problems:
Differential Evolution Algorithm”, Turk J Elec. Engin.,Vol. 12, No.1, 2004, pp. 53-60.
[16] K. Iba, “Reactive power optimization by genetic algorithm,” IEEE trans. on power systems, Vol. 9 No. 2, 1994 , pp
685-692.
[17] Lee K.Y. Park Y.M. and Ortiz J.L. (1985). ‘A United Approach to Optimal Real and Reactive Power dispatch’,
IEEE Trans. On Power Apparatus and Systems, May, Vol.PAS.104, No.5, pp 1147-1153.
[18] Granville, S. 1994.’Optimal Reactive Power Dispatch Through Interior Point Methods’,IEEE Trans. on Power
Systems Vol.9.No.1,pp.98-105.
[19] S.Durairaj, D.Devaraj, P.S.Kannan ,’ Genetic algorithm applications to optimal reactive power dispatch with voltage
stability enhancement’ , IE(I) Journal-EL Vol 87,September 2006.
AUTHOR
Dr.P.KANTARAO born in Andhra Pradesh, India, in 1969. He received the B.Tech. M.Tech degree in Electrical and
Electronics Engineering from Affiliated College of Sri Venkateswara University, A.P. He has the experience of 22 years
teaching Experience. His research areas are in power systems security, stability, load management and voltage stability,
and has published more papers in these areas. Currently, he is with the Department of Electrical and Electronics
Engineering, in GMR Institute of Technology, Rajam, and Andhra Pradesh as a Professor.
P.SURYA KUMARI received B.E (EEE) degree, First class from Jawaharlal Nehru Technological University Kakinada
in April 2010. At present she is pursuing his M.Tech (Power & Industrial Drives) at GMR Institute of Technology,
Rajam, Affiliated to JNTU, Kakinada, A.P, India.
Volume 2, Issue 9, September 2013
Page 181