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Modal Analysis of Core Inertial Dynamics: Re-evaluating Grid-Forming Control Design Principles

Gerardo Medrano, Santiago Cóbreces

TL;DR

This paper challenges the prevailing practice of forcing grid-forming converters to mimic legacy synchronous generators by showing, through state-space modeling and modal analysis, that low droop and low virtual inertia in GFM converters can yield superior damping and tightly bounded frequency variations. It demonstrates that in GC-SG–GFM hybrids, the conventional damping achieved via large droop is suboptimal, whereas GFM droop control inherently provides stronger damping with smaller droop, and virtual inertia can be freely selected. Replacing a GC-SG with a GFM, and especially reducing GFM inertia, markedly improves damping of swing and governor-related modes, suggesting a paradigm shift in GFM control design and grid-code requirements. The work also discusses RoCoF implications, arguing that instantaneous spikes can be acceptable under modern, high-damping GFM schemes, and calls for regulatory reevaluation to unlock the benefits of IBRs.

Abstract

This paper employs modal analysis to study the core inertial dynamics of governor-controlled synchronous generators (GC-SG), droop-based grid-forming (GFM) converters, and their most fundamental interactions. The results indicate that even in the simplest cases, the prevailing industry paradigm of emulating legacy GC-SG behaviour in GFM converters (high inertia to slow down the system and large droop to increase damping) could be a suboptimal policy. It is shown that GC-SGs exhibit a fundamental trade-off: adequate damping of the turbine-governor mode requires large droop constants, inevitably increasing steady-state frequency deviation and dependence on secondary regulation. In contrast, droop-based GFM converters invert this relationship: decreasing the droop constant simultaneously reduces steady-state frequency deviations and increases damping, while allowing virtual inertia to be freely chosen. When two GC-SGs are coupled, the poorly damped electromechanical swing mode emerges. Results show that replacing one GC-SG with a GFM converter of equivalent droop and inertia already significantly improves damping of both swing and turbine-governor modes. Counter-intuitively, further and remarkable damping gains are achieved by substantially lowering the GFM virtual inertia constant. These findings suggest that current industry trends may be constraining the potential benefits of Inverter Based Resources (IBRs). Optimal stability and performance are instead obtained with low droop and low virtual inertia, yielding tightly bounded frequency variations and strongly-damped electromechanical modes. The results indicate a need to re-evaluate GFM control design principles and emerging grid-code requirements.

Modal Analysis of Core Inertial Dynamics: Re-evaluating Grid-Forming Control Design Principles

TL;DR

This paper challenges the prevailing practice of forcing grid-forming converters to mimic legacy synchronous generators by showing, through state-space modeling and modal analysis, that low droop and low virtual inertia in GFM converters can yield superior damping and tightly bounded frequency variations. It demonstrates that in GC-SG–GFM hybrids, the conventional damping achieved via large droop is suboptimal, whereas GFM droop control inherently provides stronger damping with smaller droop, and virtual inertia can be freely selected. Replacing a GC-SG with a GFM, and especially reducing GFM inertia, markedly improves damping of swing and governor-related modes, suggesting a paradigm shift in GFM control design and grid-code requirements. The work also discusses RoCoF implications, arguing that instantaneous spikes can be acceptable under modern, high-damping GFM schemes, and calls for regulatory reevaluation to unlock the benefits of IBRs.

Abstract

This paper employs modal analysis to study the core inertial dynamics of governor-controlled synchronous generators (GC-SG), droop-based grid-forming (GFM) converters, and their most fundamental interactions. The results indicate that even in the simplest cases, the prevailing industry paradigm of emulating legacy GC-SG behaviour in GFM converters (high inertia to slow down the system and large droop to increase damping) could be a suboptimal policy. It is shown that GC-SGs exhibit a fundamental trade-off: adequate damping of the turbine-governor mode requires large droop constants, inevitably increasing steady-state frequency deviation and dependence on secondary regulation. In contrast, droop-based GFM converters invert this relationship: decreasing the droop constant simultaneously reduces steady-state frequency deviations and increases damping, while allowing virtual inertia to be freely chosen. When two GC-SGs are coupled, the poorly damped electromechanical swing mode emerges. Results show that replacing one GC-SG with a GFM converter of equivalent droop and inertia already significantly improves damping of both swing and turbine-governor modes. Counter-intuitively, further and remarkable damping gains are achieved by substantially lowering the GFM virtual inertia constant. These findings suggest that current industry trends may be constraining the potential benefits of Inverter Based Resources (IBRs). Optimal stability and performance are instead obtained with low droop and low virtual inertia, yielding tightly bounded frequency variations and strongly-damped electromechanical modes. The results indicate a need to re-evaluate GFM control design principles and emerging grid-code requirements.

Paper Structure

This paper contains 12 sections, 48 equations, 12 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Modeling Assumptions
  3. A Simplified Microgrid with a Governor-Controlled System
  4. A Simplified Microgrid with a PE-GFM Converter
  5. A More Comprehensive System
  6. Modal Analysis of the Two-Generator System
  7. Small-signal time-domain simulation
  8. On RoCoF
  9. Conclusions
  10. The Swing Mode
  11. Calculation of Partial Derivatives
  12. Per Unit Notation

Figures (12)

  • Figure 1: Configuration of a governor-controlled synchronous generator feeding a simplified load.
  • Figure 2: Linearized small-signal block diagram of the governor-controlled synchronous generator.
  • Figure 3: Droop-controlled grid-former feeding a load.
  • Figure 4: Linearized small-signal block diagram of the PE-GFM converter.
  • Figure 5: 3-bus system with two droop-controlled generators and a load.
  • ...and 7 more figures