Outline Short-Term Hydro-Thermal Scheduling Problem Operating Cost & Emission Minimization Bacterial Foraging Algorithm Improved Bacterial Foraging Algorithm Simulation Results Conclusions
To use up the maximum amount of available hydroelectric energy so that the operating cost of the thermal plants is minimum.
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
M : number of objective functions W k : weight assigned to the k th objective
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
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
Source: T. Audesirk and G. Audesirk, Biology: Life on Earth, Prentice Hall, Englewood Cliffs, NJ, 5th edition, 1999.
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
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
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
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
Coefficients for cost and emission functions Cost F 1 ($/h) Generator Objective Coefficient 1 2 a 0.0025 0.0008 b 3.20 3.40 c 25.00 30.00 NO X SO 2 CO 2 F 2 (kg/h) F 3 (kg/h) F 4 (kg/h ) d 1 0.006483 0.006483 e 1-0.79027-0.79027 f 1 28.82488 28.82488 d 2 0.00232 0.00232 e 2 3.84632 3.84632 f 2 182.2605 182.2605 d 3 0.084025 0.084025 e 3-2.944584-2.944584 f 3 137.7043 137.7043
B-coefficient matrix
Load demand Hour P D MW Hour P D MW Hour P D MW Hour P D MW 1 400 7 450 13 1200 19 1330 2 300 8 900 14 1250 20 1250 3 250 9 1230 15 1250 21 1170 4 250 10 1250 16 1270 22 1050 5 250 11 1350 17 1350 23 900 6 300 12 1400 18 1470 24 600 Water discharge rate
Case 1: Optimization of each of the objectives individually Min F 1 ($) Min F 2 (kg) Min F 3 (kg) Min F 4 (kg) F 1 ($) 52753.291 55828.427 54762.238 55784.252 F 2 (kg) 22803.775 19932.248 20978.468 19987.685 F 3 (kg) 72355.712 72287.658 71988.754 72133.264 F 4 (kg) 383106.467 337846.583 374222.436 334231.219 Hourly generation schedule and demand (Minimizing F1) 1600 1400 PD Pg1 Pg2 PH1 PH2 Power (MW) 1200 1000 800 600 400 200 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time interval 16 17 18 19 20 21 22 23 24
Case 2: Optimization of fuel cost and emissions: Non-dominated solutions Solution Weight Objective No. w 1 w 2 w 3 w 4 F 1 ($) F 2 (kg) F 3 (kg) F 4 (kg) 1 1.0 0.0 0.0 0.0 52753.291 22803.775 72355.712 383106.467 2 0.7 0.3 0.0 0.0 52997.479 22251.424 72336.488 372854.232 3 0.4 0.6 0.0 0.0 54876.785 20864.758 72242.424 354512.426 4 0.1 0.9 0.0 0.0 55642.429 20015.000 72201.548 351444.615 5 0.7 0.0 0.3 0.0 51878.475 24857.649 72455.145 387506.232 6 0.4 0.3 0.3 0.0 53295.875 22136.425 72322.315 367475.643 7 0.1 0.6 0.3 0.0 55224.436 20303.563 72381.413 352245.218 8 0.4 0.0 0.6 0.0 52522.419 23642.865 72384.762 384542.254 9 0.1 0.3 0.6 0.0 54774.275 21341.543 72154.412 357577.563 10 0.1 0.0 0.9 0.0 54811.549 21177.424 72018.488 355214.215 11 0.7 0.0 0.0 0.3 55037.275 20883.423 72342.514 352242.385 12 0.4 0.3 0.0 0.3 55163.241 20851.812 72274.414 352111.254 13 0.1 0.6 0.0 0.3 55296.419 20832.155 72312.546 352223.549 14 0.4 0.0 0.3 0.3 54974.769 20863.215 72382.215 352256.541 15 0.1 0.3 0.3 0.3 55263.216 20841.421 72362.215 352238.453 16 0.1 0.0 0.6 0.3 55214.362 20845.414 72354.142 352214.715 17 0.4 0.0 0.0 0.6 55198.473 20845.215 72374.235 352224.542 18 0.1 0.3 0.0 0.6 55232.422 20829.958 72354.242 352214.521 19 0.1 0.0 0.3 0.6 55250.864 20841.413 72363.241 352265.413 20 0.1 0.0 0.0 0.9 55244.136 20844.431 72352.125 352278.379
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
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