Binary Gravitational Search based Algorithm for Optimum Siting and Sizing of DG and Shunt Capacitors in Radial Distribution Systems

doi:10.4236/epe.2013.54B192

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Energy and Power Engineering, 2013, 5, 1005-1010

doi:10.4236/epe.2013.54B192 Published Online July 2013 (http://www.scirp.org/journal/epe)

Binary Gravitational Search based Algorithm for

Optimum Siting and Sizing of DG and Shunt Capacitors

in Radial Distribution Systems*

N. A. Khan1, S. Ghosh2, S. P. Ghoshal2

1Department of Electrical Engineering, Aliah University, Salt Lake, Kolkata, India

2Department of Electrical Engineering, National Institute of Technology, Durgapur, India

Email: [email protected]

Received March, 2013

ABSTRACT

This paper presents a binary gravitational search algorithm (BGSA) is applied to solve the problem of optimal allot ment

of DG sets and Shunt capacitors in radial distribution systems. The problem is formulated as a nonlinear constrained

single-objective optimization problem where the total line loss (TLL) and the total voltage deviations (TVD) are to be

minimized separately by incorporating optimal placement of DG units and shunt capacitors with constraints which in-

clude limits on voltage, sizes of installed capacitors and DG. This BGSA is applied on the balanced IEEE 10 Bus dis-

tribution network and the results are compared with convention al binary particle swarm optimization.

Keywords: Normal Load Flow; Radial Distribution System; Distributed Generation; Shunt Capacitors; Binary Particle

Swarm Optimization; Binary Gravitational Search Algorithm; Total line Loss; Total Voltage Deviation

1. Introduction

Distribution systems are usually radial in nature for op-

erational simplicity. The Radial Distribution Systems

(RDS) are fed at only one point, which is the substation.

The substation receives power from the centralized gen-

erating stations through interconnected transmission

network. The end users of electricity receive electrical

power from the substation through RDS, which is a pas-

sive network. Hence, the power flow in the RDS is uni-

directional. The high (R/X) ratio of the distribution lines

results in large voltage drops, low voltage stability and

power losses. Under critical loading conditions in certain

industrial areas, RDS experiences sudden voltage col-

lapse due to low value of voltage stability index at most

of its nodes. The sizing and sitting of DG units and shunt

capacitors in distribution systems is a very complex

combinational optimization problem. This optimization

problem involves not only integer and binary decision

variables but also nonlinear, non-continuous,

non-differential objective functions and constraints. The

problems of this type are regarded as nondeterministic

polynomial-time hard (NP-hard) problems, which pose

computational complexities with some conventional

analytical optimization techniq ue s. In th e literatures, very

few papers [1-5] use the optimization of voltage profile

as objective functions the integration of DG and shunt

capacitor placement certain heuristic methods [1-5] have

been reported in the literature for obtaining promising

results. Recently, Rashedi et al. [6] proposed a new op-

timization algorithm called Gravitational Search Algo-

rithm (GSA), which has been demonstrated to be very

interesting to find solutions of unimodal and multimodal

functions. GSA is based on the law of attraction of

masses supported by the Newtonian gravity, which says

that” a particle in the universe attracts every other one

with a force that is directly pro portional to the pr oduct of

their masses and inversely proportional to the square of

the distance between them”. The original version of GSA

was designed for search spaces of real valued vectors.

However, many optimization problems are set in binary

discrete space, such as feature selection and dimensional-

ity reduction [7-11] data mining [12], unit commitment

[13], and cell formation [14], in which it is natural to

encode solutions as binary vector s. In addition, problems

defined in the real space, may be considered in the binary

space, too. The solution is to display real digits with

some bits in the binary mode. The binary search space is

considered as a hypercube in which an agent may move

to nearer and farther corners of the hypercube by flipping

various numbers of the bits. In the literatures, very few

papers use the optimization of voltage profile as objec-

tive functions. In this work, a binary version of GSA

(BGSA) [15] is utilized to decide the optimal lo cation s of

DGs and shunt capacitors to obtain an overall better vol-

tage profile for a radial distribution system. In the binary

N. A. KHAN ET AL.

1006

version of GSA (BGSA), the outcome of these forces is

converted into a pro bability valu e for each ele ment of the

binary vector, which guides whether that elements will

take on the value 0 or 1. The objective function is to mi-

nimize Total Line Loss (TLL) and maximize the lowest

voltage level of the system i.e nothing but minimize To-

tal Voltage Deviation (TVD) to reach a better voltage

profile. The locations of DGs and capacitors are formu-

lated by binary variables as decision variables in the con-

straints.

