A Max-Affine Approximation Model to Solve Power Flow Problem with Controllable Accuracy

This paper proposes a max-affine power flow (MAPF) model to solve the power flow (PF) problem based on linear approximation. Both active and reactive power loss variables in the original power flow equations are approximated by multiple sets of affine functions. The derivations of the proposed MAPF model are based on the branch flow equations which have been validated in the literature. The problem of solving PF equations is then equivalently reformulated in an linear optimization model. The proposed MAPF model works by minimizing the approximation error in the objective function of the formulated optimization model while satisfying all the power flow equations serving as the constraints of the formulated optimization model. Since the proposed MAPF model is linear, it is advantageous in that the accuracy of the approximation is controllable by the number of affine functions. The fast convergence and accuracy of the proposed MAPF model are proved by numerical results for various IEEE test cases. A comparison with DC power flow (DCPF) results using AC power flow (ACPF) as the benchmark shows that the accuracy of MAPF is better especially in power distribution networks where power loss is un-neglectable due to larger resistance to reactance (RIX) ratio of the power lines. The proposed MAPF model is applicable for both radial and mesh power networks.