simultaneous multi-objective locating and sizing of ... · pdf filea major share of losses ......

Applied mathematics in Engineering, Management and Technology 2 (4) 2014:304- 315

www.amiemt-journal.com

304

Abstract

Today, application of shunt capacitors and distributed generation resources due to

increase in demand and power quality parameters improvement has increased.

Appropriate location and size of these two elements plays important role in bus

voltage profile and stability improvement, reducing active power losses and

economical aspect of the system. Due to the advantages of using DGs and

capacitors simultaneously, Using from this two element has additional capabilities

for the electrical power distribution system. The mentioned is related to the location

and sizing of DGs and capacitors, when it is presented under a nonlinear

optimization problem. In this paper, the imperialist competitive algorithm for

solving multi-objective problem of locating and tracking the amount of distributed

generation resources and shunt capacitors are employed simultaneously. This

objective functions for this problem are voltage profile improvement, increase in

voltage stability and decrease in active power losses. The proposed method has

implemented on standard IEEE 69 bus and the 33 bus models. The results indicate significant improve in power quality

parameters.

Keywords: distributed generation; shunt capacitor; distributed system; locating and sizing; Imperialist Competitive Algorithm

1. INTRODUCTION

A major share of losses in a power is related to the distribution system. Studies show that almost 13% of the

generated power is being dissipated in distribution systems. High R/X ratio and also a significant voltage drop in

these systems are causing significant losses. Feeders are usually in the form of radial distribution systems. Today,

the increased demand and load have led to the development of distributed systems and its dimensions and it will

cause voltage drop and losses increase which will result in reduction of nodes voltage and load imbalance [1].

Today, utilization of distributed generation sources has increased. Installation of such sources will prevent the

construction of new transmission and distribution lines to supply power system and also will avoid changes in the

topology which has many economic benefits [2]. Installation of distributed generation resources in distributed

systems will reduce network losses, improve network performance, delaying investment, increase reliability,

peak shaving, and electricity cost decrease and also improve voltage profiles [3]. The location and generating

capacity of these resources has an important effect on improving the mentioned features. Cost, size, limited

number and limitation of active and reactive power of the DGs are factors that have prevented the widespread

use of these resources in distributed systems. So it is necessary to use an element, such as a shunt capacitor

voltage to compensate the losses due to large scale distributed systems. Shunt capacitors will inject reactive

power at a lower cost than a distributed generation system and has not installation limit and they will improve

power quality parameters, contribute to compensating for the reactive power loss. Due to the advantages of DG

and shunt resistances, simultaneous use of these equipment’s will provide additional capabilities for the electrical

power distribution system. This factor depends on the simultaneous locating and sizing of these systems is posed

as a two objectives of a nonlinear optimization problem.

Location and size of the distribution system have a significant impact in improving the properties of these

sources. In [4] the optimal location of DG in different loading conditions has investigated. In this paper, the

honey bee optimization algorithm for solving optimization is employed. In [5] an analytical method for solving

the problem of locating distributed generation resources is used to reduce the power loss of the system. In [6]

Simultaneous Multi-objective Locating and Sizing of Distributed

Generation Sources and Shunt Capacitors Using Imperialist

Competitive Algorithm

Mostafa Karami 𝟏, Gholam-hossein Sheysi 𝟐, Shahram Karimi 𝟑 (1) Electric Engineering Department, Science and Research branch, Islamic Azad University Kermanshah, Iran

(2) Electric Engineering Department, Faculty of Engineering, Razi University, Kermanshah, Iran

(3) Faculty of Engineering, Higher Education and Research West Complex, Kermanshah, Iran

[email protected], [email protected], [email protected]

Applied mathematics in Engineering, Management and Technology 2014

M. Karami et al

305

combined sensitivity and load flow analysis for solving DG locating problem is used. In [7] a method of

combination the genetic algorithm and banned search for solving DG locating problem. In [8], a combined

approach is used for DG locating. In this paper, in addition to reduce losses and improve the voltage profile,

busses voltage stability is studied as a goal function. In [9], the ant colony algorithm is used to solve the problem

of locating and sizing of the DG. In this paper, the whole network cost and the cost of DG set are considered as

the target function. In [10], difference algorithm is used for locating the capacitor banks. In reference [11] the

genetic algorithm for solving the capacitor problem. In [12] immune system algorithm is applied to the capacitor

problem.

