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PE-13-119PSE-13-135
1/6Conference of Joint Technical Meeting of Power System Technology of IEEJ, Kyushu Institute of Technology, Kitakyushu, Japan, September 11-13, 2013
A New Approach Computation for Determining Committed Power
Outputs of Economic Power System Operation using HSABC
Considering Space Areas
A.N. Afandi, (Kumamoto University & State University of Malang)
Hajime Miyauchi, (Kumamoto University)
An economic power system operation (EPSO) can be expressed by a total operating cost. Technically, this
payment is presented by individual cost of generating units based on a schedule of committed power outputs
(CPOs) to meet a total load demand. Presently, a minimum operating cost is performed by considering an
economic dispatch and an emission dispatch, which are composed into a combined economic and emission
dispatch (CEED) problem. This paper introduces a newest artificial intelligent computation, harvest season
artificial bee colony (HSABC) algorithm, for determining CPOs based on a minimum total cost of CEED using
IEEE-62 bus system. Simulation results show that HSABC has short time computations and fast convergences.Space areas give different implications on HSABC’s performances.
Keywords: Artificial bee colony, economic dispatch, emission, combined economic and emission dispatch
1. Introduction
Recently, an economic power system operation (EPSO)
considers a global warming caused by pollutant
emissions in the air from thermal power plants. These
pollutants are released from combustions of fossil fuels
in various types like CO, CO2, SOx and NOx(1)-(4).Presently, the EPSO becomes complex with considering
pollutant discharges as an emission dispatch (EmD)
under operational limitations. Practically, an EPSO is
managed using economical cost strategies for providing
electric energy from generator sites to supply load
demand areas. These strategies are used to decide the
minimum total cost of EPSO to meet a total load demand
at a certain time. In particular, a minimum total cost is
obtained by minimizing a total fuel cost of generating
units troughout an economic dispatch (ED) problem and
reducing pollutant emissions in the EmD problem. By
involving an EmD, the ED problem is transformed into a
combined economic and emission dispatch (CEED)
problem for determining a committed power outputs
(CPOs) of generating units during operations(5).
Many methods have been introduced to solve CEED
problems using traditional and evolutionary methods(3),
(6)-(15). Evolutionary methods have been composed to
attempts the natural phenomenons for creating various
algorithms. These methods are frequent used to compute
CEED problems because of traditional methods sufferfor large systems and multidimension spaces. For a
couple of years, the most popular evolutionary method is
genetic algorithm and this algorithm is inspired by a
phenomenon of natural evolution(16). Recently, the
newest evolutionary method is artificial bee colony
(ABC) algorithm. This method was proposed in 2005,
based on foraging behavior of honeybees in nature (17).
The latest generation of ABC is harvest season artificialbee colony (HSABC) algorithm intoduced in this paper
for determining the CPOs of EPSO. The HSABC is
applied to a CEED problem for the power system model
of IEEE.
2. Harvest Season Artificial Bee Colony
The HSABC is inspired by a harvest season situation
in nature for providing flowers. In the HSABC, multiple
food sources (MFS) express many flowers located
randomly at certain positions in the harvest season
area(18), (19). This space area (SA) is explored by bees to
search food sources. To exploit a large number of food
sources, bees can fly randomly during foraging for foods
and move from a selected current food source to another
positions(16), (19), (20). In the HSABC, MFS are consisted of
the first food source (FFS) and other food sources (OFSs).
Each position of OFSs is directed by a harvest operator
(ho) from the FFS(18), (19). Mathematically, HSABC
algorithm is introduced as following expressions:
, ………………...(1)
, …………………………………..(2)
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, ….....(3)
, ……………………………..(4)
. ……………………………………………….(5)
Here, xij is a current food, i is the ith solution of the food
source, j{1,2,3,…,D}, D is the number of variables of the
problem, xminj is a minimum limit of xij, xmaxj is a
maximum limit of xij, vij is the food position, xkj is a
random neighborof xij, k{1,2,3,…,SN}, SN is the
number of solutions, Øi,j is a random number within
[-1,1], Hiho is the harvest season food position,
ho{2,3,…,FT}, FT is the total number of flowers for
harvest season, xfj is a random harvest neighborof xkj, f
{1,2,3,…,SN}, R j is a randomly chosen real numberwithin [0,1], MR is the modified rate of probability food,
Fi is an objective function of the ith solution of the food,
fiti is the fitness value of the ith solution and pi is a
probability of the ith quality of food.
