Research Journal of Applied Sciences, Engineering and Technology 4(19): 3610-3617, 2012
ISSN: 2040-7467
© Maxwell Scientific Organization, 2012
Submitted: February 02, 2012
Accepted: March 01, 2012
Published: October 01, 2012
Optimal Multi-type DGs Placement in Primary Distribution System by NSGA-II
K. Buayai
Electrical Engineering Department, Engineering and Architecture Faculty, The Rajamunagala
University of Technology Isan, Suranarai Rd, Nakronratchasima 30000, Thailand
Abstract: The study proposes a multiobjective optimal placement of multi-type DG for enhancement of
primary distribution system performance. A Pareto-based non-dominated sorting genetic algorithm II (NSGAII) is proposed to determine locations and sizes of specified number of Distributed Generator units (DG) within
the primary distribution system. Three objective functions are considered as the indexes of the system
performance: average Load Voltage Deviation (LVD) minimization of the system real power loss and
minimization of the annualized investment costs of DG. A fuzzy decision making analysis is used to obtain the
final trade off optimal solution. The proposed methodology is tested on modified IEEE 33-bus radial system.
Test results indicate that NSGA-II is a viable planning tool for practical DG placement and useful contribution
of DG in improving the steady state system performance of the distribution system by the optimal allocation,
setting and sizing multi-type DG.
Keywords: Distributed Generation (DG), Load Voltage Deviation (LVD), multi-objective optimization, nondominate sorting genetic algorithm II (NSGA-II)
INTRODUCTION
Distributed Generators (DG), based on renewable
energy technologies are becoming popular as they address
climate change and energy security issues to some extent.
Renewable energy based DGs do not contribute to GHG
emission and also diversity of sources also increases due
to different renewable energy options that address energy
security concerns. Apart from climate change and energy
security concerns, there are other driving forces for
increasing penetration of DG in distribution system
(Student Member and Member,). There are a number of
technical benefits that the DG can bring such as better
voltage profile, loss reduction and reliability
improvement.
The share of DGs in primary distribution systems has
been fast increasing in the last few years. Studies have
indicated that inappropriate selection of the location and
size of DG may lead to greater system losses than losses
without DG (Mithulananthan et al., 2004; Griffin et al.,
2000). By optimum allocation, utilities take advantage of
a reduction in system losses, improved voltage regulation
and an improvement in the reliability of supply
(Mithulananthan et al., 2004; Reliability, 2003). It will
also relieve the capacity of transmission and distribution
systems and hence defer new investments which have a
long lead-time. In addition, the modular and small size of
the DG will facilitate the planner to install it in a shorter
time frame compared to the conventional solution. It
would be more beneficial to install in a more
decentralized environment where there is a larger
uncertainty in demand and supply. However, given the
choices, they need to be placed in appropriate locations
with suitable sizes. Therefore, analysis tools are needed to
be developed to examine locations and the sizing of such
DG installations. Several approaches to solve the DG
siting and sizing problem in distribution system have been
proposed. In Bharathi Dasan et al. (2009), they use
evolutionary programming approach for optimal
placement and size of DG in a radial feeder. The objective
is minimize the system real power loss, hybrid distributed
generation for a mixed realistic load model is considered.
A technique to determine optimal location and sizing of
DG units in a MG based on loss sensitivity factor and
priority list compare with analytical approach is
developed by Acharya Mahat and Mithulananthan (2006).
A simple methodology for placing a distributed generator
with the view of increasing the loadability of the
distribution system is presented in Mithulananthan and Oo
(2006). In Parizad et al. (2010), they use exact loss
formula for optimal placement and size of DG in radial
distribution system. The objective is minimizing the
system real power loss, loadability and voltage stability
index. A Genetic Algorithm (GA) combined with power
analysis to evaluate DG impacts in system power losses
and voltage profile for radial network. A fuzzy model in
optimal siting and sizing of DG for loss reduction and
improvement voltage profile in power distribution is
presented in Shayeghi and Mohamadi (2009). In Ramírezrosado and Domínguez-navarro (2006), DG siting and
sizing problem is fulfilled to compromise multi-objective
function consisting of energy not-supplied cost,
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
improving cost of network and energy loss cost. In
Sookananta and Kuanprab (2010); Prommee and
Ongsakul (2008), DG siting and sizing problem in
distribution network are analyzed to improve only power
loss by particle swarm.
