Environmental constrained electric power generation and dispatch via genetic algorithm

JECET; March 2018- May 2018; Sec. B; Vol.7. No.2, 101-116.. E-ISSN: 2278–179X
[DOI: 10.24214/jecet.B.7.2.0000]
Journal of Environmental Science, Computer Science and
Engineering & Technology
An International Peer Review E-3 Journal of Sciences and Technology
Available online at www.jecet.org
Section B: Computer Science
Review Article
1 JECET; March 2018 - May 2018; Sec. B; Vol.7. No.2, 101-116.
DOI: 10.24214/jecet.B.7.2.7179.
Multi-Objective Bi-Level Programming for Environmental
Constrained Electric Power Generation and Dispatch via
Genetic Algorithm
Papun Biswas1*
, Tuhin Subhra Das2
1
JIS College of Engineering, Kalyani, West Bengal, INDIA
2
JIS College of Engineering, Kalyani-741235, West Bengal, INDIA
Received: 11 February 2018; Revised: 08 March 2018; Accepted: 00 March 2018
Abstract: This article presents how multi-objective bi-level programming (MOBLP)
in a hierarchical structure can be efficiently used for modeling and solving
environmental-economic power generation and dispatch (EEPGDD) problems
through Fuzzy Goal Programming (FGP) based on genetic algorithm (GA) in a
thermal power system operation and planning horizon. In MOBLP formulation, first
the objectives associated with environmental and economic power generation are
considered two optimization problems at two individual hierarchical levels ( top level
and bottom level ) with the control of more than one objective, that are inherent to the
problem each level. Then, the optimization problems of both the levels are described
fuzzily to accommodate the impression arises for optimizing them simultaneously in
the decision situation. In the model formulation, the concept of membership functions
in fuzzy sets for measuring the achievement of highest membership value (unity) of
the defined fuzzy goals in FGP formulation to the extent possible by minimising
under-deviational variables associated with membership goals defined for them on
the basis of their weights of importance is considered. Actually, the modeling aspects
of FGP are used here to incorporate various uncertainties arises in generation of
power and dispatch to various locations. In the solution process, a GA scheme is used
in the framework of FGP model in an iterative manner to reach a satisfactory decision
on the basis of needs in society in uncertain environment. The GA scheme is
employed at two different stages. At the first stage, individual optimal decisions of
objectives are determined for fuzzy goal description of them. At the second stage,

Multi-Objective … Papun Biswas and Tuhin Subhra Das
DOI: 10.24214/jecet.B.7.2.7179.
evaluation of goal achievement function to arrive at the highest membership value of
the fuzzy goals in the order of hierarchical of optimizing them in the decision
situation. The effective use of the approach is tested on the standard IEEE 6-
Generator 30-Bus System.
Keywords: Bi-level programming, Environmental-economic power dispatch, Fuzzy
goal programming, Goal programming, Genetic algorithm, Membership function,
Transmission-losses.
INTRODUCTION
The major electric power generation sources are thermal plants, where more than 75% of the power
plants across the countries use fossil fuel coal for generation of power. But, generation of electric
power by burning coal leads to produce various harmful pollutants like oxides of carbon, oxides of
nitrogen and oxides of sulphur. These by-products not only affect the human but also the entire living
beings in this world. So, economic-dispatch problem of electric power plant is actually a combined
optimization problem where real-power generation cost and environmental emission from a plant
during generating of power has to be optimized simultaneously, where several operational constraints
need be satisfied for smooth running of power generation system.
Actually, the thermal power operation and management problems in1
are optimization problems with
multiplicity of objectives and various system constraints. The general mathematical programming
model for optimal power generation was introduced by Dommel and Tinney in2
. The constructive
optimization model for minimization of thermal power plant emissions was first introduced by Gent
and Lament in3
. Thereafter, the field was explored by Sullivan and Hackett in4
among other active
researchers in the area of study.
Now, consideration of both the aspects of economic power generation and reduction of emissions in a
framework of mathematical programming was initially studied by Zahavi and Eisenberg in5
, and
thereafter optimization models for EEPGD problems were investigated in6, 7
in the past.
The study on environmental power dispatch models developed from 1960s to 1970s was surveyed by
Happ in8
. Thereafter, different classical optimization models developed in the past century EEPGD
problems have been surveyed in9-11
in the past.
During 1990s, emissions control problems were seriously considered and different strategic
optimization approaches were developed with the consideration of 1990’s Clean Air Amendment12
by the active researchers in the field and well documented in13-15
in the literature. Here, it is to be
mentioned that in most of the previous approaches the inherent multiobjective decision making
problems are solved by transforming them into single objective optimization problems. As a result,
decision deadlock often arises there concerning simultaneous optimization of both the objectives.
To cope with the above situations and to overcome the shortcomings of the classical approaches, the
concept of membership functions in fuzzy sets theory (FST) in16
has appeared as a robust tool for
solving the optimization problems.
Now, since an EEPGD problem is multiobjective in nature, the GP approach can be used as a robust
and flexible tool for multiobjecive decision analysis and which is based on the satisficing (coined by
the noble laureate H. A. Simon in17
philosophy has been studied in18
to obtain the goal oriented
solution of economic-emission power dispatch problems.

