# Modeling Heat Consumption of an Office Building During COVID-19 Restrictions
## 2 Materials and Methods  
Our analysis focuses on evaluating the heat consumption of an office building using a quantitative methodology. The primary method employed is based on the heating degree day (HDD) concept, which calculates heating demand by comparing the outdoor temperature to a baseline indoor temperature, typically 18 \({}^{\circ}\)C for office settings. To regulate the secondary supply and return temperatures of the heating system, the analysis uses a method that adjusts these temperatures based on the current level of heat consumption relative to the design demand. This adjustment incorporates factors such as the convective heat transfer rate and the ratio of design to actual heat demand. The daily heat demand is calculated by summing overall heat losses, internal heat gains from occupancy, and solar heat gains while also considering the thermal inertia of the building. Heat losses are estimated through design heat losses via building envelopes and additional losses due to feedback mechanisms caused by indoor temperature fluctuations. These feedback losses are approximated using empirical formulas that account for ventilation rates, infiltration, air properties, and temperature variations. Heat gains from internal sources are determined based on occupancy and specific internal heat generation rates. Solar heat gains are computed considering the glazing area and solar radiation intensity, oriented by cardinal directions. Several adjustment factors refine the analysis, including those for thermal inertia (considering radiator adjustments and setback schedules), wind influence (accounting for direction and speed), and operational patterns like night or day temperature setbacks. Due to the computational complexity of modeling detailed feedback losses, the paper employs simplified empirical formulas for practicality. This approach allows for reasonable estimations without requiring extensive numerical simulations. Finally, the methodology integrates elements from existing practices such as the Dwelling Energy Assessment Procedure (DEAP). It enhances them by including building-specific and dynamic factors, making the approach suitable for analyzing heat consumption in the context of changing operational conditions such as those seen post COVID-19. The first step is usual and is based on the HDD method [24]:  
\[HDD=(t_{in}-t_{out,a})\cdot z. \tag{1}\]  
Here, \(\mathrm{t_{out,a}}\) and \(\mathrm{z}\) are the daily average outdoor temperature [\({}^{\circ}\)C] and its duration [h], respectively; \(\mathrm{t_{in}}\) is design (minimal allowed) indoor temperature in an office [\({}^{\circ}\)C], typically 18 \({}^{\circ}\)C.  
As the authors solve the problem of heat consumption of an existing building, the traditional method for regulating secondary supply temperature is applied [24]:  
\[\mathrm{t_{1 TP}}=t_{in}+0.5\Big{(}\mathrm{t_{1}^{p}-t_{2}^{p}}\Big{)}\frac{ \overline{\mathrm{Q}}}{K}+\left(\frac{t_{1}^{p}+t_{2}^{p}}{2}-t_{in}\right) \left(\frac{\overline{\mathrm{Q}}}{K}\right)^{\frac{1}{1+m}}, \tag{2}\]  
\[t_{2 TP}=t_{1 TP}-\left(t_{1}^{p}-t_{2}^{p}\right)\frac{\overline{\mathrm{Q}}} {K}. \tag{3}\]Here, t\({}_{\rm{ITP}}\) and t\({}_{\rm{2 TP}}\) are secondary supply and return temperatures for each value of outdoor temperature (current), respectively [\({}^{\circ}\)C]. \(\overline{Q}\): the relative value of the current level of heat consumption (Equation (4));  
t\({}_{\rm{I}}\)P, t\({}_{\rm{2}}\)P: design secondary supply and return temperatures, respectively [\({}^{\circ}\)C];  
m: factor to account for the fact that convective heat transfer from a radiator depends on supply temperature, typically m = 0.25;  
K: ratio between the design heat demand and its actual annual average value.