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GRD Journals | Global Research and Development Journal for Engineering | International Conference on Innovations in Engineering and Technology
(ICIET) - 2016 | July 2016
e-ISSN: 2455-5703
Optimal Location and Sizing of Distributed
Generation Using Krill Herd Algorithm
1A.
Marimuthu 2Dr.K.Gnanambal 3J. Kokila
1
Associate Professor 2Professor 3Student
1,2,3
Department of Electrical and Electronics Engineering
1,2,3
K.L.N College of Engineering Madurai
Abstract
Distributed generator (DG) is recognized as a viable solution for controlling line losses and represents a new era for distribution
systems. This paper focuses on developing an approach for placement of DG in order to minimize the active power loss and
reactive power loss of distribution line of a given power system. The optimization is carried out on the basis of optimal location
and optimal size of DG. This paper developed a new, efficient and novel krill herd algorithm (KHA) method for solving the
optimal DG allocation problem of distribution networks. To test the feasibility and effectiveness, the proposed KH algorithm is
tested on standard 33-bus radial distribution networks. The simulation results indicate that installing DG in the optimal location
can significantly reduce the power loss of distributed power system. A detailed performance analysis is carried out on IEEE 33
Radial bus distribution system to express the effectiveness of the proposed method. Computational outcomes obtained showed
that the proposed method is capable of generating optimal solutions.
Distributed generation (DG), Radial Distribution Network (RDN), Krill Herd Algorithm (KHA), Loss reduction
__________________________________________________________________________________________________
I. INTRODUCTION
The modern power distribution network is constantly being faced with an ever-growing load demand and it is observed that under
certain critical loading conditions, the distribution system experience voltage collapse in certain areas. Moreover, at heavy loads,
the reactive power flow becomes very significant which cause an increase in real power losses. The basic reason behind these huge
power losses is resistive loss, as well as distribution system is operated at much lower voltages compared to transmission systems.
Traditionally, capacitor and distributed generator (DG) are installed in power networks to compensate for power loss reduction.
Among these devices, DG is most widely used in distribution network because it has a unique property of supplying active as well
as reactive power, whereas capacitor supplies only reactive power to the network. However, studies of DG over few years have
indicated that the inappropriate selection of location and size of DG, may lead to greater system losses than the losses without DG
[1]. Therefore, the optimal location and size of DG is an important task for the researchers. A mixed integer linear programming
(MILP) [2] was introduced by Keane et al.to solve optimal DG allocation problem. Borghetti proposed (MILP) model [3] to
minimize system real power loss of radial distribution network. Rueda-Medina et al.also proposed MILP [4] approach to solve
optimal DG allocation problem at different load levels for the radial distribution network. The sensitivity factor based on equivalent
current injection was employed in [5]for the determination of the optimum size and location of DG to minimize total power losses
of radial systems. Khan et al. presented an analytical approach [6] to improve voltage profile and to minimize power loss of radial
distribution network. The simulation results indicated that the proposed algorithm was capable of identifying the optimal location
and size of DG in distribution system effectively. However, this analytical study is based on phasor current injection method which
has unrealistic assumptions such as:uniformly, increasingly, centrally distributed load profiles. These assumptions may cause
erroneous solution for the real systems. Rezaei et al. used dynamic programming (DP) technique [7] to place DG in the distribution
system to minimize power loss, improve reliability and voltage profile of the system. Aman et al. presented power stability index
(PSI) [8] for DG placement and sizing for distribution systems. The proposed method was implemented on12-bus, modified 12bus and 69-bus systems, and its performance was compared with golden section search (GSS) algorithm. However, all above
mentioned classical methods suffer from the disadvantage of finding the optimal solution for the nonlinear optimization problem.
Placement of DG in the radial distribution system is highly nonlinear optimization problem. Conventional optimization techniques
are not suitable for solving such type of problems. Moreover, there is no criterion to decide whether a local solution is also a global
solution. Large computational time is another drawback of most of these techniques. The advent of stochastic search algorithms
has provided alternative approaches for solving optimal DG allocation problems. These population-based techniques exterminate
most of the difficulties of classical methods. Many of these stochastic search algorithms have already been developed and
successfully implemented to solve optimal DG placement problem. Vankatesh et al. proposed evolutionary programming (EP) [9]
for optimal reconfiguration of radial distribution system to maximize loadability index. Popovic et al.proposed genetic algorithm
(GA) [10] for optimal sitting and sizing of DG in distribution systems.
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
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II. LOAD FLOW ANALYSIS
To meet the present growing domestic, industrial and commercial load day by day, effective planning of radial distribution network
is required. To ensure the effective planning with load transferring, the load flow study becomes utmost important. Load flow
analysis is concerned with describing the operating state of an entire power system, by which we mean a network of generators,
transmission lines, and loads. Given certain known quantities, typically, the amount of power generated and consumed at different
locations, load flow analysis allows one to determine other quantities. The most important of these quantities are the voltages at
