multi-objective thermal generation sheduling

7/29/2019 Multi-objective thermal generation sheduling

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PROJECT ON

MULTI-OBJECTIVETHERMAL

GENERATIONSCHEDULING

PREPARED BYSUNIL AGRAWAL


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ABSTRACT

In the multi-objective framework, fuzzy decision-making methodology is exploited

to decide the generation schedule of a multi-objective thermal dispatch problem.

The multi-objective problem is formulated considering two objectives: (i) cost and

NO x emission. The solution set of such formulated problems is non-inferior due tocontradictions among the objectives considered. The weighting method is used to

simulate the trade-off relation among the conflicting objectives in the non-inferior

domain. Once the trade-off has been obtained, fuzzy set theory helps the system

operator to choose the weighting pattern and thus the operating point thatmaximizes the overall satisfaction of all the objectives. The results are

demonstrated using a sample test system.


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INTRODUCTION Environmental pollution is on the increase due to industrial advancement. Though technology has

made economic development possible, it at the same time produces enormous quantities of harmfulproducts and wastes. Also, the existing energy production processes are not ecologically clean. For

instance, thermal power plants pollute air, soil and water. The combustion of fossil fuels gives rise to

particulate material and gaseous pollutants apart from the discharge of heat to water courses. The

particulate material does not cause a serious problem in air contamination but the three principle

gaseous pollutants, oxides of carbon (CO x), oxides of sulphur(SO x), and oxides of nitrogen(NO x),

cause detrimental effects on human beings. The usual control practice is to reduce offensive emission

through post-combustion cleaning system such as electrostatic precipitators, stack gas scrubber, or

switching permanently to fuels with low emission potentials. Post-combustion removal system

requires time for engineering design, construction, and testing before they can be brought online.

Hence, the obvious alternative is go for fuels having low emission potentials, i.e. from coal to oil; oil

is however extremely expensive and supplies are uncertain. Thus, there is a sheer need for optimum

operating strategy, which can ensure minimum pollution level at minimum operating cost.


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Weighting method The weighting method identifies the non-inferior set, in which the best

compromise solution lies, also known as the parametric approach, has been

the most common method used for solving multi-objective problems until

recently. Multi-objective problem is converted in this method into scalar

optimization as given below:

Minimize

Where

where w i (i=1,2,..G) are the weighting coefficients.

1

( )G

i ii

w f x

1

1, 0G

i ii

w w x X


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GENERATOR OPERATING COST Rs/h2( )gi i gi i gi iF P a P b P c


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FUZZY SET THEORY IN POWERSYTEM

Advancements in computer technology associated with intellectual activities resulted in new fields of

inquiry such as system science, decision analysis. A mathematical formulation within which these various

types of uncertainties can be properly characterized and investigated is now available in terms of the theory

of fuzzy and fuzzy measure. In fact, one of Lofti Zadehs contribution to system modeling is the

representation of vague, incomplete knowledge that does not have a random nature and therefore cannot be

represented by a probabilistic approach. Fuzzy set theory provided a basis for the interpretation of member

function as possibility distributions, which is a very useful concept in many practical applications.

Applications of fuzzy set theory within the field of decision making have, for the most part, consisted of

extensions or fuzzifications of the classical theories of decision making. Decision making under conditions

of risk and uncertainty has been modeled by probabilistic decision theories. Fuzzy decision theories attemptto deal with fuzziness inherent in imprecise determinations of preferences, constraints, and goals. The

interaction with the decision maker, the fuzzy goal of the decision maker, was quantified by eliciting the

corresponding membership functions, including nonlinear function.


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Constraints

1. To ensure a real power balance, an equality constraints is imposed, i.e .

2. The inequality constraints imposed on generator output are

3.Weight constraint

Minimize

1

0 NG

gi D Li

P P P

min maxgi gi giP P P

1

( )G

i ii

w f x


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Initial values of and powerallocations

Initial values of and power allocations canbe found by assuming losses equal to zero.

Initial value of is

And the initial power allocations are

1 2 2

1 1( ( / )) / (1/ )

NG NG

i iPD t t t

1 2 1 2( ) / (2 2 )gi i i i iP w b w e w a w d


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Fuzzy Decision making Considering the imprecise nature of decision makers judgment, it is natural to assume that the decision

maker may have fuzzy or imprecise goals for each objective functions. The fuzzy sets are defined by

equations called membership functions. These functions represent the degree of membership in some fuzzy

sets using values from 0 to 1. The membership value 0, indicates incompatibility with the sets, while 1

means full compatibility by making account of minimum and maximum values of each objective.

Function together with the rate of increase of membership satisfaction, the decision maker must detect

membership function in a subjective manner. Here it is assumed that is strictly a monotonic decreasing

and continuous function defined as

(i=1,2,.,M)

The value of membership function suggests how far (in the scale from 0 to 1) a non-inferior (non-

dominated) solution has satisfied the objective. The aggregate or average of membership function values

(i=1,2,,M) for all the objectives can be computed in order to measure the accomplishment of each

solution in satisfying the objectives.

min

maxmin max

max min

max

1;

( ) ;

0;

i i

i

i i i ii i

i i

F F

F F

F F F F F F

F F


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TEST SYSTEM AND SIMULATIONS

Test System

A six-generator system is considered. The fuel cost and NO x emissions are given. Transmission losscoefficients are given in Table.The power demand is 1800 MW


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RESULTS

Weight combinations and corresponding power allocations

Gives the power allocations for weight combinations varying from [1 0] to [0

1], where w 1 represents the weight attached to cost function and w 2 is the

weight attached to emission function of NOx.


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Weight vectors and corresponding fitness values


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Conclusion In this work,the Multi-objective optimal generation scheduling problem is solved

using Weighting method The focus of the work concentrated on minimization of two objectives

1. Cost of generation and2. NOx. Emission

Non inferior solution are obtained for a few fed-in weight combination. The above two objectives were found conflicting in nature.When cost objective

was given a weight of 1,cost was minimum and emission was maximum and when

Emission objective was given a weight of 1,the cost was found maximum andemission was minimum.

Fuzzy membership function of cost and emission was found for each weightcombination.The best compromise solution was the one which gave 0.5 weight foreach objective.


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Scope for future work Multi-objective optimization problem can be solved by a varity of method

which includes traditional and heuristic search method fuzzy multiplierscan be introduce d to a modify in each iteration a which accelerates theprogram.

If Genetic Algorithm is used for genratind and modifying weightcombination,the search can be effectively explored for globaloptimum,which yields the best possible overall satisfactory resultcombination.


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multi-objective thermal generation sheduling

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