Unit commitment with load uncertainty by joint chance-constrained programming

This paper presents an algorithm to solve a unit commitment problem that takes into account the uncertainty in the demand. This uncertainty is included in the optimization problem as a joint chance constraint that bounds the minimum value of the probability to jointly meet the deterministic power balance constraints. The demand is modeled as a multivariate, normally distributed, random variable and the correlation among different time periods is also considered. A deterministic mixed-integer linear programming problem is sequentially solved until it converges to the solution of the chance-constrained optimization problem. Different approaches are presented to update the z-value used to transform the joint chance constraint into a set of deterministic constraints. Results from a realistic size case study are presented and the values obtained for the multivariate normal distribution probability are compared with the ones obtained by using a Monte Carlo simulation procedure.