Comparative performance Evalution of Combined
Economic Dispatchand Emission Dispatch using
Hybrid Search Algorithm.
Hareesh Sita
Research Scholar, Electrical Engineering
JNTUA
Ananthapuram, India
Prof. P.Umapathi Reddy
Department of Electrical Engineering
SVEC (Autonomus)
Tirupathi, India
Prof. R. Kiranmayi
H.O.D of Electrical Engineering
JNTUA
Ananthapuram, India
Abstract-This paper illustrates about CEED evalution using
Hybrid Search Algorithm.This paper discuseed about the
combined algorithms of firefly and differentinal evoluation
algorithm to i ‘Cost of the generating units’, NOx Emissions
Dispatch and CEED problems(Combined Economic Dispatch
and Emissions Dispatch) in base load power plants.The instant
energy yielding process are ecologically unclean as the coal
used plants desecrate the earth.The intermixture of the fossil
fuels, separate the Carbon, Nitrogen andndu sulphar cause
detrimental effects on Homo-sapiens. materials and gaseous
pollutants from discharge of heat to water.This adverse effects
induced by the Emission of particulate and gaseous pollutants
will be reduced by fair distribution of load between the plants of
a power system.As such, the operation cost of the plants rasies
noticeably.To reduce the ecological and environmental
constraints, optimized algorithms have been proposed for
minimum cost, minimum NOx Emissions and Combined
economic and emissions dispatches.The proposed algorithms
hase been tested for IEEE 30 bus system and results are
compared with DE and firefly technique.
Keywords – Economic load dispatch, Emission dispatch, CEED,
Firely and DE.
I. INTRODUCTION
The Resource programming is isolated in two stages.
The commitment stage and the constrained economic dispatch
estage. The OPF constraints are relevant to the real power
such as transmission capacity constraints, different types of
emission requirements (i.e., SO2 and NOx). The constrained
economic dispatch incorporates transmission capacity, load
and reserve requirements as well as generating unit limits. For
rapid and efficient solutions, the constrained economic
dispatch problem can be split into two sub problems, each
corresponding to constrained economic dispatch of committed
units at a given period. The common problem in economic
power dispatch pertains to the allocation of the amount of
power to be generated by different plans in the system on
optimum economic basis. Some of the states in India expertise
severe power shortage, for which optimization of fuel costs
during peak load periods. But during lean load periods,
economic dispatch reduce fuel costs and line losses. The
particulate materials do not cause a serious problem in air
contamination, but the three major pollutants precisely, the
oxides of carbon, nitrogen and sulphur threaten determinal
effects on homo-sapiens. So, when distributing load between
the stations, the planner should not only strive for minimizing
the system generation costs, but also will take into account the
impact of each station on the environment under a particular
load. Cost should not be minimized in the goal of operation if
the society is to have a clean atmosphere. Minimum emission
dispatching is one method in which all power supplying
authorities and consumers have within their grasp to meet the
problems of air pollution [2]-[3].
.
II.Mathematical Modelling For CEED Problem Formulation
A. Economic Dispatch:
In power systems Economic Dispatch Problem is the one of
the important issues.For economic feasibility the fuel cost of
base load power plants is regarded as a crucial criterion.The
fuel cost curve is approximated by quadratic function of
generator power output as [7]
GiGiiiGii
ng
i
Giiit PPPPC
min2
1
sin ------ Eqa(1)
Where i= 1,2,3,………n,
Ct is the fuel cost in the system ($/hr).
PGI is the power output of ith generating unit(MW).
αi,βi,δi the fuel cost coefficients of ith unit.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
354
B.Emission Dispatch:
Considering the environment the dangerous and harmful
emission of pollutants produced be minimized.Many possible
solutions are proposed to solve this problem such as
installation of cleaning equipment, change of fuels with less
pollutant.
