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Small-Signal Stability Impacts of Load and Network Dynamics on Grid-Forming Inverters

Rodrigo Henriquez-Auba, Jose Daniel Lara, Duncan S. Callaway

TL;DR

The paper investigates how load dynamics and transmission-line electromagnetic effects influence the small-signal stability of grid-forming inverters in increasingly inverter-dominated grids. It combines quasi-static phasor (QSP) and electromagnetic transient (EMT) modeling to perform eigenvalue and bifurcation analyses on a two-bus test system with CPL, ZIP, and active-load models across multiple GFM controls (droop, VSM, dVOC). Key findings show that stability regions and bifurcation types are highly sensitive to load representation and network modeling, with singularity-induced bifurcations arising for CPL in GFM but distinct Hopf/transcritical behavior under EMT for other loads. The work underscores the need for realistic composite load modeling and careful network representation to ensure stability as inverter-based resources scale up.

Abstract

This paper presents several stability analyses for grid-forming inverters and synchronous generators considering the dynamics of transmission lines and different load models. Load models are usually of secondary importance compared to generation source models, but as the results show, they play a crucial role in stability studies with the introduction of inverter-based resources. Given inverter control time scales, the implications of considering or neglecting electromagnetic transients of the network are very relevant in the stability assessments. In this paper, we perform eigenvalue analyses for inverter-based resources and synchronous machines connected to a load and explore the effects of multiples models under different network representations. We explore maximum loadability of inverter-based resources and synchronous machines, while analyzing the effects of load and network dynamic models on small-signal stability. The results show that the network representation plays a fundamental role in the stability of the system of different load models. The resulting stability regions are significantly different depending on the source and load model considered.

Small-Signal Stability Impacts of Load and Network Dynamics on Grid-Forming Inverters

TL;DR

The paper investigates how load dynamics and transmission-line electromagnetic effects influence the small-signal stability of grid-forming inverters in increasingly inverter-dominated grids. It combines quasi-static phasor (QSP) and electromagnetic transient (EMT) modeling to perform eigenvalue and bifurcation analyses on a two-bus test system with CPL, ZIP, and active-load models across multiple GFM controls (droop, VSM, dVOC). Key findings show that stability regions and bifurcation types are highly sensitive to load representation and network modeling, with singularity-induced bifurcations arising for CPL in GFM but distinct Hopf/transcritical behavior under EMT for other loads. The work underscores the need for realistic composite load modeling and careful network representation to ensure stability as inverter-based resources scale up.

Abstract

This paper presents several stability analyses for grid-forming inverters and synchronous generators considering the dynamics of transmission lines and different load models. Load models are usually of secondary importance compared to generation source models, but as the results show, they play a crucial role in stability studies with the introduction of inverter-based resources. Given inverter control time scales, the implications of considering or neglecting electromagnetic transients of the network are very relevant in the stability assessments. In this paper, we perform eigenvalue analyses for inverter-based resources and synchronous machines connected to a load and explore the effects of multiples models under different network representations. We explore maximum loadability of inverter-based resources and synchronous machines, while analyzing the effects of load and network dynamic models on small-signal stability. The results show that the network representation plays a fundamental role in the stability of the system of different load models. The resulting stability regions are significantly different depending on the source and load model considered.
Paper Structure (8 sections, 4 equations, 6 figures, 1 table)

This paper contains 8 sections, 4 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Instability aspects for Constant Power Loads
  3. Maximum loadability analysis
  4. QSP P-V curves for CPLs
  5. EMT P-V curves for ZIP and IM models
  6. EMT P-V curves for an active load
  7. Importance of Composite Load Modeling in GFM dominated systems
  8. Conclusions

Figures (6)

  • Figure 1: $v$-$i$ curves for common voltage sources and ideal CPLs.
  • Figure 2: Problem set-up for load studies.
  • Figure 3: P-V curves for (a) QSP/CPL model, (b) EMT/active load model. Colored regions depict stable operating points, while a black line showcase small-signal unstable operating conditions
  • Figure 4: Phase portrait $v_\text{DC}$--$\zeta$ for droop GFM supplying active load at $P^\star$.
  • Figure 5: ZIP Load example.
  • ...and 1 more figures