Turkish Journal of Electrical Engineering & Computer Sciences
http://journals.tubitak.gov.tr/elektrik/
Research Article
Turk J Elec Eng & Comp Sci
() : 1 – 14
c TÜBİTAK
⃝
doi:10.3906/elk-1203-7
Optimal placement and sizing of DG units and capacitors simultaneously in radial
distribution networks based on the voltage stability security margin
1
Hamid Reza ESMAEILIAN1 , Omid DARIJANY1 , Mohsen MOHAMMADIAN2,∗
Department of Electrical and Computer Engineering, Kerman Graduate University of Technology, Kerman, Iran
2
Department of Power Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
Received: 03.03.2012
•
Accepted: 01.10.2012
•
Published Online: ..2014
•
Printed: ..2014
Abstract: This paper presents a novel manner to reach the optimal quantity, placement, and sizing for distributed
generation (DG) units and capacitors simultaneously in a radial distribution network as a multiobjective optimization
problem. The objective function includes the DG units’ and capacitors’ costs, power losses, and voltage stability margins
as a multiobjective optimization problem, which uses a developed genetic algorithm as the first stage in the proposed
hierarchical optimization strategy. In order to model the optimization problem, different types of DG units are modeled
and the results are investigated and evaluated on an IEEE-33 bus radial distribution network.
Key words: Voltage stability, multiobjective optimization, distributed generation allocation, radial distribution networks
1. Introduction
Due to the low voltage level and high current in distribution systems, the largest power loss portion among the 3
power system sections, which are generation, transmission, and distribution, belongs to the distribution section,
such that the line losses at the distribution level constitute about 5%–13% of the total power generation [1].
Hence, many efforts have been made to decrease the losses in distribution networks. The capacitor placement
and the usage of distributed generation (DG) resources are among those efforts to mitigate this problem.
Shunt capacitors have been commonly employed to locally compensate for the reactive power in the
network and, in consequence, reduce the power loss in the lines and improve the voltage profile. Optimal
capacitor placement and sizing was applied to minimize the power loss in many previous researches, such as
in [2–5]. In [6], capacitor placement was applied as a multiobjective problem to reduce the annual cost sum
of the power loss and the capacitors, as well as to improve the voltage profile. Moreover, in [7], it was shown
that shunt capacitors can enhance the system reliability as lines redundant in distribution networks. Therefore,
capacitors are applied as an effective economic tool to improve the network performance by providing appropriate
placement.
DG units are employed at the distribution level to supply power and reduce losses. The optimal sizing
and placement of these resources to minimize the power loss, improve the voltage profile, enhance the system
reliability indices, etc. is a significant matter that was investigated in many previous studies [8–10].
Nowadays, because of the industrialization of societies and overloading of distribution networks, the
voltage stability of these networks has become an important issue. Based on this fact, many objects have been
∗ Correspondence:
m.mohammadian@uk.ac.ir
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
considered to place and size DG units in distribution networks, but the voltage stability issue has been given
less attention. Hence, the present study will address the voltage security margin in the cost function of the
proposed optimization problem.
In order to evaluate the voltage stability in distribution networks, usually the system equivalence method
from the point of each node with a transmission line is used. In [11], an index was introduced to evaluate
the system voltage stability. In this method the system voltage stability is evaluated without calculating
theZ impedance matrix and only by performing the power flow of the power system. In [12], the mentioned
index was used to evaluate the distribution network voltage stability in the presence of DG resources. Because
of the features of this index and the simplicity of using it in radial networks, it is also used in this paper.
To date, many studies have been done in the field of optimal placement for capacitors and DG units with
different aims. In [13,14], a capacitor and DG unit were used to reduce the power loss and improve network
performance, but the authors considered these placements separately and the mutual impact of the capacitor
placement and DG unit placement on the power system operation indices were not considered. In [15], capacitor
and DG unit placement was considered simultaneously to reduce power loss; however, the authors did not take
into account the impact of the capacitor and the different types of DG units in the cost function. As mentioned
before, the placement and sizing of DG units and capacitors should be modeled simultaneously in the form of
an optimization problem. Otherwise, the operation of the power system will not be optimal.