DOI: 10.24214/jecet.B.7.2.7179.
However, in most of the practical decision situations, it is to be observed that decision parameters of
problems with multiplicity of multiplicity of objectives are inexact in nature owing to inherent
impressions in parameter themselves as well as imprecise in nature of human judgments of setting
parameter values. To cope with the situation, fuzzy programming (FP) approach to EEPGD problems
has been discussed in19, 20
. The traditional stochastic programming (SP) approaches to EEPGD
problems was studied in21, 22
in the past. But, the extensive study in this area is at an early stage.
During the last decade, different multiobjective optimization methods for EEPGD problems have been
studied in23-25
by considering the Clean Air Act Amendment.
In the context of solving MODM problems by employing conventional approaches in crisp/ fuzzy
environment, it is worthy to note that uses of such an approach often leads to local optimal solution to
owing to competing in nature of objectives in optimizing them in actual practice. Again, when
nonlinearity occurs in objectives / constraints, computational difficulties arises in most of the decision
situations. To overcome the difficulty, gas based on natural selection and natural genetics in
biological system and as a goal satisficer rather than objective optimizer can be used to solve MODM
problems. The GA based several soft computing approaches to EEPGD problems have been studied
by the active researchers in26-28
in the past.
Now, it is to be observed that the objectives of power system operation and control are highly conflict
each other. As an essence, optimization of objectives in a hierarchical structure on the basis of needs
of decision makers (dms) can be considered. As such, bilevel programming (BLP) in29
in hierarchical
decision system might be an effective one for solving the problems. Although, the problem of
balancing thermal power supply and market demand have been studied in30
the recent past, but the
study in this area is yet to be explore in the literature. Moreover, the MOBLP approach to EEPGD
problem by employing GA based FGP method is yet to appear in the literature.
In this article, the GA base FGP approach is used to formulate and solve MOBLP for EEPGD
problem. In the model formulation, the minsum FGP in31
the most widely used and simplest version of
FGP is used to achieve a rank based power generation decision in an inexact decision environment. In
the decision making process, a GA scheme is employed at two different stages. At the first stage,
individual optimal decisions of the objectives are determined for fuzzy goal description of them. At
the second stage, evaluation of goal achievement function for minimization of the weighted under-
deviational variables of the membership goals associated with the defined fuzzy goals is considered
for achieving the highest membership value (unity) of the defined fuzzy goals on the basis of
hierarchical order of optimizing them in the decision situation. A case example of IEEE 6-Generator
30-Bus System is considered to illustrate the potential use of the approach.
The paper is organizing as follows. Section 2 contains the description of proposed problem by
defining the objectives and constraints in power generation system. Section 3 provides the MOBLP
model formulation by defining the leaders and followers objectives and decision vector. In Section 4,
computational steps of the proposed GA scheme for modeling and solving the problem is presented.
In Section 5 the FGP Model formulation of the proposed problem is presented. Section 6 gives an
illustrative case example in order to demonstrate the feasibility and efficiency of the proposed
approach. Finally, Section 7 provides some general conclusions and future research.
Now, the general mathematical structures of various objectives and system constraints of an EEPGD
problem are discussed in the following section.