locations throughout the transmission system, which, for alternating current (AC), consist of both a magnitude and phase angle.
Once the voltages are known, the currents flowing through every transmission link can be easily calculated.
A. Need for Power Flow Analysis
Load flow study is instrumental in the planning, design, and operation of distribution system for industrial facilities. This study
can be used to evaluate the effects of various equipment configurations, additions or modifications to generators, motors, or other
electrical loads. Modern systems are complex and have many paths or branches over which power can flow. Electric power flow
will divide among these branches until a balance is reached in accordance with Kirchhoff’s laws. Power flow analysis is required
for many other analyses such as transient stability and contingency studies. Power-flow studies are important for planning future
expansion of power systems as well as in determining the best operation of existing systems. The principal information obtained
from the power-flow study is the magnitude and phase angle of the voltage at each bus, and the real and reactive power flowing in
each line.
B. Load flow analysis
Load flow analysis is the most important and essential approach to investigating problems in power system operating and planning.
Based on a specified generating state and transmission network structure, load flow analysis solves the steady operation state with
node voltages and branch power flow in the power system. Load flow analysis is a steady state analysis of power system, which
provides information about the current state of the system for a given generation and load conditions. The R/X ratios of branches
in a distribution system are relatively high compared to a transmission system and makes the distribution system ill conditioned.
Newton-Raphson method exploits the radial nature of the distribution system and it is computationally more efficient.
The Newton-Raphson method, or Newton Method, is a powerful technique for solving equations numerically. The
Newton Method, properly used, usually homes in on a root with devastating efficiency. Moreover, it can be shown that the
technique is quadratic ally convergent as we approach the root. There are several different methods of solving the resulting
nonlinear system of equations. The most popular is known as the Newton-Raphson method.
The Algorithmic Steps for the Newton Raphson Load flow Analysis
Step 1: Make an initial guess of all unknown voltage magnitudes and angles. It is Common to use a “Flat Start” in which all voltage
angles are set to zero and all voltage magnitude are set to 1.0 pu.
Step 2: Solve the power balance equation using the most recent voltage angle and Magnitude v
n
Pi   v i v j v ij cos(θ ij  δ i  δ j )
(1)
j1
n
Q i   v i v j v ij sin(θ ij  δ i  δ j )
j1
(2)
Step 3: Linearize the system around the most recent voltage angle and magnitude Values.
Step 4: Solve for the change in voltage magnitude and angle.
Step 5: Update the Voltage Magnitude and Angle.
Step 6: Check the stopping conditions, if met then terminate, or else go to Step 2
III. DISTRIBUTED GENERATION
Distributed Generation is an emerging concept and it is a useful technology for providing electric power in the heart of the power
system. Distributed Generation mainly concentrates on the installation and operation of a portfolio of small size, compact, and
clean electric power generating units at or near an electrical load that is on the customer side. According to new technology, electric
power generation trend uses DG sizing from kW to MW at load sites instead of using traditional centralized generation units sized
from 100MW to GW and located far from the loads where the natural resources are available.
DG can be beneficial if it meets the basic requirements of the system’s operating philosophy and feeder design. However,
the insertion of DG into the distribution system could either have a positive or negative impact depending on the operating
characteristics of the DG and the distribution network.
A. Distributed Generation Technologies
From the constructional and technological points of view there are different types of DGs are available. Different DG technologies
can be used for small-scale electricity generation. Distributed resources compose of range of technologies including micro turbines,
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
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fuel cells and PV cells. Distributed energy resources involves power electronics interfaces, as well as communications and control
devices for effective dispatch and operation of single generating units, multiple system packages, and aggregated blocks of power.
A Renewable energy source that damages the nature and it come from the sun, from wind from water and from waves. Other
sources of renewable energy are available from organic matters, sometimes called bio-energy. Each of these energy sources has
unique characteristics and can play an important role in conservation and the reduction of pollutants. Most Renewable energy
resources can only be used on the power grid with the help of energy storage and power electronic support.
B. Types of distributed generation
Based on the DG technology and the terminal characteristics, they can be classified into four types.
Type 1) DG injects active power (P) only, eg. Photovoltaic
Type 2) DG injects reactive power (Q) only eg. Synchronous compensator
Type 3) DG injects active power but absorbs reactive power, eg. Induction generator .The reactive power Consumed by
an induction generator in a simple form is given in
QDG = - (0.5 +0.04P2)
(3)
Type 4) DG injects both active and reactive power, eg. Synchronous generators
The four types of DG units are employed to obtain the proper size and location, assuming fuel resources are evenly
distributed throughout the system in order to minimize the reactive power loss in the system. The maximum rating of DG that
can be connected to a distribution system depends on the capacity of that system, which is correlated to the voltage level within
the distribution system.
C. Objective functions and constraints
1) Minimization of total real power losses
Min f x   min
 G V
i, j B
2
i
ij
 Vj2  2Vi Vjcosθ ij

