SOLUTION FOR ECONOMIC LOAD DISPATCH USING
MODIFIED BAT ALGORITHM
P.Girish1, T.Yuvaraj2, R. Hariharan3.
1UG Student, Department of Electrical and Electronics Engineering, Saveetha School of
engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India
2,3Assistant Professor, Department of Electrical and Electronics Engineering, Saveetha
School of engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, India
1,2,[email protected],[email protected], [email protected]
ABSTRACT
This paper presents a Bio nature inspired Modified Bat algorithm for solving the Economic load dispatch problem. The objective is to minimize the total fuel cost of the generating units through optimal utilization of available sources. This study will further propose modifications
to the original bat algorithm to solve economic load dispatch problem. The simulation results are compared with the previously existing algorithms by using IEEE 6-Bus system, IEEE 14-
Bus system. Keywords: Modified Bat algorithm, Economic load dispatch
1. INTRODUCTION
Economic load dispatch tries to minimize the total operating cost of generating units while
satisfying system equality and inequality constraints. Therefore the main objective of the
optimization of ED problem is to reduce the total generation cost of units while satisfying
constraints. Various mathematical approaches have been suggested to solve the multi-
objective optimization of power plant such as reduction of fuel cost and minimization of the
transmission losses. In the past decade, many efforts have been focused towards solving the
ED problem, incorporating different kinds of constraints through the various optimization
techniques such as conventional methods which include lambda iteration method, base point
International Journal of Pure and Applied MathematicsVolume 119 No. 12 2018, 15957-15968ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu
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and participation factor method, gradient method, Newton based method, Nonlinear
programming (NLP), Linear programming (LP), Quadratic programming (QP), Mixed-
Integer programming (MIP). In lambda iteration and gradient based methods, the solution to
ELD is obtained by approximately representing the cost function for individual generators in
terms of single quadratic function. These techniques require incremental fuel cost curves
which are piecewise linear and monotonically increasing to find the global optimal solution.
For generators with non-monotonically incremental cost curves, conventional methods
ignores or flattens out portions of incremental cost curve that are not continuous or
monotonically increasing . These limitations of conventional methods were overcome by
modern meta-heuristic approaches like Artificial Neural Networks (ANN), Genetic
Algorithms (GA), Tabu Search (TS), Simulated Annealing (SA), Particle Swarm
Optimization (PSO),Ant colony optimization (ACO),Artificial immune systems (AIS),
Differential Evolution (DE), Bacterial Foraging Algorithm (BFA), Artificial bee colony
(ABC) algorithms [1-4]. Though these methods are not capable in attaining global best
optimal solutions to the ELD problems, to a great extent they produce near optimal solutions.
The purpose of economic dispatch is to produce energy at the low cost to dependably serve
customers, recognizing any operational limits of generation and transmission facilities. The
main plan is that, so as to satisfy the load at a minimum total value, the set of generators with
the bottom marginal costs should be used initial, with the incremental cost of the ultimate
generator required to full fill load setting the system incremental cost. The economic dispatch
involves the solutions of two problems i.e., unit commitment and on-line dispatch. The two
fundamental components of economic dispatch are planning for tomorrow’s dispatch and
dispatching the power today. Planning for tomorrow’s dispatch means scheduling generating
units based on load forecast for each hour of the next day dispatch. The factors that are
considered for planning for tomorrow’s dispatch are generating units operating limits (ramp
rate, maximum and minimum generation levels, amount of time that generator is running),
generating unit characteristics (efficiency, fuel and non-fuel costs) and start-up costs. This is
performed by independent market operator or by generation group. The factors that are
considered for dispatching the power today are ensuring balance of supply and load by
monitoring load, generation and interchange and monitoring transmission system. It is
performed by transmission operator. Normally the input output characteristics of modern
generating units are highly non-linear in nature due to value-point effects, ramp-rate limits
etc. having multiple local minimum points in the cost function.