2. Power Flow Solution in Radial

Distribution System

The load flow solution is carried by the following set of

recursive equations (1) and (2) derived from the single

line diagram as shown in Figure 1.

11,1

.ii

iiLiii

PPPRV









 





(1)

11,1

.ii

iiLiii

QQQXV









 





(2)

where is the real power flow into the sending end of

branch connecting bus and bus ; 1

i1i1i



real component of load at bus ; ,1ii is the re-

sistance of line section between buses and i

1iR



and

i is the bus voltage magnitude at bus i. i is the

reactive power flow into the sending end of branch

VQ 1i



connecting bus and bus ; 1

i1i

i is reactive

component of load at bus ; ,ii is the reactance

of line section between buses and i.

1



i1

X

The problem of DG and shunt capacitors allotment

with their proper capacities is of great importance. The

installation of DG and shunt capacitors at non-optimal

places can result in an increase in system losses, voltage

deviations and costs. Therefore, a power system planning

engineer requires an efficient and fast optimization me-

thod capable of indicating the best solution for a given

Figure 1. Single line diagram of a Radial distribution sys-

tem.

distribution network. The selection of the best places for

installation and the preferable sizes DG and shunt ca-

pacitors banks in large distribution systems is a complex

discrete optimization proble m.

In order to incorporate the proposed method recursive

equations (1) and (2) are modifi ed as follows:

a) Real Power Flow with installation of DG

11,1 1

.ii

iiLiii i

PPPRAP



 





  (3)

where 1i



is real power magnitude injected at bus



; P



is real power multiplier, set to zero when

there is no real power source or set to 1 when there is DG

power source;

b) Reactive Power Flow with shunt capacitors place-

ment

11,1 1

.ii

iiLiii i

QQQXRPQ



 



 (4)

where 1i



is reactive capacitor power magnitude in-

jected at bus 1i



; Q



is reactive capacitor power

multiplier, set to zero when there is no capacitor power

source or set to 1 when there is a capacitor power source;

c) Computation of Bus Voltages

1,1,1

,1 ,12

2(.. )

()*

ii iiiiii

ii ii

VV RPXQ

RX V





 



 (5)

3. Problem Formulation

The following sections describe the details of the pro-

posed problem formulation.

a) The Objective Functions

The main advantages of Shunt capacitors in the distri-

bution system are loss minimization in the feeders and

the improvement in the voltage profile, i.e. maintaining

the voltages at customer terminals with reactive power

compensation.

The following functions are computed using the pro-

posed algorithm: Total Line Loss (TLL), Total Voltage

Deviatio n (TVD).

b) Total Line Loss (TLL)

The installation capacitor banks should not result in an

increase in the system losses. The power loss of the line

section connecting buses and is computed as:

i1i

,1 2

(,1)* ii

lossi i

Pii RV



 (6)



1,1

loss

TLLPi i









 (7)

c) Total Voltage Deviation (TVD)

N. A. KHAN ET AL. 1007

Voltage deviation can also be minimized with integra-

tion of Shunt capacitors. The total voltage deviation

(TVD) in the system, which is to be minimized, is ex-

pressed as:

TVD V





 (8)

where = 1, 2, 3……..n and i is the voltage of ith

bus in per unit for the system buses; the ideal magnitude

of each bus voltage is unity.

i V

d) Constraints

The following constraints are considered [16].

i) Total Power Conservation:

The algebraic summation of all incoming and outgoing

powers over the feeders, taking into consideration the

feeders’ losses and the powers supplied by Shunt capaci-

tors should be equal to the total demand at that bus.

ii) Distribution Feeder’s Thermal Capacity:

Power flows in feeders must be within their capacities.

iii) Distribution Substation’s Capacity:

The summation of total powers delivered to the net-

work by the substation’s transfo rmers must be with in the

substation’s capacity limit.

iv) Shunt capacitor Operation Limits:

The Shunt capacitor’s generated power must be within

the Shunt capacitor’s capacity.

v) Voltage Drop Limits:

The voltage levels at different buses must be within

predetermined v alues.

