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Stability Constrained Voltage Control in Distribution Grids with Arbitrary Communication Infrastructure

Zhenyi Yuan, Jie Feng, Yuanyuan Shi, Jorge Cortés

TL;DR

The paper tackles stable Volt/Var control in distribution grids equipped with arbitrary communication by introducing a unified framework that enforces stability by design. It replaces per-bus monotonicity with a network-wide monotonicity constraint and uses input convex neural networks (ICNNs) to realize equilibrium functions that satisfy this constraint under any communication topology. A systematic design procedure partitions the communication graph into subgraphs, trains convex functions on each subgraph, and derives the global equilibrium functions via gradients, enabling supervised learning to mimic OPF solutions while preserving stability. Validation on the UCSD microgrid demonstrates that increased communication improves control performance and brings learned controllers closer to OPF, while maintaining robustness to measurement noise and disturbances.

Abstract

We consider the problem of designing learning-based reactive power controllers that perform voltage regulation in distribution grids while ensuring closed-loop system stability. In contrast to existing methods, where the provably stable controllers are restricted to be decentralized, we propose a unified design framework that enables the controllers to take advantage of an arbitrary communication infrastructure on top of the physical power network. This allows the controllers to incorporate information beyond their local bus, covering existing methods as a special case and leading to less conservative constraints on the controller design. We then provide a design procedure to construct input convex neural network (ICNN) based controllers that satisfy the identified stability constraints by design under arbitrary communication scenarios, and train these controllers using supervised learning. Simulation results on the the University of California, San Diego (UCSD) microgrid testbed illustrate the effectiveness of the framework and highlight the role of communication in improving control performance.

Stability Constrained Voltage Control in Distribution Grids with Arbitrary Communication Infrastructure

TL;DR

The paper tackles stable Volt/Var control in distribution grids equipped with arbitrary communication by introducing a unified framework that enforces stability by design. It replaces per-bus monotonicity with a network-wide monotonicity constraint and uses input convex neural networks (ICNNs) to realize equilibrium functions that satisfy this constraint under any communication topology. A systematic design procedure partitions the communication graph into subgraphs, trains convex functions on each subgraph, and derives the global equilibrium functions via gradients, enabling supervised learning to mimic OPF solutions while preserving stability. Validation on the UCSD microgrid demonstrates that increased communication improves control performance and brings learned controllers closer to OPF, while maintaining robustness to measurement noise and disturbances.

Abstract

We consider the problem of designing learning-based reactive power controllers that perform voltage regulation in distribution grids while ensuring closed-loop system stability. In contrast to existing methods, where the provably stable controllers are restricted to be decentralized, we propose a unified design framework that enables the controllers to take advantage of an arbitrary communication infrastructure on top of the physical power network. This allows the controllers to incorporate information beyond their local bus, covering existing methods as a special case and leading to less conservative constraints on the controller design. We then provide a design procedure to construct input convex neural network (ICNN) based controllers that satisfy the identified stability constraints by design under arbitrary communication scenarios, and train these controllers using supervised learning. Simulation results on the the University of California, San Diego (UCSD) microgrid testbed illustrate the effectiveness of the framework and highlight the role of communication in improving control performance.

Paper Structure

This paper contains 16 sections, 4 theorems, 33 equations, 8 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Distribution Grid Modeling
  4. Communication Network
  5. Problem Formulation
  6. Unified Stability Conditions on Volt/Var Controllers
  7. Existence and Uniqueness of the Equilibrium
  8. Global Asymptotic Stability of the Equilibrium
  9. The Case When Only a Subset of Buses Are Controllable
  10. Learning Stable Voltage Controllers under Arbitrary Communication Infrastructures
  11. Simulations
  12. UCSD Microgrid Testbed and the Dataset
  13. Controller and Training Setups
  14. Simulation Results
  15. Discussion
  16. ...and 1 more sections

Key Result

Proposition 3.2

(Existence and uniqueness of the equilibrium): Consider the closed-loop system eq:sys_dyn. If $\boldsymbol{\phi}$ is a monotonically decreasing function w.r.t. $\mathbf{v}$, i.e., or equivalently, holds $\forall~\mathbf{v},\mathbf{v}^\prime \in \mathbb{R}^{N}$, then eq:sys_dyn admits a unique equilibrium.

Figures (8)

  • Figure 1: Road map of the development of Volt/Var control methods with stability guarantees. The green nodes represent controllable DERs in the DG.
  • Figure 2: Examples of different communication infrastructure in DGs. Note that the difference between (b) and (c) is that the former is connected and the latter is not.
  • Figure 3: Illustration of the proposed design procedure to compute equilibrium functions under the distributed communication infrastructure example in Fig. \ref{['fig:communication_setups_distributed']}.
  • Figure 4: Reduced-order model of the UCSD microgrid testbed with 13 PV generators equipped with voltage controllers located at nodes $\mathcal{C} = \{14,15,17,19,20,27,29,30,32,34,38,39,41\}$.
  • Figure 5: The load and generation curves across the UCSD microgrid on February 2, 2020 (Sunday).
  • ...and 3 more figures

Theorems & Definitions (10)

  • Remark 3.1
  • Proposition 3.2
  • proof
  • Theorem 3.3
  • proof
  • Remark 3.4
  • Proposition 3.5
  • proof
  • Proposition 4.1
  • proof