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Hybrid Particle Swarm Optimization Approach for Optimal Distribution
Generation Sizing and Allocation in Distribution Systems
Conference PaperinCanadian Conference on Electrical and Computer Engineering · May 2007
DOI: 10.1109/CCECE.2007.328·Source: IEEE Xplore
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Hybrid Particle Swarm Optimization Approach for
Optimal Distribution Generation Sizing and
Allocation in Distribution Systems
M. F. AlHajri
∗
,M.R.AlRashidi
†
, and M. E. El-Hawary
‡
,
Department of Electrical and Computer Engineering
Dalhousie University, Halifax, NS B3J 2X4 Canada
Email:
∗
malhajri@dal.ca,
†
malrash@dal.ca,
‡
elhawary@dal.ca
Abstract— This paper presents a novel particle swarm opti-
mization based approach to optimally incorporate a distribution
generator into a distribution system. The proposed algorithm
combines particle swarm optimization with load flow algorithm to
solve the problem in a single step, i.e. finding the best combination
of location and size simultaneously. In the developed algorithm,
the objective function to be minimized is the total network power
losses while satisfying the voltage constraints imposed on the
system. It is formulated as constrained mixed integer nonlinear
programming problem with the location being discrete. The
69−bus radial distribution system has been used to validate the
proposed method. Test results demonstrate the effectiveness and
robustness of the developed algorithm.
Keyword: Distributed Generation, Particle Swarm Optimiza-
tion, Distribution System.
I. INTRODUCTION
Distribution systems usually encompass distribution feeders
configured radially and exclusively fed by utility substation.
The 1978 Public Utilities Regularitorty Policy Act (PURPA)
legislation revamped the 1935 legislation of the Public Utilities
Holding Company Act (PUHCA) to allow qualified facilities
to generate and sell electricity to utilities [1]. Due to advances
in small generation technologies, electric utilities began to
change their electric infrastructure and start adapting on-site,
multiple, small, and scattered Distribution Generations (DGs).
Typically, their power output ratings ranges from 1 kW to
20 MW [2].
Distribution Generation (DG) is expected to gain more
popularity in future generation system as a result of several
factors like the liberalization of the electricity market, recent
developments in distribution generation technologies, grow-
ing interest toward environmentally friendly energy sources,
transmission lines congestion and increased electricity costs.
Recent studies predicted that in the near future DG will play
a vital role in the electric power system. An Electric Power
Research Institute’s (EPRI) study forecasted that by the year
2010, 25% of the newly installed generation will be DGs, and
a similar study by Natural Gas Foundation believes that the
share of DG in new generation will be 30% [3].
DG technologies include a variety of conventional (fuel-
based) and green energy sources. Conventional sources for
DG include gas and diesel, while green sources are the
renewable energy sources like wind, biomass, geothermal,
and solar energies. The DG technologies available in the
market are diesel and gas reciprocating engines, microturbines,
photovoltaic systems, wind energy conversion systems, gas
turbines, and fuel cell systems [4], [5].
Incorporating DG into the distribution system may have
positive and/or negative impacts on the customer and on the
utility equipment depending on the operation condition of the
DG and the distribution system. Negative issues might be
instability of the voltage profile due to the bi-directional power
flows, quality of supply and/or harmonics [6], [7]. Positive
impacts and benefits could be summed as follows [8], [9]:
• Line loss reduction,
• Reduced environmental impacts,
• Peak shaving,
• Relieved transmission and distribution congestion,
• Reducing fossil fuel emissions,
• Postponing transmission and distribution upgrade costs
by providing electric power at a site closer to the cus-
tomer,
• improving the distribution feeder voltage conditions,
• Improved utility system reliability.
Optimal locating and sizing of the DG that minimize the
radial distribution network loses is one area that is attracting
more researchers recently. Installing the DG does not always
minimize the distribution network losses efficiently. Some
important factors such as DG rating, location and operating
power factor have to be considered carefully when analyzing
the distribution system.
