economic emission load dispatch using fuzzy new

8/13/2019 Economic Emission Load Dispatch Using Fuzzy New

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OBJECTIVE OF THE PROBLEM

Purpose is to optimize the real and reactivepower of a thermal power plant along withemission control.

Fuzzy decision making methodology isexploited to decide the generation schedule.

Weighting method is employed to generate thenon-inferior solutions.


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OBJECTIVE OF THE PROBLEM (contd)

Decision making theories attempt to deal with thefuzziness inherent with the determination ofgoals.

Regression analysis is performed between theobjectives and simulated weights to decide theoptimal operating point.

The validity of the proposed method isdemonstrated on a 5-bus,7-line system comprising3 - generators


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Problem Formulation

Optimal system in general involves theconsideration of economy of operation, systemsecurity, emission of certain fossil fuel.

The problem deals with dual objectivemathematical problem i,e, to minimize the costand NOx emission satisfying the equality and

inequality constraints.

We try to set an equality between the generatedpower and load demand.


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Calculation of Transmission loss The transmission loss is been given by Krons formula

where Pi=Pgi-Pdi and Qi=Qgi-Qdi

where are the load angles at ith an jth buses.

1 1

Nb Nb

loss ij i j i j ij i j i j

i j

P A P P Q Q B Q P PQ

1 1

Nb Nb

LOSS IJ I J I J IJ I J I J

I j

Q C P P Q Q D Q P P Q

cos( )| || |

ij

ij i j

i j

RA

V V

sin( )| || |

ij

ij i j

i j

RB

V V

sin( )| || |

ij

ij i j

i j

XD

V V

cos( )| || |

ij

ij i j

i j

XC

V V

iand j


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Weighting Method

The dual objective is being converted into single objectiveto generate non-inferior solution .

The optimization problem is being converted to scaledoptimization problem

Minimize

Subject to and the equality andinequality constraints.

where Wk are the level of weighing coefficients,L denotes the total number of objectives ,so K=1,2,

weighing coefficients vary from 0 to 1.


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Non Inferior solution

The concept of non-inferiority is being used to dealwhere there are multi objective.

A non-inferior solution is one in which an improvement

in one objective requires a degradation of another.


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Formation of Augmented Function

The generalized augmented function is given as:

-

Where and are Lagrange multipliers, ispenalty factor, Newton-Raphson algorithm is

applied to obtain the non inferior solution for theweight combinations.

p q kr


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Algorithm

Stepwise procedure to compute optimal weights is givenbelow :

Input the system data consisting of line data, fuel cost and

NOx emission coefficients , limits on active and reactivepower generations and demand etc.

Compute the loss coefficients,Ploss,Qloss.

Find the min and max values of each objective .This iscarried out by giving full weightage to one objective andneglecting the other.

Simulate weight combinations by varying in a step size of0.1 ,such that their sum remains one.


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Algorithm(contd)

Generate non inferior solutions by solving theequation of generalized augmented function.

Compute membership functions of the obtained noninferior solutions.

Perform linear and quadratic regression analysisbetween min values of membership functions of the

objectives and simulated weights.Normalize thecalculated weights.


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Cost and Emission Equations

Fuel cost($/h) equation NOx emission (kg/h) equation

F11= 21.82P1+742.890P1+847.1484 F21= 63.23P1-38.128P1+080.9019

F12=13,45P2+830.154P2+247.2241 F22=64.83P2-79.027P2+028.8249

F13=20.35P3+843.205P3+0.85.6348 F23=31.74P3-136.061P3+324.1775


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Line data

Line From To R (p.u.) X (p.u.) B (p.u)

1 1 2 0.02 0.06 0.030

2 1 3 0.08 0.24 0.025

3 2 3 0.06 0.18 0.020

4 2 4 0.06 0.18 0.020

5 2 5 0.04 0.12 0.0156 3 4 0.01 0.03 0.010

7 4 5 0.08 0.24 0.025


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Load data

Bus P (MW) Q (MVAR)

1 0.00 0.00

2 0.20 0.10

3 0.45 0.15

4 0.40 0.05

5 0.60 0.10

F1min=2510.1890 $/h F1

max=2630.7660 $/h

F2min=288.9621 kg/h F2

max=472.0815 kg/h

Minimum and maximum values of objectives.


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weights objectives Membershipfunction

StandardError

Case-1 Cost ($/h) 0.531403 2548.6830 0.6807518 0.003532

Nox

emission(kg/h)

0.46859 322.2189 0.8183873 0.012301

Case-2 Cost ($/h) 0.58467 2541.9070 0.7369482 0.011931

Noxemission(kg/h)

0.415321 330.8562 0.7712197 0.026760

Comparison of Results


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Bus PG QG PD QD P Q V

1 0.6038 -0.0641 0.00 0.00 0.6040 -0.0703 1.060000 0.00

2 0.3028 0.0887 0.20 0.20 0.1021 -0.0111 1.05184 -.025513 0.7602 0.1137 0.45 0.15 0.3109 -0.0364 1.05077 -.02864

4 0.00 0.00 0.40 0.05 -0.4001 -0.0499 1.04591 -.04105

5 0.00 0.00 0.60 0.10 -0.5999 -0.1000 1.02883 -.07370

Generation Load Injected power Voltage Profile

Best power schedule and voltage profile of proposed method


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Conclusions

In the dual objective problem it is realized that costand NOx emission are conflicting in nature.

Fuzzy decision making methodology is exploited todecide the bestgeneration schedule.

Regression analysis is performed between minsatisfaction level of the objectives and simulated

weights to decide the optimaloperating point. Cost and NOx emission are calculated at the optimal

values of weights.


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References:

[1]- Fuzzy Decision making for economic-emissionload dispatch problem, Lakhwinder Singh, J.S.Dhillon.

[2]- Fuzzy satisfying multi-objective generationscheduling based on simplex weightage patternsearch, Y.S.Brar, J.S.Dhillon and D.P.Kothari

[3]- Secure multi objective real and reactive power

allocation of thermal power units, Lakhwinder Singh,J.S.Dhillon.


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Thank You

economic emission load dispatch using fuzzy new

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