 Open Access
 Total Downloads : 505
 Authors : Mannem Saicharan Reddy, Dr. P. S. Subramanyam
 Paper ID : IJERTV3IS100573
 Volume & Issue : Volume 03, Issue 10 (October 2014)
 Published (First Online): 21102014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
A MetaHeuristic Approach of Bat Algorithm to Evaluate the Combined EED Problem
1 M. SaiCharan Reddy,
PG Student (M.Tech Electrical Power Systems), VBIT Engineering College, Hyderabad,India,
2Dr. P. S. Subramanyam.
Dept. of EEE, VBIT Engineering College, Hyderabad, India,
Abstract: Electrical Power Systems are designed and operated to meet continuous variation of power demand. In power system, minimization of operation cost is very important. This paper presents an application of BAT algorithm for multi objective optimization problem in power system. Considering the environmental impacts that grow from the emissions produced by fossilfuelled power plant, the economic dispatch that minimizes only the total fuel cost can no longer be considered as single objective. Application of BAT algorithm in this paper is based on mathematical modelling to solve economic, emission and combined economic and emissions dispatch problems by a single equivalent objective function. BAT algorithm has been applied to two realistic systems at different load condition. Results obtained with proposed method are compared with other techniques presented in literature. BAT algorithm is easy to implement and much superior to other algorithms in terms of accuracy and efficiency.
Index Terms: Economic dispatch, BAT algorithm, Artificial Bee Colony algorithm, Combined economic and emission dispatch, Mathematical modelling.
1 INTRODUCTION
Economic load dispatch can be defined as process of allocating generation levels to generating units so that the system load is supplied entirely and most economically. This paper introduces the economic dispatch problem in a power system to determine the optimal combination of power output for all generating units which will minimize the total fuel cost while satisfying load and operational constraints. The economic dispatch problem is very complex to solve because of its colossal dimension, a non linear objective function and a large number of constraints.
Well known longestablished techniques such as integer programming [2], dynamic programming [3] and lagarangian relaxation [4] have been used to solve the economic dispatch problem. Recently other optimization methods such as Simulated Annealing [5], Genetic Algorithm [6], Particle Swarm optimization [7] and Tabu Search Algorithm [8] are presented to solve the economic dispatch problem. This single objective economic dispatch can no longer be considered along due to the environmental concerns that arise from the emission produced by fossil fuelled electric power plants. Economic and environmental dispatch is a multiobjective problem.
Recently, various modern heuristics multi objective evolutionary algorithms such as Nondominated Sorting Genetic Algorithm II (NSGAII) [9], Evolutionary Programming algorithm (EP) [10], Strength Pareto Evolutionary Algorithm (SPEA) [11] and MultiObjective Particle Swam Optimization algorithm (MOPSO) [12] may prove to be efficient in solving EED problem by tackling both two objectives of EED problem simultaneously as competing objectives. But all these methods seem to be lack of ability to find the Pareto optimal front due to their drawbacks: NSGAII and SPEA may obtain only near Paretooptimal front with long simulation time when applied to solve EED problem because of the premature convergence of Genetic Algorithm (GA). EP suffers from the oscillation of the solution and computational time may be too long when applying EP to solve EED problem. The premature convergence of PSO may lead optimization progresses of MOPSO methods to the local Paretooptimum front, which would degrade their performance in solving EED problem. Including emission constrains to the economic dispatch and unit commitment problems have been analysed under cost minimization environment.
In this paper a multiobjective optimization problem i.e., BAT algorithm is proposed to solve combined economic and emissions dispatch problems and the effectiveness of proposed algorithm is demonstrated using three and six generating unit test systems.
2 COMBINED ENVIRONMENTAL ECONOMIC DISPATCH (CEED)
The traditional economic dispatch problem has been defined as minimizing of an objective function i.e., the generation cost function subject to equality constraints i.e., total power generated should be equal to total system load plus losses for all solutions and inequality constraints
i.e. generations should lie between their respective maximum and minimum specified values.
The objective function equation (1) is minimised subjected to equality constraint equation (2) and inequality constraints equation (3).
………. (1)
………. (2)
…….. (3)
Where x is a state variable, Pi is the control variable, i.e., real power setting of generator and n is the number of units or generators.
There are several ways to include emission into the problem of economic dispatch. There are various algorithms for solving environmental dispatch problem with different constraints [19]. One approach is to include the reduction of emission as an objective. In this work, only reduction is considered because it is a significant issue at the global level. A price penalty factor (h) is used in the objective function to combine the fuel cost, Rs/hr and emission functions, kg/hr of quadric form.
The combined economic and emission dispatch problem can be formulated as to minimize
……………. (4)
..(5)
Subject to equality and inequality constraint defined by equations (2), (3). Once price penalty factor (h) is known, equation (5) can be rewritten as
..(6)
This has the resemblance of the familiar fuel cost equation, once h is determined. A practical way of determining is discussed by Palanichamy and Srikrishna [6]. Consider that the system is operating with a load of PD MW, it is necessary to evaluate the maximum cost of each generator at its maximum output, i.e.