Rahman et al. [10] and Jurado et al. [11] discussed the
placement of the DG and the size in two seperate steps, i.e.
not simultaneously. In both cases, the authors determined the
optimal location first, then solved for the optimal sizing of
the DG second. Studies conducted by Griffin et al. [12] and
Gandomkar et al. [13] investigated only the location aspects of
DG with respect to network real power losses. Willis applied
the 2/3 rule that is commonly used in capacitor placement
studies to the DG optimal sizing and placement problem [14].
That is to install a DG with a rating of 2/3 of the applied load
at 2/3 the radial feeder length. However, this rule assumes
uniformly distributed loads in a radial configuration. This
assumption limits its applicability to real distribution system.
This paper presents a novel particle swarm optimization
0840-7789/07/$25.00 ©2007 IEEE
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based approach to optimally incorporate distribution generator
into a distribution system. The algorithm is utilized to search
for the optimal DG size and bus location simultaneously that
minimize the total network power losses while satisfying the
voltage constraints imposed on the system.
This paper is organized as follows: section 2 states the
problem formulation and model constraints. Then, a brief
overview of PSO algorithm and development is presented in
section 3. Simulation results and discussion are presented in
section 4 and finally concluding remarks are summarized in
section 5.
II. M
ATHEMATICAL FORMULATION
The problem investigated in this research is to find the
optimal DG power rating and bus location simultaneously that
make the radial distribution network real losses a minimum.
The real power losses are given as:
P
Loss
=
N
i
|I
br
i
|
2
R
i
(1)
where
• I
br
i
is the current in branch i,
• N is the total number of branches in the system,
• R
i
is the branch resistance.
Based on equation 1, the line power losses could be reduced
by lowering the branch currents in the distribution network.
One way to reduce the current in certain parts of the network
is to introduce the DG.
The problem is formulated as one of constrained mixed
integer nonlinear programming with the location being discrete
and the size being continuous. In the developed algorithm,
the objective function to be minimized is the total network
power losses while satisfying certain constraints imposed on
the system variables.
The objective function is as follows:-
Minimize P
Loss
(2)
• The equality constrains are the non-linear power flow
equations of the radial distribution system. They can be
written in vector form as follows:-
H(x,u) = 0 (3)
where
–xis the state vector which represents the dependent
variables.
–uis the control vector that represents the independent
variables.
• The inequality constraints are the voltage limits imposed
on the radial distribution system as follows:-
V
min
j
≤ V
j
≤ V
max
j
,j=1,...,K (4)
where j is the distribution bus number.
• The inequality constraint associated with the DG real
power output is as follows:-
P
min
DG
≤ P
DG
≤ P
max
DG
(5)
The DG can be treated as PV or PQ models in the
distribution system. The PV model represents a DG which
delivers power at a specific terminal voltage; while the DG PQ
model delivers power at a designated power factor [15]. The
latter DG model representation is adopted in this paper. It is
customary for the DGs to operate at a power factor between
0.85 and unity [8]. The proposed DG delivers constant real
power with a lagging power factor of 0.85. Such source will be
modeled as a negative load delivering a real and reactive power
to the distribution system regardless of the system voltage.
III. P
ARTICLE SWA R M OPTIMIZATION
Kennedy and Eberhart first introduced Particle Swarm Op-
timization (PSO) in 1995 as a primitive optimizer [16], [17].
They adopted a nonlinear stochastic model developed by
Heppner that mimics bird flocking movement. They realized
that, with some modifications, the model can serve as an
optimizer. The first version of PSO was meant to handle
only nonlinear continuous optimization problems. However,
several versions of PSO were subsequently proposed to cope
with constrained and combinatorial optimization problems.
PSO is a population-based evolutionary technique capable of
handling a wide class of optimization problems. It has many
key advantages over other optimization techniques like:
• It is a derivative-free technique.
• It does not make assumptions about the nature of the
objective function, i.e. convexity or continuity.
• It has few parameters to tune when compared to other
evolutionary techniques.
• It has the capability of detecting global solutions.
• It uses simple mathematical and logic operations.