The HSABC has three agents for exploring the SA,
those are employed bees, onlooker bees and scout bees.
Each agent has different taks and it is colaborated to
obtain the best food as the optimal solution. An
employed bee is defined to search a neighbor food source
in the SA. Each food source chosen represents a possible
solution to the problem. An onlooker bee is subjected to
select the best food for the optimal solution. This bee
chooses a food source based on the probability value each
nectar quality. A scout bee is used to explore food sources
for replacing abandoned values.
A set of MFS is prepared for providing candidate foods
in the SA for every foraging cycle. A foraging for the
foods of HSABC is preceded by searching the FSS and it
will be accompanied by OFSs located randomly at
different positions in the SA. A set initial population is
generated as candidate solutions and it is createdrandomly by considering objective constraints. For each
solution, it is corresponded to the number of parameter
to be optimized, which is populated using equation (1).
The nectar quality is evaluated using equation (4) and
the probability of each food source is determined using
equation (5). Each position of candidate food is searched
using equation (2) for the FSS and it is followed by OFSs
using equation (3).
3. Economic Power System Operation
Technically, the EPSO is presented by a minimum
total operating cost. This payment is optimized using a
CEED problem considered operational constraints for
determining the CPOs of generating units(7), (12), (15), (21),
(22). Basically, the CEED problem of the EPSO considers
a total cost of ED as shown in (7) with a fuel cost of each
generating unit is given in (6). Pollutant emissions are
also included in the CEED (15), (22), (23). Each pollutant
discharge of generating unit is formed in (8) and the
minimized function of EmD is given in (9) for a total
pollutan emission.
Currently, a minimizing total fuel cost and a reducing
total pollutant emission become an important thing in
the EPSO. An objective function of CEED is composed
using ED and EmD problems with including penalty and
compromised factors. Each penalty factor is performed
in (10) to shows the rate coefficient of each generating
unit at its maximum output for the given load(7), (12). A
compromised factor shows the contribution of ED andEmD in CEED’s computations(19). The CEED problem is
expressed in (11) and this single objective function is
constrained using equations (12) – (19). In general, the
dispatching problem is formulated by using
mathematical functions as follows:
Fi(Pi) =ci+biPi +aiPi2 , ………………………………….…(6)
ED minimize ………….(7)
, ………………………………(8)
EmD minimize ………..(9)
, ……………………………………….(10)
CEED minimize , ….……..(11)
, ………………………………………...(12)
…(13)
..(14)
, ……… (15)
, ……………………………………….(16)
, ……………………………………….(17)
………………………………………(18)
, ……………………………………………….(19)
where Fi is a fuel cost of the ith generating unit ($/h), Pi is
a output power of the ith generating unit, ai, bi, ci are fuel
cost coefficients of the ith generating unit, Ei is an
emission of the ith generating unit (kg/h), Ftc is a total
fuel cost, i, i, i are emission coefficients of the ith
generating unit, Et is a total emission of generating
units (kg/h), Etc is a total emission cost ($/h), hi is each
penalty factor of the ith generating unit, is the CEED
($/h), w is the compromised factor, h is the penalty factor
selected from ascending of hi, ng is the number of
generators, Pimin is a minimum output power of the i th
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generating unit, Pimax is a maximum output power of the
ith generating unit, PD is the total demand, PL is the total
transmission loss, Pp and Pq are power injections at bus
p and q, PGp and QGp are active and reactice power
injections at bus p from generator, PDp and QDp are load
demands at bus p, Vp and Vq are voltages at bus p and q,
Qimax and Qimin are maximum and minimum reactive
powers of the ith generating unit, Vpmax and Vpmin are
maximum and minimum voltages at bus p, Spq is a total
power transfer between bus p and q, Spqmax is a limit of
power transfer between bus p and q.
4. Sample System and HSABC’s Procedures
In these works, IEEE-62 bus system is adopted as a
sample model of power system. This system is shown in
Figure 1 cosisted 62 buses, 89 lines and 32 load buses.
This figure also shows locations of generating units andload positions in the power system. Load data, fuel cost
coefficients, power limits and emission coefficients are
listed in Table 2, Table 3 and Table 4, respectively. Bee’s
parameter are listed in Table 1.
