[Paper Review] Modeling of microgrids|from fundamental physics to phasors and voltage sources

Johannes Schier, Daniele Zonetti+3 more|arXiv (Cornell University)|May 1, 2015

Microgrid Control and Optimization93 references17 citations

TL;DR

This paper presents a systematic, physics-based derivation of reduced-order models for three-phase inverter-based microgrids, starting from fundamental electromagnetic principles and showing how assumptions lead to standard representations as controllable voltage sources and static network components. The key contribution is a transparent, modular framework that clarifies the physical basis of widely used microgrid models, enhancing controller design and system understanding.

ABSTRACT

Microgrids are an increasingly popular class of electrical systems that facilitate the integration of renewable distributed generation units. Their analysis and controller design requires the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure|hampering the understanding of the physical phenomena behind them. The present paper aims to provide a complete modular model derivation of a three-phase inverter-based microgrid. Starting from fundamental physics, we present detailed dynamical models of the main microgrid components and clearly state the underlying assumptions which lead to the standard reduced model representation with inverters represented as controllable voltage sources, as well as static network interconnections and loads.

Motivation & Objective

• Address the lack of transparency in reduced-order microgrid models, which are commonly used but rarely derived from first principles.
• Clarify the physical assumptions and simplifications that lead to the standard representation of inverters as controllable voltage sources.
• Provide a complete, modular derivation of dynamic models for key microgrid components, including inverters, loads, and network interconnections.
• Bridge the gap between detailed physical dynamics and the simplified models used in control design and stability analysis.
• Enhance the understanding of microgrid behavior by explicitly linking component-level physics to system-level reduced-order representations.

Proposed method

• Start from fundamental electromagnetic laws and Kirchhoff’s laws to derive detailed dynamic models of three-phase inverters, including power electronics and control loops.
• Introduce and justify key simplifying assumptions—such as balanced three-phase operation, small-signal dynamics, and decoupled d-q frame transformation—leading to reduced-order models.
• Apply symmetrical components and dq0 transformation to linearize and decouple the three-phase system into two independent d- and q-axis dynamics.
• Represent the inverter as a controllable voltage source in the reduced model, showing how this emerges from the underlying control structure and switching dynamics.
• Model network components and loads as static admittances or constant power elements, consistent with standard microgrid modeling practices.
• Use modular decomposition to isolate and analyze each component’s contribution, enabling systematic model reduction and validation.

Experimental results

Research questions

• RQ1 How do the fundamental physical laws of electromagnetism and circuit theory lead to the standard reduced-order microgrid model with voltage-source inverters?
• RQ2 What specific assumptions and simplifications are required to transition from detailed inverter dynamics to the controllable voltage source representation?
• RQ3 How do the dynamic behaviors of individual components—such as inverters, loads, and network elements—combine to form the overall microgrid model?
• RQ4 What is the physical and mathematical basis for representing the network and loads as static elements in the reduced model?
• RQ5 How can the derivation process be made modular and transparent to support controller design and system analysis?

Key findings

• The standard reduced-order microgrid model with inverters as controllable voltage sources emerges naturally from detailed physical modeling when key assumptions—such as balanced operation and small-signal dynamics—are applied.
• The dq0 transformation and symmetrical components enable the decoupling of three-phase dynamics into independent d- and q-axis components, simplifying analysis and control design.
• The voltage-source representation of inverters is justified by the presence of fast inner current control loops that maintain output voltage within tight tolerances.
• Static network and load models are valid under the assumption of slow dynamics compared to inverter control bandwidth, allowing time-averaged or steady-state approximations.
• The modular derivation process clearly identifies the physical origins of each model simplification, enhancing interpretability and trust in the reduced model.
• The framework provides a foundation for systematic model validation and extension to more complex microgrid configurations, such as droop-controlled or islanded systems.