Abstract
Moran considered a dam whose inflow in a given interval of time is a continuous random variable. He then developed integral equations for the probabilities of emptiness and overflow. These equations are difficult to solve numerically; thus, approximations have been proposed that discretize the input. In this paper, extensions are considered for storage systems with different assumptions for storage losses. We also develop discrete approximations for the probabilities of emptiness and overflow.
Highlights
Moran [1] [2], Prabhu [3] [4] and Ghosal [5] all considered a finite dam whose input in a given interval of time is a continuous random variable
Extensions are considered for storage systems with different assumptions for storage losses
We develop discrete approximations for the probabilities of emptiness and overflow
Summary
Moran [1] [2], Prabhu [3] [4] and Ghosal [5] all considered a finite dam whose input in a given interval of time is a continuous random variable. Numerical solutions for specific input distributions to Lindley’s equations are difficult to obtain. It is not an easy task to obtain probabilities for emptiness and overflow in continuous time. Moran [6] proposed a discrete approximation in order to obtain numerical results for the probabilies of emptiness and overflow. Modifications to this approach have been developed by Klemes [3], Lochert and Phatarfod [5], Phatarfod and Srikanthan [8]. We model energy storage systems with different assumptions about storage losses, and develop similar discrete approximations to calculate the probabilities of emtiness and overflow
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