Evaluate the maximum cost of each generator at its maximum output, i.e.,
..(7)

Evaluate the maximum emission of each generator at its maximum output, ie,
(8)

Divide the maximum cost of each generator by its maximum emission, i.e.,
……….. (9)
Recalling that
Rs/kg ………………. (10)

Arrange hi (i = 1, 2,……,n) in ascending order.

Add the maximum capacity of each unit, one at a time, starting from the smallest hi unit until total demand is met as shown below.
……………… (11)
At this stage, hi associated with the last unit in the process is the price penalty factor h Rs/Kg for the given load.
Arrange hi in ascending order. Let h be a vector having h values in ascending order.
……………. (12)
For a load of PD starting from the lowest hi value unit, maximum capacity of unit is added one by one and when this total equals or exceeds the load, hi associated with the last unit in the process is the price penalty factor for the given PD. Then equation (6) can be solved to obtain environmental economic dispatch using lambda iteration method.
3 BAT ALGORITHM
Bats are fascinating animals. They are the only mammals with wings and they also have advanced
capability of echolocation. Most of bats uses echolocation to a certain degree, among all the species, microbats are famous example as microbats use echolocation extensively, while mega bats do not. Microbats use a type of sonar, called echolocation, to detect prey, avoid obstacles, and locate their roosting revices in the dark.
If we idealize some of the echolocation characteristics of microbats, we can develop various bat inspired algorithms or bat algorithms. For simplicity, we now use the following approximate or idealized rules:

All bats use echolocation to sense distance, and they also know the difference between food/prey and background barriers.

Bats fly randomly with velocity at position with a fixed frequency (or wavelength ), varying wavelength (or frequency f) 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 targets.

Although the loudness can vary in many ways, we assume that the loudness varies from a large (positive) to a minimum .
Another obvious simplification is that no ray tracing is used in estimating the time delay and three dimensional topography. In addition to these simplified assumptions, we also use the following approximations, for simplicity. In general the frequency f in a range
[ ] corresponds to a range of wavelengths [ ]. For example, a frequency range of [20 kHz,500 kHz] corresponds to a range of wavelengths from 0.7mm to 17mm.
In simulation, we use virtual bats naturally. We have to define the rules how their positions and velocities in a ddimensional search space are updated. The new solutions and velocities at time step t are given by
…………. (13)
……………… (14)
where [0, 1] is a random vector drawn from a uniform distribution. Here is the current global best location (solution) which is located after comparing all the solutions among all the n bats. As the product is the velocity increment, we can use either (or ) to adjust the velocity change while fixing the other factor (or ), depending on the type of the problem of interest. 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
………………….. (15)
Where [1, 1] is a random number, while
=< > is the average loudness of all the bats at this time step.
Based on the above approximations and idealization, the pseudocode of the Bat Algorithm (BA) can be summarized below.
3.1 PSEUDOCODE OF THE BAT ALGORITHM
Objective function f(x), x =
Initialize the bat population (i = 1, 2, .., n) and Define pulse frequency at
Initialize pulse rates and the loudness
while (t <Max number of iterations)
Generate new solutions by adjusting frequency,
and updating velocities and locations/solutions [equations (13) to (15)]
if (rand > )
Select a solution among the best solutions
Generate a local solution around the selected best solution
end if
Generate a new solution by flying randomly
if (rand < & ) < )) Accept the new solutions Increase and reduce
end if
Rank the bats and find the current best
end while
Post process results and visualization
4 SIMULATION RESULTS AND DISCUSSIONS
The applicability and efficiency of BAT algorithm has been applied to two test cases. The programs are developed using MATLAB 7.14.
The Parameters for BAT algorithm considered
here are:
n=20, A=0.9, r=0.1, , .
Test case 1: The system consists of three thermal units. The parameters of all thermal units are adapted from [1].
Table: 1 Comparison of test results for Three Generating units
Load demand 
h*, Rs/kg 
Performance 
Conventional Method [7] 
SGA [7] 
RGA [7] 
ABC 
BAT 
400MW 
44.788 
Fuel cost, Rs/hr 
20898.83 
20831.54 
20801.81 
20838.729 
208378.277 
Emission, kg/hr 
201.5 
201.35 
201.21 
200.198 
200.211 

Power loss, MW 
7.41 
7.69 
7.39 
7.403120 
7.401407 

Total cost, Rs/hr 
29922 
29820 
29812 
29805.615 
29804.905 

500MW 
44.788 
Fuel cost, Rs/hr 
25486.64 
25474.56 
25491.64 
25494.904 
254939.128 
Emission, kg/hr 
312.0 
311.89 
311.33 
311.125 
311.133 

Power loss, MW 
11.88 
11.80 
11.70 
11.679210 
11.67600 

Total cost, Rs/hr 
39458 
39441 
39433 
39429.646 
39429.040 

700MW 
47.82 
Fuel cost, Rs/hr 
35485.05 
35478.44 
35471.4 
35462.826 
35462.501 
Emission, kg/hr 
652.55 
652.04 
651.60 
354.628 
651.505 

