The Price of Uncertainty: Chance-constrained OPF vs. In-hindsight OPF
For power system operators, this work provides theoretical insight into the cost of uncertainty in OPF, but the results are incremental and limited to a tutorial example.
This paper investigates the relationship between chance-constrained optimal power flow (ccOPF) and the hypothetical full-information in-hindsight OPF (hOPF), introducing dimensions of the price of uncertainty and providing sufficient conditions for their equivalence under mild assumptions. The total variational distance is proposed to quantify the performance gap.
The operation of power systems has become more challenging due to feed-in of volatile renewable energy sources. Chance-constrained optimal power flow (ccOPF) is one possibility to explicitly consider volatility via probabilistic uncertainties resulting in mean-optimal feedback policies. These policies are computed before knowledge of the realization of the uncertainty is available. On the other hand, the hypothetical case of computing the power injections knowing every realization beforehand---called in-hindsight OPF(hOPF)---cannot be outperformed w.r.t. costs and constraint satisfaction. In this paper, we investigate how ccOPF feedback relates to the full-information hOPF. To this end, we introduce different dimensions of the price of uncertainty. Using mild assumptions on the uncertainty we present sufficient conditions when ccOPF is identical to hOPF. We suggest using the total variational distance of probability densities to quantify the performance gap of hOPF and ccOPF. Finally, we draw upon a tutorial example to illustrate our results.