EEL6266_Lecture_03

# EEL6266_Lecture_03 - EEL 6266 Power System Operation and...

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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 total output power is within a specified tolerance of the load demand 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? | | 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 ( 29 ( 29 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
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EEL6266_Lecture_03 - EEL 6266 Power System Operation and...

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