From the previous works, we can conclude that most
of the problem of optimal location and sizing of DG is
generally formulated as a mono-objective optimization
problem. Unfortunately, the formulation of DG location
and sizing problem as a mono-objective optimization is
not quite practical. While, planners the power systems
aim to take advantage of multi-type DG considering
several objectives at the same time.
This study proposes a multi-objective optimal
placement of multi-type of DG for enhancement of
primary distribution system performance. A Pareto-based
NSGA-II is proposed to find locations and sizes of a
specified number of DG within distribution system.
Multiobjective functions include LVD, minimize system
real power loss and annualized investment cost. The final
decision will be made by the fuzzy method to find the
trade off solutions among three different objective
functions.
METHODOLOGY
DG planning problem formulation: The multi-objective
optimization technique to determine the optimal locations
and sizes of DG units within primary distribution system
is as follows:
C
(i / 100)(1 + i / 100) T
(1 + i / 100) T − 1
(1)
(5)
Dependent and control variables: In the three objective
functions, x is the vector of dependent variables such as
slack bus power PG1, load bus voltage VL, generator
reactive power outputs QG1 and apparent power flow Sk. x
can be expressed as:
XT = [PGI, VLI…VLNB, QGI, SI…SNL]
(6)
Furthermore, u is a set of the control variables such
as generator real power outputs except at the slack bus
PG1, generator reactive power outputs except at the slack
bus QG1, the locations of DG units, L and their setting
parameters. u can be expressed as:
ur = [PG2…PGNF,QG2…QGNF,LI…LNF]
where, f1,f2 and f3 represent average load voltage
deviation, system real power loss and annualized
investment, cost respectively.
(7)
where, NF is the total number of DG devices to be
optimally located within distribution system. The equality
and inequality constraints of the load flow problem
incorporating DG are given bellow.
Equality constrains: These constraints represent the
typical load flow equations as follows:
Minimize the average load voltage deviation:
⎛ Vkref − VK ⎞
⎟
Vkref ⎠
k =1
n
Min f 1 ( x , u) =
C
AFi =
Multi-objective:
Min f(x, u) = [f1(x, u),f2(x, u),f3(x, u)]
C
The annualized investment cost of DG unit i is
assumed to be proportional with the maximum rating of
DG (Buayai et al., 2011), where the unit cost UCi is in
($/KVA). The UCi is different for different type of
generating units. The total of investment cost is
transformed to cash value in the beginning of the planning
period by using economical expression (i.e., annual cost
based on certain interest rate and life span). AFi is the
annualized factor associated with the installation cost
(annual cost based on certain interest rate ‘i’ and life span
‘T’) as shown in (5):
∑ ⎜⎝
N
⎧N
∑
∑
P
=
⎪⎪ i =1 Gi i =1 PLDi + PL
⎨N
N
⎪∑ Q = ∑ Q + Q
Gi
LDi
L
⎪⎩ i =1
i =1
2
(2)
Minimize the system real power loss:
Min f2(x, u) = PL
(3)
where, N is the number of buses, PGi and QGi are real
power reactive power generated by generating unit i
(including slack bus), respectively, in MW.