In [13] combination of fuzzy logic algorithms and evolutionary optimization methods have employed to solve

the capacitor problem. In [14] the particle swarm optimization algorithm is used to optimize the installed

capacitor. In [15], the optimal location of DG and shunt capacitors been solved by a multi-objective genetic

algorithm method. In [16], the optimal locating of DG in the presence of a capacitor has been performed and the

effects of these two elements of the distribution system parameters simultaneously and independently

investigated.

Optimal locating and sizing of distributed generation systems and capacitance is a nonlinear objective function

with equal and unequal constraints. This problem is a combination of a continuous problem (DG) and a discrete

problem (shunt capacitance). This objective is intended to improve the voltage profile, increased voltage stability

and decrease active power loss. The proposed algorithm is implemented in 69 and 33 bus systems.

2. FORMULATION OF THE PROBLEM

The simultaneous and optimal placing and sizing of distributed generation systems is an optimization problem

with a nonlinear objective function which has equality and inequality constraints. The objective function used for

the method includes reduction in system losses due to DGs and capacitors, improve the voltage profile, voltage

stability and load balancing lines.

Mathematical form of the objective function is as follows:

1 1 2 2 3Min. f f k f k f

(1)

The f1, f2 and f3 are defined below.

2.1 Power Losses

One of the benefits of distributed generation sources and capacitors is reducing of the total system active power

losses. Optimal placement of these two elements in the system by considering the inequality constraints, cause

maximum loss decrease at the grid.

1 . { }lossMin f min P

(2)

where Ploss is the active power losses.

2.2 Voltage Profile Improvement

The f2 is the voltage deviation index which is defined as follows:

(3)

2

12

( )nN

i ratedi

n

V Vf

N

where Vrated the bus nominal voltage which assumed to be 1 pu, Vi is the bus voltage and Nn is the number of

system busses.

2.3 Voltage Stability


M. Karami et al

306

The f3 function is related to voltage stability index in the distribution system. The criteria for the evaluation of

distributed network nodes have been proposed by Mr. M.Charkravortry and colleagues in [17]. A simple two-

bus system is shown in the following figure, based on the equations have been derived. Using the following

equation stability indices is calculated for all buses.

Fig. 1 A branch of the distribution system

4 2( ) | | 4[ ] | | 4[ ]

2 1 2 1 2 1 1 2 1 2 1SI n V P R Q X V P R Q X

(4)

Whatever the SI value is lower for a bus, the bus is more unstable. The Voltage stability index for a grid is

determined by the lowest SI value, which is a most unstable bus between all busses.

To improve the stability of the buses, the maximum index should be modified, i.e. the following objective

function has to be minimized.

'

3 i nmin(SI n ) ,i 2,3, , Nf

(5)

3 '

3

1f

f

(6)

3. PROBLEM CONSTRAINTS

The locating of the DG and capacitors has equal and unequal constraints that can be expressed as follows.

3.1 Voltage Constraint

The total effective voltage of any bus should have be in Vmin and Vmax range. In this range, Vmax is 1 pu and Vmin

is 0.9 pu [14].

min maxnV V V

(7)

3.2 Power and Power Factor Constraint

Power generation and power factor range for each DG unit:

min maxDG DG DG

niS S S

(8)

min maxDG DG DG

nipf pf pf

(9)

3.3 Line Loading Constraint

Current flow through each section should not exceed a maximum value.

maxiI I

(10)


M. Karami et al

307

3.4 Number and Value of The Shunt Capacitances

The capacitors are commercially available in discrete values. The shunt capacitors are multiples of the smallest

capacitor available.

(11 ) .

0. 1,2,..ciQ L Q L nc where Q0 is the smallest capacitor available.

