Electrical Power and Energy Systems 32 (2010) 849–856

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Optimal sizing and placement of distributed generation in a network system

Sudipta Ghosh *, S.P. Ghoshal, Saradindu GhoshDepartment of Electrical Engineering, National Institute of Technology, Durgapur 713209, India

a r t i c l e i n f o

Article history:Received 28 March 2009Received in revised form 22 December 2009Accepted 28 January 2010

Keywords:Distributed generation (DG)Newton Raphson (N-R)Objective function (OF)Weighting factor

0142-0615/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.ijepes.2010.01.029

* Corresponding author. Tel.: +91 98321 54472.E-mail address: sudiptarit@gmail.com (S. Ghosh).

a b s t r a c t

With ever-increasing demand of electricity consumption and increasing open access particularly inrestructured environment, transmission line congestion is quite frequent. For maximum benefit and mit-igation of congestion, proper sizing and position of distributed generators are ardently necessary. Thispaper presents a simple method for optimal sizing and optimal placement of generators. A simple con-ventional iterative search technique along with Newton Raphson method of load flow study is imple-mented on modified IEEE 6 bus, IEEE 14 bus and IEEE 30 bus systems. The objective is to lower downboth cost and loss very effectively. The paper also focuses on optimization of weighting factor, which bal-ances the cost and the loss factors and helps to build up desired objectives with maximum potentialbenefit.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Electric utilities are now seeking upcoming new technologies toprovide acceptable power quality and higher reliability to theircustomers in restructured environment. Non-conventional genera-tion is growing more rapidly around the world, for its low size, lowcost and less environmental impact with high potentiality [1–3].Investments in distributed generation (DG) enhance environmen-tal benefits particularly in combined heat and power applications.

A multitude event, such as, system efficiency, environmentalbenefits and transmission congestion management have createda new arena in electric power system. The key element of thisnew arena is to operate several DG units near load centers insteadof expanding central generation station. DG may come from a vari-ety of sources and technologies. DGs from renewable sources, likewind, solar and biomass are often called as ‘Green energy’. In addi-tion to this, DG includes micro-turbines, gas turbines, diesel en-gines, fuel cells, stirling engines and internal combustionreciprocating engines [4–6]. Now-a-days, wind energy has becomethe most competitive among all the renewable energy availablewith us [7]. DG refers to small sources ranging between 1 kWand 50 MW electrical power generations, which are normallyplaced close to consumption centers. So, DG means a generationunit, which is connected to the distribution network rather thanthe high voltage transmission network.

DG renders a group of advantages, such as, economical, environ-mental and technical. The economical advantages are reduction oftransmission and distribution cost, electricity price and saving of

ll rights reserved.

fuel. Environmental advantages entail reductions of sound pollu-tion and emission of green house gases. Technical advantages cov-er wide varieties of benefit, like, line loss reduction, peak shaving,increased system voltage profile and hence increased power qual-ity and relieved transmission and distribution congestion as wellas grid reinforcement. It can also provide the stand-alone remoteapplications with the required power. So, optimal placement ofDGs and optimal sizing attract active research interests. Severalresearchers have worked in this area [8–14]. DGs are placed atoptimal locations to reduce only losses [8]. Some researchers pre-sented some power flow algorithms to find the optimal size of DGat each load bus [9,10]. Wang and Nehrir have shown analyticalapproaches for optimal placement of DG in terms of loss [11]. Chir-adeja has quantified the benefit of reduced line loss in radial distri-bution feeder with concentrated load [12]. Further, manyresearchers have used evolutionary computational methods forfinding the optimal DG placement [15–20]. Mithulananthan hasused GA for placement of DG to reduce the losses [16]. Celli andGhiani have used a multiobjective evolutionary algorithm for thesizing and placement of DG [19]. Nara et.al., have used Tabu searchalgorithm to find optimal placement of distributed generator [20].

This paper presents a simple search approach determining foroptimal size and optimal placement of DG using N-R method ofload flow study. Both optimal DG size and optimal bus locationare determined to obtain the best objective. The multiobjectiveoptimization covers optimization of both cost and loss simulta-neously. The cost coefficients of DG are taken from Ref. [21]. TheIEEE 6 bus and IEEE 30 bus data are obtained from Refs. [9] and[22] respectively. Ref. [23] is used to obtain IEEE 14 bus systemdata. Further, using DGs at various buses the systems are modifiedand employed for load flow study.

850 S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856

2. Methodology

As mentioned, this paper focuses on a simple conventional N-Rmethod to solve a system of non-linear algebraic equation of theform f (x) = 0. Here, N-R method is applied to solve power flowequation in polar form. Bus data have been changed to incorporatethe effect of DG. When the DG is connected to a bus, correspondingbus is assumed to be a P � V bus. Further, it is assumed that thereactive power of DG is 20% of the active power generated. N-Rmethod is available in standard books [23,24].