The emsission dispatch power problem is defined as
GiiiGiiGiii
ng
i
G PedPcPbaPE exp.10 2
1
2
------Eqa (2)
Where Ei is the total NOx Emission (ton/hr),PGI is the power
output of the ith generator (MW);ai,bi,ci,di,and ei are the NOx
emission coefficients of ith unit and N is the number of
thermal units.
C.Combined Economic Dispatch and Emission Dispatch
Problem
The above Multi objective CEED problem can be converted
in to single optimization problem by introducing modified
price penalty factor as follows.
GtG PEhCPFMin
($/hr)------Eqa (3)
Where h=price penalty factor ($/ton), which is the cost
incurred to reduce 1Kg of NOx emission output.This is
subjected to the generating unit constraint.
The price penalty factor can be defiened as ratio between
maximum fuel cost and emission of the generator.
Where max
max
G
Gti
PE
PCh - -----Eqa (4)
C.Procedure for finding modified price penalty factor:
1.Find the ratio between fuel cost of maximum value and
maximum value emission of each generator.
2.Find the ratio between fuel cost and maximum emission of
each generator .
3.Arrange the values hi in ascending order. M is an array
formed by adding Pimax, one by one from the lowest hi value
unit.
4.Add the elements of mi one at a time, starting from the
smallest hi until ∑ M > PD.The modified price penalty factor
hpd is calculating by inter polating method [6].
III.Hybrid based –Combined Economic and Emission Based
Problem.
There are many conventional techniques for solving the
economic dispatch problem by considering different
constraints of the power system operation.Many mathematical
techniques are solved to CEED such as
a.Newton Raphson method. b.Lambda iteration method.
c.Interior point method. d.Linear programming
the drawbacks of the conventional methods are a)Unable to
provicde local optimal solution.b)get stuck at local optimal.
Conventional method are usually based on assumption of
continuity and differentiabiliy.So these methods are suitable to
applied with discerte variables.
Natural inspired procedures such as Genetic algorithm,
differential evaluation algorithm and hybrid algorithm
overcome the difficulties of classical methods.These
algorithms are provide optimal solution and pollution.
A.Fire fly algorithm :
To find optimal solution for engineering problems fire fly
algorithm initialize fire fly intelligent techniques for
minimization (or) maximization probem.
Features of the fire fly algorithm are
In spite of being unisex firefly is attracted by another
firefly.
The movement of fire fly is always towards the
brightest.
Nature problems is affected by brigntness of fire fly.
B. Attractiveness:
Fire fly responds more towards attraction.This attraction of a
fire fly with others is calculating using the function when the
distance between fireflies increases the attraction
decreases.Vital reasons for reduction in attraction are
absorption factors in nature.
These factors can be calculated by using absorption cofficeints
which is monotonically decreasing function can be given as
2
0 exp r
------Eqa (5)
B.Distance:
In two –dimension space, the distance between ith and jth
firefly are calculated as
d
k
kjkijiij xxxxr1
2
,,||||
------Eqa (6)
B.Movement:
Movement of the ith firefly and jth firefly are calculated and
distance between them
i
k
i
kj
k
i
ki xxrxx 2
0
1exp
------Eqa (7)
In above equation the left hand side consists of three terms
where the first term is the initial position of ith firefly.
Second term reprensents attractiveness towards jth firefly.
Thrid term introduce the random movement in ith firefly
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
355
C:Stopping criteria:
Random movement of firefobly helps in attraction towards
brighter firefly. FA refines problem iteration by iteration till
better solutions are obtained.The iteration has stops either
when the problem is converged (or) the iteration reaches its
predefined valve.Complexity is reduced by halting
iteration[10].
C:Algorithm for firefly :
Step:1 Group of control varbiles in CEED is nothing but
firefly.
Step:2 Intialise fireflies in the population which solution
space.
Step:3 Glow of firefly can be detected by objective function
in CEED.
Step:4 Attractiosbetween fireflies is calculated.
Step:5 Space in between fireflies can be measured.
Step:6 Equation (7) helps to draw one of the firefly to other.
Step:7 Current global best is found by ranking the firefly.
