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Optimal Singular Perturbation-based Model Reduction for Heterogeneous Power Systems

Yue Huang, Dixant B. Sapkota, Manish K. Singh

TL;DR

The paper tackles the challenge of reducing dynamic power-system models in heterogeneous grids without relying on explicit timescale separation. It develops two SP-based approaches—greedy state selection and nonlinear optimization with state transformations—to identify fast states for reduction while preserving stability and, when possible, zero direct feedthrough. Through a six-bus test system featuring synchronous machines and grid-following inverters, the methods demonstrate generalizability and offer accuracy gains, with complementary strengths depending on the desired reduction level. This work extends SP-based model reduction to modern, data-rich power systems and lays groundwork for structure-preserving and data-driven reductions.

Abstract

Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often reduced using techniques based on singular perturbation. However, several technical assumptions enabling traditional approaches are being challenged due to the heterogeneous, and often black-box, nature of modern power system component models. This work proposes two singular perturbation approaches that aim to optimally identify fast states that shall be reduced, without prior knowledge about the physical meaning of system states. After presenting a timescale-agnostic formulation for singular perturbation, the first approach uses greedy optimization to sequentially select states to be reduced. The second approach relies on a nonlinear optimization routine allowing state transformations while obtaining an optimally reduced model. Numerical studies on a test system featuring synchronous machines, inverters, and line dynamics demonstrate the generalizability and accuracy of the developed approaches.

Optimal Singular Perturbation-based Model Reduction for Heterogeneous Power Systems

TL;DR

The paper tackles the challenge of reducing dynamic power-system models in heterogeneous grids without relying on explicit timescale separation. It develops two SP-based approaches—greedy state selection and nonlinear optimization with state transformations—to identify fast states for reduction while preserving stability and, when possible, zero direct feedthrough. Through a six-bus test system featuring synchronous machines and grid-following inverters, the methods demonstrate generalizability and offer accuracy gains, with complementary strengths depending on the desired reduction level. This work extends SP-based model reduction to modern, data-rich power systems and lays groundwork for structure-preserving and data-driven reductions.

Abstract

Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often reduced using techniques based on singular perturbation. However, several technical assumptions enabling traditional approaches are being challenged due to the heterogeneous, and often black-box, nature of modern power system component models. This work proposes two singular perturbation approaches that aim to optimally identify fast states that shall be reduced, without prior knowledge about the physical meaning of system states. After presenting a timescale-agnostic formulation for singular perturbation, the first approach uses greedy optimization to sequentially select states to be reduced. The second approach relies on a nonlinear optimization routine allowing state transformations while obtaining an optimally reduced model. Numerical studies on a test system featuring synchronous machines, inverters, and line dynamics demonstrate the generalizability and accuracy of the developed approaches.

Paper Structure

This paper contains 12 sections, 1 theorem, 18 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Overview
  3. Model Reduction Setup
  4. Singular Perturbation Preliminaries
  5. Desirable reduced model properties
  6. Optimal SP-based Model Reduction
  7. Greedy optimization-based singular perturbation
  8. Nonlinear optimization-based singular perturbation
  9. Numerical Tests
  10. Test setup
  11. Model reduction results
  12. Conclusions and Future Work

Key Result

Lemma 1

Given Eq. eq:partitionP and eq:RWV, the orthonormality requirement of eq:PQ_cons, $PP^\top=I_r$ is equivalent to $WW^\top = I_{r-p}$.

Figures (2)

  • Figure 1: Test network with synchronous machine and grid-following inverter-based generation, RLC line models, and passive constant current loads Sapkota-SM-GFL-Model_2025.
  • Figure 2: Approximation error $\|\Sigma_{\mathrm{err}}\|_{\mathcal{H}_2}$ attained by models reduced by greedy and nonlinear optimization methods for varying order of reduced model.

Theorems & Definitions (2)

  • Lemma 1
  • proof