DOI: 10.24214/jecet.B.7.2.7179.
PROBLEM DESCRIPTION
Let there be N generators in the power generation system, and Pgi , i = 1,2, ..., N, be the decision
variables associated with power generation (in p.u) from the i-th generator. Then, let PD be the total
demand of power (in p.u.), TL be the total transmission- loss (in p.u), PL be the real power losses
associated with the system.
Then, the objectives and constraints that are associated with the proposed EEPGD problem are
discussed as follows.
A. Description of Objective Functions
1. Economic Power Generation Objectives
a) Fuel-cost Function: The total fuel-cost ($/h) function associated with generation of power
from all generators of the system can be expressed as:
,)cPbPa(F igii
2
gii
N
1i
C  
(1)
where ii b,a and ic are the estimated cost-coefficients associated with generation of power from i- th
generator.
b) Transmission-loss function: The function associated with power transmission lines involves
certain parameters which directly affect the ability to transfer power effectively. Here, the
transmission-loss (TL) (in p.u.) occurs during power dispatch can be modeled as a function of
generator output and that can be expressed as:
,BPBPBPT
N
1i
N
1j
N
1i
00gi0gijgL iji   
 (2)
where 0iij B,B and 00B are called Kron’s loss-coefficients or B-coefficients in20
associated with the
power transmission network.
2. Environmental Objectives
In a thermal power plant operational system, various types of pollutions are discharged to the earth’s
Environment due to burning of coal for power generation.
The amount of NOx emission (kg/h)) is given as a quadratic function of generator output Pgi as:
,fPePdE iNgiiN
2
giiN
N
1i
N  
(3)
where iNiNiN f,e,d are NOx emission-coefficients associated with generation of power from i-th
generator.
Similarly, the amount of SOx emission (kg/h) is given as a quadratic function of generator output Pgi
as:
,fPePdE iSgiiS
2
giiS
N
1i
S  
(4)
where iSiSiS f,e,d are SOx emission-coefficients associated with generation of power from i-th
generator.

DOI: 10.24214/jecet.B.7.2.7179.
The amount of COx emission (kg/h) is also represented as a quadratic function of generator output Pgi
as: ,fPePdE iCgiiC
2
giiC
N
1i
C  
(5)
where iSiSiS f,e,d are COx emission-coefficients associated with generation of power from i-th
generator.
B. Description of System Constraints
The system constraints which are commonly involved with the problem are defined as follows.
1. Power Balance Constraint: The generation of total power must cover the total demand (PD) and
total transmission-loss inherent to a thermal power generation system.
The total power balance constraint can be obtained as:
,0)T(PP
N
1i
LDgi
 (6)
2. Generator Constraints: In an electric power generation and dispatch system, the constraints on the
generators can be considered as:
N...,2,1,i,VVV
,PPP
max
gg
min
g
max
gigi
min
gi
iii


(7)
where Pgi , and Vgi are the active power, and generator bus voltage, respectively. ‘N’ is the number of
generators in the system.
Now, MOBLP formulation of the proposed problem for minimizing the objective functions is
presented in the following section III.
MOBL FORMULATION OF THE PROBLEM
In MOBLP formulation of the proposed problem, environmental objectives are considered as leader’s
problem and economic objectives are considered as follower’s problem in the hierarchical decision
system.
Now, the MOBLP model formulation of the proposed problem is presented in the following sectionA.
A. MOBLP Model Formulation: In a BLP model formulation, the vector of decision variables are
divided into two distinct vectors and assigned them separately to the DMs for controlling
individually.
Let D be the vector of decision variables in a thermal power supply system. Then, let LD and FD be
the vectors of decision variables controlled independently by the leader and follower, respectively, in
the decision situation, where L and F stand for leader and follower, respectively.
Then, BLP model of the problem appears as in29
:
Find )D,(DD FL so as to:
,fPePdEMinimize iNgiiN
2
giiN
N
1i
N
DL
 