This paper attempts to model the DG units and capacitors’ allocation simultaneously as a nonlinear
multitask optimization problem, including the voltage stability margin as a security index. Moreover, the
mentioned optimization manner also improves other tasks, such as power losses and costs. Meanwhile, this
paper shows that the optimal operation planning of the network will be achieved by the capacitors’ and DG
units’ simultaneous placement, in comparison with planning separately or individually.
The sizing and placement of DG units and capacitors is a discrete, nonlinear, and nondifferentiable
problem; hence, the genetic algorithm (GA) is employed to solve the optimization problem in this paper. The
GA is a metaheuristic search algorithm that has been used in many power system problems, such as in unit
commitment [16], transmission expansion planning [17], placement of reactive power resources [18], and so
on. Moreover, in this paper, the backward/forward sweep method is utilized to perform the power flow in
the distribution network. In order to consider the impact of a photovoltaic (PV) type of DG unit on power
flow equations, the developed backward/forward power flow is used to calculate the power loss and the voltage
stability index (SI) in the fitness function of the optimization problem.
This paper is organized as follows: Section 2 presents the voltage SI to evaluate the distribution network
security level. Different types of DG units, with the characteristics of each, are described in Section 3. Section 4
introduces the backward/forward power flow as a precise method to perform the power ?ow in the distribution
networks containing DG units. The optimization problem formulation is presented in Section 5. The GA as an
evolutionary search algorithm is described in Section 6. The proposed algorithm for solving the optimization
problem is presented in Section 7. Section 8 shows the simulation results of applying the proposed algorithm
to the IEEE 33-bus network for different combinations of DG units and capacitors. Finally, the conclusion is
given in Section 9.
2. Voltage SI
Voltage stability is considered as the potential of a power system in maintaining its buses’ voltage amplitude
against the increment of the load demand. To date, many different indices have been introduced to evaluate the
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
power systems’ security level from the point of voltage static stability. By considering the radial distribution
networks’ properties, the following index is used for the present paper [11].
SIi = Vs4 − 4Vs2 (Ri PLi + Xi QLi ) − 4(Xi PLi + Ri QLi )2
i = 1, ..., N
(1)
In the i th node of Figures 1 and 2, Vs is the source voltage (substation voltage) and Ri , Xi are the equivalent
resistance and reactance, which are gained using the following equation:
∑
Zeqi = Ri + jXi =
Zk Ik
.
Ii
(2)
In Eq. (2), the sigma is applied to all of the branches that belong to the path from the i th node to the source
(substation) (S).
c
Im
Ic
a
b
h
i
S
Ia
Ib
Ih
m
VS
Ii
Zeqi = Ri + jXi
Vi
S
In
n
Ii
Figure 1. A typical radial distribution network.
Figure 2. Equivalent network from the point of the i th
node.
PLi and QLi are the total active and reactive powers flowing through the i th node, respectively, which
are gained using the following equations:
PLi = Re[Vi Ii∗ ],
(3)
QLi = Im[Vi Ii∗ ].
(4)
If N is the total number of system nodes, the voltage SI for all of the nodes of 2 through N is calculated using
the mentioned method (the first node is the substation node and the SI is considered as 1 for it). The node with
the smallest voltage SI is the weakest node and the voltage collapse phenomenon will start from that node. In
other words, the weakest node voltage SI proposes the potential of a distribution network against the increment
of the load demand and is defined as follows:
SIsystem =
min {Vs4 − 4Vs2 (Ri PLi + Xi QLi ) − 4(Xi PLi + Ri QLi )2 }.
i∈2,...,N
(5)
3. Different types of DG resources
DG resources are classified into 4 groups based on the ability of delivering active and reactive powers [19,20]:
Type 1: Active power producers like PV arrays and fuel cells, which are connected to the grid by means
of inverters. This type can only produce active power.
