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Grid-Forming Storage Networks: Analytical Characterization of Damping and Design Insights

Kaustav Chatterjee, Ramij Raja Hossain, Sai Pushpak Nandanoori, Soumya Kundu, Subhrajit Sinha, Diane Baldwin, Ronald Melton

Abstract

The paper presents a theoretical study on small-signal stability and damping in bulk power systems with multiple grid-forming inverter-based storage resources. A detailed analysis is presented, characterizing the impacts of inverter droop gains and storage size on the slower eigenvalues, particularly those concerning inter-area oscillation modes. From these parametric sensitivity studies, a set of necessary conditions are derived that the design of droop gain must satisfy to enhance damping performance. The analytical findings are structured into propositions highlighting potential design considerations for improving system stability. The findings are illustrated via numerical studies on an IEEE 68-bus grid-forming storage network.

Grid-Forming Storage Networks: Analytical Characterization of Damping and Design Insights

Abstract

The paper presents a theoretical study on small-signal stability and damping in bulk power systems with multiple grid-forming inverter-based storage resources. A detailed analysis is presented, characterizing the impacts of inverter droop gains and storage size on the slower eigenvalues, particularly those concerning inter-area oscillation modes. From these parametric sensitivity studies, a set of necessary conditions are derived that the design of droop gain must satisfy to enhance damping performance. The analytical findings are structured into propositions highlighting potential design considerations for improving system stability. The findings are illustrated via numerical studies on an IEEE 68-bus grid-forming storage network.
Paper Structure (15 sections, 6 theorems, 40 equations, 3 figures)

This paper contains 15 sections, 6 theorems, 40 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Description
  4. Synchronous Generator Model
  5. Inverter Model
  6. Network Model
  7. Grid Strength and Bounds on $K_{ii}$
  8. State-Space Representation and Oscillation Modes
  9. Main Results: Eigen-Analysis and Damping
  10. Characterization of Slow Eigenvalues
  11. Parametric Sensitivity of Slow Eigenvalues
  12. Analytical Design Insights
  13. Numerical Results and Simulation Studies
  14. Conclusions
  15. Proof of Proposition \ref{['prop:intermediate_result']}

Key Result

Proposition 1

Consider an $n$-dimensional complex square matrix $C$ , and some $n$-dimensional complex vector $v$ . Then

Figures (3)

  • Figure 1: Loci of the four dominant eigenvalues (corresponding to the 4 inter-area modes) of the IEEE $68$-bus system for variation in the droop gain $\hat{m}_{p,j}$.
  • Figure 2: Loci of four dominant eigenvalues (corresponding to the inter-area modes) for a wide range of $\hat{m}_{p,j}$ variation. In the standard range of droop gains, damping increases with a decrease in $\hat{m}_{p,j}$, however, at very low droop values the trend is reversed.
  • Figure 3: Loci of four dominant eigenvalues (corresponding to the inter-area modes) with variation in the storage size.

Theorems & Definitions (15)

  • Proposition 1
  • proof
  • Remark 1
  • Lemma 1: Eigenvectors
  • proof
  • Proposition 2
  • proof
  • Theorem 1: Damping
  • proof
  • Theorem 2: Design Insight
  • ...and 5 more