Download Optimal sizing and placement of distributed generation in a network

Electrical Power and Energy Systems 32 (2010) 849–856
Contents lists available at ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
Optimal sizing and placement of distributed generation in a network system
Sudipta Ghosh *, S.P. Ghoshal, Saradindu Ghosh
Department 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 2009
Received in revised form 22 December 2009
Accepted 28 January 2010
Keywords:
Distributed generation (DG)
Newton Raphson (N-R)
Objective function (OF)
Weighting factor
a b s t r a c t
With ever-increasing demand of electricity consumption and increasing open access particularly in
restructured environment, transmission line congestion is quite frequent. For maximum benefit and mitigation of congestion, proper sizing and position of distributed generators are ardently necessary. This
paper presents a simple method for optimal sizing and optimal placement of generators. A simple conventional iterative search technique along with Newton Raphson method of load flow study is implemented on modified IEEE 6 bus, IEEE 14 bus and IEEE 30 bus systems. The objective is to lower down
both cost and loss very effectively. The paper also focuses on optimization of weighting factor, which balances the cost and the loss factors and helps to build up desired objectives with maximum potential
benefit.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Electric utilities are now seeking upcoming new technologies to
provide acceptable power quality and higher reliability to their
customers in restructured environment. Non-conventional generation is growing more rapidly around the world, for its low size, low
cost and less environmental impact with high potentiality [1–3].
Investments in distributed generation (DG) enhance environmental benefits particularly in combined heat and power applications.
A multitude event, such as, system efficiency, environmental
benefits and transmission congestion management have created
a new arena in electric power system. The key element of this
new arena is to operate several DG units near load centers instead
of expanding central generation station. DG may come from a variety of sources and technologies. DGs from renewable sources, like
wind, solar and biomass are often called as ‘Green energy’. In addition to this, DG includes micro-turbines, gas turbines, diesel engines, fuel cells, stirling engines and internal combustion
reciprocating engines [4–6]. Now-a-days, wind energy has become
the most competitive among all the renewable energy available
with us [7]. DG refers to small sources ranging between 1 kW
and 50 MW electrical power generations, which are normally
placed close to consumption centers. So, DG means a generation
unit, which is connected to the distribution network rather than
the high voltage transmission network.
DG renders a group of advantages, such as, economical, environmental and technical. The economical advantages are reduction of
transmission and distribution cost, electricity price and saving of
* Corresponding author. Tel.: +91 98321 54472.
E-mail address: [email protected] (S. Ghosh).
0142-0615/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.ijepes.2010.01.029
fuel. Environmental advantages entail reductions of sound pollution and emission of green house gases. Technical advantages cover wide varieties of benefit, like, line loss reduction, peak shaving,
increased system voltage profile and hence increased power quality and relieved transmission and distribution congestion as well
as grid reinforcement. It can also provide the stand-alone remote
applications with the required power. So, optimal placement of
DGs and optimal sizing attract active research interests. Several
researchers have worked in this area [8–14]. DGs are placed at
optimal locations to reduce only losses [8]. Some researchers presented some power flow algorithms to find the optimal size of DG
at each load bus [9,10]. Wang and Nehrir have shown analytical
approaches for optimal placement of DG in terms of loss [11]. Chiradeja has quantified the benefit of reduced line loss in radial distribution feeder with concentrated load [12]. Further, many
researchers have used evolutionary computational methods for
finding the optimal DG placement [15–20]. Mithulananthan has
used GA for placement of DG to reduce the losses [16]. Celli and
Ghiani have used a multiobjective evolutionary algorithm for the
sizing and placement of DG [19]. Nara et.al., have used Tabu search
algorithm to find optimal placement of distributed generator [20].
This paper presents a simple search approach determining for
optimal size and optimal placement of DG using N-R method of
load flow study. Both optimal DG size and optimal bus location
are determined to obtain the best objective. The multiobjective
optimization covers optimization of both cost and loss simultaneously. The cost coefficients of DG are taken from Ref. [21]. The
IEEE 6 bus and IEEE 30 bus data are obtained from Refs. [9] and
[22] respectively. Ref. [23] is used to obtain IEEE 14 bus system
data. Further, using DGs at various buses the systems are modified
and employed for load flow study.
850
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
The unknown variables updated after mth iteration are given
2. Methodology
as:
As mentioned, this paper focuses on a simple conventional N-R
method to solve a system of non-linear algebraic equation of the
form f (x) = 0. Here, N-R method is applied to solve power flow
equation in polar form. Bus data have been changed to incorporate
the effect of DG. When the DG is connected to a bus, corresponding
bus is assumed to be a P V bus. Further, it is assumed that the
reactive power of DG is 20% of the active power generated. N-R
method is available in standard books [23,24].