Type 2: Reactive power (Q) producers like synchronous condensers, which can only produce reactive
power.
Type 3: Active power producers and reactive power consumers (PQ). This type of DG unit produces
active power and absorbs reactive power from the grid. For example, fixed speed wind turbines that use an
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
induction generator to produce electricity are placed within this type of DG. In fixed speed, wind turbines’
reactive power is consumed to produce active power.
Type 4: Active and reactive power producers (PV bus voltage regulator). This type of DG unit produces
reactive power to maintain the voltage of the bus to which they are connected. Wind turbines that have
converters and diesel generators are categorized as this type of DG.
By considering the properties of these resources and in order to model them in the mentioned optimization
problem, the injected active and reactive powers to the i th node are modeled as follows:
Pi = PDGi − PDi ,
Qi = QDGi − QDi = αi × PDGi − QDi
αi = (sign) × tan(cos−1 (P FDGi )),
(6)
,
(7)
(8)
where PDi and QDi are the demanding active and reactive powers of the i th node load; PDGi and QDGi are
the generating active and reactive powers of the DG unit connected to the i th node; and P FDGi is the DG
power factor.
The power factor depends on the DG type and the operating condition of the DG unit. For type 1:
P FDG = 1 , for type 2: P FDG = 0, for type 3: 0 < PF DG < 0 and sign = −1 ; and, finally, for type 4: 0
<PF DG < 0 and sign = +1.
In this paper, all of the DG types except for type 2 are studied. The power factor of DG type 3 is
considered as 0.9 lag, and the reactive power maximum and minimum limits of DG type 4 is ±0.8 times the
active power [21].
4. Backward-forward power flow in the presence of DG
The R/X ratio in distribution networks is high and so the conventional power flow methods like the Newton–
Raphson and fast decoupled methods, considering their procedure of derivation, may not converge in solving
the power flow problem of this type of network. Hence, these methods are not suitable. Based on this, for
solving the power flow problem of distribution networks, the known backward-forward method is used. The
backward-forward sweep method has been widely used to solve power flow problems in distribution networks
because it converges very fast and consumes less computational memory. The common algorithm of the power
flow consists of 2 basic steps of the backward-forward sweep, which iterates in a loop so that the convergence
of the power flow is gained [22,23].
One of the recent challenges in the backward-forward sweep power flow calculations is the penetration of
DG units in distribution networks. In the presence of PV-type DG units, the conventional power flow method
is not suitable for the distribution system and some changes need to be done in this method. The forwardbackward power flow method is divided into 3 types, which are current summation, power summation, and
impedance summation. In this paper, the power summation method [24] with an added term for the DG unit
management is used.
4.1. Power flow modeling
The first step in performing the power flow is numbering the branches or, in other words, the distribution lines.
In order to do this, first the network needs to be layered. For layering the network, the proposed strategy starts
from the main node and moves forward to the ending nodes. The lines between this node and the next nodes
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
constitute the first layer. The second layer consists of the lines between these layers and the next layers located
after them. After the network layering, it starts from the main node and the branches are numbered from 1
to Nb . The number allocated to the branches of the lower layer is bigger than the number of the upper layer
branches (in radial networks,Nb = N − 1, where N is the number of nodes and Nb is the number of branches).
The algorithm steps are as follows.
4.1.1. Backward sweep
By starting from the ending buses and moving backward to the slack bus, the power flow through each branch
is calculated using Eq. (9).
∑
Sn = Si +
Sm + Lossn
(9)
m∈M
Here, Sn is the power flowing through the n th branch, i is the last node of the n th branch, Si is the power
of the load connected to the i th node, M is the sum of the branches that are connected to the nth branch in
i th node, Sm is the power of the mth branch, and Lossn is the nth branch loss (which is considered as 0 in
the first iteration).
