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Data-Driven Koopman Predictive Control for Frequency Regulation of Power Systems using Black-Box IBRs

Sohrab Rezaei, Xiaomo Wang, Sijia Geng

Abstract

Model uncertainty of inverter-based resources (IBRs) presents significant challenges for power system control and stability. This work studies secondary frequency regulation in inverter-based power systems using a Data-driven Koopman Predictive Control (DKPC) framework. The method employs Koopman theory to lift the nonlinear system dynamics into a higher-dimensional space where they can be approximated as linear. Based on Willems' fundamental lemma, a behavioral model is constructed directly from lifted input-output data. A receding-horizon predictive control formulation is then provided that operates entirely using observed data, without requiring a parametric model, while satisfying explicit constraints on the control input and system output. The proposed approach is particularly suited for IBRs with complex or uncertain dynamics. Numerical results demonstrate its effectiveness for frequency control as benchmarked against the Data-enabled Predictive Control (DeePC). The trade-off between tracking performance and control effort is illustrated through tuning of the weighting parameters.

Data-Driven Koopman Predictive Control for Frequency Regulation of Power Systems using Black-Box IBRs

Abstract

Model uncertainty of inverter-based resources (IBRs) presents significant challenges for power system control and stability. This work studies secondary frequency regulation in inverter-based power systems using a Data-driven Koopman Predictive Control (DKPC) framework. The method employs Koopman theory to lift the nonlinear system dynamics into a higher-dimensional space where they can be approximated as linear. Based on Willems' fundamental lemma, a behavioral model is constructed directly from lifted input-output data. A receding-horizon predictive control formulation is then provided that operates entirely using observed data, without requiring a parametric model, while satisfying explicit constraints on the control input and system output. The proposed approach is particularly suited for IBRs with complex or uncertain dynamics. Numerical results demonstrate its effectiveness for frequency control as benchmarked against the Data-enabled Predictive Control (DeePC). The trade-off between tracking performance and control effort is illustrated through tuning of the weighting parameters.

Paper Structure

This paper contains 15 sections, 21 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Willem's Fundamental Lemma
  4. Koopman Operator
  5. Problem Formulation
  6. Data-Driven Frequency Control of IBR-Based Systems
  7. Data-Driven Koopman-Based Predictive Control
  8. System Model for Data Generation
  9. Simulation Studies
  10. Dataset Generation
  11. Receding-Horizon Predictive Control
  12. Numerical Results on Control Performance
  13. Impacts of weights on tracking and control costs
  14. Comparison with Data-Enabled Predictive Control
  15. Conclusion

Figures (7)

  • Figure 1: Frequency deviation and angle of the ten inverters in the IBR-based IEEE 39-bus system.
  • Figure 2: Control inputs of the ten inverters in the IBR-based IEEE 39-bus system.
  • Figure 3: Frequency deviation of inverters under various $q/r$ ratios.
  • Figure 4: Control inputs of inverters under various $q/r$ ratios.
  • Figure 5: Quantitative performance comparison under various $q/r$ ratios.
  • ...and 2 more figures