In PSO, numbers of particles or “possible solutions” fly as
a swarm or “group” in the problem feasible hyperspace. Each
particle i is associated with two vectors namely the position
(x
i
) and velocity (v
i
) vectors. The size of these vectors is
determined by dimension of the problem at hand. Information
about the best solution achieved throughout the optimization
process is being shared among different particles. The strength
of PSO rises from its balance between individuality and
sociality interaction. Each particle updates its position and
velocity vectors according to the following equations:
v
k+1
i
= wv
k
i
+ c
1
r
1
(pbest
i
− x
k
i
)+c
2
r
2
(gbest
i
− x
k
i
) (6)
x
k+1
i
= x
k
i
+ v
k+1
i
(7)
where
• c
1
and c
2
are two positive acceleration constants.
• r
1
and r
2
are two randomly generated numbers with a
range of [0, 1].
• w is the inertia weight.
• pbest is the best solution achieved by individual particle.
• gbest is the best solution achieved among the entire
swarm.
The PSO algorithm can be summarized in the following steps:
1) Randomly initialize a swarm with feasible discrete posi-
tion vectors.
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2) Randomly assign a suitable velocity vector to each par-
ticle.
3) Record the fitness of the entire population.
4) Determine the best particle performance among the
group.
5) Update velocity and position vectors according to (6)
and (7) for each particle.
6) Discretize the position vector.
7) If any particle flies outside the feasible solution space,
restore the particle to its best previously achieved feasible
solution.
8) Repeat steps 1 − 7 until maximum number of iterations
is reached.
IV. T
EST RESULTS AND DISCUSSION
Simulations were carried out within MATLAB
computing
environment to test the proposed algorithm. The 69−bus
distribution test system shown in Fig.1 was used to validate
our approach with a total real and reactive power demand of
3802.19 kW and 2694.60 kVAR respectively [18].
1
2
5
4
3
10
9
8
7
6
18
17
16
15
14
13
12
11
23
22
21
20
19
24
25
26
27
29
28
34
33
32
31
30
35
49
48
47
50
54
53
59
58
57
56
55
60
64
63
62
61
65
38
37
36
43
42
41
40
39
44
45
46
52
51
67
66
68
69
Substation
Fig. 1. 69-bus radial distribution system
The PSO parameters used in this study are 20 particles and
c
1
= c
2
=2.0. They were selected based on our experiments
conducted on this given system to ensure proper convergence
characteristics. The DG real power output ranges from 10 to
2500 kW while all network bus voltage magnitudes are kept
within 0.9 − 1.00 per unit. After conducting 20 independent
runs, the algorithm selected bus 61 to be the optimal location
with an optimal DG power output of 1904.2 kW.
To study the impact of the DG installation on the system
performance, the following two cases are considered:
Case 1 Calculate the distribution network losses, minimum
bus voltage magnitude, and deviation in bus voltage
angle before the DG inclusion.
Case 2 Repeat case 1 with the DG included once its optimal
location and sizing are determined.
Results for both cases are reported in Table I. It is clear from
the obtained results that the DG placement has significantly
improved the distribution network performance in terms of
power losses, voltage magnitudes and phase angle deviations.
The voltage profiles before and after the DG inclusion are
shown in Table II. DG addition has released about 52% of the
substation capacity allowing future expansion to take place
without the need to upgrade the existing infrastructure.
To study the DG sizing impact on a network’s power losses,
the real power output of a DG installed on bus 61 is varied
between its rating limits and the distribution network power
losses are calculated for each given power output. Fig.2 shows
that once the DG power output exceeded the optimal value,
power losses will tend to increase beyond the minimal value.
TAB LE I
R
ESULTS FOR CASES 1 AND 2
Case 1 Case 2 % Improvement
Real Power Losses
(kW)
225.006 23.867 89.39
Minimum Bus
Voltage (p.u.)
0.9092@65 0.9725@27 6.51
Voltage Angle
Deviation
∆θ = θ
max
− θ
min
1.36
◦
0.6411
◦
52.86
Power Losses vs DG Real Power Output
0
50
100
150
200
250
0 500 1000 1500 2000 2500
DG Power Output (kW )
Power Losses (kW)
Fig. 2. Total network losses as a function of the DG power output installed
at bus 61.