DOI: 10.24214/jecet.B.7.2.7179.
,fPePdEMinimize iSgiiS
2
giiS
N
1i
S
DL
 
,fPePdEMinimize iCgiiC
2
giiC
N
1i
C
DL
 
(Leader’s problem)
and, for given FL DD , solves ,)cPbPa(FMinimize igii
2
gii
N
1i
C
DF
 

,BPBPBPTMinimize
N
1i
N
1j
N
1i
00gi0gijgL
D
iji
F
   
 (Follower’s problem)
subject to the system constraints in (6) - (7),
(8)
where φ FL DD , DDD FL  and φ)S(}and;{  TVPD gg , and where S denotes the feasible
solution set,  and stand for the mathematical operations ‘intersection’ and ‘union’, respectively.
Now, the GA scheme employed for modeling and solving the problem in (8) in the framework of an
FGP approach is presented in the following section IV.
GA SCHEME FOR THE PROBLEM
In the literature of GAs, there is a variety of schemes in32, 33
for generating new population with the
use of different operators: selection, crossover and mutation.
In the present GA scheme, binary representation of each candidate solution is considered in the
genetic search process. The initial population (the initial feasible solution individuals) is generated
randomly. The fitness of each feasible solution individual is then evaluated with the view to optimize
an objective function in the decision making context.
Now, FGP formulation of the problem in (8) by defining the fuzzy goals is presented in the next
section V.
FGP MODEL FORMULATION OF THE PROBLEM
In a power generation decision context, it is assumed that the environmental and economic objectives
in both the levels are motivated to cooperative to each other and each optimizes its benefit by paying
an attention to the benefit of other one. Here, since leader is in the leading position to make own
decision, relaxation on the decision of leader is essentially needed to make a reasonable decision by
follower to optimize the objective function to a certain level of satisfaction. Therefore, relaxation of
individual optimal values of both the objectives as well as the decision vector LD controlled by
leader up to certain tolerance levels need be considered to make a reasonable balance of execution of
decision powers of the DMs.
To cope with the above situation, a fuzzy version of the problem in (8) would be an effective one in
the decision environment.
The fuzzy description of the problem is presented as follows Section.

DOI: 10.24214/jecet.B.7.2.7179.
A. Description of Fuzzy Goals: In a fuzzy decision situation, the objective functions are
transformed into fuzzy goals by means of assigning an imprecise aspiration level to each of them.
In the sequel of making decision, since individual minimum values of the objectives are always
acceptable by each DM, the independent best solutions of leader and follower are determined first as
)E,E,E;,( CSN
lblblblblb
FL DD and )T,F;,( LC
fbfbfbfb
FL DD , respectively, by using the GA scheme, where lb and,
fb stand for leader’s best and follower’s best, respectively.
Then, the fuzzy goals of the leader and follower can be successively defined as:
NE ~
lb
NE , SE ~
lb
SE and CE ~ lb
CE
CF ~
bf
CF and LT ~
bf
LT
(9)
where ‘
~
 ’ Refers to the fuzziness of an aspiration level and it is to be understood as ‘essentially less
than’ in 34
.
Again, since maximum values of the objectives when calculated in isolation by the DMs would be the
most dissatisfactory ones, the worst solutions of leader and follower can be obtained by using the
same GA scheme as )E,E,E;,( CSN
lwlwlwlwlw
FL DD and )T,F;,( w
LC
ffwfwfw
FL DD , respectively, where lw and, fw
stand for leader’s worst and follower’s worst, respectively.
Then, w
LCCSN TandF,E,E,E fwflwlwwl
would be the upper-tolerance limits of achieving the aspired levels
of LCCSN TandF,E,E,E , respectively.
The vector of fuzzy goals associated with the control vector LD can be defined as:
LD
~
 bl
LD (10)
In the fuzzy decision situation, it may be noted that the increase in the values of fuzzily described
goals defined by the goal vector in (10) would never be more than the corresponding upper-bounds of
the power generation capacity ranges defined in (7).
Let ),D(D,D max
L
t
L
t
L  be the vector of upper-tolerance limits of achieving the goal levels of the vector
of fuzzy goals defined in (10).
Now, the fuzzy goals are to be characterized by the respective membership functions for measuring
their degree of achievements in a fuzzy decision environment.
B. Characterization of Membership Function: The membership function representation of
the fuzzy objective goal of NOx function under the control of leader appears as:
 