(4)
B
- Susceptance of network
(i,j)єB
- (i,j)are two nodes of a branch
Vᵢ and Vⱼ - voltage magnitude of node i and j
Gᵢⱼ
- Conductance between nodes i and j
- Difference b/w nodal phase angle i &  j
 ij
2) Minimization of total reactive power losses
Min f x1   min
  B V
i, jG
ij
2
i
 Vj2  2Vi Vjsinθij

(5)
G
-Conductance of network
(i,j)єG
-(i,j)are two nodes of a branch
Vi and Vj -voltage magnitude of node i and j
Bij
-Susceptance between nodes i and j
- Difference b/w nodal phase angle i &  j
 ij
3) Constraints
 Equality constraints
PGi  Pdi  Vi  Vj G ijcosθ ij  Bijsinθ ij 
(6)
QGi  Qdi  Vi  Vj G ijsinθ ij  Bijcosθ ij 
(7)
N
j1
N
j1

Inequality constraints
PGimin  PGi  PGimax
min
Gi
Q
 QGi  Q
max
Gi
(8)
(9)
D. Load bus voltage constraints
Vimin  Vi  Vimax
Vimax andVimin
N
PGi and QGi
(10)
-Upper and lower limits at the ith bus
- Number of buses
- Active and reactive generation
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
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PdiandQd
Gij and Bij
- Active and reactive loads at node i
- Real and imaginary parts of the nodal admittance matrix
PGimin , PGimax , Q Gimin , Q Gimax -Lower/upper active and reactive
generating unit limits of DG.
IV. OPTIMAL LOCATION AND SIZING OF DISTRIBUTED GENERATION VARIOUS COMPONENTS
The optimal location and sizing of distributed generation are formulated as a multi-objective constrained optimization problem.
This paper uses KHA for solving the problems of optimal location and sizing DG.
A. Krill herd algorithm
The Krill herd algorithm (KHA) is a new efficient biologically-inspired population-based algorithm developed by Gandomi et al.
The algorithm is based on the herding behaviour of krill individuals. Each krill moves through a multi-dimensional search space
to look for a potential solution by moving towards the highest density of food. The distance of the highest density of food from the
krill swarm is analogous to fitness value. Krill individuals move around in the multidimensional space and each krill adjusts its
position based on three main processes namely movement induced by the presence of other individuals, foraging activity and
random diffusion. The concept and mathematical formulation of these operators are briefly described below.
𝑑𝑋𝑖/𝑑𝑡=𝑁𝑖+𝐹𝑖+𝐷𝑖
(11)
B. Motion Induced by other Krill Individuals
The fitness function of the algorithm mainly depends on the density of the krills in the search space. So, it is essential to maintain
a high krill density in order to achieve an optimum solution. The individuals keep on rebuilding the system maintaining this high
density under the influence of the other individuals.
Vinew  αi Vimax  ωn Viold
Where, αi
α
α
new
i
Ns
fi  f j
j1
fw  fb
α inew  
(12)
target
i
(13)
xi  x j

x i  x j  rand(0,1)

i  best best
f i x i
α itarget  2 rand 0,1 
i max 

sdi 
1
5Np
Np
f
j1
i
(14)
(15)
 fj
(16)
C. Foraging action
Each individual krill adjusts its foraging velocity based on both of its own current food location and that of its previous experience
about the food location which is mathematically expressed as follows
Vf i  0.02 i  ω x Vfold
i

i
 i  21 
 i max

f i


Ns
(17)
xj
j1
fj
 f ibest x ibest
Ns 1
 j1 f
j
(18)
D. Random diffusion
The diffusion process of the krill individuals is considered as a random phenomenon. It may be expressed in terms of a maximum
diffusion speed and a random directional factor. It may be formulated as follows:
Vdi  λVdmax
E. Position update
The position of the ith krill during the interval t to
(19)
 t may be given by
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
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
N

