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The operation of power systems has become more challenging due to feed-in ofvolatile renewable energy sources. Chance-constrained optimal power flow(ccOPF) is one possibility to explicitly consider volatility via probabilisticuncertainties resulting in mean-optimal feedback policies. These policies arecomputed before knowledge of the realization of the uncertainty is available.On the other hand, the hypothetical case of computing the power injectionsknowing every realization beforehand---called in-hindsight OPF(hOPF)---cannotbe outperformed w.r.t. costs and constraint satisfaction. In this paper, weinvestigate how ccOPF feedback relates to the full-information hOPF. To thisend, we introduce different dimensions of the price of uncertainty. Using mildassumptions on the uncertainty we present sufficient conditions when ccOPF isidentical to hOPF. We suggest using the total variational distance ofprobability densities to quantify the performance gap of hOPF and ccOPF.Finally, we draw upon a tutorial example to illustrate our results.

The Price of Uncertainty: Chance-constrained OPF vs. In-hindsight OPF