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

• We successfully apply a distributed accelerated gradient algorithm for an MPC problem.
• We deal with a hydro power valley with distributed modeling, control, and estimation.
• We propose a systematic method to decompose a globally coupled cost as 1-norm term.
• The proposed method is distributed, its performance is as good as a centralized one.
• The computation time of the proposed distributed solver is better than commercial ones.

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/k2)O(1/k2), 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.