# Modeling Heat Consumption of an Office Building During COVID-19 Restrictions
## 2 Materials and Methods
The relative value of the current level of heat consumption varies between 0 and 1, according to Equation (4) [24]:  
\[\overline{Q}=Q_{c}/Q_{d}=\left(t_{in}-t_{out}\right)/\left(t_{in}-t_{out}{}^{ d}\right). \tag{4}\]  
Here, t\({}_{\rm{out}}\) is the current outdoor temperature [\({}^{\circ}\)C];  
t\({}_{\rm{out}}\)d: design outdoor temperature (DOT) [\({}^{\circ}\)C];  
Q\({}_{c}\): current level of heat consumption [kW];  
Q\({}_{d}\): design heat demand for DOT [kW]. An equation with adjusting factors is applied to assess the daily average SH demand of the office building described above [24]:  
\[\mathrm{Q}_{\rm{SH}}^{\rm{an}}=\left[\mathrm{Q}_{\rm{hl}}^{\rm{an}}-\left( \mathrm{Q}_{\rm{int}}^{\rm{an}}+\mathrm{Q}_{\rm{ins}}^{\rm{an}}\right)\
u\xi \right]\beta\mu. \tag{5}\]  
Here, Q\({}_{\rm{hl}}\)an overall heat losses [kWh];  
Q\({}_{\rm{int}}\)an: internal heat gains [kWh];  
Q\({}_{\rm{ln}}\)an: heat gains due to solar irradiation [kWh];  
v: a factor to take thermal inertia into account, which is calculated as [24]  
\[\
u=0.7+0.000025(HDD-1000). \tag{6}\]  
Here, \(\xi\), is the factor that takes into account the number of radiators equipped with TRVs:  
* \(\xi=1.0\), i.e., 100% of radiators are equipped, and their flow rate is adjusted with the help of a TRV;
* \(\xi=0.95\), ditto, 90-99%;
* \(\xi=0.9\), ditto, 80-89%;
* \(\xi=0.85\), ditto, 70-89%;
* \(\xi=0.7\), ditto, 60-69%;
* \(\xi=0.5\), ditto, 59% or less. \(\beta\): shutdown factor:  
* \(\beta=1.13\) for a 6-8-h long night setback;
* \(\beta=1.11\), 3-6-h long day setback;
* \(\beta=1.07\), 3-4-h long night setback;
* \(\beta=1.05\), in case of a day or night setback lasting less than 3 h.  
\(\mu\): factor representing wind influence:  
* \(\mu=1.1\), if the wind direction predicted (recorded) is opposite compared to the design one;
* \(\mu=1.15\) if the wind speed expected (recorded) is 2 or more times stronger than the design one. To compare, in [PERSON] et al. [2], this daily heat demand was assumed to remain fixed throughout the year as heat consumption for DHW was declared to be a social heat load rather than a physical energy demand. The determination of the overall heat losses [kWh] for the outlined problem is quite a challenging task [24]:  
\[Q_{\text{{d}it}}^{an}=Q_{\text{{d}os}}^{an}+Q_{\text{{d}it}}^{an}, \tag{7}\]  
Here, \(Q_{\text{{d}os}}^{an}\) is the design heat loss through the envelopes (Equation (8)) [kWh];  
\(Q_{\text{{d}it}}^{an}\): additional heat losses/savings due to indoor temperature feedback [kWh]. The design heat losses through the envelopes [kWh] [24]:  
\[Q_{\text{{d}os}}^{an}=24\cdot 10^{-3}\cdot U\cdot HDD\cdot A_{\text{{e}nv}}, \tag{8}\]  
Here, U is the overall heat transfer coefficient [W/m\({}^{2}\)\({}^{\circ}\)C], calculated as [24]:  
\[U=n\frac{(A_{\text{{u}ull}}/R_{\text{{u}ull}}+A_{\text{{u}win}}/R_{\text{{u} win}}+A_{\text{{d}door}}/R_{\text{{d}oor}}+A_{\text{{d}att}}/R_{\text{{d}att}}+A_{ \text{{d}bs}}/R_{\text{{d}bs}})}{A_{\text{env}}}, \tag{9}\]  
Here, \(A_{\text{{u}ull}}\) and \(R_{\text{{u}ull}}\) are for envelopes: surface area [m\({}^{2}\)] and thermal resistance [m\({}^{2}\)\({}^{\circ}\)C/W], respectively;  
\(A_{\text{{u}win}}\), \(R_{\text{{win}}}\): ditto, for glazing;  
\(A_{\text{{d}door}}\), \(R_{\text{{d}oor}}\): ditto, for doors and gates;  
\(A_{\text{{u}att}}\), \(R_{\text{{u}att}}\): ditto, for an attic (if any);  
\(A_{\text{{d}bs}}\), \(R_{\text{{d}bs}}\): ditto, for a ground floor (basement);  
\(A_{\text{env}}\): overall area of envelopes [m\({}^{2}\)];  
n: factor representing thermal inertia:  
* for a light structure building n = 1;
* for a medium structure building, n = 0.9;
* for a heavy structure one [24]:  
\[\text{n}=(t_{in}-t_{out})/\left(t_{in}-t_{out}^{d}\right). \tag{10}\]  
Here, \(t_{\text{{d}adj}}\) is the indoor temperature within an adjoining space [\({}^{\circ}\)C]. The adjoining spaces for the second floor are the first and third ones; for the top floor, an attic and the second-to-last floor; for the first floor, a basement or a ground floor; and so on.