4. Proposed Binary Gravitational Search

Algorithm

The conventional GSA was originally designed to solve

problems in continuous valued space [6]. The search al-

gorithm is based on the metaphor of gravitational inter-

action between masses in the Newton theory. A j-th bit of

the i-th agent



in a system is represented as a bit 0

or 1 where a combination of bits gives the i-th agent po-

sition.

The next agent’s velocity





v is calculated based on

its current velocity and its acceleration as expressed in

(9). Then, a new agent’s position



is updated using

a condition as shown in (11). However, the velocity is

limited in interv al [-6, 6] so as to achieve a good con ver-

gence rate.

 

tatvrtv ijijij *1 (9)



vSigmoid



1

1 (10)









otherwise

vsigmoidr

i,1

if,0



(11)

5. Simulation Results and Discussions

To demonstrate the performance of the proposed BGSA

in solving the optimal DG and shunt capacitor placement

problem, the IEEE 10 bus distribution system is used in

this study. In this paper, for this particular test system,

Total Line Loss (TLL) and Total Voltage Deviation

(TVD) were minimized and compared to the conven-

tional BPSO as to illustrate its p e rformance in solving the

same problem. All the optimization parameters are stan-

dardized where population size and maximum population

are set to 60 and 100, respectively. In the BPSO, two

positive coefficients are set to 2 () and inertia

weight, () monotonously decreases from 0.9 (max ) to

0.4 (min ). In the BGSA, the initial gravity constant, G0

is set to 100 and the best applying force, (

122cc

) is mo-

notonously decreased from 100% (maxbest ) to 2.5%

(minbest ).The proposed BGSA algorithm has been im-

plemented on IEEE 10-bus radial distribution network.

a) Test System-I

IEEE 10 Bus [17] is a single line main feeder (Base

Voltage = 23 KV, Base MVA=100 MVA) without later-

als and sublaterals having total active and reactive pow-

ers of 12.368 MW and 8.372 MVAR, respectively.

Without any injection of DG active powers and Shunt

capacitors’ reactive powers, the normal load flow yields

Total Line Loss (TLL) and total voltage deviation (TVD)

as 78.3712 KW and 0.6989 p.u., respectively.

b) Total Line Loss (TLL) minimization

Figure 2(a) represents voltage profile of IEEE 10 bus

radial distribution system obtained by different optimiza-

tion techniques (BPSO, BGSA) and normal power flow

(NPF). TLL is improved more in the case of BGSA

(87.67%) as that of BPSO (81%) over NPF, it can be

seen from Table 1. It is observed, voltage profile is im-

proved as that of BPSO, lowest bus voltage increased

6.38% by BPSO whereas in Binary GSA, it is improved

by 8.69 % as shown in Table 3. Convergence character-

istic is depicted in Figure 2(b). Loss and corresponding

total voltage deviation is more reduced than that of

BPSO as observed from Figures 2(c) and (d) in TLL

minimization.

12345678910

0. 88

0. 9

0. 92

0. 94

0. 96

0. 98

1. 02

Bus nu mb e

Bus voltage m agnitude in p.u.

NPF

BPSO

BGSA

(a)

N. A. KHAN ET AL.

1008

020 40 6080100 120 140 160 180 200

Iterati on cyc l e s

T.L.L in kW

(b)

(c)

(d)

Figure 2. TLL Minimization Characteristics of IEEE 10

Bus Radial Distribution System; (a) Voltage profile ob-

tained by different algorithms, (b) Convergence character-

istic, (c) Comparison of TLL, (d) Comparison of TVD.

Table 1. Comparative study of Tll minimization of Ieee 10

bus test system.

Comparative Study Of TLL Minimization

Test System % Improvement in

BPSO over NPF % Improvement

in BGSA over NPF

IEEE 10 Bus

system 81 87.67

From Table 2, it is observed that same capacities of DG

and shunt capacitor are used for minimizing the fitness

function (TLL) in th is wo rk. Two DG o f 100 0 KW (at 3rd

and 7th bus position) and two Shunt capacitors (at 2nd and

5th bus position), each of 400 KVAR are optimally

placed in BGSA.

c) Total Voltage Deviation (TVD) minimization

Figure 3(a) represents voltage profile of IEEE 10 bus

radial distribution system obtained by optimization tech-

niques (BPSO, BGSA) and normal power flow (NPF). It

can be seen that voltage profile is improved as that of

BPSO, lowest bus voltage increased 4.47% by BPSO

whereas in Binary GSA, it is improved by 8.67 % corre-

sponds to Table 4. Convergence characteristic of TVD

minimization is shown in Figure 3(b). Total voltage de-

viation and correspon ding line loss is decreased than that

of BPSO as observed from Figures 3(c) and (d). One DG

set of 1000 KW capacity (at 2nd bus position), and two.

