comparative performance evalution of combined economic ... · -this paper illustrates about ceed...

Comparative performance Evalution of Combined

Economic Dispatchand Emission Dispatch using

Hybrid Search Algorithm.

Hareesh Sita

Research Scholar, Electrical Engineering

JNTUA

Ananthapuram, India

[email protected]

Prof. P.Umapathi Reddy

Department of Electrical Engineering

SVEC (Autonomus)

Tirupathi, India

[email protected]

Prof. R. Kiranmayi

H.O.D of Electrical Engineering

JNTUA

Ananthapuram, India

[email protected]

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


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.


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


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


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



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


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


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


361

comparative performance evalution of combined economic ... · -this paper illustrates about ceed...

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