IEEE 2011 Electrical Power and Energy Conference

Transcription

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2 Outline Short-Term Hydro-Thermal Scheduling Problem Operating Cost & Emission Minimization Bacterial Foraging Algorithm Improved Bacterial Foraging Algorithm Simulation Results Conclusions

3 To use up the maximum amount of available hydroelectric energy so that the operating cost of the thermal plants is minimum.

4 Hydro-thermal generation system Source: A.J. Wood, B.F. Wollenberg, Power Generation, Operation and Control, 2nd ed., John Wiley & Sons, Inc., New York, NY, 1996 Hydro-thermal Scheduling Source: A.J. Wood, B.F. Wollenberg, Power Generation, Operation and Control, 2nd ed., John Wiley & Sons, Inc., New York, NY, 1996

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

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11 Characteristic equation of the discharge rate q jk :discharge rate coefficients F 1 : cost function over scheduling time intervals N k F 2 : NO x emission function over scheduling time intervals N k F 3 : SO 2 emission function over scheduling time intervals N k F 4 : CO 2 emission function over scheduling time intervals N k n k : number of hours in scheduling time interval k a i, b i, c i : cost coefficients of the i th thermal unit d i, e i, f i : emission coefficients

12 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

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

14 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

15 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

16 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) and C(1): predefined parameters

17 The IBFA is applied to find the optimal scheduling of a hydro-thermal generation system The system consists of 2 thermal and 2 hydro plants Minimization of the NOx, SOx and COx emissions are considered

18 Coefficients for cost and emission functions Cost F 1 ($/h) Generator Objective Coefficient 1 2 a b c NO X SO 2 CO 2 F 2 (kg/h) F 3 (kg/h) F 4 (kg/h ) d e f d e f d e f

19 B-coefficient matrix

20 Load demand Hour P D MW Hour P D MW Hour P D MW Hour P D MW Water discharge rate

21 Case 1: Optimization of each of the objectives individually Min F 1 ($) Min F 2 (kg) Min F 3 (kg) Min F 4 (kg) F 1 ($) F 2 (kg) F 3 (kg) F 4 (kg) Hourly generation schedule and demand (Minimizing F1) PD Pg1 Pg2 PH1 PH2 Power (MW) Time interval

22 Case 2: Optimization of fuel cost and emissions: Non-dominated solutions Solution Weight Objective No. w 1 w 2 w 3 w 4 F 1 ($) F 2 (kg) F 3 (kg) F 4 (kg)

23 An IBFA for solving the Multi-objective STHT scheduling problem considering the emission minimization has been introduced The algorithm applies a dynamic 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 relationships

24 Thanks!