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A Case Study on Modeling Adequacy of a Grid with Subsynchronous Oscillations Involving IBRs

Lilan Karunaratne, Nilanjan Ray Chaudhuri, Amirthagunaraj Yogarathnam, Meng Yue

TL;DR

The paper investigates the modeling adequacy of grids with inverter-based resources, focusing on grid-forming converters and subsynchronous oscillations. It develops a space-phasor-based ($d$-$q$) SPC modeling framework and contrasts it with quasistationary phasor calculus (QPC) and EMT simulations on a modified IEEE 4-machine test system with GFCs. A key finding is that SPC models that include transmission-line dynamics capture a subsynchronous oscillation near $43$ Hz that QPC models miss, validated by EMT and Prony analysis. The work highlights the practicality and limitations of lumped-network SPC models for planning studies and calls for more accurate transmission-line representations in GFC-dominated grids.

Abstract

A case study on modeling adequacy of a grid in presence of renewable resources based on grid-forming converters (GFCs) is the subject matter of this paper. For this purpose, a 4-machine 11-bus IEEE benchmark model is modified by considering GFCs replacing synchronous generators that led to unstable subsynchronous oscillations (SSOs). We aim to: (a) understand if transmission network dynamics should be considered in such cases, (b) revisit the space-phasor-calculus (SPC) in d-q frame under balanced condition that captures such phenomena and lends itself to eigenvalue analysis, and (c) emphasize limitations of such models while underscoring their importance for large-scale power system simulations. Time-domain and frequency-domain results from SPC and quasistationary phasor calculus (QPC) models are compared with electromagnetic transient (EMT)-based simulations. It is shown that models with transmission line dynamics in SPC framework can capture the SSO mode while QPC models that neglect these dynamics fail to do so.

A Case Study on Modeling Adequacy of a Grid with Subsynchronous Oscillations Involving IBRs

TL;DR

The paper investigates the modeling adequacy of grids with inverter-based resources, focusing on grid-forming converters and subsynchronous oscillations. It develops a space-phasor-based (-) SPC modeling framework and contrasts it with quasistationary phasor calculus (QPC) and EMT simulations on a modified IEEE 4-machine test system with GFCs. A key finding is that SPC models that include transmission-line dynamics capture a subsynchronous oscillation near Hz that QPC models miss, validated by EMT and Prony analysis. The work highlights the practicality and limitations of lumped-network SPC models for planning studies and calls for more accurate transmission-line representations in GFC-dominated grids.

Abstract

A case study on modeling adequacy of a grid in presence of renewable resources based on grid-forming converters (GFCs) is the subject matter of this paper. For this purpose, a 4-machine 11-bus IEEE benchmark model is modified by considering GFCs replacing synchronous generators that led to unstable subsynchronous oscillations (SSOs). We aim to: (a) understand if transmission network dynamics should be considered in such cases, (b) revisit the space-phasor-calculus (SPC) in d-q frame under balanced condition that captures such phenomena and lends itself to eigenvalue analysis, and (c) emphasize limitations of such models while underscoring their importance for large-scale power system simulations. Time-domain and frequency-domain results from SPC and quasistationary phasor calculus (QPC) models are compared with electromagnetic transient (EMT)-based simulations. It is shown that models with transmission line dynamics in SPC framework can capture the SSO mode while QPC models that neglect these dynamics fail to do so.
Paper Structure (8 sections, 7 equations, 9 figures, 1 table)

This paper contains 8 sections, 7 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Different Representations of Time-Varying Phasor Calculus
  3. Modeling in SPC and QPC Frameworks
  4. Modeling of transmission network and loads
  5. Modeling of SG including stator transients
  6. Modeling of GFC and its controls
  7. Case Studies
  8. Limitations & Conclusions

Figures (9)

  • Figure 1: Signal spectrum of (a) an analytic and (b) a baseband signal.
  • Figure 2: Interconnection between SG model and transmission network.
  • Figure 3: Circuit model of GFC [parameters: $\tau_{c}$ = $0.05s$, $G_{c}$ = $0.45~pu$, $C_{c}$ = $325.73~pu$, $k_{dc}$ = $1080~pu$, $R$ = $5.5556e{-5}~pu$, $L$ = $0.0042~pu$, $C$ = $2.0358~pu$, $S_{base}$ = $100MVA$, $V_{dc,base}$ = $48.98kV$, $V_{ac,base}$ = $20kV$].
  • Figure 4: (a) Power-frequency droop control, and (b) outer loop voltage control of GFCs [parameters: $\omega_{s}$ = $120\pi~rads^{-1}$, $P_{c}^*$ = $7.00~pu$, $K_{p,ac}$ = $0.0010$, $K_{i,ac}$ = $0.5000$, $S_{base}$ = $100MVA$].
  • Figure 5: Inner current and voltage control loops of GFC [parameters: $K_{p,i}$ = $0.0411~pu$, $K_{i,i}$ = $1.7389e{-4}~pu$, $K_{p,v}$ = $9.3600~pu$, $K_{i,v}$ = $0.0554~pu$, $S_{base}$ = $100MVA$, $V_{ac,base}$ = $20kV$].
  • ...and 4 more figures