2. LITERATURE REVIEW
Several authors have given extra comparatively cheap algorithms within the utility of linear
and non-linear programming strategies. Advocate the conversion of the nonlinearly
constrained dispatch trouble to a chain of restricted linear programming issues [5]. Introduces
the combined use of the differential set of rules and therefore the simplex method of
optimization in the safety compelled dispatch [6]. Mentioned a linearized formulation of the
overall finest load float problem and observe minimization technique to an augmented price
characteristic which includes a piecewise differentiable penalty cost characteristic term [7].
Planned a multipored premiere power glide, nicely modelling the begin-up and shut-down of
thermal devices [8]. Stated regarding Dynamic financial dispatch is companion degree
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extension of the usual economic dispatch downside that takes into thought the boundaries at
the ramp fee of the producing devices [9]. Proposed in order to enhance pace and robustness
and those have been implemented successfully [10]. Introduces a brand new method based on
PS optimization to solve various problems of energy gadget ELD [11]. Proposed a unique
heuristic-hybrid op- atomization method designed to remedy the nonconvex monetary
dispatch hassle in energy structures [12]. Discussed the artificial bee colony optimization
that's successfully implemented to economic strength dispatch issues [13]. Discussed about
international warming and haze, environmental difficulty has drawn more attention in every
day optimization operation of electric electricity structures [14]. The blended-integer linear
software is used in [15] for the ED problem. The author proposed an aggregate of C-GRASP
and differential evolution (DE) [16]. Provided a green allotted auction optimization algorithm
(DAOA) based totally on the gossip conversation mechanism for the non-convex economic
dispatch problem [17]. The proposed a multi-objective optimal dispatch model for micro grid
under grid-connected mode [18]. The authors from the above Literature review paper as
proposed mainly forced on the economic problem and also overcome the ELD problem they
were introduced several optimization algorithm to overcome the ELD problem even though
there are several existing algorithm we are concentrated on BAT algorithm due to have the
edible of solving a wide range of problems and highly nonlinear problem efficiently and it
gives promising optimal solution it works well with complicated problems having the quick
response within a short time period
3. PROBLEM FORMULATION
The main aim of this work is to minimize the fuel cost of the generating units through optimal utilization of the available sources. This has to carry out with satisfying all the
operating constraints.
The objective function of the economic dispatch is formulated in mathematically.
(1)
3.1 Operating Constraints
The equality and in equality constraints for economic load dispatch problem are real power
balance
(2)
(3)
Where PD is the total power demand
Is the minimum power generation limits
Is the maximum power generation limits
is the line loss.
4. BAT ALGORITHM
Bat algorithm is proposed by Yang in 2010 [19-22], It is a meta-heuristic algorithm inspired by fascinating abilities of bats such as finding their prey and discriminating different types of
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insects even at complete darkness. The advanced echolocation capability of bats makes them fascinating. Such abilities inspired to researchers on many fields. Bats use typical sonar
called as echolocation to detect prey and to avoid obstacles. Bats, in particular micro-bats, are able to recognize positions of the objects by spreading high and short audio signals and by
collision and reflection of these spread signals. In Bat Algorithm, the echolocation characteristics are idealized within the framework of the
following rules by benefitting such features of bats.
1. All bats use echolocation to sense distance, and they also know the difference between food/prey and background barriers in some magical way. 2. Bats fly randomly with velocity at position with a frequency varying wavelength
and loudness to search for prey. They can automatically adjust the wavelength (or
frequency) of their emitted pulses and adjust the rate of pulse emission r [0, 1], depending on the proximity of their target.
3. Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) to a minimum constant value Amin. In general the frequency f in a range [Fmin , Fmax] corresponds to a range of wavelengths [min,
max]. Furthermore, we do not necessarily have to use the wavelengths themselves; instead, we can also vary the frequency while fixing the wavelength λ. This is because λ and f are
related due to the fact λf is constant. We will use this later approach in our implementation. For simplicity, we can assume f ∈ [0,
Fmax ]. We know that higher frequencies have short wavelengths and travel a shorter distance. For bats, the typical ranges are a few meters. The rate of pulse can simply be in the range of
[0, 1] where 0 means no pulses at all, and 1 means the maximum rate of pulse emission. Based on these approximations and idealization, the basic steps of the Bat Algorithm (BA) can be summarized. In algorithm we have define the rules for the updating the positions Zi
and velocities Vi in the search space. The position and velocity is given by
(4)
(5)
Where is the random number between [0,1]. is the current best global location.
