A convex-optimization method to propagate uncertainty in power flow

Hyungjin Choi, Peter J. Seiler, Sairaj V. Dhople

Abstract: This paper presents a convex-optimization-based method to estimate maximum and minimum bounds on state variables in the power flow problem while acknowledging worst-case parametric and input uncertainties in the model. The approach leverages a second-order Taylor-series expansion of the states around a nominal (known) power-flow solution. Maximum and minimum bounds are then estimated from semidefinite relaxations of quadratically constrained quadratic programs. The objective of these problems is to maximize / minimize the quadratic approximation of the states recovered from the Taylor series expansion over the convex set in which the uncertainties lie. Numerical case studies validate the approach for the IEEE 118-bus system.