Energy and Power E ngineering, 2013, 5, 774-779
doi:10.4236/epe.2013.54B149 Published Online July 2013 (http://www.scirp .o rg/journal/epe)
Copyright © 2013 SciRes. EPE
A New Evolutionary Method for Solving Combined
Economic and Emission Dispatch
A. N. Afandi, Hajime Miyauchi
Computer Science and Electrical Engineering, GSST, Kumamoto University, Kumamoto, Japan
Received April, 2013
This paper presents a new evolutionary method called in Harvest Season Artificial Bee Co lony (HSABC) algorit hm for
solving constrained problems of Combined Economic and Emission Dispatch (CEED). The IEEE-30 bus system is
adopted as a sample system for determining the best solutions of the CEED problems considering operational con-
straints. Running outs of designed programs for the HSABC show that applications of various compromised factors
have d ifferent implicatio ns o n the CEED’s results, that minimum cost co mputations are started at different values, and
that increasing load demands have affected costs, pollutant emissions and generate d powers.
Keywords: Bees; Cost; Economic; Emission; Harvest; Minimum
1. Introduction
A power system is constructed by using interconnected
structures for feeding an electric energy from generator
sites to the some areas considering a sharing amount of a
total power to meet a load demand at a certain period
time of operation. One purpose of this strategy is to re-
duce the total technical operating cost through the com-
bination various types of power plants. A minimizing
cost problem of power system operation can be ex-
pressed by using an Economic Load Dispatch (ELD) for
obtaining a minimum total fuel cost of generating units.
In general, ELD’s primary objective is to schedule the
committed generating unit outputs to meet a certain load
demand at a certain time under some operational con-
straints [1-3].
Presently, since the public awareness of the environ-
mental protection has been increased to reduce atmos-
pheric emissions, the ELD considers pollutant emissions
in the air from combustions of fossil fuels at thermal
power plants [4]. By considering an Emission Dispatch
(EmD), the power system operation has to modify opera-
tional strategies o f the thermal power plants for r educing
pollutants in the air [5]. The ELD problem has become a
crucial task to optimize a fuel cost with reducing a poll u-
tant emission for scheduling the generating unit outputs
based on a minimum total cost [6]. To avoid complexity
problems of both dispatching types for determining solu-
tions with difference targets, ELD and EmD are trans-
formed into single objective function as a Combined
Economic and Emission Dispatch (CEED).
Currently, many previous works have been success-
fully applied to solve the CEED problems [5,7-11]. The
proposed methods have been introduced by using appli-
cations of mathematical programmings and optimization
techniques [12]. Specifically, those methods can be de-
vided into traditional and evolutionary types. Traditional
methods cover several approaches such as linear pro-
gramming, lagrangian relaxation, langrange multiplier
and it can be applied to many problems [7,13-15]. On the
other hand, evolutionary methods have become alterna-
tive ways to solve the problems. These methods are
compo se d by usin g int el l ige nt tec hniq ue s fo r de te rmining
an optimum result like genetic algorithm, evolutionary
programming, particles swarm optimization and neural
network [5 ,16-20].
A novel computation of evolutionary methods is an
Artificial Bee Colony (ABC) algorithm. This method
was proposed by Karaboga in 2005 based on foraging
behaviors of honeybees in nature [21]. This algorithm
has abilities to o vercome difficultie s of evolutionary me-
thods for solving real problems with multidimesional
spaces and reducing time of computation [22-24]. These
points are covered by using bee’s interaction on the ga-
theri ng and shar ing i nfor mati on d urin g sea rchi ng t he be st
soluti o n. T he AB C al so has a p o werful co mp utati o n con-
trasted to other evolutionary methods, an ability to get
out of a local and a global minimum, a capability of ha n-
dling c o mplex problems, and a n effectiveness for solving
optimizing problems [4,6,25, 26]. The newest generation
of this algorithm is a Harvest Season Artificial Bee Co-
lony (HSABC) algorithm as a new evolutionary method.
Copyright © 2013 SciRes. EPE
The HSABC is introduced in 2013 and it is composed by
Multiple Food Sources (MFS) for mimicing flowers of a
harvest season to provides candidate solutions of the
problem [27].
This paper presents the HSABC for obtaining the best
solution of the CEED problems. The objective function
of the CEED is subjected to some operational constraints.
In t hese works , IEEE-30 bus system is adopted as a sam-
ple system for the simulations.
2. Problem Statement
2.1. Combined Economic and Emission Dispatc h
A problem of ELD is related to a nonlinear equation [28].
