A Genetic algorithm based optimization of DG/capacitors units
considering power system indices
Hossein Afrakhte1, Elahe Hassanzadeh2
1
Assistant Prof. of Guilan Faculty of Engineering, ho_afrakhte@guilan.ac.ir
2
Elahehassanzadeh@yahoo.com
Abstract: In this paper, both Distributed Generators (DG) units
and shunt capacitors are allocated and sized optimally and
simultaneously for line loss reduction, voltage profile
improvement and the reliability rising of the power system. The
objective function which includes power losses (active and
reactive), voltage profile and reliability indices is maximized
using genetic algorithm. Power system operation limits are
considered as constraints. The problem of optimal distributed
generation and capacitor sizing and placement is solved for a
9-buses test system and the results of applying the proposed
method illustrate the best answer is found by optimizing both
DGs and capacitors in distribution networks.
determine the optimal sitting and sizing of DG with
multi-system constraints. In [3] a simulated annealing is
proposed to determine the locations, the types and sizes
of capacitors and the control settings of them. A PSO
based multi objective formulation was proposed in [4] for
optimal capacitor placement incorporating the cost of
reliability, coasts of losses and investments as objective
function and in [5] to optimize the cost of power losses
and energy not supplied in presence of DG.
Ref [6] represented a Fuzzy model for optimal DG sitting
and sizing and determines its operation mode (PV or PQ).
In [7], the distributed generation impacts on total losses,
voltage profile and short circuit currents were used as
objective function based on a steady-state analysis to
search the best points for connecting distributed
generators. In [8,] the problem of the optimal allocation
and sizing of capacitors in unbalanced distribution
systems is formulated as a multi-objective optimization
problem by using a micro genetic algorithm. Ref [9]
proposed a approach for capacitor placement through
sensitivity factors and self adaptive hybrid differential
evolution (SaHDE) technique.
In this paper, the genetic algorithm is applied to
determine the optimal location and size of a DG unit
along with four shunt capacitors for power losses
reduction, voltage profile and reliability improvements.
Keywords: Capacitors, Distribution Generation (DG),
Genetic Algorithms (GA), Power Loss, Reliability,
Voltage Profile.
1.
Introduction
The primary and main function of electric utilities is
providing a reliable and secure energy supply for
customers with specific voltage and stable frequency. So,
they try to obtain this goal by means of different solutions
such as the application of Distributed Generation (DG)
units and shunt capacitors.
Technological progress, economical analyses,
environmental considerations, and power system
deregulation are known as efficient reasons of DG
employment. DG could contain any small power
generators near to utilization points that complement
central power stations regardless of energy source. The
impact of DG in system operating characteristics needs to
be evaluated properly because the performance of power
system can be improved or destroyed via proper location
and sizing of DG and system operating conditions [1]-[2].
Shunt capacitors can also be considered in parallel
with DG units due to their applications in voltage
stabilization, power/energy loss minimization, system
capacity release, and reliability enhancement [3]-[4].
A wide variety of research work has been done to
address the placement and sizing of DG and capacitor via
different methods and for different reasons. In [1] a linear
programming and Genetic algorithm were used to
2.
Problem Formulation
Determining the optimum location and sizing of DG
and capacitor units and studies their impact on loss,
voltage profile and reliability is the overall goal of this
paper. The objective function is composed of active and
reactive power losses, voltage profile and reliability
indices that are explained below:
2.1
Power Loss
Studies have indicated that as much as 13% of total
power generated is wasted in the form of losses at the
distribution level [10]. One of the main advantages
offered by DG is the line loss reduction because of its
proximity to the load canters.
٦٤١
In the heavy load conditions, the cost of losses will be
added to customers' costs. Therefore, in feeders with high
losses, using small-scale distributed generation (10-20%
of the feeder load) could cause a significant reduction of
losses [11].
DG and capacitor operations in minimizing the loss are
similar. The difference is that the DG units cause impact
on both the active and reactive power, while the capacitor
banks only have impact on the reactive power flow.
The line losses index is given as:
N
F1 

r = Maintenance time
U = λ × r = average annual off time
In this paper, the ENS index (the amount of energy that
has not been supplied) has been used as a reliability
improvement index illustrated as:
N
F3 
N
  Pl N  PlwDGor C   PlN
m 1
λ = Failure rate
m 1
N
N
m 1
m 1
(1)
ENSi  LiU i (KWh/year)
OF  Max w1 F1  w2 F 2  w3 F3 
(6)
 Vmin  Vi  Vmax

 Pl  Pl max
 min
max
Subject to :  PDG
 PDG  PDG
 min
max
 QDG  QDG  QDG
 PF
min  PF  PF max

