Recovery and Occupancy Period Point Temperature
The economic interest of intermittent heating systems in intermittently-occupied buildings (e.g. schools, office buildings) is no longer in doubt. Nevertheless, optimal energy consumption requires that the heating restart time be defined with great precision. In many cases, for fear of ill evaluation, the lowering of the temperature during non-occupancy period is minimal, which leads to reductions in energy savings.
The aim of this article is to compare the precisions of the different methods for calculating heating restart times, and to study their impacts on comfort and on energy consumption. Several classical methods are studied. For example, the method where the system is restarted at a fixed time and the methods for which the recovery duration is analytically calculated according to internal and/or external temperatures. We also propose two new methods. The first of these determines the duration of the recovery period according to the external and internal temperatures, by means of fuzzy logic. The second is based on the use of a two time-constant building model. Apart from the presentation of these two new methods, the originality of the study is that it carries out the comparison using a heating law, during occupancy periods, adapted to intermittent heating.
An intermittent heating controller allows the internal temperature to be lowered during non-occupancy periods, while maintaining the desired temperature during occupancy periods. The different phases of heating are as follows:-
• upper control during occupancy period. The internal air temperature Ta must be maintained at the upper set-point temperature Tu by means of the heating law.
• minimum power: switching-off of heating at the end of the occupancy period.
• lower control during the non-occupancy period if the internal temperature reaches the lower set-point temperature Tl. The lower set-point temperature avoids the risk of condensation or frost.
• recovery at maximum power, so as to reach the upper set-point temperature Tu from the beginning of the following occupancy period. Restart time is optimized by the controller.
As far as restart optimization is concerned, the controller estimates at each time step, throughout the non-occupancy period, the recovery duration, Dur, which corresponds to the duration needed to reach the upper set-point temperature. When this period is equal to the period remaining until the next occupancy-period, the heating is restarted automatically. If the recovery period continues into the occupancy period, the comfort of the occupants is not ensured. On the contrary, if the start-up is anticipated, there will be a corresponding loss of energy. It is therefore necessary that duration, Dur, calculated before the restart, should correspond as closely as possible to the real recovery duration, Durr, which is observed a posteriori.
The simplest solution consists in determining a fixed duration, by distinguishing Monday from the other days of the week. This solution may be adequate as far as regulations are concerned, but it is imprecise because no account is taken of the climatic conditions.
Seem et al. has shown that the duration of the recovery period depends essentially on the internal temperature at the beginning of the recovery period. But, when recovery time is long, climatic factors are more important and it is thus necessary to take the external temperature into account.
The use of a building model within the controller allows us to evaluate the duration of the recovery period. The precision is of course dependent on that of the model. Different types of models are possible. For example, Visier et al. consider a physical model for optimal control. A neural network is used by Glorennec to model the coupling of a building and an underfloor-heating system. Finally Botte considers an Armax type model.
In this article, we will use a two time-constant building model. This model has the double advantage of being both simple and sufficiently accurate to correctly estimate recovery duration.
Fuzzy logic is based on the theory of fuzzy subsets, first introduced in 1965 by Professor Zadeh of the University of California. In this theory, an element belonging to a set (a fuzzy subset) is between 0 and 1. It is not equal to either 1 or 0 as is the case in classical logic.
Fig. 2 presents a breakdown of the Te discourse universe into three fuzzy subsets: Low, Medium and High (two trapezes and one triangle). When variable Te is equal to 2°C, the degree of membership to each of these fuzzy substets is respectively 0.8, 0.2 and 0.
The controller developed in this study allows us to define different optimization laws in order to compare them.
The classical law determines the supply power in relation to the external temperature so as to compensate for the building’s steady-state thermal losses. Thus it is not entirely suitable for intermittent heating since the energy consumption needs are greater on Monday morning after a weekend set-back, than for other days of the week. This is why we use a surface heating law, based at once on Te, and on a State variable, which takes into account the thermal state of the building.
We considered six cases corresponding to different methods of optimization. The duration of the recovery period Dur can be calculated either directly from internal and/or external temperatures (cases 1 to 5), or indirectly, repeatedly by means of a building model (case 6). The various cases studied are based on classical analytical functions, with the exception of case 5 which is based on fuzzy logic. Cases 5 and 6 constitute new methods of determining heating-restart times.
A learning mechanism based on the recursive least squares routine automatically modifies the three parameters defining each of the two laws. The use of a recursive method, as opposed to a direct method, avoids stocking too great a number of parameters in the controller.
Tags: occupancy period
