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# lecture2 - EEL 6266 Power System Operation and Control...

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EEL 6266 Power System Operation and Control Chapter 3 Numerical Methods for Economic Dispatch

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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 2 The Lambda-Iteration Method ° The solution to the optimal dispatch can be approached by graphical methods ± plot the incremental cost characteristics for each generator ± the operating points must have minimum cost and satisfy load ° that is, find an incremental cost rate, λ that meets the demand P R ° graphically: Σ d F 1 d P 1 (\$/MWh) d F 2 d P 2 (\$/MWh) d F 3 d P 3 (\$/MWh) P 1 (MW) P 2 (MW) P 3 (MW) P R = P 1 + P 2 + P 3 λ
© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 3 The Lambda-Iteration Method ° An iterative process ± assume an incremental cost rate λ and find the sum of the power outputs for this rate ° the first estimate will be incorrect ± if the total power output is too low, increase the λ value, or if too high, decrease the λ value ° with two solutions, a closer value of total power can be extrapolated or interpolated ± the steps are repeated until the desired output is reached λ [1] λ [3] λ [2] [1] [3] [2] λ 0 error ( e ) solution: (| e | < tolerance) R N i i P P e - = ° = 1 Lambda projection

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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 4 The Lambda-Iteration Method ° This procedure can be adopted for a computer implementation ± the implementation of the power output calculation is rather independent of the solution method ° each generator output could be solved by a different method ± as an iterative procedure, a stopping criterion must be established ° two general stopping rules are appropriate for this application ² total output power is within a specified tolerance of the load demand ² iteration loop count exceeds a maximum value start set λ calculate P i for i = 1 to N calculate ° = - = N i i load P P 1 ε first iteration? | ε | tolerance? project λ print schedule end
© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 5 The Lambda-Iteration Method ° Example ± consider the use of cubic functions to represent the input- output characteristics of generating plants ± for three generating units, find the optimum schedule for a 2500 MW load demand using the lambda-iteration method ° generator characteristics: ° assume that the fuel cost to be \$1/MBtu ° set the value of λ on the second iteration at 10% above or below the starting value depending on the sign of the error ( ( MW in MBtu/h 3 2 P DP CP BP A H + + + = Unit 1 749.55 6.95 9.68 × 10 -4 1.27 × 10 -7 320 800 Unit 2 1285.0 7.051 7.375 × 10 -4 6.453 × 10 -8 300 1200 Unit 3 1531.0 6.531 1.04 × 10 -3 9.98 × 10 -8 275 1100 A B C D P max P min

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© 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 6 The Lambda-Iteration Method ° Example ± initial iteration: λ start = 8.0 ° incremental cost functions ° find the roots of the three incremental cost functions at λ = 8.0 ² P 1 = (–5575.6, 494.3), P 2 = (–8215.9, 596.7), P 3 = (–7593.4, 646.2) ² use only the positive values within the range of the generator upper and lower output limits ° calculate the error °
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