(2)
2.2
Voltage Profile
Proper location and sizing of DG and capacitors lead
to boost the voltage profile of the grid Voltage profile at
the customer site is improved depending on the amount
of reactive power injected by the shunt capacitor. In
addition, DG relieves the load demand that will cause an
improvement in the voltage magnitude. The proposed
index of voltage profile improvement has been
determined as:
VPN 
(5)
Where, Li is the average load connected to load point i in
kW. ENS N , ENSDG or C are the total average energy not
supplied when the fault happened in all sections of system
in the case of without and with DG and capacitor
respectively.
2.4
Objective Function
Where, Pl N and Ql N are the total active and reactive line
losses of th total active and reactive line losses with DG
and capacitors. High value of index F1 indicates low
power losses meaning better system performance.
Active and reactive load models are presumed
constant and the grid total MVA is expressed as [12]:
F2  VPDG or C VPN
(4)
i 1
  QlN  QlwDGor C   QlN
1/ 2

2


S   PN  PDG  


 Q  Q
2

DG  QC  
 N

Q DG  0 asynchrono us generators
 ENSN  ENSDG or C  ENSN 
3
 wi  1
 wi  0 1
(7)
1
٢
٣
٤
Table I shows wi values (weight coefficients) for
indices. Those values may vary according to the network
operator’s concerns.
(3)
1 N  Vi Vmin  Vmax Vi  

