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An Approach to Evaluate Modeling Adequacy for Small-Signal Stability Analysis of IBR-related SSOs in Multimachine Systems

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

Abstract

Time-varying phasor-based analysis of subsynchronous oscillations (SSOs) involving grid-following converters (GFLCs) and its benchmarking with electromagnetic transient (EMT) models have so far been restricted to highly simplified grid models with constant voltage sources behind series R-L circuits. In this paper, modeling adequacy of bulk power systems with synchronous generators (SGs), transmission systems, loads, and GFLCs are considered. To this end, we revisit the notions of time-varying phasor calculus, highlighting the distinction between space-phasor-calculus (SPC) and two often interchangeably used frameworks namely baseband-abc and generalized averaging. We present the models of grids in SPC framework that include transmission line dynamics, load dynamics, and SG stator transients. Next, we propose a generic approach to study modeling adequacy in small-signal sense by (a) identifying critical modes through eigenvalue and singular value analysis followed by (b) using weighted maximum singular value error magnitudes as metrics, and (c) further cross-validation. Using a modified 4-machine IEEE benchmark model with up to 3 GFLCs we show that SPC framework can be used for analysis of SSOs. Further, we consider the quasistationary phasor calculus (QPC) framework that neglects transmission line, load, and SG stator dynamics to show its adequacy in SSO modeling and analysis. Time-domain and frequency-domain results with EMT models are also presented.

An Approach to Evaluate Modeling Adequacy for Small-Signal Stability Analysis of IBR-related SSOs in Multimachine Systems

Abstract

Time-varying phasor-based analysis of subsynchronous oscillations (SSOs) involving grid-following converters (GFLCs) and its benchmarking with electromagnetic transient (EMT) models have so far been restricted to highly simplified grid models with constant voltage sources behind series R-L circuits. In this paper, modeling adequacy of bulk power systems with synchronous generators (SGs), transmission systems, loads, and GFLCs are considered. To this end, we revisit the notions of time-varying phasor calculus, highlighting the distinction between space-phasor-calculus (SPC) and two often interchangeably used frameworks namely baseband-abc and generalized averaging. We present the models of grids in SPC framework that include transmission line dynamics, load dynamics, and SG stator transients. Next, we propose a generic approach to study modeling adequacy in small-signal sense by (a) identifying critical modes through eigenvalue and singular value analysis followed by (b) using weighted maximum singular value error magnitudes as metrics, and (c) further cross-validation. Using a modified 4-machine IEEE benchmark model with up to 3 GFLCs we show that SPC framework can be used for analysis of SSOs. Further, we consider the quasistationary phasor calculus (QPC) framework that neglects transmission line, load, and SG stator dynamics to show its adequacy in SSO modeling and analysis. Time-domain and frequency-domain results with EMT models are also presented.
Paper Structure (20 sections, 11 equations, 21 figures, 6 tables)

This paper contains 20 sections, 11 equations, 21 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Motivation behind studying modeling adequacy
  3. Literature review
  4. Contributions of this work
  5. Different Representations of Time-Varying Phasor Calculus
  6. Modeling in SPC and QPC Frameworks
  7. Modeling of transmission network and loads
  8. Modeling of SG including stator transients
  9. Modeling of GFLC and its controls
  10. Proposed Approach for MIMO Modeling Adequacy Study in Small-Signal Sense
  11. Step 1
  12. Step 2
  13. Step 3
  14. Step 4
  15. Step 5
  16. ...and 5 more sections

Figures (21)

  • 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 GFLC [parameters: $\tau_{c}$ = $0.05s$, $C_{c}$ = $1.7370~pu$, $k_{dc}$ = $1080~pu$, $R$ = $0.0033~pu$, $R_{on}$ = $0.0023~pu$, $L$ = $0.2454~pu$, $R_{t}$ = $0~pu$, $L_{t}$ = $0.1500~pu$, $S_{base}$ = $100MVA$, $V_{dc,base}$ = $48.9873kV$, $V_{ac,base}$ = $20kV$].
  • Figure 4: Phase-locked loop (PLL) [parameters: $k_{p}$ = $101$, $k_{i}$ = $2562$ for $20$ Hz bandwidth and $k_{p}$ = $76$, $k_{i}$ = $1455$ for $15$ Hz bandwidth pll_impact, $\tau_{m}$ = $1ms$].
  • Figure 5: (a) Active power control, (b) outer voltage control, and (c) inner current control. [parameters: $P_{ref}$ = $7.00pu$, $\tau_{f}$ = $50ms$, $S_{base}$ = $100pu$, $V_{ac,base}$ = $20kV$].
  • ...and 16 more figures