3.5 Equality Constraints

The DG in the network should be such that all system variables and control variables are valid in load flow

analyses. Active and reactive power flow according to the known equations (2-40) and (2-41) are shown.

1

cos 0N

gi di i j ij i j ij

j

P P V V Y

(12)

1

sin 0N

gi di i j ij i j ij

j

Q Q V V Y

(13)

Where Pgi and Qgi are active and reactive power in ith

bus respectively, δi and Vi are angle and amplitude of bus

voltage, θijand Yij are extracted from grid's matrix determinant.

4. The Imperialist Competitive Algorithm

The ICA algorithm was first presented in [18]. The optimization algorithm, proposes a new optimization

strategy based on political and social evolution of humans. Like other evolutionary algorithms, this algorithm

starts with random initial population called a country. Some of the best elements of the population are selected

as the imperialist. The rest of the colony's population is considered as a colony. Depending on the imperialist

power, they attract the colonies with a particular process. The total power of the empire depends on the both

parts of the country which are the imperialist as core and dependent colonies. In mathematics, this dependence

is modeled by defining the empire power as total power in the imperialist countries, plus a percentage of the

average of colonies power. Each empire, which fails to compete successfully in the colonial rivalry and increase

their power or at least prevent its influence reduction, will be deleted from the scene of imperialist rivalry. So

the survival of an empire depends on its ability to attract and dominate rival imperialist empires and removing

them. Therefore during the imperial rivalries, the power of larger empires will increase gradually and the

weaker empires will be removed. The ultimate competition limit is when there is a unique empire in the world

[10].

The Imperialist Competitive Algorithm Procedure

4.1 Create the Initial Countries

To start the algorithm, arrays from the optimization variables are formed. In the algorithm, this array is known

as "Country".

1 2 3 var[ , , ,...... ]Ncountry p p p p

(14)

To start the algorithm, Nc, we create a number of initial countries. (Nimp). Countries with the lowest cost

function will be chosen as the imperialist. The remaining populations of the countries that form up the colonial

empires belonging to each empire (Ncol). To divide the primary colonies between the imperialists, some of the

colonies will be assigned to each imperialist, which the number of the assigned colonies is proportional to the

imperialist power.

To do this, with the cost of all imperialists, the normalized cost of doing this is considered as follows.


M. Karami et al

308

maxn i iC c c

(15)

The normalized relative power of each imperialist is calculated as follows:

1

nn Nimp

ii

CP

c

(16)

The initial number of a colonies belong to an imperialist is:

. { , }n colN C round P N

(17)

4.2 Colonial Assimilation Policy

The imperialists by means of assimilation policy, try to attract colonies.

Colonization process of the optimization algorithm, is modeled as the colonies movement towards imperialist

countries. As been shown in the figure, colony will be move by X units toward the imperialist and will be

dragged to the new position of the colony. X is a uniformly distributed random number, or is an number

obtained by any of other distribution which is appropriate.

~ (0, )x U d

(18)

Distance between the colony and the imperialist is shown by d.

Fig. 2 Colonial Assimilation Policy

4.3 Revolution

Sudden changes occurred in some countries and in some cases caused the function to find the minimum.

Fig. 3 Revolution Politics

4.4 Displacement of colonial and imperialist position

While moving towards the colonial settlements, some of the colonies may reach a point on the cost function that

they cost be much less than the cost function of imperialist positions (reaches a better position than the

imperialists).


M. Karami et al

309

In this case, the colonialist and colonized countries, switch places with each other, and the algorithm continues

with the new position of colonialism in this country as the new imperialists. The following figure explain this

event.

Fig. 4 The colonialist and colonized countries place switching

4.5 Power

An imperial power takes effect from its central government. Also the colonial have a small effect on the power.

Therefore, the total power of an empire is the power of central government plus a small percentage of its

colonies power

. . { }n n nT C Cost imperialist mean Cost colonies of empire

(19)

where T. Cn is the nth empire total cost and ζ is a positive number which is usually considered between 0 and 1.

In this paper ζ considered to be 0.05.

