EEL6266_Lecture_02

EEL6266_Lecture_02 - EEL 6266 Power System Operation and...

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Unformatted text preview: EEL 6266 Power System Operation and Control Chapter 3 Economic Dispatch of Thermal Units © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 2 The Economic Dispatch Problem Consider a system that consists of N thermal-generating units serving an aggregated electrical load, P load input to each unit: cost rate of fuel consumed, F i output of each unit: electrical power generated, P i total cost rate, F T , is the sum of the individual unit costs essential constraint: the sum of the output powers must equal the load demand the problem is to minimize F T T G 1 P 1 F 1 T G 2 P 2 F 2 T G N P N F N P load © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 3 The Economic Dispatch Problem The mathematical statement of the problem is a constrained optimization with the following functions: objective function: equality constraint: note that any transmission losses are neglected and any operating limits are not explicitly stated when formulating this problem Problem may be solved by optimizing the Lagrange function The Lagrange function establishes the necessary conditions for finding an extrema of an objective function with constraints ( 29 ∑ = = N i i i T P F F 1 ∑ =- = = N i i load P P 1 φ ( 29 - + = + = ∑ ∑ = = N i i load N i i i T P P P F F L 1 1 λ φ λ © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 4 The Economic Dispatch Problem Principles taking the first derivatives of the Lagrange function with respect to the independent variables allows us to find the extreme value when the derivatives are set to zero there are N F + N λ derivatives, one for each independent variable and one for each equality constraint the derivatives of the Lagrange function with respect to the Lagrange multiplier λ merely gives back the constraint equation the N F partial derivatives result in ( 29 d d =- = ∂ ∂ λ i i i i P P F P L © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 5 The Economic Dispatch Problem Principles summary of equations: taking into account the inequality constraints upper and lower power limits of the generating units the necessary conditions expand into the following set of equations when a limit is reached on a generating unit load n i i i i P P P F = = ∑ = 1 d d λ i i i i i i i i i i i i i P P for P F P P for P F P P P for P F = ≥ = ≤ < < = min , max , max , min , d d d d d d λ λ λ © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 6 The Economic Dispatch Problem Example determine the economic operating point for the three...
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This note was uploaded on 07/15/2011 for the course EEL 6266 taught by Professor Thomasbaldwin during the Fall '04 term at FSU.

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EEL6266_Lecture_02 - EEL 6266 Power System Operation and...

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