Ddiðmþ1Þ ¼ DdðmÞ
þ Ddi
i
ð2Þ
jV i jðmþ1Þ ¼ jV i jðmÞ þ DjV i j
ð3Þ
2.1. Injected power
Power flow from ith bus to jth bus through the line connected
between these buses is given by
2.2. Line power flow
The complex injected power at bus ‘i’ is given as:
Sij ¼ V i Iij ¼ V i
Y ik V k
ð1Þ
Vi Vj
þ V i Y ij0
Z ij
ð4Þ
k¼1
700
600
500
OF
Increasing DG size
400
300
200
100
0
0
100
200
300
400
500
600
700
800
900
1000
Weighting factor
Fig. 1. Variation of OF with weighting factor for IEEE 6 bus.
14000
12000
10000
Increasing DG size
8000
OF
Si ¼ V i
n
X
6000
4000
2000
0
0
100
200
300
400
500
600
Weighting factor
700
800
Fig. 2. Variation of OF with weighting factor for IEEE 14 bus .
900
1000
851
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
Similarly, the power flow from the jth bus to ith bus is given
2.4. Objective function (OF)
as:
Sji ¼
V j Iji
Vj Vi
¼ Vj
þ V j Y ji0
Z ji
ð5Þ
OF ¼ CðP DG Þ þ W E
2.3. Line losses
The total line losses for all the buses connected to the system is
the sum total of all power flows given by:
bus
no: bus
no:
X
X
¼
i¼1
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 cost
coefficient of specified DG.
3. Results and discussion
ðSij þ Sji Þ
j¼1
3.1. Calculation of OF
fðPij þ jQ ij Þ þ ðP ji þ jQ ji Þg
ð6Þ
j¼1
Eqs. (1)–(6) are solved to obtain total line losses of a system and
thus total active and reactive power loss may be obtained sepa-
18000
16000
14000
12000
Increasing DG size
10000
OF
i¼1
bus
no: bus
no:
X
X
ð7Þ
8000
6000
4000
2000
0
0
100
200
300
400
500
600
700
800
900
1000
Weighting factor
Fig. 3. Variation of OF with weighting factor for IEEE 30 bus.
800
700
Incresing DG size
600
500
OF
Pi ¼
The main objective of the power flow solution has been directed
towards optimization of OF governed by the relation:
400
300
200
100
2
3
4
5
6
Bus number
Fig. 4. Variation of OF with variation of position of DGs 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 considered. Fig. 1 shows the variation of OF as a function of weighting
factor for different ratings of DG in the range of 1–20 MW for modified IEEE 6 bus system. It may be seen from the figure that the
optimum value of weighting factor is close to 500 for any range
of DG. Similarly, the weighting factor is 150 for both modified IEEE
14 bus and IEEE 30 bus systems, as depicted in Figs. 2 and 3 respectively. Thus, weighting factor values of 500 and 150 are considered
for optimization search in modified IEEE 6 bus, 14 bus and 30 bus
respectively. 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 placement of DG for modified IEEE 6 bus system. It is seen that a minimum value of OF is obtained when DG (irrespective of its rating) is
placed at bus no. 3. It is clear from the figure that the magnitude of
OF increases with the increase of DG rating with DG placed at higher bus number. Similarly, optimum location of DG is obtained for
IEEE 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 placed
at bus numbers 8 and 11 (which are low voltage buses) for IEEE
14 bus and IEEE 30 bus systems respectively. Although it is apparent from Fig. 5 that placement of DG at bus number 3 gives lower
value of OF than that at bus no 8, but bus number 3 is not considered since it is a high voltage bus. Similarly, for IEEE 30 bus system
the lower values of OF appears with bus numbers 5, 7 and 8, but
those buses are again high voltage buses. Therefore, bus number
11, 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 of
DG. A 6 MW DG seems to be the optimum size for IEEE 6 bus sys-
2900
2800
increasing DG
size
2700
2600
OF
2500
2400
2300
2200
2100
2000
1900
2
3
4
5
6
7
8
9
Bus number
10
11
12
13
14
Fig. 5. Variation of OF with variation of position of DGs having different ratings for IEEE 14 bus system.