The ELD’s objective function is expressed by a total cost
for providing a total power from generation stations and
it can be computed by using equation (1). Presently, an
ELD includes a pollutant emission as a constraint. Vari-
ous p ollutan ts have been c ome fr om the bur ning o f fossi l
fuels in the thermal power plants [8,9,14]. The total pol-
lutant emissio n is formulated by equatio n (2) as the EmD.
The ELD and EmD are composed into single objective
function of CEED problem with considering a price pe-
nalty [8] and a weighting factor as a compromised factor
[5] as formed in equation (4). The penalty factor shows
the rate coefficient of each generating unit at its maxi-
mum output for the given load. The compromised factor
shows a sharing contribution of ELD and EmD. Several
limitations for performing CEED are given by equation
(5) to (10). Specifically, a total transmission loss is not
constant a nd it depends on the power outputs of generat-
ing units [28,29]. The transmission loss can be appeared
fro m a load flo w ana lys is. In ge neral, the CEED problem
can be formulated by using ex p r essions as follo ws :
ELD min i mi ze , (1)
EmD min i mi ze , (2)
, (3)
CEED minimize , (4)
, (5)
, (6)
, (7)
, (8)
, (9)
. (10)
where Pi is output power of ithgenerating unit (MW), ai,
bi, ci are fuel cost coefficients of ith gener ating uni t, Ftc is
total fuel cost ($/hr), αi, βi, γi are emission coefficients of
ith genera ting u nit, Et is total emis sion of genera ting unit s
(kg/hr), hi is individual penalty factor of ith generating
unit, Pima x is maximum output power of ith generating uni t ,
Ei is total e missio n o f ith gene r a ti ng u ni t (k g/ hr ) , Fi is f uel
cost of ith generating unit ($/hr), Φ is CEED ($/hr), w is
compromised factor, ng is number of generator, h is pe-
nalty factor of ascending order selection of hi, PD is
power load demand, PL is transmission loss, PGp and QGp
are power injections of load flow at bus p, PDp and QDp
are load demands of load flow at bus p, Vp and Vq are
voltages at bus p and q, Pimin is minimum power of ith
generating unit, Qimax and Qimin are maximum and mini-
mum reactive powers of ith generating unit, Vpma x and
Vpmin ar e maximum and minimum voltages at bus p.
2.2. Harvest Season Artificial Bee Colony
The HSABC algorithm is composed by MFS to presents
many flowers of the harvest season located randomly at
certain positions in the harvest season area [27]. Specifi-
cally, HSABC is inspired by a harvest season situation in
nature for providing flowers. In the HSABC, a flower is
presented by a food source and MFS express man y flow-
ers. To exploit food sources, bees fly randomly during
foraging for the foods and the position moves from a
selected current food source to another one [25,30]. In
the HSABC, MFS are consisted by the First Food Source
(FFS) and Other Food Sources (OFS). Each position of
OFS is directed by a harvest operator (ho) from the FFS.
A set of OFS is preceded by foraging for the FFS. As in
the ABC, the HSABC has four phases for searching the
best food as a final solution, those are initial phase, em-
ployed bees phase, onlooker bees phase and scout bees
An initial phase is a set population generation of can-
didate solutions. This population is created randomly by
considering the constraints. For each solution is corres-
ponded to the number of parameter to be optimized
which populated using equation (11). An employed bees
phase is a searching mechanism of a neighbor food
source. Each food source chosen represents a possible
solution to the problem. The new food source is searched
by an employed bee as the FFS. After the FFS is found
by bee, OFS have been created to express the harvest
season situation. An onlooker bees phase is a food source
selection for the best food. Onlooker bee chooses a food
source based on the probability value each nectar quality.
The nectar quality is evaluated by using equation (14)
and probability of each food source is determined by
using equation (15). Each position of candidate food is
searched by using equation (12) for the FSS and it is ac-
companied by OFS using equation (13). A scout bees
phase is a random searching for a new food source used
to replace an aband oned value.
