The energy transition, from a centralized to a decentralized and sustainable power supply using small scale power plants, presents new challenges to the distribution grid provider who is responsible for maintaining the stability of the electricity network. New procedures to ensure the overall network stability need to be developed, which are flexible with respect to the underlying network and scalable, to be able to handle the amount of data of a fast growing network of renewable energy producers.
To this end, we examine model predictive control (MPC) and hierarchical distributed optimization algorithms. In particular, we use a network of residential energy systems (RESs), connected to a grid provider through a point of common coupling, where every resident is equipped with solar photovoltaic panels and local storage devices to examine three different hierarchical distributed optimization algorithms. The flexibility of the algorithms allows for a plug and play manner of implementation. Scalability is obtained by solving the optimization problems on the level of the RESs and not on the level of the grid provider. Furthermore, with respect to a specific centralized optimization problem, convergence of the distributed optimization algorithms to the central optimum can be proven. The performance of the distributed optimization algorithms and the corresponding MPC schemes are illustrated using a dataset on power generation and power consumption of residential customers of the company Ausgrid.