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

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 cost-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.


Tillmann Muehlpfordt    
Karlsruhe Institute of Technology

Veit Hagenmeyer    
Karlsruhe Institute of Technology

Timm Faulwasser    
Karlsruhe Institute of Technology


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