Distribution Sensitivity for a Chance Constrained Model of Optimal Load Dispatch

Roemisch, W. & Schultz, R. (1989). Distribution Sensitivity for a Chance Constrained Model of Optimal Load Dispatch. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-89-090

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Abstract

Using results from parametric optimization we derive for chance constrained stochastic programs (quantitative) stability properties for (locally) optimal values and sets of (local) minimizers when the underlying probability distribution is subjected to perturbations. Emphasis is placed on verifiable sufficient conditions for the constraint-set-mapping to fulfill a Lipschitz property which is essential for the stability results. Both convex and non-convex problems are investigated.

We present an optimal-load-dispatch model with considering the demand as a random vector and putting the equilibrium between total generation and demand as a probabilistic constraint. Since in optimal load dispatch the information on the probability distribution of the demand is often incomplete, we discuss consequences of our general results for the stability of optimal generation costs and optimal generation policies.

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