*2.5. Simulations*

The final energy consumption simulation for space heating and DHW preparation in apartments was carried out for various variants of the use of premises (simulations 0–4), as follows:

• Simulation 0: The results show the actual final energy consumption for space heating and DHW preparation during the research period (14 January to 9 March 2020). The results of this simulation correspond to the apartment use conditions (see Table 3) and weather conditions observed during the tests.


#### *2.6. Methods of Energy Performance Gap Calculation*

The energy performance gap is determined by the di fference between the measured and calculated heating energy consumption in a given period. In this paper, the *EPG* indicator is defined at several levels.

*EPGh*<sup>+</sup>*w*(<sup>0</sup>→<sup>3</sup>) in Equation (1) describes the gap between the measurement results (simulation 0) and engineering calculations (simulation 3) of total final energy consumption for space heating and DHW preparation (*h* + *w*). This indicator includes all factors that a ffect the size of the energy gap.

$$EPG\_{h+w(0\to3)} = \frac{q\_{h,0} + q\_{w,0} - \left(q\_{h,3} + q\_{w,3}\right)}{q\_{h,3} + q\_{w,3}}\tag{1}$$

*EPGh*(<sup>0</sup>→<sup>3</sup>) in Equation (2) describes the gap between the measurement results (simulation 0) and engineering calculations (simulation 3) of final energy consumption for space heating (*h*).

$$EPG\_{h(0\to 3)} = \frac{\left(q\_{h,0} - q\_{h,3}\right)}{q\_{h,3}}\tag{2}$$

*EPGw*(<sup>0</sup>→<sup>3</sup>) in Equation (3) describes the gap between the measurement results (simulation 0) and engineering calculations (simulation 3) of final energy consumption for DHW preparation ( *w*).

$$EPG\_{w(0\to3)} = \frac{(q\_{w,0} - q\_{w,3})}{q\_{w,3}} \tag{3}$$

*EPGh*(<sup>1</sup>→<sup>3</sup>) in Equation (4) describes the gap between the results of simulation 1 and engineering calculations (simulation 3) of final energy consumption for space heating (*h*). This indicator determines

the energy gap between engineering calculations and the simulation of the proper use of the apartment in the observed meteorological conditions.

$$EPG\_{h(1\to 3)} = \frac{\left(q\_{h,1} - q\_{h,3}\right)}{q\_{h,3}}\tag{4}$$

*EPGw*(<sup>1</sup>→<sup>3</sup>) in Equation (5) describes the gap between the results of simulation 1 and engineering calculations (simulation 3) of final energy consumption for DHW preparation (*w*). This indicator determines the energy gap between engineering calculations and the simulation of the proper domestic hot water consumption.

$$\text{LEPG}\_{\text{w}(1\to 3)} = \frac{(q\_{\text{w},1} - q\_{\text{w},3})}{q\_{\text{w},3}} \tag{5}$$

*EPGh*(<sup>2</sup>→<sup>3</sup>) in Equation (6) describes the gap between the results of simulation 2 and engineering calculations (simulation 3) of final energy consumption for space heating (*h*). This indicator determines the energy gap between engineering calculations and the simulation of the proper use of the apartment for the meteorological conditions corresponding to the data used in engineering calculations.

$$EPG\_{h(2\to 3)} = \frac{\left(q\_{h,2} - q\_{h,3}\right)}{q\_{h,3}}\tag{6}$$

*EPGh*(<sup>4</sup>→<sup>3</sup>) in Equation (7) describes the gap between the results of simulation 4 and engineering calculations (simulation 3). This indicator can be understood as the energy gap resulting from the difference in the meteorological conditions used for the calculations.

$$EPG\_{\rm h(4\to 3)} = \frac{\left(q\_{\rm h,4} - q\_{\rm h,3}\right)}{q\_{\rm h,3}}\tag{7}$$

*EPGw*(<sup>2</sup>→<sup>3</sup>) and *EPGw*(<sup>4</sup>→<sup>3</sup>) have not been defined, because, in these cases, the use of the DHW system (the consumption of domestic hot water) in apartments does not change, and the influence of the ambient temperature on energy consumption for DHW preparation is not included in the calculations.

#### **3. Results and Discussion**

#### *3.1. Final Energy Use: Measurement vs. Calculation*

The actual unit consumption of final energy for space heating and DHW preparation and the demand calculated according to the assumptions of simulation 3 (engineering calculations) are shown in Figure 4. The results for individual apartments are very different. These differences were expected due to the location of the apartment in the building and its insulation. For example, apartments A10, A12, A14, A15 are in a good technical condition and have lower than other average heat transfer coefficient (Table 1), so their unit energy demand should be the lowest. Despite this, the lowest values are observed in A5–A9, and the most significant differences between energy consumption compared to expectations are in A1–A10. The reasons for such unlike energy consumption compared to expectations are very low temperature of indoor air in the premises, insufficient ventilation, and/or the influence of the environment, i.e., the flow of thermal energy from zones adjacent to the apartment. Little insulation of interior walls causes intensive heat exchange between zones in the building. In the case of A9 these zones are exceptionally warm (for example the temperature in the staircase adjacent to apartment A9 exceeded 22 ◦C), so its unit energy demand is low. The opposite effect was observed in apartment A1, where the adjacent spaces are extremely underheated. This shows how important it is to analyze in detail the temperature of adjacent spaces, such as staircases, basements, and attics. These are important elements that influence the energy gap, which are discussed in detail later in the paper.