EEif,0
EEEif,
EE
EE
EEif,1
Eμ
NN
NNN
NN
NN
NN
NEN
lw
lwlb
lblw
lw
lb
(11)

DOI: 10.24214/jecet.B.7.2.7179.
where )E(E NN
lblw
 is the tolerance range for achievement of the fuzzy goal defined in (9).
Similarly, the membership functions of the other two leader’s objectives and follower’s objectives can
be calculated.
The membership function of the fuzzy decision vector LD of the leader appears as:
 














if,0
if,
if,1
μ
t
LL
t
LLL
L
t
L
L
t
L
LL
LD
DD
DDD
DD
DD
DD
DL
bl
lb
bl
(12)
where )bl
L
t
L DD ( is the vector of tolerance ranges for achievement of the fuzzy decision variables
associated with LD defined in (9).
Note 1: ].[μ represents membership function.
Now, minsum FGP formulation of the proposed problem is presented in the following section.
C. Minsum FGP Model Formulation: In the process of formulating FGP model of a problem, the
membership functions are transformed into membership goals by assigning the highest
membership value (unity) as the aspiration level and introducing under- and over-deviational
variables to each of them. In minsum FGP, minimization of the sum of weighted under-
deviational variables of the membership goals in the goal achievement function on the basis of
relative weights of importance of achieving the aspired goal levels is considered.
The minsum FGP model can be presented as in31
:
Find ),( FL DDD so as to:
Minimize: 


  66 dwk
5
1k
k dwZ and satisfy
,1dd
EE
EE
:μ 11
NN
NN
EN


 
lblw
lw
,1dd
EE
EE
:μ 22
SS
SS
ES


 
lblw
lw
,1dd
EE
EE
:μ 33
CC
CC
EC


 
lblw
lw
,1dd
FF
FF
:μ 44
CC
Cc
FC


 
fbfw
fw
,1dd
TT
TT
:μ 55
LL
LL
TL


 
fbfw
fw
Idd
PD
DD
66lb
LG
t
L
L
t
L


 
:μ LD
subject to the set of constraints defined in (6) - (7), (13)
where 0d,d kk 
, (k = 1,…,5) represent the under- and over-deviational variables, respectively,
associated with the respective membership goals. 0, 
66 dd represent the vector of under- and
over-deviational variables, respectively, associated with the membership goals defined for the vector
of decision variables in LD , and where I is a column vector with all elements equal to 1 and the

DOI: 10.24214/jecet.B.7.2.7179.
dimension of it depends on the dimension of LD . Z represents goal achievement function, 0wk 
,
k = 1, 2, 3, 4, 5 denote the relative numerical weights of importance of achieving the aspired goal
levels, and 0w5 
is the vector of numerical weights associated with 
5d , and they are determined by
the inverse of the tolerance ranges31
for achievement of the goal levels in the decision making
situation.
Now, the effective use of the minsum FGP model in (13) is demonstrated via a case example
presented in the next section.
A DEMONSTRATIVE CASE EXAMPLE
The standard IEEE 30-bus 6-generator test system in23
is considered to illustrate the potential use of
the approach.
The system has 6 generators and 41 lines and the total system demand for the 21 load buses is 2.834
p.u. The data description of generators limit and load data is given in23
. The detailed data of
generation cost-coefficients and emission-coefficients are given in Table 1 - 4.
Table 1: Data description of power generation costs –coefficients.
Generator g1 g2 g3 g4 g5 g6
Cost-Coefficients
a 100 120 40 60 40 100
b 200 150 180 100 180 150
c 10 12 20 10 20 10
Table 2: Data description of NOx emission-coefficients.
NOx
Emission-
Coefficients
dN 0.006323 0.006483 0.003174 0.006732 0.003174 0.006181
eN -0.38128 -0.79027 -1.36061 -2.39928 -1.36061 -0.39077
fN 80.9019 28.8249 324.1775 610.2535 324.1775 50.3808
Table 3. Data description of SOx emission-coefficients.
SOx Emission-Coefficients
dS 0.001206 0.002320 0.001284 0.000813 0.001284 0.003578
eS 5.05928 3.84624 4.45647 4.97641 4.4564 4.14938
fS 51.3778 182.2605 508.5207 165.3433 508.5207 121.2133

