Optimal Adaptive Linearizations of the AC Power Flow Equations

The power flow equations are at the heart of many optimization and control problems relevant to power systems. The non-linearity of these equations leads to computational challenges in solving power flow and optimal power flow problems (non-convergence, local optima, etc.), Accordingly, various linearization techniques, such as the DC power flow, are often used to approximate the power flow equations. In contrast to a wide variety of general linearization techniques in the power systems literature, this paper computes a linear approximation that is specific to a given power system and operating range of interest. An “adaptive linearization” developed using this approach minimizes the worst-case error between the output of the approximation and the actual non-linear power flow equations over the operating range of interest. To compute an adaptive linearization, this paper proposes a constraint generation algorithm that iterates between 1) using an optimization algorithm to identify a point that maximizes the error of the linearization at that iteration and 2) updating the linearization to minimize the worst-case error among all points identified thus far. This approach is tested on several IEEE test cases, with the results demonstrating up to a factor of four improvement in approximation error over linearizations based on a first-order Taylor approximation.