4.6 Colonial Competitive

Weak empire, lost its colonies and more powerful empires, conquer these colonies and increase their power. To

model these competition between empires, at the first, chance to seize the empire is proportional to the strength

of the empire, taking the total costs of empire into account, will be calculate as follows:

The total normalized cost of the empire, will be determined by the total cost of the empire.

. . max . .n i nN T C T C T C

(20)

Where T. Cn is the total empire cost and N. T. Cn is the total empire power.

Probability (power) takeover of colonies by the Empire is calculated as follows.

1

. .

. .

npn Nimp

ii

N T CP

N T C

(21)


M. Karami et al

310

Fig. 5 Foreign competition

4.7 Fall of The Weak Empires

During the imperialist competition, weak empires eventually fall into the hands of the stronger colonial

empires. In the proposed algorithm, when an empire considered to be removed that has lost all of its colonies.

4.8 .Colonial Competitive Algorithm Steps

1- Initial countries generation.

2- Choosing the best countries as the imperialist.

3- Allocation of the other countries to colonizers as colonized countries.

4- Move the colonials toward the imperialist countries (Matching Policy).

5- Apply revolution operator.

6- If there is a colony in an empire which would have cost less than colonial, change place of colonial and

imperialist.

7- Calculate total cost of an empire ( considering the imperialist and their colonial cost)

8- Choose one (or more) colonies of the weakest empires and give it to an empire that has the highest take-over

chance.

9- Remove weak empires.( empires with no colonial).

10- If only one empire exists, stop, else, go to the 4th step.

5. Simulation Result

To solve the problem, the optimization algorithm been implemented on the 33- bus and 69 bus standard

systems. In first stage, locating of a type-1 DG in a 33bus and 69 bus system has been simulated and the results

compared to the other sources. At the second stage, simultaneous locating of DG and capacitor has been

performed.in this study, DGs are 1.2 MW size and a 150 kvar capacitor bank used.

5.1 The 33 Bus System

The line and load data are obtained from [19]. The system voltage is 6/12 kv. Total system active and reactive

loads are MW 715/3 and 3/2 MVar respectively. 33-bus system is schematically shown in Fig. 5.


M. Karami et al

311

Fig. 6 The 33 bus system schematic

Table 1: Weighted index values are considered for the objective functions

Power loss Voltage Profile improvement Stability index

1 0.6 0.4

Table 2. The results of multi-objective optimization of DG and capacitor banks installed on the 33 bus system

DG location DG value in Kw Power factor Capacitor

Location

Capacitor value

13

24

30

817

1142

1168

0.896

0.919

0.768

2

26

750

150

Table 3. Comparison of the results of the system before and after DG and capacitor banks installation in the 33

bus system

After DG installation Before DG and Capacitor

installation

33 bus system

Bus 22 – 0.9944 Bus 18 – 0.9038 Lowest voltage in pu

Bus 30 – 1.006 Bus 2 – 0.9970 Highest voltage in pu

12.34 kW 210.98 kW Power loss in kw

10.34 KVAR 143.12 KVAR Power loss in KVAR

Bus 22 – 0.9776 Bus 18 – 0.6667 Minimum stability index (pu)

Fig. 7 33 bus voltage profile before and after a DG installation and capacitor banks

0.9

0.92

0.94

0.96

0.98

1

1.02

1 4 7 10 13 16 19 22 25 28 31

Vo

ltag

e in

pu

bus number

Default

With3 DG& Cap


M. Karami et al

312

Fig. 8 Network voltage stability index charts for the 33 bus system before and after the installation of a DG and

capacitor banks

Table 4. Comparison of a type-1 DG installation in 33 bus system with other algorithms

Proposed algorithm GA [3] ABC[4] Analytical[1] Optimization Algorithm

61 61 61 61 Optimized location

2590 2380 2400 2490 Optimized value

1 1 1 1 Optimized power factor

48.47 44.83 48.19 47.33 Value of power loss decrease

5.2 The 69 Bus System

The line and load data are obtained from [18]. The system voltage is 6/12 kv. Total system active and reactive

loads are MW 8.3 and 69.2 MVar respectively.