4.1.2. Forward sweep
By starting from the branches connected to the slack bus and moving forward to the ending branches, the
currents in the sending bus of the nth branch (j) and the voltages in the receiving bus of the nth branch (i)
are calculated using Eqs. (10) and (11). The branch losses are calculated using Eq. (12). Hence:
(
Jn =
Sn
Vj
)∗
,
V i = V j − Zn × Jn
(10)
,
(
)
Lossn = V j − V i × J ∗n
(11)
.
(12)
4.2. Calculating the voltage deviation
After performing steps 4.1.1. and 4.1.2. in each iteration, the voltage deviation for all of the buses is calculated
using Eq. (13):
(k) (k−1) (k)
∆V i = V i − V i
(13)
,
where k is the numerator of the iteration numbers.
If any of the ∆V i values are bigger than the convergence criterion ( ε), steps 4.1.1. and 4.1.2. are
repeated so that the convergence is gained.
4.3. Considering DG units in the power flow algorithm
The DG units are controlled like PQ buses. Hence, they can be modeled as passive (negative) loads, but for
considering DG units that are controlled like PV buses, more complicated procedures are needed in the power
flow calculations.
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
In order to control the voltage of PV nodes, the compensation technique from [25] is used. For gaining
the voltage profile in a PV node, the accurate generated reactive current injection is specified by the unit. For
this purpose, in each PV bus, the constant values for the DG are specified. The mentioned parameters are
the active power (P) and voltage amplitude (V). Next, in the power flow algorithm, this bus is considered as
a PQ bus. After the power flow is converged, the voltage deviation of the PV bus from the specified value is
calculated using Eq. (14):
i i − Vcal ≤ ε i = 1 : nP V ,
(14)
∆V i = Vsp
i
is the specified value of
where ∆V i is the voltage deviation in the ith node, nP V is the PV node number, Vsp
i
the voltage amplitude in the i th bus, and Vcal
is the calculated value of the voltage amplitude in the i th bus.
If the voltage deviation is at a specified limit, the PV node voltage is converged to the specified value.
Otherwise, by the DG reactive power compensation, this voltage remains at the specified value.
The amount of reactive power required for compensation is calculated by:
X.∆Q = ∆V,
(15)
where X is the sensitivity matrix of the PV node (with the size of nP V −unconverged × nP V −unconverged ).
The diagonal elements of the X matrix are the summation of the reactance of the branches between each
unconverged PV node and the source node. The off-diagonal elements of the X matrix are the summation of
the reactance of the common branches between each unconverged PV node and source node.
nP V −unconverged is the number of PV nodes in which the voltage magnitude has not converged to the
specified value, ∆Q is the injected reactive power vector and its size is nP V −unconverged × 1 , and ∆V is the
voltage deviation vector and its size is nP V −unconverged × 1 .
If ∆V > , the DG should generate active power to maintain the voltage in the specified value.
If ∆V < 0, the DG should absorb reactive power to maintain the voltage in the specified value (the DG
should decrease the reactive power injection to the network).
Hence:
Qicalnew = Qicalold ± ∆Qi i = 1 : npv ,
(16)
where Qicalnew is the new calculated value for the i th bus DG injection and Qi≀↕⌈ is the calculated value for the
i th bus DG reactive power generation in the previous iteration.
After calculating ∆Q, the generated reactive power value should be controlled using Eq. (17). If the
reactive power (Q) is outside the limit, its value should be adjusted to the limit.
Qimin ≤ Qicalnew ≤ Qimax
(17)
After performing the aforementioned procedure, the power flow calculation is performed again and the mentioned
steps are repeated. If the voltages of all of the PV nodes converge to the specified value, then the proposed
algorithm has also converged.