D:Credits and limitations of firefly :
FA has credits over other optimized techniqes.A few of them
are catalogued below.
1.FA are promising intelligent algorithm helps to find global
optima.
2.Random reduction and Automatic sub division.
3.Complex function of optimization is solved.
4.It is a static objective fitness function.
5.Population based search technique.
6.Solutions to non linear and multi model problems are
formed.
7.Solutions to continuous or discontinuous functions.
E :Differential evaluation:
Differential evaluation was initially proposed during the year
1996 by Strom and pride were responsible for it.The aptitude
of differential evaluation is to optimize non linear, non
continuous and non differential substantial world problems.
Differential evaluation focus on mutation rather than cross
over when compared with meta heuristic algorithms.
Minimization Ct = G
NG
i
i Pf1
$/hour
Subject to : 0, Vg
-- Eqa (8)
maxmin XXX
Differential evalution does not need any encoding and
decoding due to merging characteristics and uses real value
control variables.This set of control variables froms a vector
which in turn forms a population.Random variables vectors
are used iteration by iteration by the evaluation to
convergence in optimal solution.The basic operations of
differential evaluation are mutation, recombination and
selection. A target vector selected by the differential
evaluation passes mutation and crossover resulting as a trail
vector.Based on their fitness selection procedure.
E :Differential evaluation based OPF:
The control variables are active power generation, generation
bus voltage and tap position of the transformer are considered
to optimize the power flow problems.These actual values
obtained are used in vectors.In population formed vectors
evaluation is carried out mutation, recombination and
selection process.
F:Encoding:
Converting set of control variables in to vector of differential
evaluation optimization problem is called as encoding.The
aptitude of differential evaluation operates on floating point.
G:Mutation:
Recombination is not given importance, more emphasises on
mutation. Enabling such diversity and directing the existing
vectors are the objectives of mutation for better results at a
suitable time mutation not only explores new areas in such
domain but also keep the search robust.Based on the fitness
function target vector is selected to find mutated vector this
can be done by random selected vector.
H:Recombination:
The generation of trail vector is due to recombination or cross
over from a target and mutated vector recombination is the apt
name since it recombines mutated or target vector
particles.Prior success in the current population is reinforced
in the process binomial recombination andss in the current
population is reinforced in the process binomial recombination
and exponentional recombination .The simplest most frequent
used one is binomial recombination.Recombination usually
ranges from 0 to 1 .Convergence speeds up when
recombination has large value so low value is good for
separable problem.
Xtrail = Xmutated if (rand)≤CR
Xtarget if (rand)>CR -- Eqa (9)
H:Selection:
In DE there are mainly selection process, Among them one to
one selection process is used to make a decision process either
by target vector or trail vector for next iteration.
Where X is a target vector and K is a iteration no.
Xk is a target vector and X k+1 is a vector for subsequent
iteration.
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
356
Fitness function is used to compute the fitiness target vector
and trial vector. if the ifitness function of trail vector is great
than the target vector is replaced by trial vector [9].
Xtrail= X0=Xmin+ rand(0,1)*(Xmax– Xmin)
Xtrail if f(trail)<f(target)Xk+1 =
-- Eqa (10)
Xtarget if f(target)≤f(trail)
IV:Simulation Results and Discussions:
Solutions for CEED problem were demonstrated on IEEE 30
bus Six generator system.The parameters used of proposed
algorithm is Maximum iteration =100, minimum and
maximum bus voltage levels are can be taken as Vmin=0.9P.U
and Vmax=1.1P.U.and it consists of 6 generators, 4transformers
and 30 bus the generators costcofficients emissionscofficients
load demands are given in the following tables. The cost
coefficients of a IEEE 30 bus as shown in table I and
emissions coefficients are shown in table II.
Table 1. Cost coefficients of IEEE 30 Bus system
Table 2. Emission coefficients of IEEE 30 Bus system
“ Fig.1. Represents the flow chart for Hybrid algorithm.In this
flow chart , The important parameters are Recombination,
cross over, selection and mutation .Initally the voltage
magnitude, Real power and Reactive power losses can be
calculated by using Newton Raphson method.