TVD is improved more in the case of BGSA (8.1%) as

that of BPSO (4.47%) over NPF as presen ted in Table 6.

Table 2. Capacities of DG and shunt capacitors in Tll

minimization of Ieee 10 bus test system.

Comparative Stu dy by two algorithms

BPSO BGSA

Test SystemDG

(kW) Shunt Capaci-

tors (kVAR) DG

(kW)

Shunt Ca-

pacitors

(kVAR)

IEEE 10

Bus system2000 800 2000 800

Table 3. Lowest bus voltage improvement in Tll minimiza-

tion for Ieee 10 bus system

Comparative Study Of TLL Minimization

Test System% Improvement in

BPSO over NPF % Improvement

in BGSA over NPF

IEEE 10 Bus

system 6.38 8.69

1 2 3 4 56 7 8 910

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

Bus numb e r

Bus voltage m agnitude in p.u.

NPF

BPSO

BGSA

(a)

N. A. KHAN ET AL. 1009

050100 150 200250 300 350400

0. 2

0.25

0. 3

0.35

0. 4

0.45

0. 5

0.55

0. 6

0.65

0. 7

B us num ber

T.V .D in p.u.

(b)

(c)

(d)

Figure 3. TVD Minimization Characteristics of IEEE 10

Bus Radial Distribution System; (a)Voltage profiles ob-

ined by different algorithms, (b) Convergence characteristic,

voltage deviation.

Table 4. Comparative study of Tvd Minimization of Ieee 10

bus test system.

Comparative Study Of TVD Minimization

Test System % Improvem ent in

BPSO over NPF % Improvement

in BGSA over NPF

IEEE 10 Bus

system 4.47 13.47

Table 5. Capacities of DG and shunt capacitors In TVD

Minimization of Ieee 10 bus test system.

Comparative Stu dy by two algorithms

BPSO BGSA

Test System

(kW)

Shunt

Capacitors

(kVAR)

(kW)

Shunt Ca-

pacitors

(kVAR)

IEEE 10 Bus

system 1000800 1000 800

Table 6. Lowest bus voltage improvement in TVD minimi-

zation for Ieee 10 bus system.

Comparative Study Of TLL Minimization

Test System % Improvement in

BPSO over NPF % Improvement

in BGSA over NPF

IEEE 10 Bus

system 4.47 8.10

Shunt Capacitors (at 4nd and 8th bus position), each of

400 KVAR capacity, are equivalent to total 800 KVAR

optimally placed in BGSA as indicated in Table 5. Same

capacity of DG and Shunt capacitors are used in BPSO

technique but for TVD minimization, required two DG

sets and two Shunt capacitors.

6. Conclusions

This paper presented a BGSA and a comparative per-

formance of BGSA and BPSO in solving the two sepa-

rate single-objective optimization problem for optimal

DG and Shunt capacitor placement in a radial distribu-

tion test systems. The optimization techniques have been

tested on IEEE 10 bus distribution test system for deter-

mining the best optimal DG and Shunt capacitor place-

ments for TLL and TVD minimization. The comparative

results showed that the proposed BGSA is the most ef-

fective and precise among the aforementioned optimiza-

tion techniques. In conclusion, the authors’ contribution

in this work is successful application of a binary GSA

algorithm for simultaneous solution of optimal number

and placements of DG powers and Shunt capacitors in a

balanced distribut ion syste m.

N. A. KHAN ET AL.

1010

REFERENCES

[1] K. Zou, A. P. Agalgaonkar, K. M. Muttaqi, S. Perera.

“Optimisation of Distributed Generation Units and Shunt

Capacitors for Economic Operation of Distribution Sys-

tems,” Power Engineering Conference; Australasian

Universities; pp. 1-7, 14-17 Dec. 2008.