The new solution or position for the bat can be generated by the equation
(6)
For the local search part, once a solution is selected among the current best solutions, a new solution for each bat is generated locally using random walk.
(7)
Where is the random number between [0, 1].
Is the average loudness of all the bats?
5. MODIFICATIONS
5.1 Add Bad Experience Component
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A new variant to the classical PSO was introduced by Selvakumar and Thanushkodi by
splitting the correction component into two components. These components were called the good and bad experience components. A particle tries to achieve a better position while
trying to avoid the bad positions it has encountered. This paper proposes to add bad experience component to the velocity update equation. This modification is intended for enhancing the exploration capability of the algorithm. The modified equation is can be
mathematically written as
(8)
Where and are the global best and worst positions. And are the
personal best and worst positions. And are parameters that accelerate the particle
towards the global best and personal best positions respectively. And are constants that
accelerate the particle away the swarm worst and personal worst positions respectively.
5.2 NONLINEAR INERTIA WEIGHT
A variant of the bat algorithm called improved bat algorithm (IBA) has recently been
presented by Jamil. He proposed adding an inertia weight coefficient to the velocity
component in the velocity update equation. The paper proposes the weight component
decrease linearly from its maximum value to its minimum value. The purpose of the weight is
to provide balance between global and local exploration and better convergence rate. This
paper proposes using a nonlinear weight. The reason for using nonlinear weight is to have to
ability to control the transition between the global and local exploitation so that it can be
tailored for a specific problem. In this paper the following three equations have been derived
to get a better control over the transition between global and local exploitation.
(9)
Where and are maximum and minimum bounds of inertia weight coefficient.
Is maximum allowed iterations? The constants calculated using the following equations.
(10)
(11)
The final modified velocity updated equation is
(12)
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6. FLOW CHART
Fig.1 Modified Bat algorithm flowchart
7. RESULTS AND DISCUSSION
The bat algorithm is used for solving the economic load dispatch problems. In this the IEEE 6
bus system is used to compare with the fruit fly algorithm(FA), practical swarm
optimization(PSO), cuckoo search algorithm (CSA), flower pollination algorithm (FPA), The
simulation results is done by MATLAB. The six generator system consists of six busses. In
the system the P, Q is the real power and the reactive power.
The table 1 shows the comparative results of proposed algorithm with compared algorithms
PSO, FA, FPA, and CSA. The proposed method shows the best results when compared to the
other algorithms. The IEEE 6 bus system power delivering units are 325.51MW, 78.24MW,
150MW, 49MW, 55.25MW, 52MW respectively.
Start
Initialize random bat position and calculate fitness where
i=1, n
Generate pulse frequency
Ca lculate new frequency and calculate new bat pos i tion
Ca lculate new fi tness
Ini tia l i ze pulse rate and loudness
U(0,1) >
Terminate
<
U(0,1) < and
Random walk around best
solution
Update and
Accept new solution update pulse and loudness
End
Yes
No
Yes
No
Yes
No
Yes
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The power loss reduced by the proposed method is 10.86MW. Here the power loss reduced
by the other algorithms is 11.03MW, 11.44MW, 11.73MW, 11.02MW. From the above
discussion it could be concluded that the proposed method shows the best results when
compared to the other algorithms.
IEEE 6-Bus system
The six unit test system consisting of six thermal units, 26 buses, and 46 transmission lines is
used for simulation of proposed problem of economic load dispatch. This system is simulated
for 50 iterations.
Fig 2 IEEE six bus generating units
Parameters CSA
[12]
FA
[12]
PSO
[12]
FPA
[12]
Proposed
method [MBA]
P1 (MW) 324.1 293.3 288.6 323.995 325.51
P2 (MW) 76.86 79.54 82.75 76.84 78.24
P3 (MW) 158.1 123.33 132.9 158.2 150
P4 (MW) 50 69.7 50 50 49
P5 (MW) 51.96 79.54 99.5 51.98 55.25
P6 (MW) 51.96 63.77 57.5 50 52
Ploss (MW) 11.03 11.44 11.73 11.02 10.86
Fuel Cost($) 8356.06 8388.4 8401.45 8356.05 8199.4
Table 1 comparative results of modified bat algorithm
The result of comparison between CSA, FA, PSO, and FPA obtained from table1 shows that
the method of modified bat algorithm gives better results. Additionally the advantages of
modified bat algorithm are it is easier to implement and there are fewer parameters to adjust
and it shows the best results when compared to the other algorithms.
