Revisiting Consensus-Based Energy-Management in Smart Grid with Transmission Losses and Directed Communication

TL;DR

This paper critically examines a distributed energy management algorithm in smart grids, identifies logical flaws in prior theorems, and proposes corrections to ensure optimality despite transmission losses and directed communication.

Contribution

It reveals contradictions in existing theorems, demonstrates the algorithm's limitations, and offers a rectified version with valid theoretical guarantees.

Findings

Identified flaws in the original theorems of [1]

Provided a counterexample showing non-optimality

Proposed an adjusted algorithm with correct theoretical proof

Abstract

We discovered a deficiency in Algorithm 1 and Theorem 3 of [1]. The algorithm called CEMA aims to solve an energy management problem distributively. However, by means of a counter example, we show that Theorem 2 and 3 of [1] contradict each other in the case of a valid scenario, proving that the suggested algorithm does not always find the optimum. Furthermore, we provide theoretic results, showing that Theorem 3 of [1] does not hold generally. At last, we provide a rectification by adjusting the algorithm and the corresponding proof of Theorem 3.