Fig. 9 - The 33-bus system schematic

Table 5. The results of multi-objective optimization of DG and capacitor banks installed on the 33 bus system

DG location DG value in Kw Power factor Capacitor Location Capacitor value

11

21

61

528.5

344

1673

0.977

0.875

0.848

4

12

64

750

300

150

Table 6. Comparison of the results of the system before and after DG and capacitor banks installation in the 33

bus system

After DG installation Before DG and Capacitor installation 33 bus system

Bus 50 – 0.9943 Bus 65 – 0.9092 Lowest voltage in pu

Bus 2 – 1.00 Bus 2 – 1.00 Highest voltage in pu

3.97 kW 224.91 kW Power loss in kw

6.59 kVAR 102.1 kVAR Power loss in kVAR

Bus 12 – 0.9923 Bus 65 – 0.6833 Minimum stability index (pu)

0.6

0.7

0.8

0.9

1

1.1

1 4 7 1013161922252831St

abili

ty in

de

x in

pu

bus number

Default

With 3 DG &Cap


M. Karami et al

313

Table 7. Summary of the power quality factors improvement

System Active power loss

reduction

Lowest bus voltage Lowest voltage

stability

33 bus 94.1 0.9038 to 0.9944 0.6667 to 0.9776

69 bus 98.2 0.9092 to 0.9944 0.6823 to 0.9923

Table 8. Comparison of a type-1 DG installation in 69 bus system with other algorithms

Proposed

algorithm

GA [3] ABC[4] Analytical[1] Optimization

Algorithm

61 61 61 61 Optimized

location

1872 1839 1900 1810 Optimized value

1 1 1 1 Optimized

power factor

63.2 62.91 62.97 62.86 Value of power

loss decrease

6. Conclusion

DG and shunt capacitors have a large impact on distribution system performance. It can be seen that after the

optimal installation of these two elements, the system reactive power loss decreased of about 94% at 33 bus

systems and has been reduced by approximately 98% at 69 bus system. Figures 4 and 5 and Figures 7 and8 in

33 bus 69 bus system shows that the increase in stability and improve in the voltage profile.

Conclusion

In this paper, the imperial competitive algorithm for the problem of locating and locating the shunt capacitor

banks and distributed generation sources were employed. The problem as modeled as a multi-objective problem

that aims to reduce the real power loss, improving voltage stability and improves the voltage profiles. The

method was implemented on the standard 33 bus and 69 bus systems. The obtained results shows, improved

power quality parameters and the high efficiency of the algorithm in complex optimization problems. The high

speed, high performance and flexibility of the algorithm shows that this algorithm can be employed as an

optimal locating method for DGs in the distribution network.

Fig. 10 - The 69 bus network voltage profile before and after DG and capacitor bank installation

0.9

0.92

0.94

0.96

0.98

1

1.02

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Vo

ltag

e in

pu

bus number

Default

3 DG & Cap


M. Karami et al

314

Fig. 11 - The 69 bus network stability index before and after DG and capacitor bank installation

REFERENCES

[1] Ng .H. N, Salama .M. M. A, and Chikhani .A. Y, "Classification of capacitor allocation techniques," IEEE Transactions

on power Delivery, vol. 15, no. 1, pp. 387-392, 2000.

[2] Mendes .A, Franca .P.M, Lyra .C, Pissarra .C, and Cavellucci .C, "Capacitor placement in large-sized radial distribution

networks, " IEEE Proceedings-Generation, Transmission and Distribution , vol. 152 ,no. 4,pp. 495-502,2005.

[3] Brown .R. E," Modeling the reliability impact of distributed generation," IEEE Power Engineering Society Summer

Meeting , vol. 1, pp 442-446, 2002.

[4] Algorithm Fahad S. Abu-Mouti, and M. E. El-Hawary, "Optimal Distributed Generation Allocation and Sizing in

Distribution Systems via Artificial Bee Colony " IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 26, NO. 4,

OCTOBER 2011 E.

