Impact of power generation uncertainty on unbalanced power systems

Continued growth in distributed generation introduces significant uncertainty for power generation in distribution systems. We continue the development of set-theoretic methods to confirm whether static state variables, such as bus voltage magnitudes and angles, are within some acceptable performance criterion while subject to the uncertainties introduced by intermittent power sources. This method considers three-phase unbalanced systems, which may include unbalanced loading and generation, by utilizing a three-phase representation of the power flow equations in the method formulation. We bound the possible values the uncertain generation can take by an ellipsoid and propagate it through a linearized power flow model. The resulting ellipsoid represents approximate bounds for the system state variables. The proposed method is applied to the IEEE 4-bus system.