Energy and Buildings 37 (2005) 181–187 State transition probability for the Markov Model dealing with on/off cooling schedule in dwellings Jun Tanimoto ∗ , Aya Hagishima Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-koen, Kasuga-shi, Fukuoka 816-8580, Japan Received 30 November 2002; received in revised form 10 February 2004; accepted 14 February 2004 Abstract We gathered field measurement data on five familial and three single dwellings during summer 2000 by deploying numerous handy type hygrothermal meters with self-recording functions to measure room air, globe and outdoor air temperatures. These measurements led to conclusions on the probability of turning on an air conditioning system versus indoor globe temperature and the ongoing probability of air conditioning versus outdoor temperature. This analysis was transformed into state transition probability functions, i.e. shifting from the off to on state and from the on to off state. Identifying these state transition probability functions is an important first step in applying the Markov Model to on/off state analysis for air conditioning systems, which is one of the significant approaches for dealing with the stochastic thermal load for HVAC system. The obtained state transition probability functions should help immeasurably in determining effective schedules for air conditioning operation from inhabitant occupancy schedules. © 2004 Elsevier B.V. All rights reserved. Keywords: On/off control for air conditioning system; State transition probability; Field measurement; Markov Model 1. Introduction Stochastic approaches have been increasingly regarded as more useful than deterministic building thermal load because they can estimate not only average thermal load but also peak, deviation and other statistical multi-order moments that can provide useful information in the design of HVAC systems. Hokoi et al. [1] and Andersen et al. [2] are exam- ples of stochastic approaches. To design a building thermal system using stochastic procedures inevitably requires the input of meteorological data and various scheduling data including HVAC system in stochastic expressions. Studies such as Remund and Kunz [3] have pointed out how the fun- damental elements such as outdoor air temperature and solar radiation can be depicted in appropriate stochastic expres- sions. However, the stochastic expression of scheduling data has not been paid much attention so far. One of the reasons is the fact that those scheduling data are generally related to inhabitants’ behaviors, which is more difficult to model. Among the studies there is a very admirable attempt by Fritsch et al. [4], to apply the Markov Model to an inhabitant’s behavior in opening or closing a window for ∗ Corresponding author. Tel.: +81-92-583-7600. E-mail addresses: tanimoto@cm.kyushu-u.ac.jp (J. Tanimoto), aya@cm.kyushu-u.ac.jp (A. Hagishima). natural ventilation. Of course, whether inhabitants’ be- haviors can be approximated by the Markov Process or not is a fundamental and substantial problem Their study nonetheless seemed a good place to start. Following their example, we discussed [5–7] whether the scheduling model using Markov Process makes sense from the standpoint of building thermal systems. If a future state of HVAC system operation, namely on or off state, can be described by the present state of HVAC system operation and some addi- tional variables such as a room air temperature and outdoor air temperature for example, you can treat a time series on operation schedule for HVAC system by the Markov Chain. Then, if you can be successful to define the state transition functions between a room air temperature and on state probability in the next time step, for instance, the significant stochastic information on building thermal load can be drawn by means of Monte-Carlo simulation process. In order to confirm both possibility and feasibility from this viewpoint a series of numerical experiments were con- ducted. And then, we concluded that it makes sense and works well if an impediment in identifying the state tran- sition probability functions is cleared This paper exists in this particular context. Herein, we report state transition probability functions derived from field measurement data of an air conditioner being shifted from off to on state and from on to off state. 0378-7788/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.enbuild.2004.02.002