Voltage Restoration After Unforeseen Disturbances in Weakly Observable Distribution Systems

Abstract

Following an unforeseen disturbance in a power system, the system state should be known to extract the emergency voltage restoration strategy. Such a condition does not usually hold in distribution systems due to the lack of enough measurements. Here, the joint probability density function ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pdf</small> ) of uncertain parameters is extracted from historical data. This <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pdf</small> is updated to comply with the measurements. A set of samples is then generated that best models the updated <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pdf</small> . These data reconciliation and sampling techniques enable the functioning of the emergency voltage control ( <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evc</small> ) with measurement scarcity. They are designed to be fast enough to meet the quasi-real-time requirements of the intended application. The <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evc</small> problem is cast as a stochastic programming problem. The resultant problem is a mixed-integer non-convex (and hence, NP-hard) optimization problem. It is solved using five distinct <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sm</small> s based on relaxation/approximation of the non-convex constraints. The results show that a novel combination of relaxation and approximation aimed at respectively mitigating the emergency under- and over-voltages outperforms the others. The propounded stochastic <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">evc</small> is validated through numerical studies.