Monotone operator approach to power flow solutions

The AC power flow equations underlie all operational aspects of power systems. In this paper, Here we solve this problem using the theory of monotone operators. We show that it is possible to characterize a “contractivity domain” in the power flow variables (voltage magnitudes and phases). The construction of these domains depends on the specific representation chosen for the power flow equations, so that different representations lead to different domains. Given this domain, there is a simple efficient algorithm that will either find a solution in the domain, or certify that no solutions exist in it. We validate the approach on several IEEE test cases