N m1  1 Vmin  Vmax  1 
TABLE I: Weight Coefficients
w1
0.35
Where, VPN and VPDG or C are the voltage profile of
system in the case of without and with DG and capacitor
respectively. Vi is the voltage magnitude of the ith bus,
Vmin and Vmax are the minimum and maximum allowed
operation voltages. A High index F2 value indicates high
quality voltage profile.
3.
w2
0.3
w3
0.35
GA Setup and Coding of the Solution
Genetic algorithms work by optimizing the fitness
function (formed by adding the objective function and
penalty terms for constraints violations). When applying
Genetic Algorithms to optimize the DG/shunt capacitors
allocation and sizing problems, an important aspect is the
coding of the potential solutions.
The initial population (coded variables) is the
candidate locations and sizes of DG/capacitor units. Each
chromosome is represented by a vector. The chromosome
coding in this study as seen in Fig. 1 is defined as a two-
2.3
Reliability
Main Power system ability in securing the supply of
electricity and delivering an acceptable quality of power
to the customers is mentioned as a reliability concept
which is one of the most important criteria and must be
considered during power system planning and operation.
The main indices (load point) used to assess the reliability
of distribution networks are [13]:
٦٤٢
vector chromosome in which the first section is a string
of bus numbers that DG/capacitor are installed, the
secondary section explains the DG/capacitors capacities.
4.
Simulation Results
The test system for the proposed methodology is a 9bus, single feeder, radial distribution network [14] shown
in Fig.3. The substation line voltage is 23kV and details
of the feeder and the load characteristics are given in
Table II. In this work, the failure rate for all branches is
assumed to be 0.1 f /km-year that "f" represents the
failure frequency. Therefore, the failure rates of the test
system are in the range [0.1, 0.5] (f/year) which the
longer line with highest impedance has the biggest failure
rate. The repair time is 4 h and the switching time is 0.5h.
By running the power flow without DG and
capacitors, calculated values of active and reactive power
losses are 0.784 MW and 0.64 MVAR and the average of
bus voltage is 0.937.
Fig. 1: Chromosome coding
BUS i is a discrete number between 1 and the total
number of buses. PDG i and QCAi are continuous
numbers ranging from zero to the maximum value of DG
capacity (MW) and capacitor capacity (MVAR)
respectively. Genetic Algorithm searches for the best
answer in a continuous way between boundary limits;
consequently the optimal case is GA output. Genetic
Algorithm parameters used for all system were:
Population size: 50, Number of generation: 300, Crossover function: Arithmetic, Mutation function: Gaussian,
Mutation Rate: 0.7, Selection type: Roulette Wheel.
The elitism mechanism is adopted for ensuring the
survival of the best performing combination. For each
location of DG/capacitor units in GA, an optimal power
flow is used to define their available sizes.
The utilization of this structure is various extensions
implementing to the standard OPF problem and easily
adding the new variables, constraints and costs to it.
Calculating of optimal power flow is used to evaluate the
branch current, bus voltage, real and reactive power flows
for the generation and load conditions at each bus. The
flow chart for the proposed method based on the GA is
given in the Fig. 2.
Fig. 3: Case study
Then, the proposed algorithm is carried out for one
DG unit and four capacitor banks individually and
simultaneously. Capacitor and DG sizes are randomly
selected from [150, 300, 450, 600, 750, and 900] KVAR
and [0.1, 0.4] MW respectively.
The total ENS value of grid before DG/capacitor
placements is about 55051 KWh/year, after 4 capacitors
allocated in their proper locations (3, 4, 5 and 9) is 45354
KWh/year, after one DG optimum locating (bus 9) and
sizing (379 KW) reduce to 42505 KWh/year and after
DG/capacitors simultaneously installing (DG at bus 8,
capacitors at buses 3, 4, 6, and 7) reduce to 40350
KWh/year. Reliability calculations of the test system are
given in Table III. The values of “r” and “U” at each
branch and for each case are not included because of the
lack of sufficient space. Tables IV shows a comparison
between the results related to a system of different
DG/Capacitor configurations that illustrates a big
difference among the system results without a
DG/capacitor and other cases.
As mentioned, choosing both DGs and capacitors are
necessary for minimizing the active and reactive power
losses and boosting the voltage profile of network.
However, DG has more efficiency at improving system
reliability. Changing optimum location and size of DG
and capacitors when they installed simultaneity, is an
important issue.
Fig. 2: Flowchart of genetic algorithm
٦٤٣
TABLE II: Load and line data of 9-bus system
Branch
PL (KW)
QL (KWAR)
R + j X (Ω)
λ (f/year)
0-1
1840
460
0.123 +
j0.413
0.107
1-2
980
340
0.014 +
j0.605
0.1
2-3
1790
446
0.746 +
j1.205
0.151
3-4
1598
1840
0.698 +
j0.608
0.15
4-5
1610
600
1.983 +
j1.728
0.249
5-6
780
110
0.905 +
j0.798
0.162
6-7
1150
60
2.055 +
j1.164
0.248
7-8
980
130
4.795 +
j2.716
0.46
8-9
1640
200
5.343 +
j3.026
0.5
TABLE III: Reliability calculations of test system for 4 cases (1- without DG/Capacitor, 2-with Capacitor, 3-with DG and 4- with DG/Capacitor)
Feeder
section
1
2
3
4
5
6
7
8
9
total
λ1
0.107
0.1
0.151
0.15
0.249
0.162
0.248
0.46
0.5
Failure rate (f/year)
λ2
λ3
0.092
0.087
0.085
0.0795
0.13
0.123
0.143
0.137
0.218
0.202
0.149
0.14
0.215
0.201
0.415
0.4
0.43
0.42
λ4
0.08
0.072
0.112
0.13
0.192
0.128
0.19
0.383
0.412
ENS1
2536.885
2879.885
3925.9
4753.664
6106.064
6548.324
7554.574
9142.664
11602.664
55050.624
ENS (KWh/year)
ENS2
ENS3
1864.288
1723.118
2159.268
1996.048
2979.983
2766.64
3774.189
3532.920
5002.619
4671.19
5409.389
5053.39
6282.814
5858.234
7706.264
7230.014
10174.464
9673.795
45353.278
42505.358
ENS4
1667.46
1914.42
2616.1
3343.16
4425.08
4774.52
5539.27
6852.96
9217.84
40350.81
Active and reactive power losses of system are shown
in Figs 4 and 5 before and after the installation of DG and
capacitors respectively. To analyse the voltage profile of
the test system, Fig 6 is plotted. Comparing the results
illustrates that the integration of both DG and capacitor
into the network can improve the voltage more than the
other situations. The value of failure rate and ENS with
and without DG and capacitors are shown in Figs 7 and 8
respectively.
Table V shows the objective function value.
Fig. 5: Network reactive power loss
Fig. 4: Network active power loss
Fig. 6: Impact of different DG/Capacitor configurations on voltage
profile
٦٤٤
TABLE V: Objective function value
Capacitor
DG
DG& Capacitor
F1
0.13
0.32
0.42
F2
0.01
0.012
0.0212
F3
0.١٨
0.٢٣
0.٢٨
OF
0.1١
0.١٩٦
0.2٤
References
[1]
Fig. 7: Network Failure Rate
[2]
[3]
[4]
[5]
[6]
[7]
[8]
Fig. 8: Network ENS index
TABLE IV: Comparison of different DG/capacitor arrangements
Capacitor bus
-
-
-
-
533
430
42505
9
379 + j
102
-
-
679.2
535
45354
-
3, 4,
5, 9
900, 900,
750, 300
P+jQ
Capacitor
size KVAR
ENS
(KWh/yr)
55051
DG size
Q ( KVAR)
640
DG bus
P ( KW)
784
[9]
[10]
[11]
[12]
[13]
448
400
40350
8
379 +
j100
3, 4,
6, 7
750, 750,
600, 300
[14]
٦٤٥
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