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