*3.1. Lighting Analysis*

The results of the electrical lighting consumption are shown in Figure 5. On the one hand, the vectorial analysis by means of box plots is shown in the first row. It can be seen that, after the refurbishment, the lighting demands of the building decreased and became more homogeneous on all floors. This is demonstrated in Table 2, where the change is quantified, and the statistical tests used (ANOVA and Kruskal) corroborate the change. In this case, the floor with the highest reduction was the third floor (2004 W less) and the floor with the lowest reduction was the second floor (489 W less). On the other hand, in the second row of Figure 5, the functional analysis, through the daily curve graph, is presented. In this case, thanks to this approach, it can be seen that, despite the decrease in the consumption, the retrofitting hardly affects the daily behaviour of the lighting consumption. As it is observable in Figure 5 that the curves have very similar shapes, with the exception on the third floor where a change in the lighting schedule was implemented. Table 2 presents the FANOVA results. The similarity of the samples is rejected on every floor. However, the impact varies among floors, as shown in Table 2. The first floor was the most benefited (2032 W less per minute on average) and the third floor the least benefited (400 W less per minute on average). The differences between the two analyses, in absolute terms, have been noticed: with the vectorial analysis the third floor obtained the highest reduction, while with functional analysis it obtained the lowest reduction. As shown in the second row of Figure 5, on the third floor, the reduction was concentrated on the last hours of the day; however, on average during the day, this reduction was lower. The vectorial approach does not take this fact into account because it distorts the sample with the calculation of daily averages.

**Figure 5.** Analysis of the electrical lighting consumption on each floor measured in W. In the first row, the vectorial results (in form of box plots) are presented. In the second row, instead, the functional data are represented with the respective mean functions. The data are divided into winter days before and after the refurbishment.

**Table 2.** Numerical results on each floor for lighting consumption. The vectorial results are presented with Dv measuring the difference between medians. The functional results, accompanied with the average minute difference (Dfunc), the L2(*l*) distance between the mean functions (Ddist) and the smoothing adjustment (R2), are also presented. For both analyses, the change in the variability of the data ( Var) and the electrical savings are displayed. Lastly, the *p*-values for the tests, both vectorial and functional, are displayed in this table.


On the other hand, the effects of the refurbishment on the illuminance conditions were studied. Figure 6 shows the analysis for the illuminance levels. Through vectorial analysis, an impact is also detected, but is different on each floor. In general, the illuminance level was improved. Table 3 indicates that the floors with the biggest increase in illuminance were the first and third floors (356 lx and 414 lx more, respectively). Ground floor was the only one with an illuminance reduction from this point of view (270 lx less). In this case, this reduction is related to the shading that was installed to have a better protection against natural light (see Table 3). Furthermore, observing the functional illuminance curves floor by floor shown in the second row of Figure 6, the conclusion is the same: there was also an improvement in the illuminance levels, and the biggest increase of illuminance took place on the first and third floors. From this point of view, Table 3 shows that the increments were about 174 lx on the first floor and 204 lx on the third floor, on average, every minute. Once again, FDA makes it possible to see that the behaviour of the illuminance was maintained on all floors. As shown in Table 3, FDA detects that the illuminance changes on the second floor, while the vectorial approach fails in this detection (the *p*-values obtained are bigger than 0.05).

**Figure 6.** Analysis of the illuminance on each floor measured in lx. In the first row, the vectorial results (in form of box plots) are presented. In the second row, instead, the functional data represented with the respective mean functions. The data are divided into winter days before and after the refurbishment.

**Table 3.** Numerical results on each floor for illuminance. The vectorial results are presented with Dvec measuring the difference between medians. The functional results, accompanied with the average minute difference (Dfunc), the L2(*l*) distance between the mean functions (Ddist) and the smoothing adjustment (R2), are also presented. For both analyses, the change in the variability of the data is displayed (Var). Lastly, the *p*-values for the tests, both vectorial and functional, are displayed in this table.


Analysing the graphs shown in Figures 5 and 6, it can be seen that the retrofitting reduced the electrical consumption of lighting while the illuminance levels were improved or maintained in proper levels. The level of illuminance on the first and third floors was improved mainly due to the replacement by LED technology, as shown in Figure 6 and Table 3. In the case of the second floor, although it obtained an average reduction of 435 W, the illuminance level was maintained according to European illuminance regulations. This regulation states that the optimal lighting level in offices is 500 lx, a level already reached before the renovation. In the case of the ground floor, as mentioned above, it had to be analysed individually. The mean function of illuminance before retrofitting on this floor had peaks above 1500 lx (see Figure 6), which indicates a high influence of natural light. After the retrofitting, the shading that was installed to protect from sunlight achieved a reduction, on average, of 286 lx each minute, as it can be seen in Table 3 (266 lx, observing the vectorial results). Furthermore, the electrical consumption associated to lighting on the ground floor is also reduced. Table 2 shows that the vectorial reduction was 587 W, and the functional reduction 609 W, on average, every minute.

Generally, monitored lighting consumption data after retrofitting have less dispersion (see Var in Table 2). This means that the monitored lighting data are more homogeneous. In this case, the reduction of the data variability reaches values higher than 30% from both methods. However, the functional analysis detects an increase of 17% in the data dispersion of the third floor, as shown in Table 2. The functional graph of this floor in Figure 5 supports this result. The vectorial approach, which summarises the days with the mean, distorts the results by considering false conclusions such as, in this case, that the data variance decreased for all floors (see Table 2). On the other hand, the homogeneity of the monitored illuminance data after the renovation is different depending on the floor. Table 3 shows that the floors where the data dispersion was reduced are the ground and the second floors.

From an energetic point of view, the relative electrical consumption savings after retrofitting are also calculated. Table 2 shows that savings of more than 18% were obtained on every floor with the functional analysis and more than 24% with the vectorial analysis. The first floor is the most benefited floor with savings around 73% from the two approaches applied. However, there are differences between the results of the vectorial analysis and the functional analysis. This is shown in Figures 5 and 6 and, specifically, in Table 2 where the savings are presented. The savings calculation of functional analysis are more accurate because it is based on the areas under the curves representing the mean functions, taking into account the entire daily behaviour. The vectorial results, instead, only quantify the differences between the medians of the samples.