3600
3400
3200
OF
Increasing DG size
3000
2800
2600
2400
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Bus number
Fig. 6. Variation of OF with variation of position of DGs having different ratings for IEEE 30 bus system.
853
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
tem. Similarly, from Figs. 8 and 9 and 16 MW and 35 MW respectively are the optimum DG sizes for IEEE 14 bus and IEEE 30 bus
systems respectively.
where P 1 = value of OF using Power World Simulator, P2 = value of
OF using proposed method.
3.4. Comparison of the results of the proposed method with those of
Power World Simulator software
3.5. Variation of bus voltage with DG size
The comparison of the results obtained by the proposed method
and those obtained by the Power World Simulator software (Simulator 11.0 Glover Sarma Education Edition) is presented in Table
1. The results of the proposed method seem to be better than those
of the Power World Simulator. The last column of Table 1 indicates
the superiority of the proposed method in percentage, as given by:
P1 P2
100%
P1
Fig. 10 shows the effect of change in DG size at bus number 3 on
the voltage magnitudes of other buses in IEEE 6 bus system. Here,
effects on bus numbers 2, 4 and 6 are taken into consideration
since they are essentially load buses. As may be seen from the figure, the bus voltages are increasing with increase in DG size for bus
numbers 2 and 4 and reach to the highest values, corresponding to
DG size 11 MW and 14 MW respectively. The bus voltages fall
afterwards with increasing DG size. In bus number 6 of course
the bus voltages are increasing continuously, throughout the considered range of DG. As stated in Section 3.3, the optimized size of
250
240
230
OF
220
210
200
190
180
170
0
2
4
6
8
10
12
14
DG size (MW)
Fig. 7. Variation of OF as a function of DG size for IEEE 6 bus system.
2030
2025
2020
OF
2015
2010
2005
2000
1995
0
4
8
12
16
20
24
28
32
DG size (MW)
Fig. 8. Variation of OF as a function of DG size for IEEE 14 bus system.
36
40
854
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
2590
2585
OF
2580
2575
2570
2565
15
20
25
30
35
40
45
50
DG size (MW)
Fig. 9. Variation of OF as a function of DG size for IEEE 30 bus system.
Table 1
Comparison results of proposed method with Power World Simulator.
IEEE modified
systems
Placement of DG
(bus no.)
Size
(MW)
Active loss (MW)
Power World
Simulator
Proposed
method
Power World
Simulator (P1)
OF
Proposed
method (P2)
% Superiority of the proposed
method
6 Bus
14 Bus
30 Bus
3
8
11
6
16
35
0.17
11.72
13.76
0.17
11.70
13.61
175.00
1998.00
2589.00
175.00
1995.00
2566.50
0
0.15
0.87
0.994
bus no 2
bus no 4
0.9935
bus no 6
Voltage (p.u)
0.993
0.9925
0.992
0.9915
0.991
0.9905
0
2
4
6
8
10
12
DG size (MW)
14
16
18
20
Fig. 10. Voltage profile of IEEE 6 bus system.
DG is 6 MW as far as OF (i.e. both cost and loss) is considered. The
variation of voltages from maximum voltage level for DG size beyond 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 size
may be chosen as 6 MW. The bus voltages of these representative
buses have increased after the optimal placement of the optimal
DG.
Similar conclusions may be drawn from Figs. 11 and 12 with respect to IEEE 14 bus and 30 bus systems respectively. In these two
systems the voltages of few representative load buses, where bus
voltages are low have increased after the optimal placement of
the optimal DG.
4. Conclusions
From the above studies on modified IEEE 6, 14 and 30 bus systems, the major contribution in the present work are:
(1) The optimized value of weighting factor is computed.
855
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
1.05
bus no 4
bus no 5
bus no 14
1.045
Voltage (p.u)
1.04
1.035
1.03
1.025
1.02
0
20
40
60
80
100
120
140
160
180
200
DG size (MW)
Fig. 11. Voltage profile of IEEE 14 bus system.
1.015
busno 7
busno 26
busno 29
busno 30
1.01
Voltage (p.u)
1.005
1
0.995
0.99
0.985
0.98
0.975
0
20
40
60
80
100
120
140
160
180
200
DG size (MW)
Fig. 12. Voltage profile of IEEE 30 bus system.
(2) The optimum locations and optimal sizes of DG are obtained.
The optimum DG location obtained by the proposed method
validates the results of observation of Wang C. and Nehrir
M.H. [11] for IEEE 6 bus system.
(3) Due to the placement of optimal DG size at its optimum
location it is observed that the voltages of load buses are
improved 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 better
than the simulation results obtained with Power World Simulator software.
