application of harvest season artificial bee colony algorithm to economic load dispatch of power...
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8/11/2019 Application of Harvest Season Artificial Bee Colony Algorithm to Economic Load Dispatch of Power System Operati
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The 2013 Annual Conference of Power and Energy Society, Toki Messe, Niigata, Japan, August 27-29, 2013
Application of Harvest Season Artificial Bee Colony Algorithm to EconomicLoad Dispatch of Power System Operation with Pollutant Emissions
A.N. Afandi
a)
, Student Member, Hajime Miyauchi
, Senior Member
This paper presents an application of Harvest Season Artificial Bee Colony (HSABC) algorithm to solve an Economic Load
Dispatch (ELD) of power system operation throughout a Combined Economic and Emission Dispatch (CEED) problem. The
IEEE-30 bus system is adopted as a sample system for testing the problem. The simulations showed that statistical, numerical,
and convergence results of the HSABC are better than the existing tested methods. The proposed method of the HSABC seems
strongly to be a new promising approach for solving an ELD throughout the CEED problem.
Keywords: CEED, cost, HSABC, problem
1. Introduction
One of the most important problems in the power system
operation is to reduce the total technical operating cost through the
various combinations of power plants. By considering this
condition, a cost optimization is a significant case for obtaining
the best schedule of the committed generating unit outputs to meet
a certain load demand at a certain time under some operational
limitations belonged in equality and inequality constraints. An
Economic Load Dispatch (ELD) is usually applied to the power
system operation for optimizing the total operating cost. Presently,
the ELD also considers pollutant emissions into the air by burning
fossil fuels as an Emission Dispatch (EmD)(1)and it is transformed
into a Combined Economic and Emission Dispatch (CEED) (1),(2).
Many previous works have been applied to solve the ELD
throughout the CEED problems categorized into classical and
evolutionary methods. For a couple years, the evolutionary
methods are common used to solve the ELD problem and the most
popular method is a Genetic Algorithm (GA)(3). Recently, the
newest algorithm of evolutionary methods is an Artificial Bee
Colony (ABC). This algorithm is inspired by natural behaviors of
honeybees in nature. A novel generation of the ABC is a Harvest
Season Artificial Bee Colony (HSABC)(4)composed by multiple
food sources for attempting the harvest season situation.
2. ELD and HSABC
The ELD problem considered an EmD is presented inliteratures(1),(2). In this section, it is expressed by a CEED problem
as single objective function of optimization problem. To obtain the
minimum total cost of the CEED, the HSABC is demonstrated by
using two strategies, a Controlled Distance Placement (CDP) and
an Uncontrolled Distance Placement (UDP). The CDP is a
creating strategy for locating food sources within a certain
distance for every cycle and the UDP locates food sources in
various distances for each other. In these works, the ABC and GA
are selected as comparators of the HSABC and both algorithms
have been clearly presented in references(2),(3). The HSABCs
processes used a collaboration of food sources are performed in a
reference(4)
for determining the best solution. In general, the mainprocedures of the HSABC are given in equations (1) to (3) as
follows:
Minimize .. (1) ... (2)
. (3)where t is the CEED ($/hr), w is a compromised factor, h is a
penalty factor, Ftis the total fuel cost of generating units ($/hr), Et
is the total emission of generating units (kg/hr), vij is a food
position, xijis a current food, i is the i
th
solution of the food source,k {1,2,3,,SN},j{1,2,3,,D}, SN is the number of solutions,
D is the number of variables of the problem, i,j is a random
number within [-1, 1], xkj is a random neighbor of xij, xfj is a
random harvest neighbor of xkj, Hiho is a harvest season food
position, ho{2,3,,FT}, f {1,2,3,,SN}, FT is the total
number of flowers for the harvest season, Rjis a randomly chosen
real number within [0,1], MR is a modified rate.
3. Simulation Results
IEEE-30 bus system is employed as a sample system for
simulating the CEED problem. The ABC, GA, and HSABC are
adopted to solve CEED problem referred to references(2), (3),(4). The
CEED problem considered 283.4 MW of total load, 0.5 of
compromised factor, equality of generating power, generating
power limits and 5% of voltage limits.The ABC and HSABC
are run out by using colony size=100, food source=50, limit food
source=50 and foraging cycles=150. The HSABC uses three food
sources for the CDP and UDP. The GA is executed by using
several controlling parameters. Its parameters are population=50,
elite count=2, generation=150, initial population=0-1, crossover
fraction=0.4, migration fraction=0.1, migration interval=20,
forward migration direction, linear ranking fitness function,
gaussian mutation and roulette selection.
