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Unformatted text preview: EEL 6266 Power System Operation and Control Chapter 3 Economic Dispatch Using Dynamic Programming © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 2 Piecewise Linear Cost Functions & Common practice ¡ many utilities prefer to represent their generator cost functions as single or multiplesegment, linear cost functions & Typical examples: P max P min F ( P ) P max P min d F ( P )/ d P P max P min F ( P ) P max P min d F ( P )/ d P © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 3 Piecewise Linear Cost Functions & Piecewise linear cost functions can not be used with gradient based optimization methods ¡ like the lambdaiteration ¡ such methods will always land on P min or P max & A tablebased method resolves this problem ¡ technique & for all units running, begin to raise the output of the unit with the lowest incremental cost segment ¢ if this unit hits the righthand end of a segment or hits P max , find the unit with the next lowest incremental cost segment and begin to raise its output & eventually, the total of all units outputs equals the total load ¢ the last unit is adjusted to have a generation, which is partially loaded for one segment © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 4 Dynamic Programming & A wide variety of control and dynamic optimization problems use dynamic programming (DP) to find solutions ¡ can greatly reduce the computation effort in finding optimal trajectories or control policies ¡ DP applications have been developed for & economic dispatch & hydrothermal economicscheduling & unit commitment ¡ methods are based on the calculus of variations & but, applications are not difficult to implement or program ¡ principles are introduced by presenting examples of one dimensional problems © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 5 Dynamic Programming & Example ¡ consider the cost of transporting a unit shipment from location A to location N & there are many short paths that connect many stops along the way, which offers numerous parallel routes from getting from A to N & each path has an associated cost ¢ e.g., distance and level of difficulty results in fuel costs & the total cost is the sum of the path costs of the selected route from the originating location to the terminating location & the problem is to find the minimum cost route © 2002, 2004 Florida State University EEL 6266 Power System Operation and Control 6 Dynamic Programming A C B D F E G I H J M L K N 1D Dynamic Programming Example 3 2 5 11 8 4 9 6 6 3 8 2 11 5 9 4 5 8 6 7 3 9 4 3 © 2002, 2004 Florida State University...
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 Fall '09
 Jhon
 Florida State University, Power System Operation and Control

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