Learning Provably Stable Local Volt/Var Controllers for Efficient Network Operation

TL;DR

The paper addresses the challenge of achieving stable and efficient voltage regulation in distribution networks with high DER penetration by learning local surrogates of the ORPF solution and embedding them in a provably stable incremental Volt/Var controller. It introduces a two-stage framework: learning equilibrium functions $\{\phi_n\}$ that map local voltages to approximate ORPF reactive injections, and a local control law that drives the system toward these equilibria with guaranteed global stability under a suitable stepsize $\epsilon$. The approach leverages monotone ReLU neural networks to enforce the required properties and uses pseudo data points to extend voltage regulation capabilities beyond nominal ranges. Numerical tests on the IEEE 37-bus feeder demonstrate improved optimality relative to standard and optimized droop controllers, with robustness to modest voltage measurement noise and under time-varying loading conditions. The framework offers a practical, data-driven path to deploy stable, locally computable Volt/Var controls without full-network centralized optimization or persistent communications.

Abstract

This paper develops a data-driven framework to synthesize local Volt/Var control strategies for distributed energy resources (DERs) in power distribution networks (DNs). Aiming to improve DN operational efficiency, as quantified by a generic optimal reactive power flow (ORPF) problem, we propose a two-stage approach. The first stage involves learning the manifold of optimal operating points determined by an ORPF instance. To synthesize local Volt/Var controllers, the learning task is partitioned into learning local surrogates (one per DER) of the optimal manifold with voltage input and reactive power output. Since these surrogates characterize efficient DN operating points, in the second stage, we develop local control schemes that steer the DN to these operating points. We identify the conditions on the surrogates and control parameters to ensure that the locally acting controllers collectively converge, in a global asymptotic sense, to a DN operating point agreeing with the local surrogates. We use neural networks to model the surrogates and enforce the identified conditions in the training phase. AC power flow simulations on the IEEE 37-bus network empirically bolster the theoretical stability guarantees obtained under linearized power flow assumptions. The tests further highlight the optimality improvement compared to prevalent benchmark methods.

Figures (9)

• Figure 1: Flowchart of the proposed data-driven control framework.
• Figure 2: An illustration of the role of the pseudo data points for DER at node $n$. Blue and orange points respectively represent true and pseudo data points, while the dark red curves are instances of learned equilibrium functions. Adding pseudo data points helps the equilibrium functions reach maximum reactive power compensation capability when voltage exceeds the limits.
• Figure 3: The IEEE 37-bus feeder.
• Figure 4: Minute-based data for the total (feeder-wise) solar power generation and active power demand.
• Figure 5: The orange solid and red dashed curves are, respectively, the learned equilibrium functions with and without considering pseudo data points for the DER at node 32. The blue dash-dotted and green dotted curves are, respectively, the optimized linear droop control function HJ-CW-PL-JZ-GS-FD-JW:18 and standard linear droop function GC-RC:17KT-PS-SB-MC:11. The comparison between the orange solid and red dashed curves illustrates the role of pseudo data points in learning equilibrium functions. The former reaches the maximum reactive power compensation capability when the voltage exceeds the limits, whereas the latter does not.

Theorems & Definitions (14)

• Proposition 3.1
• Proposition 3.2
• Remark 3.3
• Remark 3.4
• Proposition 4.1
• Remark 4.2
• Remark 4.3
• Remark 4.4
• Lemma A.1
• Lemma A.2