1:0.9725
1:0.91
P=55MW
Q=13MV
ar 1.05/0
P=50MW
Q=5MVar
P=30MW
Q=18MVar
P=50MW
V=1.1
1
2
3
6 5
4
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Fig 3 The performance analysis of six bus system
the above figure 3 shows the performance analysis of six bus system.the graph has been
drawn for fuel cost and power loss from the above graph it is very clear that our proposed
method shows the least values of power lost and fuel cost.whereas the other alogirthms
csa,fa,pso,fpa alogirthms shows the highest values of power loss and fuel cost when
compared to our proposed alogirthm mba.
IEEE 14-Bus system
The IEEE 14 bus system consists of 14 busses and 16 inter connecting nodes among
the busses and 32 transmission lines is used for simulation of proposed problem of economic
load dispatch.
parameters QP GA Proposed
method MBA
PG1(MW) 200 199.8 203
PG2(MW) 25.79 24.28 26
PG3(MW) 15 15.77 16
PG6(MW) 10 10.41 8
PG8(MW) 10 10.48 8
Power loss(MW)
13.54 13.42 13.24
Fuel cost($) 860.7250 805.55 803.45
Table 2 comparative results of MBA with other optimization algorithms
8356.06
8388.4 8401.45
8356.05
8199.4
711.03
711.4
711.73
711.02
710.86
710.4
710.6
710.8
711
711.2
711.4
711.6
711.8
8050
8100
8150
8200
8250
8300
8350
8400
8450
CSA FA PSO FPA
MBA
PO
WER
LO
SS(M
W)
FUEL
CO
ST($
)
FUEL COST($) POWER LOSS(MW)
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Fig 4 IEEE 14 bus generating units
The table 2 shows the comparative results of proposed method with compared algorithm
CSA, FPA, PSO, FA. The proposed method shows the best result by using IEEE 14 bus
system the power delivering units are 13.54 MW, 13.42 MW, 13.24 MW respectively.
The fuel cost reduced by the proposed method is 803.45 where the fuel cost obtained by the
other algorithms QP, GA are 860.7250, 805.55 respectively.
21
C
c
16
11
G1
3
C
2
G1
Bus 14 Bus 13
Bus 11
Bus 12
Bus 10
Bus 8
Bus 9
Bus 6 Bus 7
Bus 2 Bus 3
Bus 1 Bus 5 Bus 4
30 22 31 32 26
18 2
29
20
19 25
24 27
17 23
3 1 5 6 14 15
16 12
2
10
11
4 13 9 7
8
8
1
7
4
6
10
9
13
14
12
15
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Fig.5 The performance analysis of 14 bus system
The above figure 5 shows the performance analysis of 14 bus system. The above graph has
been plotted for fuel cost and power loss. Whereas our proposed method modified bat
algorithm shows the least values where compared with other optimization alogirthms
quadratic programming and genetic algorithm shows the higher values.
CONCLUSION
This paper proposes a new bio-nature inspired Modified Bat algorithm for solving the
economic load dispatch problem. For a normal bat algorithm the modification s have done.
And the Modified bat algorithm is compared with the Cuckoo search algorithm(CSA),
Practical swarm optimization(PSO), Fruit fly(FA) ,Flower pollination(FPA), algorithms but
from the graph that is very clear that the MBA shows best results when compared to the other
algorithms. From the graph it is clear that the modified bat algorithm has more accuracy and
computational time when compared to the other optimization algorithms, although the
proposed algorithm had been successfully applied to Economic load dispatch with valve point
loading effect including a few constraints.
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13.54
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13.05
13.1
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FUEL COST($) POWER LOSS(MW)
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