Ellipsoidal Approximation to Uncertainty Propagation in Boundary Power Flow

Boundary load flow exemplifies a class of power (load) flow solution procedures that explicitly incorporates uncertainties in system data. Its importance for operation and control of modern power systems is increasing due to changes in system operation following deregulation and due to the emergence of new types of sources (e.g., distributed generation). The quantification of effects of uncertainties in system parameters (e.g., branch admittances) and in measurements (e.g., SCADA) is a fundamental task in generalized boundary (robust) power flow methodology. In this paper we propose a family of ellipsoidal approximations to uncertainty propagation in linearized power flow equations. After providing a precise uncertain power flow problem formulation, we describe an approximate solution based on the geometry of ellipsoids in high dimensions. While computationally intensive, the method is potentially applicable to large-scale power systems. We illustrate its capabilities on a benchmark example of the New England/New-York interconnection with 68 nodes