(4)
Inequality constrains: The inequality constraints are
limits of control variables and state variables. Generator
active power PG, reactive power QG and voltage VG are
restricted by their limits as follows:
Minimize the annualized Investment Cost:
Min f 3 ( x , u) =
NDG
∑ AF × UC × C
i =1
i
i
DGi ,max
(8)
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
⎧ PDGi ,min ≤ PDGi ≤ PDGi , max
⎪
⎪ QDGi ,min ≤ QDGi ≤ QDGi ,max
⎨
⎪ Vi min ≤ Vi ≤ Vi max
⎪
⎩ Pbi ≤ Pbi ,max
(9)
Distributed generation model: DG units are modeled as
synchronous generators for small hydro power,
geothermal power, combined cycles and combustion
turbines. They are treated as induction generators for wind
and micro hydro power. DG units are considered as power
electronic inverter generators such as micro gas turbines,
solar power, photovoltaic power and fuel cells (Puttgen
et al., 2003). In general, DG can be classified into four
types:
C
C
C
C
Type 1: DG capable of injecting constant P only
(PV)
Type 2: DG capable of injecting both P and Q (Gas
Turbine)
Type 3: DG capable of injecting constant P but
consumes Q (Wind Turbine)
Type 4: DG capable of delivering Q only
(Synchronous condenser)
NSGA-II is one of the most efficient algorithms for
multiobjective optimization on a number of benchmark
problems (Deb et al., 2002). In addition, with NSGA-II
based approach, the multiobjective of DG planning is
retained without the need for any tunable weights or
parameters. As a result, the proposed methodology is
applicable to solving distributed generation planning in a
distribution network. NSGA-II has been developed to
determine locations and sizes of DG units within
distribution system. The NSGA-II procedure can be found
in Deb et al. (2002).
Load flow analysis: The distribution systems are
structurally weakly meshed but are typically with a radial
structure. The Distribution Load Flow (DLF) based on
iterative backward/forward sweep methods had been
applied for a radial distribution system (Bompard et al.,
2000). The effectiveness of the backward/forward sweep
method in the analysis of radial distribution systems has
already been demonstrated over traditional NR (Lin and
Huang, 1987). Because of high R/X ratio of distribution
networks and it radial structure, these equations are
commonly based on iterative backward/forward sweep
methods. In this case, the method described in Bompard
et al. (2000) was used:
Vnode ← Vgrid
NSGA-II for dg placement: A NSGA-II combined with
distribution load flow NRPF based on MATPOWER
(Zimmer and Deqiang, 1997) is used to solve multiobjective optimization to identify appropriate sizes and
locations of a specified number DG unit within
distribution system. The final trade off solution is
determined by the fuzzy method. The fitness function for
the above problem can be written as:
f(x,u) = [f1(x, u),f2(x,u ),f3(x, u)]
(11)
⎧ I node = f load mod el ( S node , S Der ,Vnode )
⎪ I = A. I
⎪ line
node
do⎨
⎪Vnode = Vgrid − Z . I line
⎪⎩ ε = g error ( S node , I node ,Vnode )
(10)
The final trade off solution is determined by the fuzzy
method.
NSGA-II algorithm: In case of multiple conflicting
objectives, there may not exist one solution which is the
best compromise for all objectives. Therefore, a “tradeoff” solution is needed instead of a single solution in
multi-objective optimization. Non-dominated Sorting
Genetic Algorithm (NSGA) uses nondominated sorting
and sharing has not been widely used mainly because of:
C
C
C
while ε ≥ ε max
High computational complexity
Nonelitism approach
The need for specifying a sharing parameter
NSGA-II is developed to overcome these difficulties
(Deb, 2003; Deb et al., 2002)
z and A are the impedance matrix and line current
summation matrix, respectively. For simplicity, here, the
constant power model is used, but this could be adapted.
All current injections are based on a static load model
where the power doses not vary with changes in voltage
magnitude. It is also known as constant MVA load model
(Mithulananthan et al., 2000). The stopping criterion is
based on the node-power convergence.
Fuzzy method for best compromise solution: Once the
Pareto optimal set is obtained, it is practical to select one
solution from all solutions that satisfies different goals to
some extent. Such a solution is the best compromise
solution. In this paper, a simple linear membership
function is considered for each of the objective functions.
The membership function is defined as follow (Sakawa
and Yano, 1989).
