A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

TL;DR

This paper introduces a distributed accelerated gradient algorithm for model predictive control in hydro power valleys, achieving fast convergence and comparable performance to centralized methods in large-scale, nonlinear, and nonsmooth systems.

Contribution

It proposes a novel distributed optimization algorithm based on accelerated gradient methods tailored for complex hydro power valley control problems.

Findings

The algorithm converges at a rate of O(1/k^2).

Distributed approach outperforms centralized solvers like CPLEX in speed.

Performance similar to centralized solutions in simulations.

Abstract

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX.