Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Stability-Constrained Learning for Frequency Regulation in Power Grids with Variable Inertia

Jie Feng, Manasa Muralidharan, Rodrigo Henriquez-Auba, Patricia Hidalgo-Gonzalez, Yuanyuan Shi

Abstract

The increasing penetration of converter-based renewable generation has resulted in faster frequency dynamics, and low and variable inertia. As a result, there is a need for frequency control methods that are able to stabilize a disturbance in the power system at timescales comparable to the fast converter dynamics. This paper proposes a combined linear and neural network controller for inverter-based primary frequency control that is stable at time-varying levels of inertia. We model the time-variance in inertia via a switched affine hybrid system model. We derive stability certificates for the proposed controller via a quadratic candidate Lyapunov function. We test the proposed control on a 12-bus 3-area test network, and compare its performance with a base case linear controller, optimized linear controller, and finite-horizon Linear Quadratic Regulator (LQR). Our proposed controller achieves faster mean settling time and over 50% reduction in average control cost across $100$ inertia scenarios compared to the optimized linear controller. Unlike LQR which requires complete knowledge of the inertia trajectories and system dynamics over the entire control time horizon, our proposed controller is real-time tractable, and achieves comparable performance to LQR.

Stability-Constrained Learning for Frequency Regulation in Power Grids with Variable Inertia

Abstract

The increasing penetration of converter-based renewable generation has resulted in faster frequency dynamics, and low and variable inertia. As a result, there is a need for frequency control methods that are able to stabilize a disturbance in the power system at timescales comparable to the fast converter dynamics. This paper proposes a combined linear and neural network controller for inverter-based primary frequency control that is stable at time-varying levels of inertia. We model the time-variance in inertia via a switched affine hybrid system model. We derive stability certificates for the proposed controller via a quadratic candidate Lyapunov function. We test the proposed control on a 12-bus 3-area test network, and compare its performance with a base case linear controller, optimized linear controller, and finite-horizon Linear Quadratic Regulator (LQR). Our proposed controller achieves faster mean settling time and over 50% reduction in average control cost across inertia scenarios compared to the optimized linear controller. Unlike LQR which requires complete knowledge of the inertia trajectories and system dynamics over the entire control time horizon, our proposed controller is real-time tractable, and achieves comparable performance to LQR.
Paper Structure (13 sections, 1 theorem, 18 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 13 sections, 1 theorem, 18 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Model and Problem Formulation
  3. Frequency Dynamics as a Hybrid Switching System
  4. Training Set Generation
  5. Methodology
  6. Candidate Lyapunov Function for the Switched System
  7. Proposed Controller
  8. Stability-Constrained Learning for Frequency Regulation
  9. Simulations
  10. Experimental Setup
  11. Results
  12. Controller Constraints
  13. Conclusion

Key Result

Theorem 1

Consider a controller defined as $u_{\psi}(x) = Kx + \Pi[\pi_{\psi}(x)]$, where $u=Kx$ is a linear controller that can stabilize the switching system eq:freq_dyn, and $\pi_{\psi}(x)$ is a neural network controller parameterized by $\psi$. For all $x \neq 0$, define the projection operation $\Pi[\pi_ where $\epsilon>0$ is a sufficiently small constant. For $x=0$, the projection is $\Pi[\pi_{\psi}(0

Figures (4)

  • Figure 1: The diagram of the proposed controller depicts a combination of a linear controller $Kx(t)$ and a neural network residual $\pi_{\psi}(\cdot)$, constrained to actions that satisfy the Lyapunov stability conditions specified in \ref{['eq:closed-form']}.
  • Figure 2: 230kV/100 MVA Kundur 12-bus 3-area test network with 0.0001 + 0.001 p.u. line impedance.
  • Figure 3: State and control trajectories for LQR, the proposed controller, Linear, and Linear-opt at bus 9 with a zoomed-in view for 0-0.2 s. The background color represents the inertia modes.
  • Figure 4: State and control trajectories of all buses with the proposed controller with a zoomed-in view for 0-0.1 s.

Theorems & Definitions (3)

  • Theorem 1
  • proof
  • Remark 1