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
Table 1: NSGA-II parameters
NSGA-II (parameters)
Population size, Np
Number of iterations
0c
0m
µ f (z)
i
1
0
f i max
f i min
3.72 MW and 2.3 Mvar, real and reactive load
respectively. The system losses are 0.211 MW and 0.143
MVar. The IEEE 33-bus radial system is depicted in
Fig. 2. All parameters of the 33-bus radial system are
shown in Table 3.
fi ( z )
Fig.1: Linear type membership function
⎧
1
⎪⎪ f max − f ( z)
i
µ f i ( z ) = ⎨ max i min
⎪ fi − fi
⎪⎩
0
Assumptions and constraints:
In this section, it is assumed that:
f i ( z ) ≤ f i min
f i min < f i ( z) < f i max
C
(12)
f i ( z) ≥ f i max
The membership function :fi(z) is varied between 0
and 1, where, :fi(z) = 0 indicates incompatibility of the
solution with the set, while :fi(z) = 1 means full
compatibility. Figure 1 illustrates the graph of this
membership function.
The compromised solution can be found by using the
normalized membership function (Sakawa and Yano,
1989). For each non-dominated solution k, the normalized
membership function :k is calculated as:
N obj
µk =
∑µ
i =1
M N obj
k
i
∑∑µ
k =1 i =1
(13)
k
i
In all optimization problems several cases in terms of
use of Multi-type DG is considered namely:
C
C
C
C
Parameter values (type)
600
100
20
20
Base case (without DG)
Case 1: PV only (Type 1)
Case 2: MT only (Type 2)
Case 3: Coordinated PV and MT (Type 1 and
Type 2)
C
C
C
C
Loads are typically represented as constant PQ loads
with constant power factor on peak load level
Line limit Sb#5.0 MVA
The maximum allowable number of DG is two
DG placement is not allowed at the same bus
All DG resources are evenly distributed within
system (except at the slack bus)
Evaluation of DG placement within primary
distribution system: The decision variables considered,
are the location and setting of DG units. The DG should
be formed at load bus, consisting of buses 2 to 33. The
NSGA-II combined with DLF approach is minimizing the
LVD (f1), system real power loss (f2) and annualized
investment cost (f3). The best parameters for the NSGAII, selected through ten runs, are given in Table 1.
Parameters of all DGs are shown in Table 4. The number
of DG to be installed will be initially specified to
two.Simulations have been carried out for optimal
placement and size of DG in three different DG
configurations compared to the base case (without DG) as
shown in Table 2.
The results were compared with the Repetitive Load
Flow (RLF) approach. The computation procedure of RLF
is given as follows:
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
SIMULATION RESULTS AND DISCUSSION
Analytical tool and test system: The load flow analysis
used Distribution Load Flow (DLF) (Bompard et al.,
2000). Multiobjective optimization problem is solved by
NSGA-II.
The distribution system is the modified IEEE 33-bus
radial system (Kashem et al., 2000), which consists of 33
buses and 32 branches. The system has 32 loads totaling
Step 6:
Run the base case load flow (without MG).
Place DG at the bus within MG area.
Change the size of DG in “small” step and
calculate loss for each by running load flow.
Store the size of DG that gives minimum loss.
Compare the system loss with previous
solution. Replace the previous solution if new
solution is lower.
Repeat from Steps 3 to 5 for all buses in MG
area.
The procedure above is used to find the best location and
size of two or more DG units within distribution system,
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
7
10
13
14
1
2
4
6
9
12
3
5
8
11
15
16
18
20
22
24
26
28
17
19
21
23
25
27
29
30
31
32
33
HV/MV
Substation
SlagBus
Bus
Line
Fig. 2: The IEEE 33-bus radial system
Fig. 3: Pareto front to find optimum location and size of DG units (Type 1) within 33-bus radial system by NSGA-II (on peak load
level)
minimizing only system real power loss. Assuming DG
units will regulate bus voltage for DG type 2, here we set
DG bus voltage as equal 1.0 p.u. The best location and
size of the first DG is obtained by RLF method. Similarly,
the second DG size and location is found by fixing the
first DG at the original location and size. For comparison,
NSGA-II and RLF system Loss, Load Voltage Deviation
(LVD), annualized investment cost and penetration level
is considered. The penetration level can be defined as the
total DG power generation PDG er the total load demand
PLD:
Penetration level (%) =
∑P
∑P
DG
× 100
(14)
LD
Optimal distributed generation placement-type 1: The
best configuration plans of DG within 33-bus radial
system are found at buses 22 and 27 for peak load level.
