Online Distributed Optimization in Radial Power Distribution Systems: Closed-Form Expressions

TL;DR

This paper derives closed-form solutions for node-level optimization in online distributed control of radial power systems, significantly reducing computational complexity and enabling faster, more efficient system management.

Contribution

It provides analytical closed-form expressions for node-level optimization, eliminating the need for iterative solvers in distributed control of radial power distribution systems.

Findings

Closed-form solutions reduce computational time.

Elimination of embedded optimization solvers.

Enhanced speed in online distributed control.

Abstract

The limitations of centralized optimization methods in managing power distribution systems operations motivate distributed control and optimization algorithms. However, the existing distributed optimization algorithms are inefficient in managing fast varying phenomena, resulting from highly variable distributed energy resources (DERs). Related online distributed control methods are equally limited in their applications. They require thousands of time-steps to track the network-level optimal solutions, resulting in slow performance. We have previously developed an online distributed controller that leverages the system's radial topology to achieve network-level optimal solutions within a few time steps. However, it requires solving a node-level nonlinear programming problem at each time step. This paper analyzes the solution space for the node-level optimization problem and derives the analytical closed-form solutions for the decision variables. The theoretical analysis of the node-level optimization problem and obtained closed-form optimal solutions eliminate the need for embedded optimization solvers at each distributed agent and significantly reduce the computational time and optimization costs.