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.