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

TL;DR

This work addresses the need for accurate, loss-aware, steady-state inverter representations in distribution-grid analysis. It introduces a physics-based TSBI that embeds semiconductor losses and inverter control directly into a unified equivalent-circuit formulation, avoiding binary decisions and enabling seamless integration with gradient-based solvers. The key contributions include closed-form, sign-aware loss expressions, twice-differentiable controlled sources for MPPT and Volt–VAR, and validation against time-domain models on large networks, plus scalable optimization results. The TSBI framework demonstrates improved accuracy, generality across control modes, and scalability to networks with tens of thousands of nodes, improving utility analyses, hosting capacity, and DER scheduling.

Abstract

This paper presents a \textit{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; and iii) inability to integrate different control modes into nonlinear solvers without loss of generality. We propose a physics-first model that explicitly captures losses in passive circuit components based on circuit-level 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. Index Terms: bidirectional inverter model, circuit-based modeling, DERs, inverter efficiency, power control, steady-state analysis.

Figures (12)

• Figure 1: ECF models for: (A) battery (zeroth-order) and (B) PV (SDM)
• Figure 2: Idealized FSC operation under forward power flow. (A) FESM: inductor charges from $V_{\text{T1}}$ via $S_1$, $S_4$. (B) FETM: energy transferred to $V_{\text{DC}}$ via $S_2$, $S_3$. (C) Equivalent transformer model relating $V_{\text{T1}}$ to $V_{\text{DC}}$.
• Figure 3: (A) FESM with current $I_{\text{T1}}$, duty $D$; (B) FETM with current $I_{\text{DC}}$, duty $1{-}D$. Losses include $V_{T0}$, $R_T$, and $R_L$, and the total voltage drop is obtained by superposition of the two subcircuits.
• Figure 4: Equivalent circuit model of non-ideal FSC, with switching and conduction losses using controlled sources.
• Figure 5: Equivalent circuit representation of the ideal SSC.