# An Incentive-Based Online Optimization Framework for Distribution Grids

## TL;DR

This paper introduces an online distributed optimization framework for distribution grids with DERs, enabling real-time voltage regulation and economic optimization amid dynamic conditions.

## Contribution

It develops a novel online algorithm that tracks time-varying solutions for social-welfare maximization in distribution grids with real-time incentives.

## Key findings

- Algorithm effectively tracks solutions under changing conditions.
- Voltage constraints are maintained within prescribed limits.
- The approach is both theoretically stable and practically effective.

## Abstract

This paper formulates a time-varying social-welfare maximization problem for distribution grids with distributed energy resources (DERs) and develops online distributed algorithms to identify (and track) its solutions. In the considered setting, network operator and DER-owners pursue given operational and economic objectives, while concurrently ensuring that voltages are within prescribed limits. The proposed algorithm affords an online implementation to enable tracking of the solutions in the presence of time-varying operational conditions and changing optimization objectives. It involves a strategy where the network operator collects voltage measurements throughout the feeder to build incentive signals for the DER-owners in real time; DERs then adjust the generated/consumed powers in order to avoid the violation of the voltage constraints while maximizing given objectives. The stability of the proposed schemes is analytically established and numerically corroborated.