Can We Compute The Worst Voltage Case Under Power Flows Uncertainty At Tso-Dso Interfaces?

This paper proposes the new problem of calculating the worst-voltage-case (WVC) under power flows uncertainty, particularly at interfaces between transmission and distribution grid operators. The goal of the calculation is to verify if the realization of the worst uncertainty scenario leads to abnormal voltages, in particular to assure where the voltage instability is not a risk, and inform the transmission system operator. The problem is formulated as a tailored non-convex, nonlinear optimal power flow (OPF) with complementarity constraints (CCs). The latter models the generator switch between under voltage control and under reactive power limit. The problem is converted into a mathematically equivalent nonlinear programming OPF problem in which CCs are handled as penalty terms in the objective function. The paper has conducted a series of experiments on the 60-bus Nordic system that have pointed out the challenges associated to such computations to obtain meaningful results and unveiled interesting new insights. The findings and scalability are confirmed using a real-world 1203-bus system.