In differential evalution , the vector has 15 control variables.
This control variables a forms atrial vector (or) target vector .
In differential evalution mutation plays avital role because the
value of mutation depands on the accuracy of solution.the
valve of mutation constant depands on the fitness function
based on their selection procedure ,if the fitness function value
is in the range of o to 1.if the value is very low then
convergence speed increases and it is very good for seperable
problem.”
S.No Bus
No
P max (MW)
P min (MW)
αi βi γi ζi λi
1 1 50 200 0 2.0 0.00375 18 0.0370
2 2 20 80 0 1.7 0.01750 16 0.038
3 5 15 50 0 1.0 0.06250 14 0.040
4 8 10 35 0
3.2
5
0.00834
12 0.045
5 11 10 30 0 3.0 0.02500 13 0.042
6 13 12 40 0 3.0 0.02500 13.25 0.041
S.
No
Bu
s
No
P max (MW)
P min (MW)
a b c d e
1 1 50 200 4.091 -5.574 6.490 2.0E-4 2.857
2 2 20 80 2.534 -6.047 5.638 5.0E-4 3.333
3 5 15 50 4.258 -5.094 4.586 1.0E-6 8.000
4 8 10 35 5.426 -3.550 3.380 2.0E-3 2.000
5 11 10 30 4.258 -5.094 4.586 1.0E-6 8.000
6 13 12 40 6.131 -5.555 5.151 1.0E-5 6.667
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
357
15x8080,41,4
80,11,1
80,61,6
80,11,1
80,61,6
80,21,2
...
.....
...
...
.....
...
...
.....
...
TT
TT
VV
VV
PP
PP
gg
gg
gg
gg
Y
Start
1 Calculate Y-bus 2 Solve Power balance equation using NR method and 3 Calculate P and Q flow and losses in each line
Calculate objective Cost
function 2
1
minζ sin λ P Pi i Gi Gi
ng
t i i Gi i Gi
i
C P P
Differential Evolution
A Vector has 15 control variables
(5 Real Power generation, 6 generator bus Voltage magnitude and 4 transformer Tap position)
No_Control_Variables=15, No_Vector=80,
Scaling Factor (SF) = 0.7, Cross Over const (CR) = 0.2
Initialize Population, Pop =
Mutation
Yi1(G) = Ya
(G) +S (Y b(G)
– Y c(G))
Crossover
otherwiseX
CifXX
Gji
RjGjiG
ji..........
..)(
,
1)(1,)(11
,
Selection
otherwiseY
YfYfifYY
G
i
G
i
G
i
G
iG
i...........................
)()(...)(
)()(11)(11
)1(
Read Bus Data, Line Data and generator costCo-efficienct
If G ≤ Gmax
Print the Minimum Generating Cost
End
NO
Fig: 1: Flow chart for hybrid algorithm
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
358
Table. 3. Optimum generation schedule obtained the proposed algorithm for IEEE 30 bus.