Fig. 1. One-line diagram of IEEE-62 bus system
Table 1. Bee’s parameters for running test
No Parameters quantity
1 Colony size 100
2 Food source 50
3 Foraging cycle 100
Fig. 2. Flow chart of HSABC’s application
Table 2. Fuel cost and emission coefficients of generators
Bus Gen
a, x10-3 ($/MWh2)
b($/MWh) c
(kg/MWh2)
(kg/MWh)
1 G1 7.00 6.80 95 0.0180 -1.8100 24.300
2 G2 5.50 4.00 30 0.0330 -2.5000 27.023
5 G3 5.50 4.00 45 0.0330 -2.5000 27.023
9 G4 2.50 0.85 10 0.0136 -1.3000 22.070
14 G5 6.00 4.60 20 0.0180 -1.8100 24.300
17 G6 5.50 4.00 90 0.0330 -2.5000 27.023
23 G7 6.50 4.70 42 0.0126 -1.3600 23.040
25 G8 7.50 5.00 46 0.0360 -3.0000 29.030
32 G9 8.50 6.00 55 0.0400 -3.2000 27.050
33 G10 2.00 0.50 58 0.0136 -1.3000 22.070
34 G11 4.50 1.60 65 0.0139 -1.2500 23.010
37 G12 2.50 0.85 78 0.0121 -1.2700 21.090
49 G13 5.00 1.80 75 0.0180 -1.8100 24.300
50 G14 4.50 1.60 85 0.0140 -1.2000 23.060
51 G15 6.50 4.70 80 0.0360 -3.0000 29.000
52 G16 4.50 1.40 90 0.0139 -1.2500 23.010
54 G17 2.50 0.85 10 0.0136 -1.3000 22.070
57 G18 4.50 1.60 25 0.0180 -1.8100 24.300
58 G19 8.00 5.50 90 0.0400 -3.000 27.010
Table 3. Power limits of generators
Bus GenPmin
(MW)Pmax
(MW)Qmax
(MVar)Qmin
(MVar)
1 G1 50 300 0 450
2 G2 50 450 0 500
5 G3 50 450 -50 500
9 G4 0 100 0 150
14 G5 50 300 -50 30017 G6 50 450 -50 500
23 G7 50 200 -50 250
25 G8 50 500 -100 600
32 G9 0 600 -100 550
33 G10 0 100 0 150
34 G11 50 150 -50 200
37 G12 0 50 0 75
49 G13 50 300 -50 300
50 G14 0 150 -50 200
51 G15 0 500 -50 550
52 G16 50 150 -50 200
54 G17 0 100 0 150
57 G18 50 300 -50 400
58 G19 100 600-100 600
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Table 4. Load demands of each bus
Bus no MW MVar Bus no MW MVar
1 0.0 0.0 32 0.0 0.0
2 0.0 0.0 33 46.0 25.0
3 40.0 10.0 34 100 70.0
4 0.0 0.0 35 107 33.0
5 0.0 0.0 36 20.0 5.0
6 0.0 0.0 37 0.0 0.07 0.0 0.0 38 166 22.0
8 109 78.0 39 30.0 5.0
9 66.0 23.0 40 25.0 5.0
10 40.0 10.0 41 92.0 910
11 161 93.0 42 30.0 25.0
12 155 79.0 43 25.0 5.0
13 132 46.0 44 109 17.0
14 0.0 0.0 45 20.0 4.0
15 155 63.0 46 0.0 0.0
16 0.0 0.0 47 0.0 0.0
17 0.0 0.0 48 0.0 0.0
18 121 46.0 49 0.0 0.0
19 130 70.0 50 0.0 0.0
20 80.0 70.0 51 0.0 0.021 0.0 0.0 52 0.0 0.0
22 64.0 50.0 53 248 78.0
23 0.0 0.0 54 0.0 0.0
24 28.0 34.0 55 94.0 29.0
25 0.0 0.0 56 0.0 0.0
26 116 52.0 57 0.0 0.0
27 85.0 35.0 58 0.0 0.0
28 63.0 8.0 59 0.0 0.0
29 0.0 0.0 60 0.0 0.0
30 77.0 41.0 61 0.0 0.0
31 51.0 25.0 62 93.0 23.0
Main procedures of the HSABC application for
determining the CPOs of EPSO are illustrated in Figure
2. This figure also describes sequencing computations for
searching the optimal solution based on a total minimum
cost of EPSO. HSABC’s procedures are consisted of three
steps. The first step is a formation of objective function
for the CEED problem, which is used to compute a
minimum total cost for every foraging cycle. The second
step is an algorithm composition using employed bees,
onlooker bees and scout bees to search the optimal
solution. The third step is programming developments
for three categories of subprograms in terms of datainput program, CEED program and algorithm program.