2.1. Injected power

The complex injected power at bus ‘i’ is given as:

S�i ¼ V�iXn

k¼1

YikVk ð1Þ

0 100 200 300 400 50

100

200

300

400

500

600

700

Weigh

O F

Increasing

Fig. 1. Variation of OF with weig

0 100 200 300 400 50

2000

4000

6000

8000

10000

12000

14000

Weigh

O F

Increasing

Fig. 2. Variation of OF with weig

The unknown variables updated after mth iteration are givenas:

Ddðmþ1Þi ¼ DdðmÞi þ Ddi ð2Þ

jVijðmþ1Þ ¼ jVijðmÞ þ DjVij ð3Þ

2.2. Line power flow

Power flow from ith bus to jth bus through the line connectedbetween these buses is given by

Sij ¼ ViI�ij ¼ Vi

Vi � Vj

Zijþ ViYij0

� ��ð4Þ

00 600 700 800 900 1000ting factor

DG size

hting factor for IEEE 6 bus.

00 600 700 800 900 1000ting factor

DG size

hting factor for IEEE 14 bus .

S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856 851

Similarly, the power flow from the jth bus to ith bus is givenas:

Sji ¼ VjI�ji ¼ Vj

Vj � Vi

Zjiþ VjYji0

� ��ð5Þ

2.3. Line losses

The total line losses for all the buses connected to the system isthe sum total of all power flows given by:

Pi ¼Xbus no:

i¼1

Xbus no:

j¼1

ðSij þ SjiÞ

¼Xbus no:

i¼1

Xbus no:

j¼1

fðPij þ jQ ijÞ þ ðPji þ jQjiÞg ð6Þ

0 100 200 300 400 50

2000

4000

6000

8000

10000

12000

14000

16000

18000

Weig

O F

Increasi

Fig. 3. Variation of OF with weig

2 3100

200

300

400

500

600

700

800

Bus

O F

Incresing DG

Fig. 4. Variation of OF with variation of position of DG

2.4. Objective function (OF)

The main objective of the power flow solution has been directedtowards optimization of OF governed by the relation:

OF ¼ CðPDGÞ þW � E ð7Þ

where, C (PDG) = total cost of DG as a function of DG rating, PDG,W = weighting factor, E = total active loss and C (PDG) = aDG + bDG

PDG + cDG (PDG)2 respectively, aDG, bDG and cDG are the quadratic costcoefficient of specified DG.

3. Results and discussion

3.1. Calculation of OF

Eqs. (1)–(6) are solved to obtain total line losses of a system andthus total active and reactive power loss may be obtained sepa-

00 600 700 800 900 1000

hting factor

ng DG size

hting factor for IEEE 30 bus.

4 5 66number

size

s having different ratings for IEEE 6 bus system.

852 S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856

rately. In this work, only the active power loss component is con-sidered. Fig. 1 shows the variation of OF as a function of weightingfactor for different ratings of DG in the range of 1–20 MW for mod-ified IEEE 6 bus system. It may be seen from the figure that theoptimum value of weighting factor is close to 500 for any rangeof DG. Similarly, the weighting factor is 150 for both modified IEEE14 bus and IEEE 30 bus systems, as depicted in Figs. 2 and 3 respec-tively. Thus, weighting factor values of 500 and 150 are consideredfor optimization search in modified IEEE 6 bus, 14 bus and 30 busrespectively. In the whole work, bus 1 is considered as a slack bus.

3.2. Optimum location of DG

Fig. 4 indicates the variation of OF as a function of bus place-ment of DG for modified IEEE 6 bus system. It is seen that a mini-mum value of OF is obtained when DG (irrespective of its rating) isplaced at bus no. 3. It is clear from the figure that the magnitude of

2 3 4 5 6 71900

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

Bus

O F

Fig. 5. Variation of OF with variation of position of DG

0 1 2 3 4 5 6 7 8 9 10 11 12 13 142400

2600

2800

3000

3200

3400

3600

Bus

O F

Fig. 6. Variation of OF with variation of position of DG

OF increases with the increase of DG rating with DG placed at high-er bus number. Similarly, optimum location of DG is obtained forIEEE 14 bus and 30 bus systems from Figs. 5 and 6 respectively.It may be seen that the OFs are minimum when the DG is placedat bus numbers 8 and 11 (which are low voltage buses) for IEEE14 bus and IEEE 30 bus systems respectively. Although it is appar-ent from Fig. 5 that placement of DG at bus number 3 gives lowervalue of OF than that at bus no 8, but bus number 3 is not consid-ered since it is a high voltage bus. Similarly, for IEEE 30 bus systemthe lower values of OF appears with bus numbers 5, 7 and 8, butthose buses are again high voltage buses. Therefore, bus number11, which is a low voltage bus, is taken into consideration.

3.3. Optimum DG rating

Fig. 7 represents variation of objective function with the size ofDG. A 6 MW DG seems to be the optimum size for IEEE 6 bus sys-

8 9 10 11 12 13 1414 number

increasing DGsize

s having different ratings for IEEE 14 bus system.