Copyright © 2013 SciRes. EPE
In general, the rules of the HSABC are a set of MFS is
consisted by FFS a nd OFS, the FSS is followed b y OFS,
every food source is located at a different position, all
food sources stay in the harvest season area, colony size
is consisted by employed bees and onlooker bees, an
employed bee of an abandoned food source becomes a
scout bee. By mathematical expressions, the HSABC are
presented as fol l owing exp res sions:
, (11)
, (12)
, (14)
. (15)
where 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 minimum limit of xij, xmaxj is maxi-
mum limit of xij, vij is food position, xkj is 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
harvest season food position, ho{2,3,…,FT}, FT is the
total number of flowers for harvest season, xfj is random
harvest neighborof xkj, f {1,2,3,…,SN}, Rj is a ran-
domly chosen real number within [0,1], MR is modified
rate of probability food, Fi is objective function of the ith
solution of the food, fiti is fitnes s value o f the ith solutio n
and pi is probability of the i th quality of food.
3. Sample System and Procedures
In these simulations, parameters listed in Table 1 to Ta-
ble 3 are used for the sample system. Figure 1 sho ws the
single line diagram of IEEE-30 b us system.
Designed programs of application HSABC for solving
CEED problems are created by considering several steps
of HSABC’s procedures as presented in Figure 2. The
listi ng p r ogr a ms ar e c at e go ri ze d into thr e e p r ogr a ms . The
data input program is consisted by a set data of parame-
ters for generating units, transmission lines, loads, con-
straints, CEED’s parameters and HSABC’s parameters.
The CEED program is designed for an objective function
to compute a minimum total cost based on the CEED
problem, compromised factors and constraints. The
HSABC program is developed by using HSABC’s steps
for searching the best solution of the CEED problem.
4. Results and Discussions
These works are addressed to solve the CEED problem
using HSABC algorithm for obtaining the best solution
Table 1. Fuel cost coefficients and mw limits.
Bus Gen a
($ / MWh2) b
($/MWh) c Pmin
(M W) Pmax
(M W)
1 G1 0.00375 2.00000 0 50 200
2 G2 0.01750 1.75000 0 20 80
5 G3 0.06250 1.00000 0 15 50
8 G4 0.00835 3.25000 0 10 35
11 G5 0.02500 3.00000 0 10 30
13 G6 0.02500 3.00000 0 12 40
Table 2. Emission coefficients and mvar limits.
Gen α
(kg/MWh2) β
(kg/MWh) γ Qmin
(Mvar) Qmax
G1 0.0126 -1.1000 22.9830 100 -100
G2 0.0200 -0.1000 25.3130 60 -60
G3 0.0270 -0.0100 25.5050 65 -15
G4 0.0291 -0.0050 24.9000 50 -15
G5 0.0290 -0.0040 24.7000 40 -10
G6 0.0271 -0.0055 25.3000 15 -15
Table 3. Load d ata for each bus.
Bus No MW Mvar Bus No MW Mvar
1 0.0 0.0 16 3.5 1.8
2 21.7 12.7 17 9.0 5.8
4 7.6 1.6 19 9.5 3.4
5 94.2 19.0 20 2.2 0.7
7 22.8 10.9 22 0.0 0.0
8 30.0 30.0 23 3.2 1.6
9 0.0 0.0 24 8.7 6.7
10 5.8 2.0 25 0.0 0.0
11 0.0 0.0 26 3.5 2.3
13 0.0 0.0 28 0.0 0.0
14 6.2 1.6 29 2.4 0.9
15 8.2 2.5 30 10.6 1.9
Figure 1 . One-line diagram of IEEE 30 bus system.
Copyright © 2013 SciRes. EPE
Figure 2 . HSABC’s flow chart for solvi ng CEED proble m.
and determining a committed power outputs of generat-
ing units. The main purpose of the used compromised
factors is to know the best combination of ELD and EmD
from possibility values of combinations. To observe
HSABC’s performances on load demand changes are
studied in this section. Effects of load demand changes
are also evaluated on the samp le s ystem.
These studies consider 283.4 MW of load demand, ±
5% of voltage limits, power balance and power limits.
The programs are executed by using colony size = 100,
number of foods = 50, limit number of foods = 50, total
foraging cycles = 100 and 3 flowers. An initial popula-
tion of a set candidate food is presented in Figure 3 as
the candidate solutions for six generating units. The best
food of each food source is located at random positions
as shown in Figure 4. Determined iterations on the
CEED’s minimum cost are presented in Table 4 and
Figure 5.
Final solutions of the committed power outputs of ge-
nerating units to meet a load demand at the minimum
total costs are listed in Table 5 and final minimum oper-
ating costs are provided in Table 6. Power losses and
pollutant emissions are presented in Figure 7. By consi-
dering combinations of ELD and EmD, according to Ta-
ble 6 and Figure 5, better results are obtained by using w
= 0.5. For this chase, the CEED has the shortest range
from a starting cost to reaches a minimum cost, the
cheapest total cost is given by using w = 0.5 and the
fastest convergence speed is also performed b y using thi s
compromised factor as presented in Figure 5. The con-
vergence speed of the CEED used w = 0.5 is illustrated
in Figure 6.