5. Optimization problem formulation
The recommended objective function of the multiobjective optimization problem is considered as below:
∑
∑
PLoss
Costcap
CostDG
SI
M inF = k1 ×
+ k2 ×
+ k3 ×
− k4 ×
,
PLoss0
Costcapmax
CostDGmax
SI0
6
(18)
ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
4
∑
ki = 1,
(19)
i=1
where PLoss0 is the total losses of the network before the installation of the DG units and the capacitors, PLoss
is the total losses of the network after the installation of the DG units and the capacitors, sumCostcap is the
sum of the cost of the installed capacitors [26], and Costcapmax is the cost of the biggest summation of capacitors
that can be installed.
Qc ≤ Qcmax
Here,
∑
(20)
CostDG is the sum of the installed DG units’ cost.
The capital cost of the DG units is different because of their types [27], but in general it can be defined
as in Eq. (21):
CostDGi = Ki × PDGi ,
(21)
where Ki is the constant coefficient (US$/kW).
In this paper, it is assumed that 8 generators exist (Table 1), where CostDGmax is the cost of the biggest
DG unit that can be installed.
PDG ≤ PDGmax
(22)
Here, SI0 is the system voltage SI before the installation of the DG units and the capacitors, SI is the system
voltage stability index, and ki is the weighting constants, which are selected as follows:
k1 = 0.6, k2 = 0.1, k3 = 0.2, k4 = 0.1.
In addition, all of the buses’ voltage constraints and thermal limits of the lines are modeled as inequality
conditions in the multiobjective optimization problem.
Table 1. Characteristics of the DG units.
Capacity (kW)
250
500
750
1000
1250
1500
1750
2000
Capital cost (USD$/kW)
2121
1500
1225
1061
949
866
802
750
6. Genetic algorithm
GAs are search algorithms based on the process of biological evolution. In this algorithm, the problem variables
are defined as binary strings that are known as genes. A set of genes constitutes a chromosome that is one of
the possible solutions of the problem. The basic structure of the GA is as follows: first, a randomly constructed
initial population of chromosomes is generated. Next, the fitness of each chromosome is defined by the objective
function. The selection operator chooses the chromosomes with better fitness among the population. Using
crossover and mutation operators, a new population is produced. The iterative loop is executed until the
termination condition is satisfied [28].
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
7. Problem algorithm
The proposed algorithm is shown in Figure 3 based on the GA. If the number of buses in the network is assumed
as N, then the number of candidate buses for the DG unit installation and the capacitor placement is N − 1
(in the slack bus, no DG unit or capacitor is installed). In this case, the length of each string or chromosome
is 2N − 2. Each chromosome presents the capacity of the installed DG unit or capacitor in the related bus. If
0 is placed in any of the bits, it shows that no DG unit or capacitor is placed in that bus. The capacity of the
DG units is within (0– PDGmax ) in the defined steps and the capacity of the capacitors changes in the defined
steps in the range of (0 − QC max ). The structure of each chromosome is shown in Figure 4.
For the studied problem in this paper, the GA parameters are selected as in Table 2.
Start
A
Acquiring
network data
A
Execution of power flow program
and calculation of power losses
and voltage stability index
Network without DGs and
capacitors to find base
o bjective f unction terms
(PLoss 0 , SI 0 )
Generating initial
population
randomly
B
Execution of power flow program
and calculation of power losses
and voltage stability index
C
A
B
Evaluation f itness of
all individuals
Yes
End
C
Best
individuals
Termination
condition met?
f i (x ) k1 ×
k3 ×
PLoss
PLoss 0
Σ Cost DG
Cost DG max
k4×
No
Crossover &
mutation
Offspring
Roulette wheel
selection
Generating new
population
Figure 3. Flowchart of the proposed method.
8
k2 ×
C
Σ Cost cap
Cost cap max
SI
SI 0
ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
X1
X2
XN-1
DGs capacity in each node
XN
XN+1
X2N-2
Capacitors capacity in each node
Figure 4. Chromosome structure.
Table 2. GA parameters.