[5] Quoc Hung .D, Mithulananthan .N and Bansal. R. C, "Analytical Expressions for DG Allocation in Primary

Distribution Networks", IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 25, NO. 3, SEPTEMBER 2010

[6] Popovic .D. H, Greatbanks .J. A, Begovic .M, and Pregelj .A, "Placement of distributed generators and reclosers for

distribution network security and reliability," International Journal of Electrical Power & Energy Systems, vol. 27,no. 5-6,

pp. 398-408, 2005.

[7] Gandomkar .M, Vakilian .M, and Ehsan .M, "A Genetic-Based Tabu Search Algorithm for Optimal DG Allocation in

Distribution Networks," Electric Power Components and Systems, vol. 33, pp. 1351-1362, Dec. 2005.

[8] Moradi .M.H, Abedini .M,"A combination of genetic algorithm and particle swarm optimization for optimal DG

location and sizing in distribution systems", Electrical Power and Energy Systems 34 (2012) 66–74

[9] Falaghi .H and Haghifam .M. R," ACO Based algorithm for distributed generation sources allocation and sizing in

distribution systems," IEEE Lausanne Power Tech, pp. 555-560, 2007.

[10] Shukla .T. N, Singh. S. P, Srinivasarao. V, and Naik .K. B, "Optimal sizing of distributed generation placed on

radial distribution systems," Elect. Power Compon. Syst., vol. 38, no. 3, pp. 260–274, 2010

[11] Chiou .J, Chang. C. F, Su. C. T, "Capacitor Placement in Large-Scale Distribution Systems using Variable Scaling

Hybrid Differential Evolution," Electrical Power and Energy Systems ,Vol. 28, No. 10, pp. 739-745, 2006.

[12] Kennedy, J. and Eberhart, R., "Particle swarm optimization," IEEE International Conference on Neural Networks,

1995.

[13] M. Dlfanti, G. P. Granelli, P. Maranninio, "Optimal Capacitor Placement using Deterministic and Genetic

Algorithm," IEEE Trans. On Power Systems, PWRS-15; Vol. 15, No. 3, pp. 1041-1046,2000

[14] T. L. Huang, Y. T. Hsiao, C. H. Chang, J. A.Jiang, “Optimal placement of capacitors in distributionsystems using

an immune multi-objective algorithm,”International Journal of Electrical Power & Energy Systems, vol. 30, no. 3, pp. 184-

192, 2008.

[15] D. Das, "Optimal Placement of Capacitors in Radial Distribution System using a Fuzzy-GA Method,"

International Journal of Electrical Power & Energy Systems, Vol. 30, No. 6, pp. 361-367, 2008.

[16] Abdelsalam A. Eajal, , , and M. E. El-Hawary, , IEEEOptimal Capacitor Placement and Sizing inUnbalanced

Distribution Systems With HarmonicsConsideration Using Particle Swarm OptimizationIEEE TRANSACTIONS ON

POWER DELIVERY, VOL. 25, NO. 3, JULY 2010

[17] Esmaeilian H, Darijany O, Mohammadian M. Optimal placement and sizing of DGs and capacitors

simultaneously in radial distribution networks based on voltage stability security margin. TUBITAK 2013; in press.

0.9

0.92

0.94

0.96

0.98

1

1.02

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69

Vo

ltag

e in

pu

bus number

Default

3 DG & Cap


M. Karami et al

315

[18] M.Wang, J. Zhong, A Novel Method forDistributed Generation and Capacitor OptimalPlacement considering

Voltage Profiles, IEEE Power and Energy Society General Meeting, 2011

[19] Charkravorty M, Das D. Voltage stability analysis of radial distribution networks. Int J Electrcal Power Energy

Syst 2001;23(2):129–35.

[20] Atashpaz-Gargari. E, Lucas. C," Imperialist competitive algorithm: an algorithm for optimization inspired by

imperialistic competition". IEEE Congress on Evolutionary Computation, 2007, CEC 2007, 2007,pp. 4661–4667.

[21] Baran ME, Wu FF. Optimal Sizing of capacitor placed on radial distribution systems. IEEE Trans Power Deliv

1989;4(1):735–43.

simultaneous multi-objective locating and sizing of ... · pdf filea major share of losses ......

Documents