DOI: 10.24214/jecet.B.7.2.7179.
Table 4. Data description of COx emission-coefficients.
COx Emission-
Coefficients
dS 0.265110 0.140053 0.105929 0.106409 0.105929 0.403144
eS -
61.01945
-
29.95221
-
9.552794
-
12.73642
-
9.552794
-121.9812
fS 5080.148 3824.770 1342.851 1819.625 13.42.851 11381.070
The B-coefficients in20
are presented as follows:





















0244.00005.00033.00066.00041.00008.0
0005.00109.00050.00066.00016.00010.0
0033.00050.00137.00070.00004.00022.0
0066.00066.00070.00182.00025.00044.0
0041.00016.00004.00025.00487.00299.0
0008.00010.00022.00044.00299.01382.0
B
 
4E8573.900B
,0030.00002.00009.00017.00060.00107.00B


Now, in the proposed MOBLP formulation of the problem, without loss of generality it is assumed
that, )Pand(P g5g3LD is under the control of the leader, and )P,P,P,(P g6g4g2g1FD is assigned to the
follower.
The data presented in Table 1- 6 is used here to solve the problem in the present decision situation.
Here, the executable MOBLP model for EEPGDD problem appears as follows.
Find )PP,P,P,P,P( g6g5g4g3g2g1D so as to:
)3808.50P39077.0P006181.01775.324P36061.1P003174.0
2535.610P39928.2P006732.01775.324P36061.1P003174.0
8249.28P79027.0P006483.09019.80P38128.0P006323.0()(EMinimize
6g
2
6g5g
2
5g
4g
2
4g3g
2
3g
2g
2
2g1g
2
1gN


D
LD
(14)
)2133.121P14938.4P003578.05207.508P45647.4P001284.0
3433.165P97641.4P000813.05207.508P45647.4P001284.0
2605.182P84624.3P002320.03778.51P05928.5P001206.0()(EMinimize
6g
2
6g5g
2
5g
4g
2
4g3g
2
3g
2g
2
2g1g
2
1gS


D
LD
(15)
)070.11381P9812.121P403144.0851.1342P552794.9P105929.0
625.1819P73642.12P106409.0851.1342P552795.9P105929.0
770.3824P95221.29P140053.0148.5080P01945.61P265110.0()(EMinimize
6g
2
6g5g
2
5g
4g
2
4g3g
2
3g
2g
2
2g1g
2
1gC


D
LD
(leader’s objectives)
(16)

DOI: 10.24214/jecet.B.7.2.7179.
and for given FL DD ; solve
)10P150P10020P180P4010P100
P6020P180P4010P150P12010P200P100()(FMinimize
6g
2
6g5g
2
5g4g
2
4g3g
2
3g2g
2
2g1g
2
1gC

D
FD
(17)
4
6g5g4g3g2g1g
6g5g6g4g5g4g6g3g5g3g
2
6g
2
5g
2
4g
2
3g
2
2g
2
1gL
10X8573.9P0030.0P0002.0P0009.0P0017.0P0060.0P0107.0
PP0010.0PP0066.0PP010.0PP0132.0PP0132.0
PP140.0PP0082.0PP0032.0PP0008.0PP0050.0
PP0016.0PP0020.0PP0044.0PP0088.0PP0598.0
P0244.0P0109.0P0137.0P0182.0P0487.0P1382.0TMinimize






