Non-local approximation of power flow equations with guaranteed error bounds

Progressive increase of distributed generation penetration levels into the power grid has motivated studies on network stability and control methods in order to maintain the grid in operational conditions. A key challenge to better study features of the power grid is to have a reliable network model under different circumstances. In this paper, we derive a structured nonlinear model for the network and then propose an approximate model that captures the system nonlinearities. We then design voltage control functions and derive a dynamic network model with embedded controllers. We analyse voltage stability of the controlled network for both the exact and approximate models. In particular, we give conditions for the voltage to ultimately lie within quantifiable bounds for both models. This result also allows to compute a bound on the difference between the exact and approximate model voltages.