The optimal DG size at bus 22 is 1.1576 and at bus 27 is
0.852 MW respectively. Figure 3 shows the Pareto front,
in the objective function space (objective function load
voltage deviation, system real power loss and annualized
investment cost) for on peak load level. This set of
solutions on the non-dominated frontier is used by the
decision maker as the input to select a final compromise
solution by using the normalized membership function in
(13).
Optimal distributed generation placement-type 2: The
best configuration plans of DG within 33-bus radial
system are found at buses 22 and 30 for peak load level.
The optimal DG sizes at buses (22 and 30) are (0.938,
0.672) MW and (0.744, 0.356) MVAR, respectively.
Optimal distributed generation placement-types 1 and
2: The best configuration plans of DG types 1 and 2
within 33-bus radial system are found at buses 22 and 30
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
DG size
---------------------------------Bus No. MW
MVAR MVA
Penetration
level (%)
f1
f2
0.1340
211.194 0
0
f3
0.472
0.325
0.286
0
0.867
0
0.472
0.926
0.286
0.0144
0.0138
0.0106
96.16
54.87
58.78
0.8100
0.7118
0.6202
82.45
75.53
74.48
27
30
30
0.852
0.6720
0.6680
0
0.3575
0
0.852
0.7659
0.668
0.0170
0.0072
00.0098
87.248
36.240
38.978
0.5314
0.3548
0.4522
54.09
43.35
46.20
respectively for peak load level. The optimal DG types 2
and 1 sizes at buses (22 and 30) are (1.048, 0.668) MW
and (1.107, 0) MVAR, respectively.
In Table 2, comparison has been made between RLF
and NSGA-II method at on-peak load level. The RLF
approach is minimizing system real power loss only
whereas NSGA-II approach is minimizing three
objectives including LVD, system real power loss and
annualized investment cost, respectively.
For DG type 1, the system loss of RLF method is
slightly more than NSGA-II method but the LVD is
300
0.12
200
(54.09, 0.017, 87.248, 0.531)
0.10
0.08
0.06
100
0.04
1.5
System loss (kW)
0.14
1.0
0.5
0.02
0
0
20
40
60
80
Penetration level (%)
100
120
0
Annualized investment cost
(million $/year)
LVD
System loss
Annualized investment cost
0.16
0
Fig. 4: Comparison of system loss, LVD and annualized
investment cost for on-peak load level of DG (Type1)
when the penetration level varies
DG type 1
System loss reduction (%)
0.452
92.69 %
81.54 %
DG type 2
100
90
80
70
60
50
40
30
20
10
0
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Annualized investment cost
(million $/year)
Annualized investent cost
0.355
100
90
80
70
60
50
40
30
20
10
0
87.31 %
System loss
94.63 %
82.84 %
Load voltage deviation
58.69 %
0.531
Table 3: 33 bus test system (base case)
Bus data
Branch data
--------------------------------------------------Pd
Qd
R
X
B
No Fn
Tn
(MW)
(Mvar)
(p.u.)
(p.u.)
(p.u.)
