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A Heterogeneous Multiscale Method for Efficient Simulation of Power Systems with Inverter-Based Resources

Kaiyang Huang, Min Xiong, Yang Liu, Kai Sun

TL;DR

The paper tackles the challenge of simulating power systems with heavy inverter-based resources, where EMT, EMch, and QSS dynamics create stiffness across vastly different time scales. It introduces a Heterogeneous Multiscale Method (HMM) that alternates between detailed EMT micro-simulations and automatically reduced macro-dynamics, using an intermediate state $\mathbf{u}_\epsilon = Q(\mathbf{x})$ and a kernel-based convolution to estimate slow dynamics without requiring explicit reduced equations. The approach provides theoretical speedup and error guidance, employs a DT-based semi-analytical micro-solver for adaptive step sizes, and demonstrates substantial performance gains on Kundur's two-area, the IEEE 39-bus with high IBR penetration, and a 390-bus large system, while preserving essential fast dynamics. This framework offers a scalable, automatic, and accurate pathway for multi-timescale EMT simulations in modern grids and can be extended to other ODE-based dynamical systems.

Abstract

As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics of synchronous generators. Consequently, the power system model becomes highly stiff, posing a challenge for efficient simulation using existing methods that focus on dynamics within a single timescale. This paper proposes a Heterogeneous Multiscale Method for highly efficient multi-timescale simulation of a power system represented by its EMT model. The new method alternates between the microscopic EMT model of the system and an automatically reduced macroscopic model, varying the step size accordingly to achieve significant acceleration while maintaining accuracy in both fast and slow dynamics of interests. It also incorporates a semi-analytical solution method to enable a more adaptive variable-step mechanism. The new simulation method is illustrated using a two-area system and is then tested on a detailed EMT model of the IEEE 39-bus system.

A Heterogeneous Multiscale Method for Efficient Simulation of Power Systems with Inverter-Based Resources

TL;DR

The paper tackles the challenge of simulating power systems with heavy inverter-based resources, where EMT, EMch, and QSS dynamics create stiffness across vastly different time scales. It introduces a Heterogeneous Multiscale Method (HMM) that alternates between detailed EMT micro-simulations and automatically reduced macro-dynamics, using an intermediate state and a kernel-based convolution to estimate slow dynamics without requiring explicit reduced equations. The approach provides theoretical speedup and error guidance, employs a DT-based semi-analytical micro-solver for adaptive step sizes, and demonstrates substantial performance gains on Kundur's two-area, the IEEE 39-bus with high IBR penetration, and a 390-bus large system, while preserving essential fast dynamics. This framework offers a scalable, automatic, and accurate pathway for multi-timescale EMT simulations in modern grids and can be extended to other ODE-based dynamical systems.

Abstract

As inverter-based resources (IBRs) penetrate power systems, the dynamics become more complex, exhibiting multiple timescales, including electromagnetic transient (EMT) dynamics of power electronic controllers and electromechanical dynamics of synchronous generators. Consequently, the power system model becomes highly stiff, posing a challenge for efficient simulation using existing methods that focus on dynamics within a single timescale. This paper proposes a Heterogeneous Multiscale Method for highly efficient multi-timescale simulation of a power system represented by its EMT model. The new method alternates between the microscopic EMT model of the system and an automatically reduced macroscopic model, varying the step size accordingly to achieve significant acceleration while maintaining accuracy in both fast and slow dynamics of interests. It also incorporates a semi-analytical solution method to enable a more adaptive variable-step mechanism. The new simulation method is illustrated using a two-area system and is then tested on a detailed EMT model of the IEEE 39-bus system.

Paper Structure

This paper contains 15 sections, 2 theorems, 49 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Heterogenous Multiscale Method for Simulating Power Systems in EMT Models
  3. Introduction of a generic HMM
  4. Overview of the Proposed HMM Approach
  5. Power System Models
  6. Proposed Algorithms for the Micro-Process
  7. Proposed Algorithms for the Macro-Process
  8. Fixed-step macro-process simulation
  9. Variable-step macro-process simulation
  10. Comparison with Other Multi-Timescale Methods
  11. Case Studies
  12. Test on Kundur's Two-area System
  13. Test on the IEEE 39-bus System
  14. Test on the Large-scale System
  15. Conclusion

Key Result

Theorem 1

Suppose the micro-process uses an $r$-th order solver with a time step of $h$, the macro-process uses an $S$-th order solver with a time step of $H$, and a $k$-th order differentiable kernel is applied to the first $\eta$ interval of each micro-process, the HMM approach---alternating between the mic such that the kernel estimation error $|\mathcal{E}_{\color{black}\text{HMM}}| \leq C_K H^S$, where

Figures (11)

  • Figure 1: A two-timescale HMM scheme.
  • Figure 2: Flowchart of the proposed HMM approach
  • Figure 3: Diagram of a grid-following IBR model
  • Figure 4: Kundur's two-area system
  • Figure 5: Convergence analysis for HMM in two-area system under three scenarios. (a) Execution time under different $H$. (b) Speedup compared with the reference simulations. (c) Integral errors. (d) Execution time for reference simulations using a 10$\mu$s time step.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Theorem 2
  • proof