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The increasing amount of controllable generation and consumption indistribution grids poses a severe challenge in keeping voltage values withinadmissible ranges. Existing approaches have considered different optimal powerflow formulations to regulate distributed generation and other controllableelements. Nevertheless, distribution grids are characterized by an insufficientnumber of sensors, and state estimation algorithms are required to monitor thegrid status. We consider in this paper the combined problem of optimal powerflow under state estimation, where the estimation uncertainty results intostochastic constraints for the voltage magnitude levels instead ofdeterministic ones. To solve the given problem efficiently and to bypass thelack of load measurements, we use a linear approximation of the power flowequations. Moreover, we derive a transformation of the stochastic constraintsto make them tractable without being too conservative. A case study shows thesuccess of our approach at keeping voltage within limits, and also shows howignoring the uncertainty in the estimation can lead to voltage levelviolations.

Stochastic Optimal Power Flow in Distribution Grids under Uncertainty from State Estimation