The data input program is consisted of a set data input
of parameters, such as generating units, transmission
lines, loads and constraints. The CEED program is
created to compute an objective function under
operational constraints and the number of CEED’s
variable is associated with exploring limits of food source.
The algorithm program is developed for searching the
optimal solution of the CEED problem based on HSABC’s
hierarchies. In these programs, three types of bee are
collaborated to explore food sources in the SA and the
programs are executed for choosing the best food as the
optimal solution of CPOs using bee’s parameters as listed
in Table 1. Specifically, the best food is selected by using
a greedy process in every cycle.
5. Simulation Results
In this section, these simulations are addressed to
determine the CPOs of EPSO considered operational
constratints given in Section 3. The HSABC is run out
using three food sources and the SA is demonstrated
using four scenarios for 100%, 75%, 50% and 45% areas.
A set population of these simulations are initialed in
Figure 3 for candidate foods considering power
constraints of generating units. The population is
created for 50 candidate solutions for G1 to G19 in every
foraging cycle. Convergence speeds of HSABC for
determining the optimal solutions are illustrated in
Figure 4. These characteristics are performed using 45%,50%, 75% and 100% of the SA. Obtained iterations and
time consumptions are listed in Table 5.
Fig. 3. Initial population
Fig. 4. Convergence speeds of HSABC
Table 5. Time consumptions of HSABC
-
100
200
300
400
500
600
700
0 10 20 30 40 50
F o o d c a n d i d a t e s ( M W )
Populations
G1 G2 G3 G4 G5 G6 G7 G8 G9 G10G11 G12 G13 G14 G15 G16 G17 G18 G19
26,000
27,000
28,000
29,000
30,000
31,000
32,000
33,000
34,000
1 6 1 1
1 6
2 1
2 6
3 1
3 6
4 1
4 6
5 1
5 6
6 1
6 6
7 1
7 6
8 1
8 6
9 1
9 6
O p t i m a l p o i n t
( $ / h r )
Iterations
HSABC 45% Area HSABC 50% Area
HSABC 75% Area HSABC 100% Area
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AlgorithmsMin.iter.
Time ofmin. iter.
(s)
Total time of100 cycles
(s)
HSABC 45% Area 25 3.31 12.91
HSABC 50% Area 32 4.43 13.02HSABC 75% Area 43 7.63 19.27
HSABC 100% Area 48 10.86 22.03
Fig. 5. Time consumptions of HSABC’s computations
Fig. 6. Statistical results of HSABC
StatisticResults
HSABC45% Area
HSABC50% Area
HSABC75% Area
HSABC100% Area
Max 30,299.16 29,601.37 31,625.36 32,773.61Min 27,005.93 27,005.93 27,005.93 27,005.93
Range 3,293.24 2,595.44 4,619.43 5,767.68Mean 27,319.18 27,361.65 27,625.08 27,767.72
Median 27,005.93 27,005.93 27,005.93 27,005.93
Mode 27,005.93 27,005.93 27,005.93 27,005.93Std.dev. 725.08 652.78 1,146.61 1,212.39
From Figure 4, it is known that the convergence speed
of HSABC using 45% of SA is faster than others. This
characteristic is demonstrated in 25 iterations for
searching a minimum solution of CEED after pointing at
30,299.16 $/h at the first iteration. HSABC used 50% of
SA is started at 29,601.37 $/h and it is converged to the
minimum value in 32 iterations. The HSABC used 75% of
SA needs 43 iterations to reach 27,005.93 $/h of a CEED’s
minimum result from 31,625.36 $/h at the first iteration.
The largest size of SA produces 48 of iterations for the
convergence speed and 32,773.61 $/h of initial cost for the
HSABC. In detail, statistical results of each HSABC
using each size of SA are given in Table 6. This table
provides values of the HSABC for max and min points,
ranges, means, medians, modes and standard deviations.
