Using voltage control for reducing standing phase angle in power system restoration

In closing transmission system loops after a blackout or a partial outage, the standing phase angle (SPA) across breakers should be below a preset value. Closing a breaker on a larger SPA can give rise to damage to system equipment, and can even provoke the recurrence of system outage. Power angle across a line is influenced by the transmitted real power, line reactance, as well as the voltage magnitude at both ends of the transmission line. SPA reduction has conventionally been made by rescheduling the production among generators or by load curtailment. In this paper, an approach is presented to achieve the desired SPA by using the generator terminal voltages as control variables. This allows the desired SPA to be attained in a shorter time. Due to the dependency of load power on voltage magnitude, load active and reactive powers are represented by a more detailed model of constant power, constant current, and constant impedance components. Constraints in operational variables which can restrict the control scheme are also taken into consideration. The effectiveness of the proposed approach in reducing the SPA is illustrated by case studies on a three-bus test system and on the IEEE 118-bus system.