Practically, generating units are associated with load
demand behaviors during operations. To performs load
dema nd cha nges a nd evaluates it in the total cost are st u-
died in these wor ks. For the se works, a sharin g contrib u-
tion of ELD and EmD use 0.5 of compromised factor.
Load demands are assumed to increase gradually at load
buses. The performances on increased load demands are
listed in Table 7. By comparing costs in Table 7 to Ta-
ble 6 for column w = 0.5, the percentage results are given
in Table 8.
Figure 3. Populations of candid ate solutions.
Figure 4. Food posit ions of f ood sources.
Table 4. CEED’s minimum of the computations.
Compr om ised factors
0 0.25 0.5 0.75 1
CEED 609.94 669.51 724.98 773.28 798.02
ELD neglected 210.78 415.14 611.92 798.02
EmD 609.94 458.73 309.84 161.36 neglect ed
Starting 612.36 671.14 726.04 776.05 806.15
Minimum 609.94 669.51 724.98 773.28 798.02
Figure 5. Cost changes and iterations at CEED’s minimum.
Copyright © 2013 SciRes. EPE
Table 5. Final result of committed power outputs.
(M W) Compromised factors
0 0.25 0.5 0.75 1
G1 112.29 117.60 126.07 140.68 177.46
G2 46.96 48.26 49.74 50.66 49.35
G3 34.87 31.48 28.40 25.25 19.63
G4 31.48 31.66 31.80 30.90 22.83
G5 30.00 29.54 26.63 21.74 12.11
G6 33.29 30.71 27.17 21.54 12.00
Total power 288.89 289.25 289.81 290.77 293.38
Total los s 5.49 5.85 6.41 7.37 9.98
Table 6. Final result of minimu m total costs.
($/hr) C om promised factors
0 0.25 0.5 0.75 1
Fuel cost 854.11 843.10 830.28 815.89 803.89
Emis. cost 610.07 611.76 619.81 645.57 765.87
Total cost 1464.18 1454.86 1450.09 1461.46 1569.76
Figure 6. Convergence speed using w=0.5.
Figure 7. Fi nal results of emissions and power losses.
Table 7. Final results on various loads.
Subjects Increased load demands (MW)
20% 30% 40%
G1 (M W)
G2 (M W)
G3 (M W) 34.44 38.53 43.20
G4 (M W)
G5 (M W) 30.00 30.00 30.00
G6 (M W) 36.59 40.00 40.00
Total G (MW)
Loss (MW)
T. Emission (kg/hr) 469.55 547.48 639.21
T. Emission Cost ($/hr)
T. Fuel Cos t ($/hr)
T. Cost ( $/hr) 1892.61 2150.89 2438.65
Table 8. Percentage results on various lo ads.
New load demands
340. 0 8 MW
(20%) 368.42 MW
(30%) 396.76 MW
Fuel costs 0.2663 0.4092 0.5578
Emis. Costs 0.3573 0.5826 0.8477
Total cost 0.3052 0.4833 0.6817
From Table 7 is known that all power outputs of com-
bined generating units are produced up by increased load
demands. Specifically, G5 and G4 feed to the power sys-
tem with 30 MW and 35 WM because of upper power
limits. Generating units produces 348.95 MW to 409.71
MW of total powers with increasing losses from 8.87
MW to 12.95 MW. The most interesting point is 40% of
increased load demand. In this case, all components of
cost exceed 50 % as listed in Table 8. The higher load
demand associates with greater payments of generating
5. Conclusions
This paper presents an application of a new evolutionary
method, Harvest Season Artificial Bee Colony Algorithm,
for solving CEED problem using IEEE-30 bus as a sam-
ple system. These works demonstrate that compromised
factors give effects to the CEED’s solutions. These stu-
dies indicate that increasing load demands affect gener-
ated power outputs, pollutant emissions and costs. By
considering compositions of ELD and EmD, the lowest
total cost is obtained by CEED using 0.5 of compromised
factor. In these simulations, the HSABC is tested on a
standard model of IEEE, a revealing real sample system
is devoted to the future works.
6. Acknowled gements
The authors gratefully acknowledge the support and
thanks to Kumamoto University (Japan) and Beasiswa
Luar Negeri DIKTI (Indonesia).
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