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Control and Stability of a Multilevel Power System for a Future Distribution Network

Xian Wu, Jan H. van Schuppen, Hai Xiang Lin

TL;DR

This work tackles stability challenges in future distribution networks with high renewable penetration and low inertia by proposing a six-level multilevel control framework that uses energy storage as buffers. It develops a nonlinear interconnected model for Levels 3–5, analyzes open-loop stability with a Lyapunov function, and designs a distributed LQR controller with bottom-up communication to reduce complexity. The study provides explicit conditions and a performance bound that quantify how far distributed control may be from an optimal centralized controller, highlighting scenarios where distributed performance approaches centralized performance. The framework offers a scalable approach to frequency and voltage regulation in decarbonized distribution networks and paves the way for extensions to time-varying parameters and additional operational constraints.

Abstract

The growing integration of renewable energy sources into distribution networks poses significant challenges to frequency and voltage stability due to their intermittent nature and low-inertia dynamics. This paper proposes a multilevel control framework for a future decarbonized power system, using energy storage systems as power buffers to mitigate frequency and voltage fluctuations. A nonlinear interconnected model is formulated to characterize the complex dynamics across multiple levels of the distribution network. To reduce operational complexity and communication overhead of these dynamics, a distributed linear quadratic regulator control strategy is developed for information exchange in a bottom-up approach, where each level implements local feedback control within a short time horizon. Stability conditions for both open-loop and closed-loop systems are established using Lyapunov-based analysis. In addition, explicit performance bounds are derived to quantify the optimal difference between the proposed distributed strategy and the centralized control method, demonstrating the effectiveness of the proposed framework.

Control and Stability of a Multilevel Power System for a Future Distribution Network

TL;DR

This work tackles stability challenges in future distribution networks with high renewable penetration and low inertia by proposing a six-level multilevel control framework that uses energy storage as buffers. It develops a nonlinear interconnected model for Levels 3–5, analyzes open-loop stability with a Lyapunov function, and designs a distributed LQR controller with bottom-up communication to reduce complexity. The study provides explicit conditions and a performance bound that quantify how far distributed control may be from an optimal centralized controller, highlighting scenarios where distributed performance approaches centralized performance. The framework offers a scalable approach to frequency and voltage regulation in decarbonized distribution networks and paves the way for extensions to time-varying parameters and additional operational constraints.

Abstract

The growing integration of renewable energy sources into distribution networks poses significant challenges to frequency and voltage stability due to their intermittent nature and low-inertia dynamics. This paper proposes a multilevel control framework for a future decarbonized power system, using energy storage systems as power buffers to mitigate frequency and voltage fluctuations. A nonlinear interconnected model is formulated to characterize the complex dynamics across multiple levels of the distribution network. To reduce operational complexity and communication overhead of these dynamics, a distributed linear quadratic regulator control strategy is developed for information exchange in a bottom-up approach, where each level implements local feedback control within a short time horizon. Stability conditions for both open-loop and closed-loop systems are established using Lyapunov-based analysis. In addition, explicit performance bounds are derived to quantify the optimal difference between the proposed distributed strategy and the centralized control method, demonstrating the effectiveness of the proposed framework.
Paper Structure (11 sections, 9 theorems, 69 equations)

This paper contains 11 sections, 9 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Multilevel power system of a distribution network
  4. Power system of Levels 3, 4, and 5
  5. Combined power system of Level 3, 4, and 5
  6. Isolated power systems of Levels 3, 4, and 5
  7. Stability analysis of the open-loop power system
  8. Distributed control structure of the power system
  9. Stability analysis of the closed-loop power system
  10. Performance of closed-loop power system
  11. Conclusion

Key Result

Lemma 5.4

Under Assumption assump:system, the matrix $\bm V_{\theta\theta}$ is positive definite. Therefore, the smallest positive eigenvalue satisfies $\lambda_{\min}(\bm V_{\theta\theta}) > 0$.

Theorems & Definitions (31)

  • Definition 2.2
  • Definition 3.1
  • Definition 4.1
  • Definition 4.2
  • Definition 5.1
  • Definition 5.2
  • Lemma 5.4
  • proof
  • Lemma 5.5
  • proof
  • ...and 21 more