Population size
120
Selection function
Roulette wheel
No. of variables
33 × 2 – 2
Crossover
Single point
Crossover rate
0.9
Mutation rate
0.035
8. Results and discussion
In order to simulate the proposed problem, the IEEE 33-bus radial network is used (Figure 5). The network
base voltage is 12.66 kV and the base apparent power is 10 MVA. The network data, including the resistance and
reactance of the lines and the loads connected to nodes, were presented in [29]. For the cost evaluation of the
capacitor banks, the given data in [26] are used. In order to show the importance of studying the simultaneous
placement and sizing of the DG units and the capacitors, first, for the proposed network, the quantity, placement,
and sizes of the different DG units and the capacitors are presented separately, and, finally, the simultaneous
quantity, placement, and sizing of the DG units and the capacitors is determined and the results are compared.
Figure 5. The studied IEEE 33-bus radial network.
8.1. The base case (network without a DG unit and capacitor)
In this case study, the network losses are equal to 202.676 kW and the security index of the nodes’ voltage
stability is shown in Figure 6. It has been shown that bus 18 is the weakest bus, which has a voltage magnitude
of around 0.913 pu and its voltage SI is 0.682.
8.2. Optimal quantity, placement, and capacities of the DG units
In this section, the quantity, placement, and capacities of different DG units regarding the minimum value of
the problem objective function are defined. In this case, the term related to the capacitors’ cost in the objective
functions is not present and the capacity of the DG units increases up to a maximum value of 2000 kW in steps
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
Voltage stability index
of 250 kW, which is shown in Table 1. The results for the different types of DG are shown in Table 3. Table 4
shows the voltage SI, system losses, and the objective function value after the installation of different DG units.
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
1
5
9
13
17
21
Bus number
25
29
33
Figure 6. The node voltage SI in the base case.
Table 3. Optimal quantity, placement, and capacities of the different DG units.
DG type
1
3
4
PDG (kW)
750
750
500
500
1000
Bus No.
14
31
14
14
30
Table 4. Losses and voltage SI of the system and the objective function value after the installation of the DG units.
DG type
1
3
4
Ploss
92.47
173.66
37.452
SISys
0.839
0.712
0.912
∆Ploss /Ploss0
54.3%
14.32%
81.52%
F
0.396
0.510
0.219
8.3. Optimal capacitor placement
In this section, the quantity, placement, and optimal capacities of the required capacitors regarding the minimum
value of the multiobjective cost function are defined. For this purpose, the term related to the cost of the DG
units in the objective function is eliminated. The maximum capacity of the capacitors is considered to be 1500
Kvar. The results of the algorithm are given in Tables 5 and 6.
Table 5. Optimal quantity, placement, and capacities of the capacitors.
Bus No.
14
30
Qc (kVar)
450
900
Table 6. Losses and voltage SI of the system and the objective function value after the installation of the capacitors.
Ploss
137.098
10
SISys
0.771
∆Ploss / Ploss0
32.35%
F
0.376
ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
8.4. Optimal placement of the DG units after installation of the capacitors
In this section, the quantity, placement, and optimal capacities of the DG units after installation of optimal
capacitors is done for the different types of DGs. This section is necessary for the simultaneous discussion of
optimal placement of DGs and capacitors. The results for different types of DGs are shown in Table 7. Table 8
presents the voltage SI, system losses, and the objective function value after the installation of different types
of DGs.
Table 7. Optimal quantity, placement, and capacities of the different DG units after of the installation of the capacitors.
Type
1
3
4
PDG (kW)
1250
750
1500
Bus No.
29
14
29
Table 8. Losses and voltage SI of the system and the objective function value after the installation of the DG units and
capacitors.
DG type
1
3
4
Ploss
60.88
82.198
56.63
SISys
0.838
0.813
0.912
∆Ploss / Ploss0
69.97%
59.44%
72.06%
F
0.3079
0.339
0.3071
8.5. Simultaneous optimal placement of DGs and capacitors
In this section, the simultaneous placements and capacities of the DG units and capacitors are done for the
different types of DG. The results gained from the algorithm shown in Figure 3 are presented in Table 9. Table
10 presents the voltage SI, system losses, and the objective function value after the installation of different DG
units and capacitors. The voltage SI of the network buses is presented in Figures 7, 8, and 9 for the 4 cases
of the base case, after the installation of the DG units, after the installation of the capacitors, and after the
simultaneous installation of the DG units and the capacitors. Moreover, the buses’ voltages before and after
the installation of the DG units and capacitors for the different types of DG are shown in Figures 10, 11, and
12.
