# Modeling Heat Consumption of an Office Building During COVID-19 Restrictions
###### Abstract
Unlike now, we used to assume a model containing the set of constraints and the Jacobian matrix configured manually based on a fixed-point iteration approach [19]. [PERSON] et al. [20] studied DH substations equipped with an additional meter to record SH heat demand only. Compared to the present paper, the shared DH substation measurements were used to establish a forecast model for winter, intermediate, and summer seasons. At the same time, the design heat demand is defined according to the equation. Using such an approach extends its applicability. As for the models and methods, [PERSON] et al. [21] studied control point temperature, defined as the last day of the SH season. If the correlation between outdoor temperature and heat demand is known, the regression function can be plotted using the least squares method for two parts of the model. The difference is the focus on control point temperature, which was identified with the help of the piecewise regression method. [PERSON] et al. [22] corroborated this idea; they found that non-negligible temperature drops of flow branches with respect to the outlet power station temperature are detected and low-temperature drops of return branches are observed. Moreover, the same as us, they attributed this to abnormal thermal response (due to the rather slight effect of the energy consumption of a few DH consumers). Based on [23], two possible reasons for high error have already been found: (1) a too-high return temperature after a DHW or SH heat exchanger and (2) a wrong design approach when assessing the surface areas of radiators of an SH system. For a building with a hydronic SH system that prevails in Russia and Europe, with a secondary supply temperature design, the return temperature fails to reach low values. Nevertheless, indoor comfort is maintained. The solution to alleviate low-temperature differences is to check and upgrade the operation of the building's HVAC system and its connected heat demand, as stated in [23]. In [8], all the neighborhood's buildings were aggregated into a single substation, representing the average heat demand of that district. Eventually, their model of a district energy system included only a DH plant and one aggregated district substation. However, such a system will not indicate variations in temperature within supply and return lines. Compared to the present paper, we developed a much more detailed model since the aggregation only excludes abnormal heat demand profiles, increasing accuracy and decreasing the number of heat demand peaks. Our contribution to the pool of knowledge is in analyzing potential savings once a building achieves the maximum energy flexibility potential and answering whether it is worth it for excessive heat to be dumped into the envelopes, increasing thermal inertia further for additional energy storage capacity and O&M savings. The relevance of this research is based on introducing adjustment factors representing the difference between heat consumption profiles before and after COVID-19 restrictions. These factors differ for light, medium, or heavy structures and low- and high-insulation dwellings since not every building can compensate for the heat losses through the envelopes. That significantly limits the recovery of accumulated heat and, thus, the total energy flexibility potential. That means that the novelty is in comparing different building models and substation control logic for the specific application of flexible operation. As highlighted in the literature, the research gaps revolve around the inadequacy of existing models and methodologies in addressing the dynamic and complex factors influencing heat consumption in office buildings, particularly under the evolving conditions induced by COVID-19 restrictions. These gaps are summarized in Table 1.  
For studies explore the performance of real-world HVAC control systems, especially in conjunction with flexible operation strategies like temperature adjustments and thermal inertia.