3.1.1. The Energy Performance of the Facility

Regarding the energy performance, the swimming facility at Jøa was identified as having an energy performance indicator (EPI) of 44.8 kWh/visitor, calculated over the period of the investigated dataset presented in Figure 4. In comparison, Norwegian swimming facilities are associated with an average EPI for a typical year of approximately 26 kWh/visitor,and a median EPI of approximately 22 kWh/visitor, where the dispersion is reported to range from 10 to 80 kWh/visitor [51]. The EPI has been recommended by Kampel [7] who found that visitors are the single variable that explains most of the variation in the energy performance of swimming facilities [35]. The poor EPI-value of the swimming facility at Jøa can be explained by the low user intensity, on average only 235 visitor/month, compared to Kampel's dataset representing a median annual user intensity of 94,261 visitors (average of 7855 visitors per month). Additionally, the outdoor climate can explain this performance indicator since the data are not climate corrected.

**Figure 4.** Energy usage for operation of the swimming facility vs. the outdoor temperature, both daily averaged.

#### 3.1.2. Energy Distribution

The delivered energy to the swimming facility is almost evenly divided between electricity and thermal energy. Figure 5 depicts the energy distribution of the building section with the swimming pool. The low thermal energy consumption for the air handling unit (AHU) in comparison with the thermal load of the pool circuit has two major causes. The low overall user intensity for the period of collected data implies that the system operates in air recycling mode (night mode) without fresh air supply for a long period of time, which reduces the air dehumidification and heating demands considerably. Another reason is the operation of the heat recovery system which recovers the latent heat in the exhaust air and supplies heat to the facility, where the order of priority is air heating and pool heating. The building automation system neither collects data regarding the performance of the subsystems nor the thermal efficiency of the heat recovery system.

#### 3.1.3. Time Step Analysis

When treating time series data of energy use in buildings with linear regression, the inertia of the building must be considered due to this impact on the autoregressive process of the variables. This is because the energy use (the dependent variable) is logged with a short time step (1 min). For the swimming pool at Jøa, this impact is partly illustrated using a duration curve depicted in Figure 6, where the data are sorted by decreasing power consumption. The range of outdoor temperatures associated with each step of power demand is wide and can be partly explained by inertia of the building. A short time step

resolution will not give any significant correlation, since the process depicted is not steady state. The impact of the time lag can be minimized by averaging the dataset, and thereby reducing the time step resolution (see Section 2.5.2).

**Figure 5.** Energy distribution for the swimming facility incl. the energy use for domestic hot water heating.

**Figure 6.** Scatter plot—sorted power consumption presented as a duration curve along with the corresponding outdoor temperature.

Figure 7 illustrates the consequences of averaging the dataset and reducing the time step resolution. The figure presents the dataset with time steps ranging from 1 min to 4 weeks. Both the power consumption and outdoor temperature are presented as timeaveraged values centered in time. Firstly, the figure gives an indication of two possible different states in the operation of the facility, represented as a pattern of a divided dataset (clouds of datapoints), for time-step resolution from 1 min up to 60 min. The same can be observed in Figure 6, which represents a pattern of two different duration curves overlapping. Secondly, without considering the significance of the simple linear regressions, a considerable increase in the coefficient of determination, the *R*2, is observed when averaging the dataset. This implies that the time step should be maximized in order to

obtain the best fitting model if prediction is the main purpose. Concerning the purpose of this study, the time step should correspond to the swimming facility operating staff's requirement to identify and handle possible operational disturbances during a reasonable period of time.