Table 9. Optimal quantity, placement, and sizes of the different DG units and capacitors.
DG type
1
3
4
PDG (kW)
750
500
1000
–
500
1000
Bus No.
32
16
12
–
14
30
Qc (kVar)
900
–
900
900
–
–
Bus No.
30
–
12
30
–
–
Table 10. Losses and voltage SI of the system and the objective function value after the installation of the DG units
and capacitors.
DG type
1
3
4
Ploss
51.92
67.689
37.452
SISys
0.862
0.837
0.912
∆Ploss /Ploss0
74.38%
66.51%
81.52%
F
0.304
0.328
0.219
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ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
1
1.05
0.95
0.9
0.85
0.8
0.75
0.8
0.75
0.7
0.65
1
5
9
13
17
21
Bus number
25
29
33
5
1
Voltage (pu)
0.95
0.85
0.8
13
17
21
Bus number
25
29
33
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
1.02
0.9
9
Figure 8. Bus voltage SI before and after the installation
of DG type 3 and the capacitor.
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
1
Voltage stability index
0.9
0.85
0.7
1.05
0.98
0.96
0.94
0.75
0.92
0.7
0.65
1
5
9
13
17
21
Bus number
25
29
0.9
33
Figure 9. Bus voltage SI before and after the installation
of DG type 4 and the capacitor.
0.96
0.92
0.92
9
13
17
21
Bus number
25
29
33
Figure 11. Bus voltages before and after the installation
of DG type 3 and the capacitor.
17
21
Bus number
25
29
33
0.96
0.94
5
13
0.98
0.94
1
9
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
1
0.98
0.9
5
1.02
Voltage (pu)
1
1
Figure 10. Bus voltages before and after the installation
of DG type 1 and the capacitor.
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
1.02
Voltage (pu)
0.95
0.65
1
Figure 7. Bus voltage SI before and after the installation
of DG type 1 and the capacitor.
12
1
Voltage stability index
Voltage stability index
1.05
Base case
With capacitor
With DG
With DG and capacitor (simultaneously)
With DG and capacitor (separately)
0.9
1
5
9
13
17
21
Bus number
25
29
33
Figure 12. Bus voltages before and after the installation
of DG type 4 and the capacitor.
ESMAEILIAN et al./Turk J Elec Eng & Comp Sci
According to the above simulation results, if the operation from the network is in the presence of DG
types 1 and 4, better conditions are provided than operation in the presence of the capacitors, which shows that
the role of these types of DG is more effective than that of the capacitors. The simulation results also show
that the optimal operation of the network occurs in the simultaneous expansion planning of DG resources and
capacitors. This matter is especially more obvious in the case of DG type 3. In the case of DG type 4, according
to the optimization problem objective function and the selected weighting factors, the simulation results in the
presence of DG units alone, and also by considering the capacitors and DG units simultaneously, are identical.
This is because of the reactive power generation by the DG units, and therefore there is no need to pay an
extra cost for the capacitors. Comparing the results, it is obvious that optimal operation from the network is
obtained by the simultaneous placement of DG units and capacitors.
9. Conclusion
In this paper, the optimal placement of DG units and capacitors simultaneously is modeled as a nonlinear
optimal problem. Hence, the quantity, placement, and sizes of the DG units and capacitors are calculated in
a novel approach based on the multiobjective problem. The voltage SI is applied in the proposed optimization
approach as a security index and it covers the security requirement in the mentioned optimal placement. The
simulation results show that the optimal operation of the network occurs in the simultaneous expansion planning
of the DG units and capacitors.
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