V. C ONCLUSION
This paper presents solving the optimal DG allocation and
sizing problem through applying novel hybrid particle swarm
optimization based approach algorithm. By combining the
particle swarm optimization with the load flow algorithm
the problem was solved in a single step, that is finding the
best combination of location and sizing simultaneously. The
effectiveness of the PSO was demonstrated and tested. The
results show that incorporating the DG in the distribution
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TAB LE II
V
OLTAGE PROFILE BEFORE AND AFTER DG
Voltage before DG Voltage after DG
Bus |V | angle
◦
|V | angle
◦
1 1.000 0.000 1.000 0.000
2 1.000 -0.001 1.000 -0.001
3 1.000 -0.002 1.000 -0.001
4 1.000 -0.006 1.000 -0.003
5 0.999 -0.019 1.000 -0.004
6 0.990 0.049 0.997 0.038
7 0.981 0.121 0.994 0.081
8 0.979 0.138 0.994 0.092
9 0.977 0.147 0.993 0.097
10 0.972 0.232 0.988 0.179
11 0.971 0.249 0.987 0.195
12 0.968 0.302 0.984 0.246
13 0.965 0.348 0.981 0.291
14 0.962 0.394 0.978 0.336
15 0.959 0.440 0.976 0.380
16 0.959 0.449 0.975 0.389
17 0.958 0.463 0.974 0.402
18 0.958 0.463 0.974 0.402
19 0.958 0.472 0.974 0.411
20 0.957 0.477 0.973 0.416
21 0.957 0.486 0.973 0.425
22 0.957 0.486 0.973 0.425
23 0.957 0.487 0.973 0.426
24 0.957 0.490 0.973 0.429
25 0.956 0.493 0.973 0.431
26 0.956 0.495 0.973 0.433
27 0.956 0.495 0.973 0.433
28 1.000 -0.003 1.000 -0.001
29 1.000 -0.005 1.000 -0.004
30 1.000 -0.003 1.000 -0.002
31 1.000 -0.003 1.000 -0.001
32 1.000 -0.001 1.000 0.000
33 0.999 0.003 0.999 0.005
34 0.999 0.009 0.999 0.011
35 0.999 0.010 0.999 0.012
36 1.000 -0.003 1.000 -0.002
37 1.000 -0.009 1.000 -0.008
38 1.000 -0.012 1.000 -0.010
39 1.000 -0.013 1.000 -0.011
40 1.000 -0.013 1.000 -0.011
41 0.999 -0.024 0.999 -0.022
42 0.999 -0.028 0.999 -0.027
43 0.999 -0.029 0.999 -0.027
44 0.999 -0.029 0.999 -0.028
45 0.998 -0.031 0.998 -0.029
46 0.998 -0.031 0.998 -0.029
47 1.000 -0.008 1.000 -0.004
48 0.999 -0.053 0.999 -0.049
49 0.995 -0.192 0.995 -0.188
50 0.994 -0.211 0.994 -0.208
51 0.979 0.139 0.994 0.092
52 0.979 0.139 0.994 0.092
53 0.975 0.169 0.994 0.106
54 0.971 0.195 0.994 0.116
55 0.967 0.230 0.994 0.130
56 0.963 0.265 0.994 0.143
57 0.940 0.662 0.997 0.194
58 0.929 0.864 0.998 0.219
59 0.925 0.945 0.998 0.228
60 0.920 1.050 0.999 0.233
61 0.912 1.119 1.001 0.253
62 0.912 1.122 1.000 0.256
63 0.912 1.125 1.000 0.259
64 0.910 1.143 0.998 0.273
65 0.909 1.149 0.998 0.278
66 0.971 0.250 0.987 0.196
67 0.971 0.250 0.987 0.196
68 0.968 0.308 0.984 0.252
69 0.968 0.308 0.984 0.252
system can reduce the total line power losses. The proposed
algorithm was tested on 69−bus distribution system to solve
the DG mixed integer nonlinear problem with both equality
and inequality constraints imposed on the system. The hybrid
PSO significantly minimized the distribution network real
power losses and converged to the same bus for the DG to
be installed in every single run.
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