x i t  Δt   x i t   c t  U i  L i  Vi  Vfi  Vdi (20)
i 1
V. KH ALGORITHM APPLIED TO OPTIMAL DG ALLOCATION PROBLEM
Step 1: Read the system data, constraints, the population size(NP), the maximum number of iterations, the number of DGs to be
installed in the distribution network and the KHA parameters namely foraging speed, maximum diffusion speed and the maximum
induced speed.
Step 2: The size of the DGs are randomly generated & normalized between the maximum and the minimum operating limits. The
rating of ith DG is normalized to Pj as given below to satisfy the capacity constraint:

j
j
j
P j  Pmin
 r * Pmax
 Pmin

(21)
The location and rating of all the installed DGs comprise a vector which represents the initial position of each krill of the
population set and it also represents a candidate solution for the optimal DG allocation problem.
Mi=[loci,1,loci.2,…loci,j….loci,ND,P i,1,P i,2,...P i,j,.Pi,ND] (22)
Depending upon the population size, initial solution M is created which is given by:
M=[M 1,M 2,..M i,…MNP]
(23)
Step3: Run the load flow to find the power losses/energy losses of the distribution network. In this article, a direct load flow
algorithm based on the bus-injection to branch-current (BIBC)matrix and the branch-current to bus-voltage(BCBV)matrix are
used.
Step 4: Update the motion of each krill individuals by adding the three motion index namely motion induced by other individual,
foraging motion and random diffusion.
Step 5: Modify the position of each krill individual.
Step 6: Applying crossover and mutation to update the position of each individual krill. The position of each krill individual
represents a potential solution as defined by optimal DG allocation problem.
Step 7: Check whether the control variables violate the operating limits or not. If any independent variable is less than the minimum
level it is made equal to minimum value and if it is greater than the maximum level it is made equal to the maximum level.
Step 8: Go to Step 3 until the current iteration number reaches the pre specified maximum iteration number.
VI. RESULTS AND DISCUSSION
The results of optimal DG placement using KHA to minimize real and reactive power loss of the system are presented. The 33bus
radial distribution system have been used to test the proposed methodology. Total Real and Reactive power loss minimization by
optimal DG Placement is executed in a 33 bus radial distribution test system. The test system consists of 33 Buses and 32 Lines.
The first bus is considered as the substation bus. Loads are connected to all buses except the first bus which is the substation bus.
Base KV is 12.66 KV and Base MVA is 10 MVA for Base case.
In order to test the mathematical statement, a 33 bus radial distribution system has been taken the total active power and
reactive power of this test system are 3715KW and 2300KVAR.Apparent power and power factor of this system are 4369.35KVA
and 0.8502.
A. Result Discussion of Krill Herd Algorithm
DGs are placed at suitable bus positions .In this work, the optimal location and size of the DG are obtained for IEEE 33-bus radial
distribution system. The results are obtained by considering placement of DG. The optimal location of buses and sizing of DG are
obtained by using Krill Herd algorithms. In all calculations of KHA the following test parameters are used:
 Base MVA =10
 Base kV = 12.66
 Maximum of Iteration=100
 Population Size=25
 DG installation cost =5000
 Rating of DG=3 $/KW
 Time duration = 8760 hrs
Parameter
Without
DG
Base case
33bus
With DG
Krill herd algorithm
best
mean
Standard
deviation
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
(GRDJE / CONFERENCE / ICIET - 2016 / 054)
Reactive
power loss
in KVAR
Optimal
location of
DG
Sizes of DG
in KW
143.1775
81.701
82.114
-
6
6
0.000032
6
0.2589
Table 1: Results of DG placement and sizing of using krill herd algo
The result depicts that KHA algorithm has less total real and reactive power loss when compared to without DG, for the same location of
distributed generation. The KHA algorithm show the effectiveness for distributed generators placement on 33-bus test system and also the size
of distributed generation is also more economical or optimal in KHA.
B. Convergence characteristics
Fig. 1: Convergence characteristics of total real power loss
Fig1.shows the convergence characteristics of total real power loss.The best value obtained in real power loss is 111.02
by using Krill herd algorithm. The average value converged is 111.41.
Fig. 2: Convergence characteristics of total reactive power loss
Fig2. Shows the convergence characteristics of total reactive power loss.The best value obtained in reactive power loss is
81.701 by using Krill herd algorithm. The average value converged is 82.114.
VII.
CONCLUSION
In this paper, a complex combinatorial problem of locating and sizing of DG for real power loss/reactive power loss minimization
of electric radial distribution networks is investigated. The KHA algorithm is employed to determine the optimal size and location
of DG. In order to prove the validity and superiority of the proposed method, it is applied on small, medium and large scale
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Optimal Location and Sizing of Distributed Generation Using Krill Herd Algorithm
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distribution network .The numerical results and the convergence profiles of the objective function value of all the test systems
confirm the effectiveness and dominancy of the proposed approach over other established algorithms.
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