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Asymmetry of Frequency Distribution in Power Systems: Sources, Estimation, Impact and Control

Taulant Kerci, Federico Milano

TL;DR

This work investigates the emergence of asymmetry in the frequency probability distribution (FPD) of inverter-dominated power systems, linking skewness to nonlinearities from network losses and wind-based primary frequency control. It introduces a nonlinear compensation strategy and a simple, robust metric based on left/right standard deviations of the FPD to quantify asymmetry, validated with real-world Irish and Australian data and IEEE 9-bus simulations. Real-system results show that narrow deadbands for wind PFC increase asymmetry and frequency-trajectory skew, while automatic generation control (AGC) mitigates it; the proposed nonlinear deadband compensation substantially reduces asymmetry in simulated and case-study scenarios. The findings have direct implications for frequency quality and resilience in high-renewable grids and offer practical guidance for TSOs on control design and assessment methodologies.

Abstract

This paper analyses an emerging real-world phenomena in inverter-based renewable-dominated power systems, namely, asymmetry of frequency distribution. The paper first provides a rationale on why asymmetry reduces the "quality" of the frequency control and system operation. Then it provides qualitative theoretical insights that explain asymmetry in terms of the nonlinearity of real-world power systems and associated models. In particular network losses and pitch angle-based frequency control of wind power plants are discussed. Then the paper proposes a nonlinear compensation control to reduce the asymmetry as well as a statistical metric based on the frequency probability distribution to quantify the level of asymmetry in a power system. Real-world data obtained from the Irish and Australian transmission systems serve to support the theoretical appraisal, whereas simulations based on an IEEE benchmark system show the effectiveness of the proposed nonlinear compensation. The case study also shows that, while automatic generation control reduces asymmetry, frequency control limits and droop-based frequency support provided by wind generation using a tight deadband of 15 mHz, namely active power control, leads to a significant increase in the asymmetry of the frequency probability distribution.

Asymmetry of Frequency Distribution in Power Systems: Sources, Estimation, Impact and Control

TL;DR

This work investigates the emergence of asymmetry in the frequency probability distribution (FPD) of inverter-dominated power systems, linking skewness to nonlinearities from network losses and wind-based primary frequency control. It introduces a nonlinear compensation strategy and a simple, robust metric based on left/right standard deviations of the FPD to quantify asymmetry, validated with real-world Irish and Australian data and IEEE 9-bus simulations. Real-system results show that narrow deadbands for wind PFC increase asymmetry and frequency-trajectory skew, while automatic generation control (AGC) mitigates it; the proposed nonlinear deadband compensation substantially reduces asymmetry in simulated and case-study scenarios. The findings have direct implications for frequency quality and resilience in high-renewable grids and offer practical guidance for TSOs on control design and assessment methodologies.

Abstract

This paper analyses an emerging real-world phenomena in inverter-based renewable-dominated power systems, namely, asymmetry of frequency distribution. The paper first provides a rationale on why asymmetry reduces the "quality" of the frequency control and system operation. Then it provides qualitative theoretical insights that explain asymmetry in terms of the nonlinearity of real-world power systems and associated models. In particular network losses and pitch angle-based frequency control of wind power plants are discussed. Then the paper proposes a nonlinear compensation control to reduce the asymmetry as well as a statistical metric based on the frequency probability distribution to quantify the level of asymmetry in a power system. Real-world data obtained from the Irish and Australian transmission systems serve to support the theoretical appraisal, whereas simulations based on an IEEE benchmark system show the effectiveness of the proposed nonlinear compensation. The case study also shows that, while automatic generation control reduces asymmetry, frequency control limits and droop-based frequency support provided by wind generation using a tight deadband of 15 mHz, namely active power control, leads to a significant increase in the asymmetry of the frequency probability distribution.
Paper Structure (15 sections, 28 equations, 6 figures, 6 tables)

This paper contains 15 sections, 28 equations, 6 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Qualitative Appraisal of Asymmetry
  3. Probability Distribution of System Variables
  4. Asymmetry due to Network Losses
  5. Asymmetry due to Wind Frequency Control
  6. Asymmetry due to Regulator Hard Limits
  7. Compensation of Asymmetry through Control
  8. Metrics
  9. Asymmetry in Real-World Power Systems
  10. Real-World Data from the Irish Grid
  11. Real-World Data from the Australian Grid
  12. Case Study
  13. Power Systems with Conventional Generation
  14. Power Systems with Non-Synchronous Generation
  15. Conclusions

Figures (6)

  • Figure 1: One-machine one-load system.
  • Figure 2: Proposed nonlinear compensation for turbine governors of synchronous machines.
  • Figure 3: FPD of the Irish power system with and without APC.
  • Figure 4: FPD of the Australian (mainland) power system for 2023 and 2019 years.
  • Figure 5: PD of: (a) Scenario 4, conventional power systems; (b) Scenario 5, high losses; (c) Scenario 9, APC On and no wind ramps; and (d) Scenario 10, APC On and wind ramps.
  • ...and 1 more figures