An analysis of stochastic properties of the heating load in an intermittently air-conditioned building by optimal control theory

Abstract The correct sizing of an air-conditioning system requires data concerning the maximum heating and/or cooling load. And, in order to reduce operating costs or energy consumption, the system must be operated at or near optimum state keeping the efficiency of the air-conditioning system high. Therefore, both the maximum value and the distribution of the heating load are required for the optimum design of the building and its air-conditioning system. Due to fluctuating conditions and their effects on the heating and cooling load, external climatic conditions are an important consideration in determining the maximum load and the load distribution. In other words, external climate must be regarded as a stochastic time series. In our previous paper, the introduction of a time-variant control concept provided a method to calculate the maximum load and the distribution of the load of the intermittently heated building, and took into account the stochastic nature of the external climate. In this paper, the stochastic characteristics of the load are analysed based on the optimal control theory. Making use of this result and other numerical examples, the influence of the criterion of the optimality is clarified, and the optimal strategy for pre-heating is obtained.