Extended Mathematical Derivations: Decentralized Model-free Loss Minimization in Distribution Grids with the Use of Inverters

TL;DR

This paper presents communication-free, model-free algorithms for loss minimization in distribution grids using inverters, proven to reduce losses without prior network information or communication, relying solely on local measurements.

Contribution

It introduces novel decentralized algorithms for loss minimization in distribution grids that operate without communication or prior network data.

Findings

Algorithms effectively reduce grid losses

No prior network information needed

Operate solely on local measurements

Abstract

This document contains extended mathematical derivations for the communication-free and model-free algorithms that can actively control converter-connected devices, and can operate either as stand-alone or in combination with centralized optimization algorithms. We address the problem of loss minimization in distribution grids, and we analytically prove that our proposed algorithms reduce the total grid losses without any prior information about the network, requiring no communication, and based only on local measurements.