IEEE 2011 Electrical Power and Energy Conference

Transcription

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2 Outline Economic Dispatch Problem Operating Cost & Emission Minimization Bacterial Foraging Algorithm Modified Bacterial Foraging Algorithm Simulation Results Conclusions

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4 M : number of objective functions W k : weight assigned to the k th objective

5 F 1 : Fuel cost function of thermal units, F 2 : NO x emission function a i, b i, c i : cost coefficients, d 1i, e 1i, f 1i : NOx emission coefficients

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7 In nature, different species of animals search for nutrients in such a way that they maximize the energy they obtain (E ) and minimize time (T ) they spent on their search This means that they intend to maximize the following objective function: This search is subject to various obstacles and constraints such as the environmental and physiological constraints and the existence of predators

8 Source: T. Audesirk and G. Audesirk, Biology: Life on Earth, Prentice Hall, Englewood Cliffs, NJ, 5th edition, 1999.

9 Chemotactic movement: -Swimming up nutrient gradient (or out of noxious substances) -Tumbling Reproduction: Elimination/ Dispersal -To explore other parts of the search space -The probability of each bacterium to experience elimination/ dispersal event is determined by a predefined fraction

10 Start Initialization of variables: j=k=l=0 Elimination/Dispersal Loop: l=l+1 No l<ned Yes Reproduction Loop: k=k+1 Terminate Compute J (i,j,k,l): J(i,j,k,l)=J(i,j,k,l)+Jcc(θ i (j,k,l),p(j,k,l)) Jlast=J(i,j,k,l) Compute θ i (j+1,k,l): θ i (j+1,k,l)=θ i (j,k,l)+c(i)ɸ(i) Compute J (i,j+1,k,l): J(i,j+1,k,l)=J(i,j+1,k,l)+Jcc(θ i (j+1,k,l),p(j+1,k,l)) Swim: m=0 (counter for swim length) m=m+1 No k<nre Yes Chemotactic Loop: j=j+1 No j<nc Yes J(i,j+1,k,l)< Jlast Yes Jlast=J(i,j+1,k,l) Let θ i (j+1,k,l): θ i (j+1,k,l)=θ i (j+1,k,l)+c(i)ɸ(i) J(i,j+1,k,l)=J(i,j+1,k,l)+Jcc(θ i (j+1,k,l),p(j+1,k,l)) Yes m<ns No No Tumble: m=ns

11 Unit length of the chemotactic step is modified to have a decreasing function in terms of the maximum and initial chemotactic step j : chemotactic step Nc : maximum number of chemotactic steps while C(Nc) : predefined parameters

12 The MBFA is applied to solve an EED case study considering the system losses The case study is the IEEE30-bus system with 6 generators and a total load demand of 1800 MW Minimization In this EED problem, two conflicting objectives are considered; the cost and NOx emission functions.

13 Fuel cost characteristics Parameter Unit i a i b i c i P gi min P gi max $/MW 2 h $/MWh $/h MW MW

14 Coefficients for cost and emission functions Cost Generator Obj. Coef F 1 ($/h) a b c NO X F 2 (kg/h) d e f

15 B-coefficient matrix

16 Individual Optimization of Cost and Emissions: Min F 1 ($/h) Min F 2 (kg/h) P g1 (MW) P g2 (MW) P g3 (MW) P g4 (MW) P g5 (MW) P g6 (MW) P loss (MW) F 1 ($/h) F 2 (kg/h)

17 Bi-objective of cost and emission: Solution Weight Objective Number w 1 w 2 F 1 ($/h) F 2 (kg/h)

18 Power generation level and losses for each non-dominated solutions: Solution Power Generation Dispatch P loss Number P g1 P g2 P g3 P g4 P g5 P g6 (MW) (MW) (MW) (MW) (MW) (MW) (MW)

19 Pareto-optimal front for cost and NOx objectives:

20 An MBFA for solving the Bi-objective Economic- Emission Dispatch problem has been introduced The algorithm applies a dynamic nonlinear function to update the solution vector The proposed algorithm has been successfully implemented to solve this complex problem The algorithm could successfully find the optimum or near optimum solutions and capture the costemission trade-off relationship

21 Thanks!