# Distributed Algorithm for Economic Dispatch Problem with Separable Losses

## TL;DR

This paper presents a distributed algorithm for solving the economic dispatch problem in power systems, incorporating power losses, using convex relaxation and dual decomposition, with robustness to operational changes.

## Contribution

It introduces a novel distributed algorithm that handles power losses in economic dispatch, without requiring initialization, and analyzes its behavior under infeasible conditions.

## Key findings

- Algorithm effectively solves the non-convex problem via convex relaxation.
- Distributed approach is robust to changing operating conditions.
- Behavior under infeasibility is thoroughly analyzed.

## Abstract

Economic dispatch problem for a networked power system has been considered. The objective is to minimize the total generation cost while meeting the overall supply-demand balance and generation capacity. In particular, a more practical scenario has been studied by considering the power losses. A non-convex optimization problem has been formulated where the non-convexity comes from the nonlinear equality constraint representing the supply-demand balance with the power losses. It is shown that the optimization problem can be solved using convex relaxation and dual decomposition. A simple distributed algorithm is proposed to solve the optimization problem. Specifically, the proposed algorithm does not require any initialization process and hence robust to various changes in operating condition. In addition, the behavior of the proposed algorithm is analyzed when the problem is infeasible.