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Online Event-Triggered Switching for Frequency Control in Power Grids with Variable Inertia

Jie Feng, Wenqi Cui, Jorge Cortés, Yuanyuan Shi

Abstract

The increasing integration of renewable energy resources into power grids has led to time-varying system inertia and consequent degradation in frequency dynamics. A promising solution to alleviate performance degradation is using power electronics interfaced energy resources, such as renewable generators and battery energy storage for primary frequency control, by adjusting their power output set-points in response to frequency deviations. However, designing a frequency controller under time-varying inertia is challenging. Specifically, the stability or optimality of controllers designed for time-invariant systems can be compromised once applied to a time-varying system. We model the frequency dynamics under time-varying inertia as a nonlinear switching system, where the frequency dynamics under each mode are described by the nonlinear swing equations and different modes represent different inertia levels. We identify a key controller structure, named Neural Proportional-Integral (Neural-PI) controller, that guarantees exponential input-to-state stability for each mode. To further improve performance, we present an online event-triggered switching algorithm to select the most suitable controller from a set of Neural-PI controllers, each optimized for specific inertia levels. Simulations on the IEEE 39-bus system validate the effectiveness of the proposed online switching control method with stability guarantees and optimized performance for frequency control under time-varying inertia.

Online Event-Triggered Switching for Frequency Control in Power Grids with Variable Inertia

Abstract

The increasing integration of renewable energy resources into power grids has led to time-varying system inertia and consequent degradation in frequency dynamics. A promising solution to alleviate performance degradation is using power electronics interfaced energy resources, such as renewable generators and battery energy storage for primary frequency control, by adjusting their power output set-points in response to frequency deviations. However, designing a frequency controller under time-varying inertia is challenging. Specifically, the stability or optimality of controllers designed for time-invariant systems can be compromised once applied to a time-varying system. We model the frequency dynamics under time-varying inertia as a nonlinear switching system, where the frequency dynamics under each mode are described by the nonlinear swing equations and different modes represent different inertia levels. We identify a key controller structure, named Neural Proportional-Integral (Neural-PI) controller, that guarantees exponential input-to-state stability for each mode. To further improve performance, we present an online event-triggered switching algorithm to select the most suitable controller from a set of Neural-PI controllers, each optimized for specific inertia levels. Simulations on the IEEE 39-bus system validate the effectiveness of the proposed online switching control method with stability guarantees and optimized performance for frequency control under time-varying inertia.
Paper Structure (27 sections, 6 theorems, 43 equations, 6 figures, 4 tables, 1 algorithm)

This paper contains 27 sections, 6 theorems, 43 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Frequency control under time-invariant inertia
  4. Frequency control under variable inertia
  5. Model and Problem Formulation
  6. Power System Model
  7. Control System Architecture
  8. Problem Formulation
  9. Exponentially Stable Controller Design Under All Modes
  10. Controller Structure
  11. Theoretical Results
  12. Monotone Neural Network
  13. Online Switching Algorithm
  14. Online Event-triggered Switching Algorithm
  15. Stability Guarantees for the Switching System
  16. ...and 12 more sections

Key Result

Theorem 1

Assume $\forall \{i,j\}\!\in\! \mathcal{E}\,\, |\delta_i-\delta_j|<\frac{\pi}{2}$, the power flow equation opt_dyn2 is feasible, and proportional term equals to zero when the frequency deviation is zero, i.e., $\pi(\bm{0}_n)=\bm{0}_n$. Then the equilibrium $(\boldsymbol{\delta}^*,\boldsymbol{\omega} where $\gamma$ is determined by

Figures (6)

  • Figure 1: The proposed online switching control method for frequency control under variable inertia with stability guarantee.
  • Figure 2: Diagram of the control system architecture.
  • Figure 3: Diagram of the Neural-PI controller defined by \ref{['eq:pi_control_nodal']}.
  • Figure 4: Online switching control for frequency control under variable inertia.
  • Figure 5: Structure of RNN for policy optimization.
  • ...and 1 more figures

Theorems & Definitions (12)

  • Definition 1: Exponential Input-to-State Stability (Exp-ISS)
  • Remark 1: Robustness to measurements error, delay, or cyber attacks
  • Remark 2: Comparison to the Neural-PI controller in cui2023structured
  • Theorem 1: Unique Closed-loop Equilibrium
  • Theorem 2: Exp-ISS of Neural-PI Controller for Frequency Control with Time-invariant Inertia
  • Corollary 1
  • Theorem 3: Exp-ISS for the switching system
  • proof
  • Lemma 1: Bounds on Lyapunov Function
  • proof : Proof of Lemma \ref{['lm1']}
  • ...and 2 more