Discrete representation of storage for stochastic reservoir optimization

In explicit stochastic dynamic programing optimization of storage reservoirs the ‘curse of dimensionality’ dictates the adoption of the smallest possible number of discrete states to represent the range of reservoir storage. This pressure makes it imperative to understand clearly the consequences of pushing the limit too far. It is shown that the number of storage states is subject to some absolute constraints and that it must increase linearly with the reservoir storage capacity in order that comparability of results be assured. It is demonstrated, both theoretically and with the aid of a numerical example, that a too coarse discrete storage representation can not only impede accuracy but may completely distort reality in most unexpected ways. Finally, charts are presented giving the numbers of storage states necessary to obtain stationary probabilities of reservoir emptiness and/or fullness with an error e ≤ 0.1% for log normal and normal input distributions.