Captured within 10 cycles from all period of running out the
designed program for the HSABC, Figure 1 and Figure 2 show thepositions of food sources. These figures illustrate food sources
positions of the placement strategies. Specifically, these figures
a) Correspondence to: A.N. Afandi. E-mail: [email protected] Computer Science and Electrical Engineering, Graduate School of
Science and Technology, Kumamoto University, 2-39-1 Kurokami,Chuo-ku, Kumamoto 860-8555, Japan
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8/11/2019 Application of Harvest Season Artificial Bee Colony Algorithm to Economic Load Dispatch of Power System Operati
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The 2013 Annual Conference of Power and Energy Society, Toki Messe, Niigata, Japan, August 27-29, 2013
describe the collaboration of three food sources in the UDP and
CDP to show the involvement of the first food source and other
food sources for determining solutions.
Fig. 1. Collaboration of food sources using CDP.
Fig. 2. Collaboration of food sources using UDP.
Fig. 3. Convergence speeds of the tested algorithms.
Table 1. Comparison of the CEEDs statistical results.
Subjects ABC GAHSABC
(UDP)
HSABC
(CDP)
Population 50 50 50 50
Max. Iteration 150 150 150 150
Min. Iteration 34 51 24 17
Start Cost CEED ($/hr) 727.63 729.42 727.11 726.45
Min.Cost CEED ($/hr) 725.04 723.68 725.04 724.60
Min.Cost ELD ($/hr) 415.13 413.97 415.13 414.80
Min.Cost EmD ($/hr) 309.91 309.71 309.91 309.80
Mean ($/hr) 725.15 725.34 725.09 725.10
Median ($/hr) 725.04 725.04 725.04 725.04Mode ($/hr) 725.04 725.04 725.04 725.04
Std. deviation 0.42 0.69 0.24 0.22
The convergences of three tested methods are given in Figure 3
for the ABC, GA and HSABC. These characteristics illustrate a
speed of each computation during searching the best value of the
final solution for the CEED problem. From this figure, it is known
that the fastest computation is obtained by using both types of the
HSABC. Specifically, HSABC used CDP has better performances
contrasted to the UDP and other tested methods. In detail, the
obtained iteration are 34 of the ABC, 51 of the GA, 24 of the
HSABC using UDP and 17 of the HSABC using CDP.
Table 2. Final results of the simulations.
Gen. UnitPower
(MW)
Fuel Cost
($/hr)
Emis. Cost
($/hr)
Tot. Cost
($/hr)
G1 126.07 311.74 151.55 463.29
G2 49.74 130.34 125.12 255.46
G3 28.40 78.81 84.22 163.03
G4 31.80 111.78 97.07 208.85
G5 26.63 97.62 80.93 178.55
G6 27.17 99.97 80.93 180.9Total 289.81 830.26 619.82 1,450.08
Statistical results for the ABC, GA and HSABC are given in
Table 1. This table compares the computing abilities of each
algorithm for determining the solution of the ELD throughout the
CEED problem in term of populations, obtained iterations, costs,
means, medians, modes, standard deviations. By considering
283.4 MW of load demand, six generating units produce 289.81
MW of total power output with 6.41 MW of total power loss. The
minimum total cost is obtained in 1,450.08 $/hr contributed by
830.26 $/hr of fuel cost and 619.82 $/hr of emission cost.
4. Conclusions
This paper presents the HSABC for solving an ELD throughout
the CEED problem using IEEE-30 bus system. The simulations
showed that the HSABC is better than the existing tested methods.
Convergence speeds of HSABC are smooth and quick to select
solutions and HSABC used CDP has better performances. The
proposed method of the HSABC algorithm seems strongly to be a
new promising approach for solving an ELD throughout the
CEED problem based on the solution quality and the
computational efficiency under several constraints. From these
works, real system applications are devoted to the future
investigations.
eferences
(1) Yunzhi Cheng, Weiping Xiao, Wei-Jen Lee and Ming Yang , A New Approach
for Missions and Security Constrained Economic Dispatch,Proc. NAPS, IEEE
Conference Publication, Starkville USA, 4-6 Oct 2009, pp. 1-5.
(2) R.Gopalakrishnan, A.Krishnan, A novel combined economic and emission
dispatch problem solving technique using non-dominated ranked genetic
algorithm, European Journal of Scientific Research, vol.64, pp. 141-151, Nov.
2011.
(3) Karaboga D, Basturk B, A Powerful and Efficient Algorithm for Numerical
Function Optimization: ABC Algorithm, J. of Global Optimization, vol. 39, no.
0925-5001, pp. 459-471, Apr. 2007.
(4) A.N. Afandi, Hajime Miyauchi, Multiple Food Sources for Composing Harvest
Season Artificial Bee Colony Algorithm on Economic Dispatch Problem, Proc.
The 2013 Annual Meeting of the IEEJ, No. 6-008, pp. 11-12, Nagoya, 20-22
March 2013.
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CostoftheCEED(
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Iterations
ABC
GA
HSABC (UDP)
HSABC (CDP)