1
1
2
0.100
0.060
0.0058
0.0030 0
2
2
3
0.090
0.040
0.0102
0.0098 0
3
2
4
0.090
0.040
0.0308
0.0157 0
4
3
5
0.090
0.040
0.0939
0.0846 0
5
4
6
0.120
0.080
0.0228
0.0116 0
6
4
7
0.090
0.050
0.0282
0.0192 0
7
5
8
0.090
0.040
0.0255
0.0298 0
8
6
9
0.060
0.030
0.0238
0.0121 0
9
7
10
0.420
0.200
0.0560
0.0442 0
10 8
11
0.090
0.040
0.0442
0.0585 0
11 9
12
0.060
0.020
0.0511
0.0441 0
12 10
13
0.420
0.200
0.0559
0.0437 0
13 12
14
0.060
0.025
0.0127
0.0065 0
14 12
15
0.200
0.100
0.0117
0.0386 0
15 14
16
0.060
0.025
0.0177
0.0090 0
16 15
17
0.200
0.100
0.1068
0.0771 0
17 16
18
0.060
0.020
0.0661
0.0583 0
18 17
19
0.060
0.020
0.0643
0.0462 0
19 18
20
0.120
0.070
0.0502
0.0437 0
20 19
21
0.060
0.020
0.0649
0.0462 0
21 20
22
0.200
0.600
0.0317
0.0161 0
22 21
23
0.045
0.030
0.0123
0.0041 0
23 22
24
0.150
0.070
0.0608
0.0601 0
24 23
25
0.060
0.035
0.0234
0.0077 0
25 24
26
0.210
0.100
0.0194
0.0226 0
26 25
27
0.060
0.035
0.0916
0.0721 0
27 26
28
0.060
0.040
0.0213
0.0331 0
28 27
29
0.120
0.080
0.0338
0.0445 0
29 29
30
0.060
0.010
0.0369
0.0328 0
30 30
31
0.060
0.020
0.0466
0.0340 0
31 31
32
0.060
0.020
0.0804
0.1074 0
32 32
33
0.090
0.040
0.0457
0.0358 0
Substation Voltage (kV): 12.66 kV; Base MVA; Rating of all branch in
the system: 5.0 MVA; Pd and Od are the lods at bus Tn
Load voltage deviation (LVD)
30
28
32
Load voltage deviation
improvement (%)
Table 2: Comparison of the results of different approaches
DG size
---------------------------------DG type
Bus No.
MW
MVAR
MVA
Case of a 33 bus radial system (without DG)
On-peak load level
Repetitive load flow (RLF)
On-peak load level
Type 1
12
2.591
0
2.591
Type 2
12
2.481
1.711
3.014
Type 1&2
12
2.481
1.7109
3.014
NSGA-II
On-peak load level
Type 1
22
1.1576
0
1.1576
Type 2
22
0.9384
0.7438
1.1975
Type 1&2
22
1.0483
1.1074
1.5249
DG type 1&2
Fig. 5: Comparison of system loss, LVD and annualized
investment cost for on-peak load level of DG (Type1,
Type 2 and Type 1&2)
smaller than NSGA-II method. This is because the best
location and size of the first DG is obtained by RLF
method then the second DG size and location is found by
fixing the first DG at the original location and size. In
contrast, the NSGA-II method is solved the optimal siting
and size of two DGs within the system at the same time.
For DG type 2, in NSGA-II method, the LVD, system
loss and anualized investment cost are less than RLF
method . This is because RLF is optimizing only system
loss while regulate bus voltages. NSGA-II method is
minimizing for all three objectives by real and reactive
power injection control. Thus, NSGA-II method is better
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
Table 4: Parameter for simulation
No
Description
Parameter of simulation
DGs
1
DG technology
Photo voltaic
2
DG type
1
3
Size (MVA)
0.001-3.00.0
4
Unit cost ( $/ kVA)
5250
5
Fuel
Solar energy
6
Equipment life (years)
20
Economic
1
Interest rate
7%
AFi is the annualized factor associated with the installation
Gas turbine (biomass)
2
01-3.0
1800
Biogas
10
Wind turbine
3
0.001-3.0
2150
Wind
20
Synchronous condenser
4
0.001-3.0
700
Non
20
cost (annual cost based on certain interest rate ‘i’ and life span
(i / 100)(1 + i / 100) T
‘T’ AFi =
(1 + i / 100) T − 1
than RLF method in terms of both system loss and LVD.
For DG type 1&2, NSGA-II is far better that RLF method
in terms of LVD, system loss and annualized investment
cost.
In Table 2, comparison has been made between the
three different DG configurations which are solved by
NSGA-II method. The NSGA-II approach is minimizing
three objectives including LVD, system real power loss
and annualized investment cost, respectively.
For DG type 1, the system loss, LVD and annualized
investment cost are more than the other types. This is
because it is only real power injection to the bus and unit
cost ($/kVA) is the highest. The system loss varies as a
function of penetration level in a U-shape trajactory. As
a penetration increases, loss will decrease until the
minimum value and will start increasing as show in
Fig. 4. Simillarly, the LVD varies as a function of
penetration level in a U-shape trajactory. As DG
penetration increases, LVD will decrease until the
minimum value and will start increasing as shown in Fig.
