Two-Stage Bidirectional Inverter Equivalent Circuit Model for Distribution Grid Steady-State Analysis and Optimization

This paper presents a physics-based steady-state equivalent circuit model of a two-stage bidirectional inverter. These inverters connect distributed energy resources (DERs), such as photovoltaic (PV) and battery systems, to distribution grids. Existing inverter models have technical gaps on three fronts: i) inadequate modeling of inverter losses ii) use of mathematical abstractions for bidirectional flow of power, iii) inability to integrate different control modes into nonlinear solvers without loss of generality. We propose an inverter model that explicitly captures losses in passive circuit components, grounded in circuitlevel principles. We enable bidirectional power flow without binary or complementarity constraints by formulating loss terms as smooth, sign-aware expressions of current. We introduce and parameterize controlled current sources with twice-differentiable continuous functions to enable inverter control modes without loss of generality. We integrate DERs with the proposed inverter model at the load buses of distribution networks to perform power flow and optimization studies on real-world distribution networks with over 20,000 nodes. We demonstrate that the proposed model is more accurate, integrates seamlessly with various control modes without loss of generality, and scales robustly to large optimization problems.