EEL6266_Lecture_04

# EEL6266_Lecture_04 - EEL 6266 Power System Operation and...

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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 multiple-segment, 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 lambda-iteration such methods will always land on P min or P max A table-based 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 right-hand 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 hydro-thermal economic-scheduling 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 1-D 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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EEL6266_Lecture_04 - EEL 6266 Power System Operation and...

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