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Verification and Validation of Physics-Informed Surrogate Component Models for Dynamic Power-System Simulation

Petros Ellinas, Indrajit Chaudhuri, Johanna Vorwerk, Spyros Chatzivasileiadis

Abstract

Physics-informed machine learning surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. The key question, however, is not only whether a surrogate matches a stand-alone component model on average, but whether it remains accurate after insertion into a differential-algebraic simulator, where the surrogate outputs enter the algebraic equations coupling the component to the rest of the system. This paper formulates that in-simulator use as a verification and validation (V\&V) problem. A finite-horizon bound is derived that links allowable component-output error to algebraic-coupling sensitivity, dynamic error amplification, and the simulation horizon. Two complementary settings are then studied: model-based verification against a reference component solver, and data-based validation through conformal calibration of the component-output variables exchanged with the simulator. The framework is general, but the case study focuses on physics-informed neural-network surrogates of second-, fourth-, and sixth-order synchronous-machine models. Results show that good stand-alone surrogate accuracy does not by itself guarantee accurate in-simulator behavior, that the largest discrepancies concentrate in stressed operating regions, and that small equation residuals do not necessarily imply small state-trajectory errors.

Verification and Validation of Physics-Informed Surrogate Component Models for Dynamic Power-System Simulation

Abstract

Physics-informed machine learning surrogates are increasingly explored to accelerate dynamic simulation of generators, converters, and other power grid components. The key question, however, is not only whether a surrogate matches a stand-alone component model on average, but whether it remains accurate after insertion into a differential-algebraic simulator, where the surrogate outputs enter the algebraic equations coupling the component to the rest of the system. This paper formulates that in-simulator use as a verification and validation (V\&V) problem. A finite-horizon bound is derived that links allowable component-output error to algebraic-coupling sensitivity, dynamic error amplification, and the simulation horizon. Two complementary settings are then studied: model-based verification against a reference component solver, and data-based validation through conformal calibration of the component-output variables exchanged with the simulator. The framework is general, but the case study focuses on physics-informed neural-network surrogates of second-, fourth-, and sixth-order synchronous-machine models. Results show that good stand-alone surrogate accuracy does not by itself guarantee accurate in-simulator behavior, that the largest discrepancies concentrate in stressed operating regions, and that small equation residuals do not necessarily imply small state-trajectory errors.
Paper Structure (13 sections, 2 theorems, 29 equations, 4 figures)

This paper contains 13 sections, 2 theorems, 29 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Surrogate Component Models and Error Notions
  3. In-Simulator Certification Problem
  4. Embedding a component surrogate in a differential-algebraic simulator
  5. Finite-horizon in-simulator bound
  6. Verification and Validation Methods
  7. Differentiable worst-case verification
  8. Statistical validation of component-output variables
  9. Results
  10. Benchmark models and setup
  11. Empirical worst-case verification of PIML surrogates
  12. Residual error, solution error, and interface-level validation
  13. Conclusion

Key Result

Theorem 1

Assume the Lipschitz and one-sided Lipschitz conditions above, and assume that the reference and surrogate-embedded trajectories share the same initial condition, so that $\boldsymbol{e}_x(0)=\boldsymbol{e}_y(0)=\boldsymbol{0}$. If then and therefore Hence, if $\Delta>0$ is the maximum admissible simulator-level deviation, then a sufficient interface requirement is

Figures (4)

  • Figure 1: Illustration of Theorem \ref{['thm:closedloop']} on a single-machine infinite-bus (SMIB) system. Top: for nearly identical maximum interface errors $\|\boldsymbol{e}_z(t)\|$, the simulator deviation $\|\boldsymbol{e}_x(t)\|+\|\boldsymbol{e}_y(t)\|$ is larger in the weak-grid case than in the strong-grid case. Bottom: at fixed target $\varepsilon$, the maximum simulator deviation increases with grid sensitivity ($K_{yz}\approx X_{\mathrm{line}}$).
  • Figure 2: Worst-case verification and coverage-oriented sampling under matched budgets.
  • Figure 3: Functional and solution errors are related but not equivalent.
  • Figure 4: Split conformal versus high-confidence UCB-based calibration across calibration ratios.

Theorems & Definitions (3)

  • Theorem 1: Finite-horizon in-simulator acceptance bound
  • Remark 1
  • Proposition 1