**Figure 4.** Final energy for space heating and domestic hot water (DHW) production: measurement vs. calculation.

### *3.2. Energy Performance Gap*

The results of energy performance gap (EPG) calculations for different levels of analysis are presented in Table 4.

**Table 4.** Energy performance gap for different levels of analysis.


The energy gap for space heating and DHW preparation between measurement and engineering calculation results (*EPGh*<sup>+</sup>*w*(<sup>0</sup>→<sup>3</sup>)) is significant and is shown in Figure 5. Apartments A1–A4 are heated with solid fuel. In this case, the energy gap is −0.55 on average (excluding A1, for which the EPG value is positive at 0.3). A5–A7 are heated with electricity and are characterized by an energy gap of −0.7 on average. A8–A11 are heated with district heat and are characterized by a slightly smaller energy gap of −0.49 on average. A11–A15, for which the energy gap is the smallest at −0.2 on average, are heated with natural gas. There are different reasons for the discrepancy between the energy gap calculated for space heating and DHW preparation. A detailed analysis of this problem was performed and described below.

In Table 4 an expected energy gap between measurement and engineering calculations, due to significant differences in ambient temperature (see Figure 2), is presented (*EPGh*(<sup>4</sup>→<sup>3</sup>)). These values range from −0.31 to −0.39. Comparing the results of *EPGh*(<sup>4</sup>→<sup>3</sup>) and *EPGh*(<sup>0</sup>→<sup>3</sup>), Table 4, by extending the analysis with the actual parameters of the use of the premises, most of the apartments (A2–A11) have a greater negative EPG, which means that they actually consume less energy than expected. Several apartments (A1, A12–A14) have higher values, i.e., they consume more energy than calculated.

**Figure 5.** Energy performance gap for heating and DHW preparation.

To understand the causes of this condition, it is necessary to examine residents' behavior. The indoor temperature and the ventilation level in many apartments differ significantly from the norm. If they were correct, the energy performance gap would be smaller. This situation is marked and calculated as (*EPGh*(<sup>1</sup>→<sup>3</sup>)) and presented in Figure 6. It is worth noting that the difference in EPG values calculated for the real (*EPGh*(<sup>0</sup>→<sup>3</sup>)) and proper (*EPGh*(<sup>1</sup>→<sup>3</sup>)) operation is the highest for apartments A2–A8 and A11. These are heated with solid fuel and electricity, and two with district heat. The differences are significant and mostly cannot be classified as positively understood energy saving. In many apartments, the effect of energy poverty is noticeable, as manifested by extreme underheating and/or insufficient ventilation. In some premises heated with solid fuel (A2, A4), energy saving may be additionally forced by difficulty with operating the system, and not by energy poverty. In only one case, A11, the energy saving effect was not forced by the financial situation and technical problems.

**Figure 6.** Energy performance gap for space heating.

Figure 6 also shows the value of the energy performance gap between the results of simulations 2 and 3 (*EPGh*(<sup>2</sup>→<sup>3</sup>)). Despite the fact that both simulations were performed with the same meteorological conditions, the EPG value in many cases does not approach 0. The obtained values are both strongly positive (1.12 for apartment A1) and negative (−0.28 for A10). These values illustrate the e ffects of imprecise assumptions regarding ventilation of rooms, internal heat gains, and temperatures in internal zones surrounding the apartment on the calculations. The latter especially contributes to significant di fferences between actual consumption, both positive and negative, and expected values, which is most noticeable in A1, A2, and A5, which are in buildings in very serious technical condition. Extremely underheated spaces and empty premises surrounding these flats increase their actual energy consumption.

The results of EPG calculations related to DHW preparation are shown in Figure 7. The discrepancies between measurement and calculation are significant (see *EPGw*(<sup>0</sup>→<sup>3</sup>)). As with space heating, in some cases they are not dictated by typical user behavior, but by energy poverty and technical limitations (e.g., lack of bathrooms). This is the case of apartments A5, A7, A8, and A9. The EPG values calculated for the situation where all inhabitants consume similar amounts of DHW (the average of the measurements) are also significant (*EPGw*(<sup>1</sup>→<sup>3</sup>)). This means that methods of estimating DHW consumption, at least in the case of Poland, require many studies, such as those shown in [34]. It is necessary to clarify the calculation methods because the current ones do not meet expectations. In pre-war tenement houses, due to their significant energy consumption related to space heating, this problem may not be very important, but in new buildings, the EPG related to DHW preparation systems may have a significant impact on the assessment of the entire facility.

**Figure 7.** Energy performance gap for DHW production.
