Scalability study for a hierarchical NMPC scheme for resource sharing problems

This paper deals with the computational efficiency evaluation of a hierarchical DMPC (distributed model predictive control) framework for resource sharing problems which has been established in the context of smart district energy management. The provided DMPC framework is based on a dual decomposition of the centralized open-loop controller which is decomposed into several subproblems and one coordinator problem. At coordinator level the bundle method is used in order to recover the globally optimal solution through an iterative process. The main focus of this paper is a detailed discussion of the impact of the bundle method´s parametrization on the computational performance of the whole scheme. Additionally a qualitative comparison with a similar scheme based on primal decomposition is provided and some rules of thumb for determining an effective parametrization of the bundle method are established. In the provided simulations the scheme is applied to a large-scale problem of the smart district context. More precisely the centralized optimization problem of a district composed of 1000 buildings sharing a globally limited power resource can be solved to optimality using our proposed framework in around 3 seconds.