Graphs for CEED using fire fly, DE, and Hybrid Algorithm for a power demand 290 MW:
0 10 20 30 40 50 60 70 80 90 100813.6
813.8
814
814.2
814.4
814.6
814.8
815
815.2
815.4
No. of Iteration
Gen
erat
img
Cos
t $/
hr
Convergence Curve for CEED
Fig.2.Convergence Characteristics for Economic dispatch
using using FFA
Fig.3. Convergence characterstics for Economic Dispatch
using DE algorithm
S.NO Method Pd
(MW)
P1
(MW)
P2
(MW)
p3
(MW)
p4
(MW)
p5
(MW)
p6
(MW)
Fuel
cost
($/Hr)
Emission
cost
(ton/Hr)
CEED
cost
($/Hr)
1
Fire fly
algorithm
290
100.023 66.041 24.254 34.099 26.012 38.0315 859.869 0.087899 1095.85
DE
98.7254 51.656 41.05 27.976 28.555 39.0125 883.594 0.076585 1077.16
Hybrid
Algorithm
88.1678 55.238 47.128 53.124 17.359 27.5987 896.115 0.072686 1052.47
2
Fire fly
algorithm
260
98.023 65.014 23.543 30.009 25.015 18.031 850.676 0.078967 1085.67
DE
90.027 50.65 37.051 23.976 24.554 25.595 876.954 0.065769 1075.64
Hybrid
Algorithm
80.18 45.238 41.124 43.124 24.059 25.595 883.113 0.062785 1046.67
0 10 20 30 40 50 60 70 80 90 100813.6
813.8
814
814.2
814.4
814.6
814.8
815
815.2
815.4
No. of Iteration
Gen
erat
img
Cos
t $/
hr
Convergence Curve for CEED
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
359
using
Fig.4.Convergence characterstics for Economic Dispatch
Using DE
Fig.5.Convergence characterstics for Emission Dispatch
Using FFA
Fig.6..Convergence characterstics for Emission Dispatch
Using DE Algorithm.
Fig.7..Convergence characterstics for Emission Dispatch
Using DE Using DE
Fig.8 CEED graph using Firefly algorithm
Fig.10.CEED graph using firefly-DE
0 10 20 30 40 50 60 70 80 90 100820
830
840
850
860
870
880
890
900
No. of Iteration
Genera
tim
g C
ost
$/h
rConvergence Curve for DE
0 10 20 30 40 50 60 70 80 90 1000.0738
0.074
0.0742
0.0744
0.0746
0.0748
0.075
0.0752
No. of Iteration
Em
issi
on t
on/h
r
Convergence Curve for CEED
0 10 20 30 40 50 60 70 80 90 1000.0765
0.077
0.0775
0.078
0.0785
0.079
No. of Iteration
Em
issi
on t
on/h
r
Convergence Curve for ff
0 10 20 30 40 50 60 70 80 90 1000.062
0.063
0.064
0.065
0.066
0.067
0.068
0.069
No. of Iteration
Em
issio
n t
on/h
r
0 10 20 30 40 50 60 70 80 90 100880
885
890
No. of Iteration
Gen
erat
img
Cos
t $/h
r
Convergence Curve
0 10 20 30 40 50 60 70 80 90 1000.0756
0.0758
0.076
No. of Iteration
Em
issi
on to
n/hr
0 10 20 30 40 50 60 70 80 90 1001078
1080
1082
No. of Iteration
CE
ED
$/h
r
0 10 20 30 40 50 60 70 80 90 100895
896
897
No. of Iteration
Gene
ratim
g Co
st $
/hr
Convergence Curve
0 10 20 30 40 50 60 70 80 90 1000.071
0.072
0.073
No. of Iteration
Emiss
ion to
n/hr
0 10 20 30 40 50 60 70 80 90 1001050
1055
1060
No. of Iteration
CEED
$/h
r
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
360
Fig.11.CEED graph for DE alorithm
V.Conclusion:
Combined economic and dispatch problem is formulated as
high non linear multi objective problem.Many conventional
methods are available to solve CEED problem.The main dis
advantages in these methods are that they use of gradients and
derviates.In order to over come such things a new version
hybrid procedure has been proposed and demostarted for
IEEE 30 bus system .The advantage in this method is to
combine the firefly and DE procedure to generate a solution of
best quality .The merits of proposed algorithm is that value of
mutataion is constant through out the process as solution
accuracy depands on constant of mutation .it shows that
hybrid procedure produces best solution and shows that
consistency characteristics.
References [1]. R.Yokoyama, S.H.Bae, “Multi Objective Generation Dispatch based
on probability security criteria” IEEE transaction on Power Systems ,
Vol. 3, No.1, February 1988.
[2]. A.A.El-keib;H.Ma;J.L.Hartames“EnvironmentallyConstrained Economic Dispatch using the Lagrangian relaxation method ’’ IEEE
transaction on Power Systems , Vol. 9, No.1, November 1994.
