Unsupervised Learning for Equitable DER Control

TL;DR

The paper tackles equitable, data-driven DER control in distribution networks by learning local equilibrium mappings that approximate OPF solutions in an unsupervised fashion. It introduces equilibrium functions $\boldsymbol{\gamma}$ and $\boldsymbol{\xi}$ that map local voltage and demand measurements to active and reactive injections, and integrates an equity penalty to reduce disparities in curtailment. A stable incremental control scheme is analyzed, with explicit sufficient conditions ensuring global asymptotic stability and a nonincreasing-in-voltages design. Empirical results on the IEEE 37-bus feeder demonstrate voltage stability and improved performance over standard local controllers, while the equity penalty fosters fairer DER participation. This framework offers a scalable, data-driven path to provably stable and fair DER control without requiring centralized optimization or extensive communications.

Abstract

In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.

Figures (5)

• Figure 1: IEEE 37-bus feeder. Red nodes represent buses hosting DERs, black nodes represent loads.
• Figure 2: Learned (a) Volt/Watt and (b) Volt/Var curves for node 25 using 795-th minute-based load and generation profiles with and without equity design.
• Figure 3: Evolution of active and reactive power setpoints under the proposed power update rule \ref{['eq:power_update']} with (a) $\epsilon = 0.1$ and (b) $\epsilon = 1$, where we use the power data profiles of the 1095-th minute and consider 100 iterations.
• Figure 4: Maximum voltage deviation and optimality gap with respect to the OPF solutions along the evolution. The linear control method induces instability between 12:00 and 13:00.
• Figure 5: Comparison of the evolution of curtailment between node 10 and node 25 (a) without and (b) with equity-promoting design and (c) the evolution of the equity cost ($\lambda = 0.0154$).

Theorems & Definitions (3)

• Theorem 4.1
• Proposition 5.1
• proof