Power loss, MW 
23.37 
23.29 
23.28 
23.334221 
23.3300 

Total cost, Rs/hr 
66690 
66659 
66631 
66617.903 
66617.505 
Table: 1 shows the summarized results of CEED problem for load demand of 400MW, 500MW and 700MW are obtained by the proposed BAT algorithm with stopping criteria based on maximumgeneration=100.
Form Table: 1, it is clear that BAT algorithm gives optimum result in terms of minimum fuel cost,
emission level and the total operating cost compared to other algorithms.
Table: 2 gives the best optimum power output of generators for CEED problem using BAT & ABC algorithm for load demand 400MW, 500MW and 700MW.
Table: 2 Optimum Power dispatch Results by ABC, Proposed BAT method for three units system
Load demand, MW 
Algorithm 
P1 
P2 
P3 
Iterations 
400MW 
ABC 
102.5546 
152.7996 
152.0485 
29 
BAT 
102.5589 
153.7197 
151.1228 
8 

500MW 
ABC 
128.8494 
191.4610 
191.3687 
56 
BAT 
128.8501 
192.5603 
190.2657 
18 

700MW 
ABC 
182.6259 
270.3542 
270.3541 
44 
BAT 
182.6477 
271.2397 
269.4426 
7 
The convergence tendency of proposed BAT algorithm based strategy for power demand of 400MW, 500MW and 700 MW is plotted in figure: 1. It shows that
the technique converges in relatively fewer cycles thereby possessing good convergence property.
Figure: 1 convergence of three generating units system for load demand values 400MW, 500MW & 700MW.
Test case II: The system consists of six thermal units. The parameters of all thermal units are adapted from [1]. The summarized result of CEED problem for load demand of
500MW an 900MW are obtained by the proposed BAT algorithm with stopping criteria based on maximum generation=100 is presented in Table: 3.
Table: 3 comparison of test Results for six generating unit system
Load demand 
h*, Rs/kg 
Performance 
Conventional Method [9] 
RGA [9] 
Hybrid GA [9] 
Hybrid GTA [9] 
ABC 
BAT 
500MW 
43.898 
Fuel cost, Rs/hr 
27638.300 
27692.1 
27695 
27613.4 
27613.247 
27612.749 
Emission, kg/hr 
262.454 
263.472 
263.37 
263.00 
263.013 
263.006 

Power loss, MW 
8.830 
10.172 
10.135 
8.93 
8.934145 
8.933858 

Total cost, Rs/hr 
39159.500 
39258.1 
39257.5 
39158.9 
39158.9 
39158.199 

900MW 
47.822 
Fuel cost, Rs/hr 
48892.900 
48567.7 
48567.5 
48360.9 
48350.683 
48350.163 
Emission, kg/hr 
701.428 
694.169 
694.172 
693.570 
693.788 
693.772 

Power loss, MW 
35.230 
29.725 
29.718 
28.004 
28.009673 
28.008975 

Total cost, Rs/hr 
82436.580 
81764.5 
81764.4 
81529.1 
81529.00 
81527.739 
Form Table: 3, it is clear that BAT algorithm gives the optimum result in terms of minimum fuel cost, emission level and the total operating cost compared to other algorithms.
Table: 4 gives the best optimum power output of generators for CEED problem using BAT & ABC algorithms for load demand 500MW and 900MW.
Table: 4 Optimum Power dispatch results by ABC Approach for six unit system
Load demand, MW 
Algorithm 
P1 
P2 
P3 
P4 
P5 
P6 
Iterations 
500 
ABC 
33.2733 
26.8554 
89.9135 
90.4852 
135.6435 
132.7631 
120 
BAT 
33.2703 
26.85061 
89.91347 
90.48638 
135.6411 
132.762 
18 

900 
ABC 
92.3297 
98.3912 
150.1948 
148.5588 
220.4043 
218.1307 
132 
BAT 
92.3288 
98.3910 
150.1132 
148.5586 
220.4007 
218.1267 
25 
The convergence tendency of proposed BAT algorithm based strategy for power demand of 500MW and 900 MW is plotted in figure:2. It shows that the technique
converges in relatively fewer cycles there by possessing good convergence property.
Figure: 2 convergence of six generating unit system for load demand values of 500MW and 900MW.
5 CONCLUSION
In this paper, a new optimization of BAT algorithm has been proposed. In order to prove the effectiveness of algorithm it is applied to CEED problem with three and six generating unit. The results obtained by proposed method were compared to those obtained conventional method, RGA and SGA and Hybrid GA and ABC. The comparison shows that BAT algorithm performs better than above mentioned methods. The BAT algorithm has superior features, including quality of solution, stable convergence characteristics and good computational efficiency. Bat algorithm gives optimum dispatch evaluation with less number of iterations. Therefore from the results it is concluded that BAT optimization is a promising technique for solving complicated problems occurring in power systems.
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*h values are considered based on literature.