[3]. R.Ran,Ranathanj “Emissions Constrained Economic Dispatch”
IEEE transaction on Power Systems , Vol. 9, No.1, November 1994
[4]. Ahmed Farag Samir,Al-Baiyat,T.C.Cheng”Economic Load Dispatch Multi Objective Optimization procedures using linear programming
techniques” IEEE transaction on Power Systems , Vol. 10, No.2, May 1995.
[5]. D.B.Das,C.Patvardhan,”New Multi Objective Stochastic search technquie for Economic load Dispatch”IEE proc-gener,Vol.14,No.6
November 1998.
[6]. P.Venkatesh,R.Gnandass an Narayana Prasad Padhy "Comparsion and Application of Evolutionary Programming Techniques to
Combined Economic Emission Dispatch with line flow constrains“ IEEE Transactions on Power systems, Vol.18, NO.2, May 2003
[7]. M.A.Abido”Enviromenatl/Economic Power dispatch using Multi
objective evolutionary algorithms” IEEE transaction on Power Systems , Vol. 18, No.4, November 2003
[8]. M.A.Abido “Multi objective evolutionary algorithms for Electric power Dispatch problem” IEEE transaction on Evolutionary
Computation , Vol. 10, No.6, June 2006.
[9]. S.R.Spea,M.A.Abido, “Multi objective Differential Evoluation algorithm for Economic Power Dispatch problem” IEEE
International energy Conference , August 2010.
[10]. A.Bedina,N.Amjady,M.S.Nadam,“Multi objective Environmental
/Economic Dispatch using Fire fly technique” International conference on Environment and Electrical Engineering, June 2012
[11]. James A.Momoh, S.Surender Reddy, "Combined Economic Dispatch and Emission Dispatch using Radial Basis Network” IEEE
Conference and Exposition, July 2014.
AUTHOR’s PROFILE:
Hareesh Sita has received the B.Tech
(Electrical and Electonics Engineering)
degree from Audi Sankara College of
Engineering and Technology, in 2007
affiliated to JNTUA and M.Tech
(Electrical Power Systems ) degree from
Sree Vidyanikethan Engineering college
in 2010. Presently, he is working as a
Research Scholar in SVEC (R&D center)
affiliated to JNTU Anantapur. His field of
interest includes Renewable Energy
Sources, Power systems operations.
Dr. P.Umapathi Reddy, is graduated in
1998, Masters in 2004 from J.N.T.U.C.E,
Anantapur and Ph.D in 2013 from the
JNTUK kakinda.He worked 17 years at Sree
Vidyanikethan Engineering college,
Tirupathi, A.ndhrapradesh. in the
cadars of Assistant Professor,
Assoc.Professor, Professor and Head of
Electrical and Electronics Engg.
Department.. He has published 20 research
papers in national and international
conferences and journals. He has attended
10 National & International workshops. His
areas of interests are Electrical Machines,
Power Systems & Solar Energy. He is a
member of I.S.T.E,&I.S.C.A.
Dr. R. Kiranmayi has completed her
Doctorate in the year 2013 in the area of
EnergySystems. She is presently working as
Professor & Head in the Department of
Electrical Engineering at JNTUA, Anantapur.
She has published 23 research papers in
national and international conferences and
journals . Her areas of interts are of Electrical
machines , Photo voltaic systems.She is a life
member of I..S.T.E.& Institue of
Engineering
0 10 20 30 40 50 60 70 80 90 100895
896
897
No. of Iteration
Gen
erat
img
Cos
t $/h
r
Convergence Curve
0 10 20 30 40 50 60 70 80 90 1000.071
0.072
0.073
No. of Iteration
Em
issi
on to
n/hr
0 10 20 30 40 50 60 70 80 90 1001050
1055
1060
No. of Iteration
CE
ED
$/h
r
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 12, Number 1 (2017) © Research India Publications. http://www.ripublication.com
361