4. By contrast, the annualized investment cost linearly
increases as a function of the penetration level.
Accordingly, the optimal solution NSGA-II would require
a high DG penetration level for voltage profile
improvement and loss reduction but require a low
annualized investment cost.
Figure 5 shows the comparison of system loss
reduction, load voltage deviation improvement and
annualized investment cost for the DG type 1, type 2 and
type 1&2 for on-peak load level. Obviously, the DG type
2 is the best plan with respect to load voltage deviation
improvement of 94.63% and system loss reduction of
82.84% compared to the base case. For economic
consideration, DG type 2 is the best plan due to the lowest
annualized investment cost. The annualized investment
cost for on peak load level is the lowest at 0.355 million
$/year.
CONCLUSION
This study proposes an efficient multi-objective DG
placement methodology. The NSGA-II is used to
determine locations and sizes of a specified number of
Distributed Generators (DG) within primary distribution
system. A fuzzy decision making analysis is used to
obtain the final trade off optimal solution. The proposed
methodology is tested on IEEE 33-bus radial system.
Using the fuzzy method, DG can improve the system
performance by trading off the minimize system LVD,
minimize system real power loss and minimize annualized
investment cost. Moreover the method does not impose
any limitation on the number of objectives. This work will
be further extended to address the problem of optimal
location of multi-type of DG units to enhance system
reliability.
LIST OF SYMBOLS AND ABBREVIATIONS
Afi
Annualized factor associated with the
installation cost of DG unit i
CDGi, ax Selected capacity of DG unit i for installation
within MG (kVA)
Minimum value of the ithobjective function
fimin
among all non-dominated solutions
Maximum value of the ithobjective function
fimin
among all non-dominated solutions
i
Interest rate (%)
n
Number of buses.
Net real power injection at bus i
Pi
System power loss, in kW
PL
Real power generated by generating unit i
PGi
(including slack bus), in kW
Load demand at bus i, in kW
PLDi
Branch power in branch i, in kW
Pbi
PDGi,min Upper real power generating limit of unit i, in
kW
PPDGi,min Lower real power generating limit of unit i, in
kW
The real power injection from DG place at bus i
PDGi
Net reactive power injection at bus i
Qi
Load demand at bus i in kVAR
QLDi
Reactive power generated by generating unit i
Qgi
(including slack bus), in kVAR
The reactive power injection from DG place at
QDGi
bus i
*i
Voltage phase angle at bus
T
Life span in year
u
Decision variables for a two-entry vector of DG
size and location
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Res. J. Appl. Sci. Eng. Technol., 4(19): 3610-3617, 2012
UCi
:k
:fi(z)
Vref k
Vi
Vk
x
Unit cost of DG unit ($/kVA)
Normalized membership function
Membership function (varied between 0 and 1)
Reference value of the voltage magnitude at bus
k, in p.u. (usually set to 1.0 p.u.)
Voltage magnitude at bus i
Actual voltage magnitude at bus k, in p.u
the vector of dependent variables such as slack
bus power PG1, load bus voltage VL
REFERENCES
Acharya, N., P. Mahat and N. Mithulananthan, 2006. An
analytical approach for DG allocation in primary
distribution network. Int. J. Elec. Power, 28(10): 669678, DOI:10.1016/j.ijepes.2006.02.013.
Bompard, E., E. Carpaneto, G. Chicco and R. Napoli,
2000. Convergence of the backward/forward sweep
method for the load-flow analysis of radial
distribution systems. Int. J. Elec. Power, 22(7):
521-530.
Buayai, K., W. Ongsakul and N. Mithulananthan, 2011.
Multi-Objective Micro-Grid Planning by NSGA-II in
Primary Distribution System: European Transactions
on Electrical Power Wiley Online Library. Retrieved
from: http:// onlinelibrary. wiley. com/doi/ 10.1002/
etep.553/full.
Bharathi Dasan, S.G., R.S. Selvi, S.G.B. Dasan, S.S.
Ramalakshmi and R.P.K. Devi, 2009. Optimal Siting
and Sizing of Hybrid Distributed Generation using
EP. ICPS ’Conference, (27-29 Dec. 2009), pp: 1-6.
