An equivalent circuit formulation of the power flow problem with current and voltage state variables

Steady state analysis of power grids is typically performed using power flow analysis, where nonlinear balance equations of real and reactive power are solved to calculate the voltage magnitude, phase, and power at every bus. Transient analysis of the same power grids are performed using circuit simulation methods. We propose a novel approach to modeling the nonlinear steady state behavior of power grids in terms of equivalent circuits with currents and voltages as the state variables that is a step toward unifying transient and steady state models. A graph theoretic formulation approach is used to solve the circuits that enables incorporation of switch models for contingency analyses. Superior nonlinear steady state convergence is demonstrated by use of current as a state variable and application of circuit simulation methods. Furthermore, current and voltage state variables will offer greater compatibility with future smart grid components and monitors.