Optimal control of heating in a two-zone building using price decomposition-coordination method

To avoid electricity peak loads in winter buildings can be pre-heated during off-peak hours using their thermal mass. A way to guarantee comfort levels while deferring electricity consumption is to solve an Optimal Control Problem (OCP) which consists in finding the heating power profile minimising the heating bill over a time horizon. An OCP continuous-time resolution method was tested at monozone buildings scale [1]. The originality of this paper is to extend this continuous resolution method to a two-zone scale. This is a first step toward multi-zone buildings control. At multi-zone scale, three resolution approaches are possible. The first is the centralised method which consists in solving a unique global OCP. However centralised approach is not suitable for large scale systems due to high computational time or a lack of modularity. At the opposite, the decentralised approach which consists in solving local OCPs at each zone scale is the most used approach nowadays. However, this approach neglects couplings between zones as thermal couplings (type 1) or energy sharing (type 2). The third approach is the decomposition-coordination one which consists in solving local OCPs at each zone scale (decomposition stage) and reintegrate neglected couplings by an iterative procedure (coordination stage). This paper deals with couplings of type 1. The decomposition-coordination method which appeared to be more appropriated was price decomposition-coordination method. It was tested and compared to the optimal reference obtained with the centralised approach in a two-zone building with residential and tertiary zones. The centralised and the decomposition-coordination methods results are close. Both methods leaded to more than 20 % of savings on the global energy bill. The computational time was heavier with the decomposition-coordination method than with the centralised methods. However, in future work concerning multi-zone building, decomposition-coordination method is expected to be more beneficial