Concerning in the number of time execution for the
designed programs during searching minimum solutions,
Table 5 provides time consumptions of HSABC using
each area. This table shows the time consumption forobtaining minimum total costs and completing the
running out programs in 100 foraging cycles. From Table
5, it is known that various sizes of SA affect to HSABC’s
performances. In details, by using 45% of SA, the
minimum of HSABC is searched in 3.31 minutes. This
computation is completed in 12.91 minutes for 100
foraging cycles with various running times of execution
as shown in Figure 5.
Fig. 6. Progressing powers of generating units
Table 6. Final results of simulations
UnitsPower(MW)
Emission(kg/h)
Fuel cost($/h)
EmissionCost ($/h)
G1 157.86 187.13 1,342.88 480.95G2 104.90 127.90 510.12 328.73G3 133.87 283.77 679.06 729.34G4 100.00 28.07 120.00 72.15G5 188.67 323.55 1,101.47 831.59G6 152.93 416.48 830.34 1,070.43G7 170.00 155.98 1,028.85 400.90G8 111.53 142.23 696.93 365.57G9 201.38 1,004.79 1,607.99 2,582.51
G10 100.00 28.07 128.00 72.15G11 150.00 148.26 406.25 381.06G12 16.01 3.86 92.25 9.91G13 183.35 297.54 573.11 764.73G14 150.00 158.06 426.25 406.25G15 102.05 97.75 627.32 251.25G16 150.00 148.26 401.25 381.06G17 100.00 28.07 120.00 72.15G18 230.91 566.11 634.40 1,455.01G19 546.37 10,328.57 5,483.15 26,546.49
Total 3,049.83 14,474.45 16,809.62 37,202.23
Progressing powers of HSABC’s computation are
presented in Figure 6. This figure is performed using
45% of SA for G1 to G19 to meet a total load demand.
This figure is also evaluated by load flow analysis and
power output constraints. The final results of CPOs
based on a total minimum cost are listed in Table 6.
These final results are performed using all size of SA in
terms of powers, emissions, fuel costs and emission costs.
Generating units produce 3,049.83 MW of a total power
for supplying 2,912 MW of a total load. The total
pollutant is emitted around 14,474.45 kg/h from
generating units. The total payment of power stations
-
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
1 6
1
1
1
6
2
1
2
6
3
1
3
6
4
1
4
6
5
1
5
6
6
1
6
6
7
1
7
6
8
1
8
6
9
1
9
6
T i m e c o n s u m p t i o n s ( s )
Iterations
HSABC 45% Area HSABC 50% Area
HSABC 75% Area HSABC 100% Area
-
100.00200.00
300.00
400.00
500.00
600.00
700.00
800.00
1 6 1 1
1 6
2 1
2 6
3 1
3 6
4 1
4 6
5 1
5 6
6 1
6 6
7 1
7 6
8 1
8 6
9 1
9 6
G e n e r a t e d p o w e r s ( M W )
Iterations
G1 G2 G3 G4
G5 G6 G7 G8
G9 G10 G11 G12
G13 G14 G15 G16
G17 G18 G19
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for providing CPOs is 54,011.85 $/h contributed by
16,809.62 $/h of total fuel cost and 37,202.23 $/h of total
emission cost.
6. Conclusions
This paper introduces a harvest season artificial bee
colony (HSABC) algorithm to compute committed poweroutputs of generating units based on a minimum total
cost. By using various size of the space area (SA), the
small size of SA produces better results in terms of time
consumption and convergence speed. Refers to
applications of SA, a size of harvest season area is able to
use for controlling HSABC’s performances. From these
works, evaluations of limited abandoned solutions are
devoted to the future works.
Acknowledgments
The authors gratefully acknowledge the support to
Kumamoto University (Japan) and the BLN DIKTI
(Indonesia).
eferences
(1). 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 (2011)
(2). K. Sathish Kumar, V.Tamilselvan, N.Murali, R.Rajaram,
N.Shanmuga Sundaram and T.Jayabarathi : “Economic load
dispatch with emission constraints using various PSO algorithm”,
WSEAS Transaction on Power System , Vol. 9, pp. 598-607 (2008)
(3). Mukesh Garg, Surender Kumar: “A survey on environmentaleconomic load dispatch using lagrange multiplier method”,
International Journal of Electronics & Communication Technology ,
Vol. 3, pp.43-46 (2012)
(4). Yunzhi Cheng, Weiping Xiao, Wei-Jen Lee and Ming Yang : “A new
approach for emissions and security constrained economic
dispatch”, Proc. NAPS IEEE Conference , pp. 1-5 (2009)
(5). H. Chahkandi Nejad, R. Jahani, M. Mohammad Abadi:
“GAPSO-based Economic Load Dispatch of Power System”,
Australian Journal of Basic and Applied Sciences , Vol. 5, pp.
