Analytical reformulation of chance-constrained optimal power flow with uncertain load control

Aggregations of controllable loads can provide reserves to power systems; however, their reserve capacity is uncertain and affected by ambient conditions like weather. Past work proposed a stochastic optimal power flow formulation that used chance constraints to handle uncertain reserves and generation from wind. The problem was solved with a scenario-based optimization method. In this paper, we assume Gaussian distributions of all uncertainties and reformulate the constraints analytically to solve a deterministic problem, which is computationally simpler than scenario-based approaches. To evaluate this idea, we implement our method on a modified IEEE 30-bus network and compare our results to those of a scenario-based method. Use of low-cost but uncertain load reserves yields lower cost dispatch solutions than those for systems with only generator reserves. The analytical approach using a cutting plane algorithm leads to fast convergence and is scalable to larger problem sizes. We explore the effect of non-Gaussian and correlated uncertainties on the reliability of the solution.