Numerical solution technique for joint chance-constrained programming problem – an application to electric power capacity expansion

We consider a joint chance-constrained linear programming problem with random right hand side vector. The deterministic equivalent of the joint chance-constraint is already known in the case that the right hand side vector is statistically independent. But if the right hand side vector is correlative, it is difficult to derive the deterministic equivalent of the joint chance-constraint. We discuss two methods for calculating the joint chance-constraint. For the case of uncorrelated right hand side, we try a direct method different from the usual deterministic equivalent, for the correlative right hand side case, we apply numerical integration. In this paper a chance-constrained programming problem is developed for electric power capacity expansion, where the error of forecasted electricity demand is defined by a random variable. Finally we show that this problem can be solved numerically using the trust region method and numerical integration, and we present the results of our computational experiments.