606-611 (2011)
(6). B.H. Chowdhury, Saifur Rahman: “ A review of recent advances in
economic dispatch”, IEEE Trans. On Power Systems , Vol. 5,
pp.1248-1259 (1990)
(7). A.A. El-Keib, H.Ma, and J.L. Hart : “Environmentally constrained
ED using the lagrangian relaxation method”, IEEE Trans. Power
Systems , Vol. 9, pp. 1723-1729 (1994)
(8). Ahmed Farag, Samir Al-Baiyat, T.C. Cheng : “Economic load
dispatch multiobjective optimization procedures using linear
programming techniques”, IEEE Trans. Power Systems , Vol. 10, pp.
731-738 (1995)
(9). S. Subramanian, and S. Ganesa : “A s implified approach for ED
with piecewise quadratic cost functions”, International Journal of
Computer and Electrical Engineering, Vol. 2, pp. 793-798 (2010)
(10). Ioannis G. Damausis, Anastasios G. Bakirtzis, Petros S.
Dokopoulos : “Network constrained economic dispatch using real
coded genetic algorithm”, IEEE Trans. Power Systems , Vol. 18, pp.
198-205 (2003)
(11). M. A. Aziz, J. I. Musirin and T. K. A. Rahman : “Solving dynamic
ED using evolutionary programming”, Proc. First International
Power and Energy Conference, pp. 144-149 (2006)
(12). M.A. Abido : “Enviranmental/economic power dispatch using
multiobjective evolutionary algorithm”, IEEE Trans. Power
Systems , Vol. 18, pp. 1529-1537 (2003)
(13). T. Yalcinoz and M. J. Short : “Large-scale ED using an improved
hopfield neural network”, IEE Proc. Gener. Transm. Distrib. Vol.
144, pp. 181-185 (1997)
(14). Y. Abdelaziz, S. F. Mekhamer, M. A. L. Badr, and M. Z. Kamh :
“ED using an enhanced hopfield neural network”, Electric Power
Components and Systems , Vol. 36, pp. 719-732 (2008)(15). Z.-L. Gaing : “Particle swarm optimization to solving the ED
considering the generator constraints”, IEEE Trans. Power
Systems, Vol. 18, pp.1187-1195 (2003)
(16). Karaboga D, Basturk B : “A powerful and efficient algorithm for
numerical function optimization ABC algorithm”, J. of Global
Optimization , Vol. 9, pp. 459-471 (2007)
(17). Dervis Karaboga : “An idea based on honey bee swarm for
numerical optimization,” Erciyes University, Turkey, Technical
Report-TR06 (2005)
(18). 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, 2013, pp. 11-12.
(19). A.N. Afandi, Hajime Miyauchi, “ A New Evolutionary Method for
Solving a Combined Economic and Emission Dispatch”,International Journal of Energy and Power Engineering , Vol. 5, No.
4B, pp. 774-779 (2013).
(20). Milos Subotic: “Artificial Bee Colony Algorithm for Constrained
Optimization Problems Modified with Multiple Onlookers”,
International Journal and Mathematical Models and Methods in
Applied Sciences , Vol. 2, pp.314-322
(21). C. Christoper Columbus and Sishaj P. Simon : “A parallel ABC for
security constrained economic dispatch using shared memory
model”, Proc. 2012 EPSCICON IEEE Conference Publication , pp.
1-6 (2012)
(22). M.A. Abido, “Multiobjective Evolutionary Algorithms for Electric
Power Dispatch Problem”, IEEE Transactions on Evolutionary
Computation, Vol. 10, pp. 315-329 (2006)
(23). Yong Fu, Mohammad Shahidehpour, Zuyi Li : “AC Contingency
Dispatch Based on Security Constrained Unit Commitment”, IEEE
Transactions on Power Systems, Vol. 21, pp. 897-908 (2006)