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Improved Algebraic Inverter Modelling for Four-Wire Power Flow Optimization

Rahmat Heidari, Frederik Geth

Abstract

This paper discusses the modeling of inverters used in distributed energy resources in steady state. Modeling the interaction between distribution grids and inverter-based resources is crucial to understand the consequences for the network's operational and planning processes. This work highlights the limitations of existing models and emphasizes the need for better representations of inverters and their control laws in decision-making contexts. Improved steady-state grid-following and grid-forming inverter models are presented, including both three-leg and four-leg converter variants. The advantages of these improved models in mathematical optimization contexts are showcased by investigating the power quality improvement capabilities of the inverters. Numerical studies integrating the proposed inverter models in a four-wire unbalanced optimal power flow engine are presented, and trade-offs between modeling detail and computational intensity are illustrated.

Improved Algebraic Inverter Modelling for Four-Wire Power Flow Optimization

Abstract

This paper discusses the modeling of inverters used in distributed energy resources in steady state. Modeling the interaction between distribution grids and inverter-based resources is crucial to understand the consequences for the network's operational and planning processes. This work highlights the limitations of existing models and emphasizes the need for better representations of inverters and their control laws in decision-making contexts. Improved steady-state grid-following and grid-forming inverter models are presented, including both three-leg and four-leg converter variants. The advantages of these improved models in mathematical optimization contexts are showcased by investigating the power quality improvement capabilities of the inverters. Numerical studies integrating the proposed inverter models in a four-wire unbalanced optimal power flow engine are presented, and trade-offs between modeling detail and computational intensity are illustrated.
Paper Structure (29 sections, 25 equations, 5 figures, 9 tables)

This paper contains 29 sections, 25 equations, 5 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Steady State Inverter Models and Controllability
  3. Scope and Contributions
  4. Review of Inverter Models and Controls
  5. Inverters in Unbalanced Optimal Power Flow
  6. Inverter Control Degrees of Freedom
  7. Steady-State Inverter Models up to Four-Leg
  8. Grid-Following Inverter (GFL)
  9. Voltage
  10. Current
  11. Power
  12. Mathematical Reduction to a 3-Leg Model
  13. Grid-Forming Inverter (GFM)
  14. Control Laws
  15. Droop control
  16. ...and 14 more sections

Figures (5)

  • Figure 1: 3-Leg vs. 4-Leg inverter power electronic circuit topologies.
  • Figure 2: Equivalent circuit of the four-leg inverter model with mathematical symbols, and current directions indicated.
  • Figure 3: Electrical diagram of 2-bus network to illustrate differences in feasibility between inverter models.
  • Figure 4: Volt-var and Volt-Watt control laws in 4-Leg GFL inverters. From left to right 1) phase-to-neutral control, 2) phase-to-phase control and 3) averaged phase-to-ground control.
  • Figure 5: Negative and zero sequence components of network voltages.