Deb, K., 2003. Multi-Objective Optimization using
Evolutionary Algorithms. Wiley, New York.
Deb, K., A. Member, A. Pratap, S. Agarwal and
T. Meyarivan, 2002. A fast and elitist multiobjective
genetic algorithm. IEEE Trans. Power Syst., 6(2):
182-197.
Griffin, T., K. Tomsovic, D.S.A. Law and A. Corp, 2000.
Placement of dispersed generations systems for
reduced losses. Proceedings of the 33rd Hawaii
International Conference on Sciences, 00(c), pp: 1-9.
Kashem, M., V. Ganapathy, G. Jasmon and M. Buhari,
2000. A Novel Method for Loss Minimization in
Distribution Networks. Electric Utility Deregulation
and Restructuring and Power Technologies, 2000.
Proceedings
of DRPT 2000, International
Conference. Retrieved from: http://ieeexplore.ieee.
org/ xpls/abs-all. jsp? arnumber = 855672. pp:
251-256.
Lin, C. and Y. Huang, 1987. Distribution system load
f l o w c a l c u l a t i o n w i t h mi c r o c o mp u t e r
implementation. Electr. Pow. Syst. Res., 13(2):
139-145
Mithulananthan, N. and T. Oo, 2006. Distributed
Generator Placement to Maximize the Loadability of
Distribution System. Int. J. Elec. Eng. Educ., 43(2):
107-118.
Mithulananthan, N., T. Oo and L.V. Phu, 2004.
Distributed generator in power distribution placement
system using genetic algorithm to reduce losses.
Thammasat Int. J. Sci. Technol., 9(3): 55-62.
Mithulananthan, N., M.M.A. Salama and C.A. Can, 2000.
Distribution system voltage regulation and var
compensation for different static. Int. J. Elec. Eng.
Educ., 37(4): 384-395.
Parizad, A., A. Khazali, M. Kalantar, 2010. Optimal
Placement of distributed generation with sensitivity
factors considering voltage stability and losses
indices. 18th Iranian Conference on Electrical
Engineering, (ICEE), Iran University of Science and
Technology, Tehran, Iran, pp:848-855
Prommee, W. and W. Ongsakul, 2008. Optimal multidistributed generation placement by adaptive weight
particle swarm optimization. IEEE International
Conference on Control, Automation and Systems,
1663-1668, pp: DOI:10.1109/ICCAS.2008.4694499.
Puttgen, H.B., P.R. MacGregor and F.C. Lambert, 2003.
Distributed generation: Semantic hyde or the drawn
of the new era. IEEE Power and Energy Magazine,
1(february 2003), pp: 22-29.
Ramírez-rosado, I.J. and J.A. Domínguez-navarro, 2006.
New multiobjective tabu search algorithm for fuzzy
optimal planning of power distribution systems.
IEEE T. Power Syst., 21(1): 224-233.
Reliability, A., 2003. Impact of distributed generation
allocation and sizing on reliability, losses and voltage
profile. Proceeding of IEEE Bolonga Power
Tachnology Conference, Barazil, Vol. 2.
Sakawa, M. and H. Yano, 1989. An interactive fuzzy
satisficing method for multiobjective nonlinear
programming problems with fuzzy parameters. Fuzzy
Set. Syst., 30(3): 221-238.
Shayeghi, H. and B. Mohamadi, 2009. Multi-objective
fuzzy model in optimal siting and sizing of dg for
loss reduction. World Acad. Sci. Eng. Technol., 52:
703-708.
Sookananta, B., W. Kuanprab and S.Hank, 2010.
Determination of the optimal location and sizing of
distributed generation using particle swarm
optimization. International Conference on Electrical
Engineering/ Eiectronics Computer
Telecommunications and Information Technology
(ECII-CON), Warinchamrap, Thailand, pp: 818-822.
Zimmerman, R.D. and D.G. Deqing, 1997.
MATPOWER-A Matlab Power System simulation
package. Power Systams Engineering Research
Center (PSERC), Cornell University, NY.
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