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 3030number

Increasing DG size

s having different ratings for IEEE 30 bus system.

S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856 853

tem. Similarly, from Figs. 8 and 9 and 16 MW and 35 MW respec-tively are the optimum DG sizes for IEEE 14 bus and IEEE 30 bussystems respectively.

3.4. Comparison of the results of the proposed method with those ofPower World Simulator software

The comparison of the results obtained by the proposed methodand those obtained by the Power World Simulator software (Sim-ulator 11.0 Glover Sarma Education Edition) is presented in Table1. The results of the proposed method seem to be better than thoseof the Power World Simulator. The last column of Table 1 indicatesthe superiority of the proposed method in percentage, as given by:

P1 � P2

P1� 100%

0 2 4 6170

180

190

200

210

220

230

240

250

DG size

O F

Fig. 7. Variation of OF as a function o

0 4 8 12 161995

2000

2005

2010

2015

2020

2025

2030

DG siz

O F

Fig. 8. Variation of OF as a function o

where P1 = value of OF using Power World Simulator, P2 = value ofOF using proposed method.

3.5. Variation of bus voltage with DG size

Fig. 10 shows the effect of change in DG size at bus number 3 onthe voltage magnitudes of other buses in IEEE 6 bus system. Here,effects on bus numbers 2, 4 and 6 are taken into considerationsince they are essentially load buses. As may be seen from the fig-ure, the bus voltages are increasing with increase in DG size for busnumbers 2 and 4 and reach to the highest values, corresponding toDG size 11 MW and 14 MW respectively. The bus voltages fallafterwards with increasing DG size. In bus number 6 of coursethe bus voltages are increasing continuously, throughout the con-sidered range of DG. As stated in Section 3.3, the optimized size of

8 10 12 14

(MW)

f DG size for IEEE 6 bus system.

20 24 28 32 36 4040

e (MW)

f DG size for IEEE 14 bus system.

15 20 25 30 35 40 45 50502565

2570

2575

2580

2585

2590

DG size (MW)

O F

Fig. 9. Variation of OF as a function of DG size for IEEE 30 bus system.

Table 1Comparison results of proposed method with Power World Simulator.

IEEE modifiedsystems

Placement of DG(bus no.)

Size(MW)

Active loss (MW) OF

Power WorldSimulator

Proposedmethod

Power WorldSimulator (P1)

Proposedmethod (P2)

% Superiority of the proposedmethod

6 Bus 3 6 0.17 0.17 175.00 175.00 014 Bus 8 16 11.72 11.70 1998.00 1995.00 0.1530 Bus 11 35 13.76 13.61 2589.00 2566.50 0.87

0 2 4 6 8 10 12 14 16 18 200.9905

0.991

0.9915

0.992

0.9925

0.993

0.9935

0.994

DG size (MW)

Vol

tage

(p.

u)

bus no 2

bus no 4

bus no 6

Fig. 10. Voltage profile of IEEE 6 bus system.

854 S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856

DG is 6 MW as far as OF (i.e. both cost and loss) is considered. Thevariation of voltages from maximum voltage level for DG size be-yond 6 MW is very small of the order of 0.00015 and 0.0002 p.u.respectively, for bus number 2 and 4. Therefore, optimum DG sizemay be chosen as 6 MW. The bus voltages of these representativebuses have increased after the optimal placement of the optimalDG.

Similar conclusions may be drawn from Figs. 11 and 12 with re-spect to IEEE 14 bus and 30 bus systems respectively. In these twosystems the voltages of few representative load buses, where bus

voltages are low have increased after the optimal placement ofthe optimal DG.

4. Conclusions

From the above studies on modified IEEE 6, 14 and 30 bus sys-tems, the major contribution in the present work are:

(1) The optimized value of weighting factor is computed.

0 20 40 60 80 100 120 140 160 180 2000.975

0.98

0.985

0.99

0.995

1

1.005

1.01

1.015

DG size (MW)

Vol

tage

(p.

u)

busno 7busno 26busno 29busno 30

Fig. 12. Voltage profile of IEEE 30 bus system.

0 20 40 60 80 100 120 140 160 180 200

1.02

1.025

1.03

1.035

1.04

1.045

1.05

DG size (MW)

Vol

tage

(p.

u)

bus no 4bus no 5bus no 14

Fig. 11. Voltage profile of IEEE 14 bus system.

S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856 855

(2) The optimum locations and optimal sizes of DG are obtained.The optimum DG location obtained by the proposed methodvalidates the results of observation of Wang C. and NehrirM.H. [11] for IEEE 6 bus system.

(3) Due to the placement of optimal DG size at its optimumlocation it is observed that the voltages of load buses areimproved and the losses are reduced substantially.

(4) The OF values (that is, combination of cost and line losses)computed with the proposed method proved to be betterthan the simulation results obtained with Power World Sim-ulator software.

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