[2] K. Zou, A. P Agalgaonkar, K. M. Muttaqi and S. Perera,

“Voltage Support by Distributed Generation Units and

Shunt Capacitors in Distribution Systems,” Power &

Energy Society General Meeting, IEEE, pp.1-8; 26-30

July 2009.

[3] K. Haghdar and H. A. Shayanfar, “Optimal Placement

and Sizing of DG and Capacitor for the Loss Reduction

via Methods of Generalized Pattern Search and Genetic

Algorithm.” Power and Energy Engineering Conference

Asia-Pacific, pp. 1-4, 28-31 March 2010.

[4] R. A. Hooshmand and H. Mohkami, “New Optimal

Placement of Capacitors and Dispersed Generators Using

Bacterial Foraging Oriented by Particle Swarm Optimiza-

tion Algorithm in Distribution Systems,” Springer Electr

Eng 93, pp. 43-53, Jan 2011.

[5] M. Kalantari and A. Kazemi, “Placement of Distributed

Generation Unit and Capacitor Allocation in Distribution

Systems Using Genetic Algorithm,” pp.1-5, 8-11 May

2011.

[6] E. Rashedi, H. Nezamabadi-pour and S. Saryazdi, “Gsa:

A Gravitational Search Algorithm,” Information Sciences,

Vol. 179, No. 13, 2009, pp. 2232-2248.

doi:10.1016/j.ins.2009.03.004

[7] P. Avishek and J. Maiti, “Development of a Hybrid Me-

thodology for Dimensionality Reduction in Mahalano-

bis–Taguchi System Using Mahalanobis Distance and

Binary Particle Swarm Optimization,” Expert Syst Appl

Vol. 37, No. 2, 2010, pp. 1286-1293.

doi:10.1016/j.eswa.2009.06.011

[8] M. Beretaa and T. Burczynski, “Comparing Binary and

Real-valued Coding in Hybrid Immune Algorithm for

Feature Selection and Classification of ECG Signals.”

Eng Appl Artif Intell, Vol. 20, 2007, pp. 571-585.

[9] X. Wang and J. Yang, “Feature Selection Based on

Rough Sets and Particle Swarm Optimization,” Pattern

Recogn Lett, Vol. 28, 2007, pp. 459-471.

[10] L. H. Chuang and H. W. Chang, “Improved Binary PSO

for Feature Selection Using Gene Expression Data,”

Comput Biol Chem,Vol. 32, No. 1, 2008, pp.29-38.

[11] X. P. Zeng and Y. M Li, “A Dynamic Chain-like Agent

Genetic Algorithm for Global Numerical Optimization

and Feature Selection,” Neurocomputing, Vol. 72, 2009,

pp. 214-1228. doi:10.1016/j.neucom.2008.02.010

[12] K. G Srinivasa and K. R Venugopal, “A Self-adaptive

Migration Model Genetic Algorithm for Data Mining

Applications. Inf Sci, Vol. 177, No. 20, 2007, pp.

4295-4313.

[13] X. Yuan and Nie, “An Improved Binary Particle Swarm

Optimization for Unit Commitment Problem,” Expert

Syst Appl, Vol. 36, No. 4, 2009, pp. 8049-8055.

doi:10.1016/j.eswa.2008.10.047

[14] T. H. Wu and C. C. Chang, “A Simulated Annealing Al-

gorithm for Manufacturing Cell Formation Problems,”

Expert Syst Appl , Vol. 34, No. 3, 2008, pp. 1609-1617.

[15] E. Rashedi, H. Nezamabadi-pour and S. Saryazdi, “Bgsa:

Binary Gravitational Search Algorithm,” Natural

Computing, Vol. 9, 2010, pp. 727-745.

doi:10.1007/s11047-009-9175-3

[16] R. Annaluru, S. Das and A. Pahwa, “Multi-level Ant Co-

lony Algorithm for Oplacement of Capacitors in Distribu-

tion Systems,” Congress on Evolutionary Computation,

Vol. 2, 2004, pp. 1932-1937.

[17] J. J Grainger and S. H Lee, “Capacity Release by Shunt

Capacitor Placement on Distribution Feeders, A New

Voltage-Dependent Model,” Power Engineering Review,

IEEE, Vol. 2, No. 5, 1982, pp. 42-43.