Modeling building occupants in CEA – Part 2: Stochastic occupant model

This post is part of a series on occupant modeling in CEA. In the previous blog post, we explored the deterministic occupant model in CEA and how the demand patterns for electricity and domestic hot water are defined. At this point, you might have noticed that the deterministic model provides a simplified occupant pattern, whereby every weekday in a given month is the same as the previous one. In real buildings, however, occupants are not that predictable. Gabriel might have a dentist’s appointment and come to the office an hour later one day. Shanshan might have a meeting at noon and go to lunch an hour later than usual. And Zhongming might need to stay in the office a bit later and will go to the gym an hour later than usual. A more realistic occupant model would therefore need to account for these random variations in occupant presence from one day to the next.

The CEA stochastic occupancy model is a simple implementation of the Markov chain model of Page et al. In this model, each building occupant is modeled individually at each time step. Based on the probabilities of an occupant being present at each time of the day discussed in the previous blog post, the probability of an occupant who is absent arriving and the probability of an occupant who is present leaving is calculated at each time step. The occupant’s state (“present” or “absent”) is then assigned randomly based on these probabilities. Thus, the number of occupants for a given building varies for each day of the week, as shown below for the same example used in the blog post about the deterministic model:

In the deterministic model, the electricity demands for appliances and lighting were shown to be dependent only on the corresponding electricity demands. However, it is the building occupants that cause these demands to arise. Hence, in the stochastic model, the demands for appliances are associated to the presence of occupants by simply assuming that the power density discussed previously correlates to the occupant density of each use. For example, according to the CEA database office buildings have a demand for appliances of 7 W/m² and an occupant density of 14 m²/p, so the demand for appliances for office workers is assumed to be 98 W/p (`7 W/m² * 14 m²/p`). Lighting is assumed to be independent of occupant presence for simplicity. The resulting electricity demand patterns again follow occupant presence a lot more closely:

The demands for fresh and domestic hot water are calculated the same way as described in the deterministic model, however since they depend on different occupant presence patterns the demands deviate from the deterministic model’s:

Stochastic_dhw.png

The CEA stochastic occupancy model therefore generates more realistic variations in occupant presence and associates final energy demands to occupants’ presence. However this comes at a computational expense! Running the stochastic model takes significantly longer than the deterministic model in CEA.

We have now seen how CEA can generate more realistic schedules to account for variations in occupant presence at different times of the year for a single building. However, these schedules are still generated from standards, meaning that any building of a given occupancy type will have the same underlying assumption regarding the probability of occupant presence throughout the day. To put it simply: the standards assume any office is the same as any other office. Our team has recently been studying the reliability of these standard schedules and the deviation caused by changing occupant modeling approaches on the simulation results.

In the next post, we will discuss the limitations to existing occupant modeling approaches and present a peek into upcoming features for occupant modeling in CEA.

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