FD
(18)
(follower’s objectives)
subject to
,0)L834.2(PPPPPP T6g5g4g3g2g1g  (19)
(Power balance constraint)
and ,50.0P05.0 1g  ,60.0P05.0 2g  ,00.1P05.0 3g  ,20.1P05.0 4g 
,00.1P05.0 5g  ,60.0P05.0 6g 
(20)
(Power generator capacity constraints)
Now, employing the proposed GA scheme the individual best and least solutions of the leader’s
objectives are determined.
The computer program developed in MATLAB and GAOT (Genetic Algorithm Optimization
Toolbox) in MATLAB-Ver. R2010a is used together for the calculation to obtain the results. The
execution is made in Intel Pentium IV with 2.66 GHz. Clock-pulse and 4 GB RAM.
Now, the following GA parameter values are introduced during the execution of the problem in
different stages.
The parameter values used in genetic algorithm solution are given in Table 5.
Table 5: The parameter values used in GA.
Parameter Value
Number of Individual in the initial population 50
Selection Roulette-wheel
Crossover function Single Point
Crossover probability 0.8
Mutation Probabiliy 0.06
Maximum Generation Number 100

DOI: 10.24214/jecet.B.7.2.7179.
Following the procedure, the individual best solutions of leaders and followers are obtained as:
1413.708);0.051.00,1.20,0.5177,0.05,(0.05,)E;P,P,P,P,P,P( N6g5g4g3g2g1g lb
)535.5491;0.600.7320,0.05,0.8379,0.60,(0.05,)E;P,P,P,P,P,P( S6g5g4g3g2g1g lb
24655.09);0.600.05,1.0985,0.05,0.60,(0.50,)E;P,P,P,P,P,P( C6g5g4g3g2g1g lb
595.9804);0.35180.5236,0.9926,0.5832,0.2863,(0.1220,)F;P,P,P,P,P,P( C6g5g4g3g2g1g fb
0.0170);0.33730.8533,0.5001,0.9764,0.0978,(0.0861,)T;P,P,P,P,P,P( L6g5g4g3g2g1g fb
Again, the worst solutions of leader and follower are found as:
1416.167);0.600.5269,0.05,0.6036,0.60,(0.50,)E;P,P,P,P,P,P( N6g5g4g3g2g1g lw
1551.043);0.051.00,1.2,0.1002,0.05,(0.50,)E;P,P,P,P,P,P( S6g5g4g3g2g1g lw
)86.47522;0,0.050.7040,1.00.05,1.00,(0.05,)E;P,P,P,P,P,P( C6g5g4g3g2g1g lw
705.2694);00,0.60097,0.05,1.0.600,0.13(0.500,)F;P,P,P,P,P,P( C6g5g4g3g2g1g lw
0.0696);0.10361.00,1.20,0.05,0.05,(0.50,)T;P,P,P,P,P,P( L6g5g4g3g2g1g fw
Then, the fuzzy objective goals appear as:
NE ~ 1413.708, SE ~ 1549.535, CE ~ 24655.09, CF ~ 595.9804 and LT ~ 0.0170
The fuzzy goals for power generation decisions under the control of leader are obtained as:
3gP ~ 0.15 and 5gP ~ 0.15 .
The upper-tolerance limits of LCCSN TandF,E,E,E are obtained as
).,0696.0,2694.705,86.24752,043.1551,167.1416()T,F,E,E,E( LCCSN fwfwlwlwlw
Again, the upper-tolerance limits of the decision variables associated with LD are considered as
).6.0,6.0()Pand,P( 5g3g tt
Then, the membership functions are constructed as follows:
708.1413167.1416
E167.1416 N
EN



, 535.1549043.1551
E043.1551 S
ES



, 09.2465586.24752
E86.24752 C
EC



,
,
9804.5952694.705
Z2694.705 1
FC


 ,
0170.00696.0
T0696.0 L
TL



,
40.060.0
P60.0 3g
P 3g



40.070.0
P60.0 5g
P 5g



Following the procedure, the executable minsum FGP model of the problem is obtained as follows.
Find )P,P,P,P,P,P( 6g5g4g3g2g1gD so as to:
Minimize Z = 
 7654321 d5.2d5.2d0114.19d0092.0d0102.0d6631.0d4067.0 and
satisfy

DOI: 10.24214/jecet.B.7.2.7179.
1dd
708.1413167.1416
fPePd167.1416
:μ 11
iNgiiN
2
giiN
N
1i
EN





