Piecewise affine approximations for the control of a one-reservoir hydroelectric system

Piecewise affine approximations for the control of a one-reservoir hydroelectric system

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Article ID: iaor19982267
Country: Netherlands
Volume: 89
Issue: 1
Start Page Number: 53
End Page Number: 69
Publication Date: Feb 1996
Journal: European Journal of Operational Research
Authors: , , ,
Keywords: programming: probabilistic, programming: markov decision, programming: dynamic
Abstract:

We analyze the computation of optimal and approximately optimal policies for a discrete-time model of a single reservoir whose discharges generate hydroelectric power. Inflows in successive periods are random variables. Revenue from hydroelectric production is represented by a piecewise linear function. We use the special structure of optimal policies, together with piecewise affine approximations of the optimal return functions at each stage of dynamic programming, to decrease the computational effort by an order of magnitude compared with ordinary value iteration. The method is then used to obtain easily computable lower and upper bounds on the value function of an optimal policy, and a policy whose value function is between the bounds.

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