References
[1] Puttgen HB, Macgregor PR, Lambert FC. Distributed generation: semantic hype
or the dawn of a new era? IEEE Power Energy Mag 2003(January/
February):22–9.
[2] Martin G. Renewable energy gets the green light in Chicago. IEEE Power Energy
Mag 2003;22(November/December):34–9.
[3] Sonderegger RC, Henderson D, Bubb S, Steury J. Distributed asset insight. IEEE
Power Energy Mag 2004(May/June):32–9.
[4] Rahman S. Green power: what is it and where can we find it? IEEE Power
Energy Mag 2003(January/February):30–7.
[5] Kishinevsky Y, Zelingher S. Coming clean with fuel cells. IEEE Power Energy
Mag 2003(November/December):20–5.
[6] Andrews CJ, Weiner SA. Visions of a hydrogen future. IEEE Power Energy Mag
2004(March/April):26–34.
[7] Slootweg JG, Kling WL. Is the answer blowing in the wind? IEEE Power Energy
Mag 2003(November/December):26–33.
[8] Griffin T, Tomsovic K, Secrest D, Law A. Placement of dispersed generation
systems for reduced losses. In: Proceedings 33rd annual Hawaii international
conference system sciences, Maui, HI; 2000. p. 1446–54.
[9] Rau NS, Wan YH. Optimum location of resources in distributed planning. IEEE
Trans Power Syst 1994;9:2014–20.
[10] Kim JO, Nam SW, Park SK, Singh C. Dispersed generation planning using
improved Hereford ranch algorithm. Electr Power Syst Res 1998;47(11).
[11] Wang C, Nehrir M Hashem. Analytical approaches for optimal placement of
distributed generation sources in power systems. IEEE Trans Power Syst
2004;19(4):2068–76.
[12] Chiradeja P. Benefit of distributed generation: a line loss reduction analysis.
IEEE/PES transmission and distribution conference & exhibition: Asia and
Pacific, China Dalian; 2005. p. 1–5.
856
S. Ghosh et al. / Electrical Power and Energy Systems 32 (2010) 849–856
[13] Singh RK, Goswami SK. Optimum allocation of distributed generations based
on nodal pricing for profit, loss reduction, and voltage improvement including
voltage rise issue. Int J Electr Power Energy Syst 2010;32(6):637–44.
[14] Frías P, Gómez T, Cossent R, Rivier J. Improvements in current European
network regulation to facilitate the integration of distributed generation. Int J
Electr Power Energy Syst 2009;31(9):445–51.
[15] Niknam T, Ranjbar AM, Sirani AR, Mozafari B, Ostadi A. Optimal operation of
distribution system with regard to distributed generation: a comparison of
evolutionary methods. IEEE Conf IAS 2005;22:2690–6.
[16] Mithulananthan N, Oo Than, Phu Le Van. Distributed generator placement in
power distribution system using genetic algorithm to reduce losses.
Thammasat Int J Sci Technol 2004;9(3):55–62.
[17] Keane A, O’Malley M. Optimal allocation of embedded generation on
distribution networks. IEEE Trans Power Syst 2005;20(3):1640–6.
[18] Kim Kyu-Ho, Lee Yu-Jeong, Rhee Sang-Bong, Lee Sang-Kuen, You Seok-Ku.
Dispersed generator placement using fuzzy-GA in distribution system. IEEE
Power Eng Soc Summer Meet 2002:1148–53.
[19] Celli G, Ghiani E, Mocci S, Pilo F. A multiobjective evolutionary algorithm for
the sizing and siting of distributed generation. IEEE Trans Power Syst
2005;20(2):750–7.
[20] Nara K, Hayashi Y, Ikeda K, Ashizawa T. Application of tabu search to optimal
placement of distributed generators. IEEE PES Winter Meet 2001:918–23.
[21] Gautam Durga, Mithlananthan Nadarajah. Optimal DG placement in
deregulated electricity market. Electric Power Syst Res 2007;77:1627–36.
[22] Yokoyama R, Bae SH, Morita T, Sasaki H. Multiobjective optimal generation
dispatch based on probability security criteria. IEEE Trans Power Syst
1988;3:317–24.
[23] Pai MA. Computer techniques in power system analysis. New Delhi: Tata
McGraw-Hill Publishing Company Limited; 2006.
[24] Saadat Hadi. Power system analysis. New Delhi: Tata McGraw-Hill Publishing
Company Limited; 2006.