1dd
535.1549043.1551
fPePd043.1551
:μ 22
iSgiiS
2
giiS
N
1i
ES





1dd
09.2465586.24752
fPePd86.24752
:μ 33
iCgiiC
2
giiC
N
1i
EC





1dd
9804.5952694.705
)cPbPa(2694.705
:μ 44
N
1i
igii
2
gii
FC





1dd
0170.00696.0
BPBPBP0696.0
:μ 55
N
1i
N
1j
N
1i
00gi0gijg
F
iji
C



  
 
1dd
40.060.0
P60.0
:μ 66
3g
P 3g


 
1dd
40.060.0
P60.0
:μ 77
5g
P 5g


 
subject to the given system constraints in (19) and (20). (21)
The goal achievement function Z in (21) appears as the evaluation function in the GA search process
of solving the problem.
The evaluation function to determine the fitness of a chromosome appears as:
pop_size,...,2,1,))()(Eval
5
1
7
6k
  
 

vdwdwZE v
k
kkkkvv ( (22)
where vZ)( is used to represent the achievement function )(Z in (21) for measuring the fitness value of
v-th chromosome in the decision process.
The best objective value )( *
Z for the fittest chromosome at a generation in the solution search process
is determined as:
pop_size},...,2,1)eval{min*
 vEZ v( (23)
The achieved values of the objectives are:
,0.0522).73,669.95,6291550.38,24(1414.69,)T,F,E,E,E( LCCSN 
with the respective membership values:
,0.0255).479,0.69120.4357,0.8(0.5978,)μ,μ,μ,μ,μ( LCCSN TFEEE 

DOI: 10.24214/jecet.B.7.2.7179.
The resultant power generation decision is:
0.47737).0.40,0.9885,0.40,0.4197,(0.1821,)P,P,P,P,P,P( 6g5g4g3g2g1g 
The graphical representation of decision of power generation is displayed in Figure 1.
Fig. 1: Graphical representation of power generation decision.
The result reflects that the solution is quite satisfactory from the view point of executing the decision
powers of DMs on the basis of hierarchical order in the decision situation.
PERFORMANCE COMPARISON
To expound the effectiveness of the proposed method, the model solution is compared with the
solutions obtained by conventional minsum FGP approach in35
.
The achieved values of the objectives are found as:
0.0175)..60,719.38,6311550.01,24(1414.847,)T,F,E,E,E( LCCSN 
The resultant power generation decision is:
0.3389).0.8938,0.4379,0.9898,0.1409,(0.05,)P,P,P,P,P,P( 6g5g4g3g2g1g 
The comparison of the result with the proposed approach shows that, 49.43 kg/hr carbon emission
reduction and 1.87 $/hr fuel cost reduction is achieved here without sacrificing the total demand.
CONCLUSIONS AND SCOPE FOR FUTURE RESEARCH
The main advantage of BLP formulation of EEPGD problem is that individual decisions regarding
optimization of objectives on the basis of hierarchy assigned to them can be taken in the decision
environment. Again, under the flexible nature of the model, hierarchical ordering of objectives as well
as fuzzy descriptions of objectives / constraints can easily be rearranged and that depend on decision
environment. Further, computational load occur for traditional use of linearization approaches to
nonlinear functions does not arise here owing to the use of bio-inspired approach for power generation
decision. Finally, it is hoped that the solution approach presented here may lead to future research for
optimal thermal power generation decision by making pollution free living environment on earth.
The GA based FGP approach to EEPGD problems presented here can be extended to formulate
multilevel programming (MLP) model with multiplicity of objectives in power plant operation and
management system to meet power demand in society as well as to protect health of environment on
Earth, which is a problem in future study.
0
0.2
0.4
0.6
0.8
1
Pg1 Pg2 Pg3 Pg4 Pg5 Pg6
Powergenerationinp.u.
Generators
Decision of Power Generation

DOI: 10.24214/jecet.B.7.2.7179.
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DOI: 10.24214/jecet.B.7.2.7179.
* Corresponding Author: Papun Biswas
1
JIS College of Engineering, Kalyani, West Bengal, INDIA
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View Sl.No. Journal
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Title Publisher ISSN E-ISSN
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and Technology
JECET 2278179X

Environmental constrained electric power generation and dispatch via genetic algorithm

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