A two-stage non-linear program for optimal electrical grid power balance under uncertainty

We propose a two-stage non-linear stochastic formulation for the economic dispatch problem under renewable-generation uncertainty. Each stage models dispatching and transmission decisions that are made on subsequent time periods. Certain generation decisions are made only in the first stage and the second stage realizes the actual renewable generation, where the uncertainty in renewable output is captured by a finite number of scenarios. Any resulting supply-demand mis-match must then be alleviated using extra, high marginal-cost power sources that can be tapped in short order. We propose two outer approximation algorithms to solve this nonconvex optimization problem to optimality. We show that under certain conditions the sequence of optimal solutions obtained under both alternatives has a limit point that is a globally-optimal solution to the original two-stage nonconvex program. Numerical experiments for a variety of parameter settings were carried out to indicate the efficiency and usability of this method of large practical instances.