## 2 Method
### Local Sensitivity Analysis--OAT  
Local sensitivity analysis in this paper refers to a one-at-a-time (OAT) variation of input parameters. Having the baseline as a starting point, each input value is varied consecutively, while the remaining parameters are kept constant. The OAT analysis is performed twofold, distinguishing between variations of boundary conditions (see Section 2.1.1) and building-specific model inputs (see Section 2.1.2). The baseline represents a multi-family building owned by a social housing association. Ergo, respecting the DS/EN 15459-1:2017 [9] guidelines for such building type means applying a decreasing real DR for a 50-year calculation period. As previously pointed out, PD for energy costs has been considered in the respective models. However, to assess their direct effect on the output, PD for electricity and DH are variated in addition to DR type and calculation period. First, the three different DR types described in Section 2.1.1 are applied in turn to the baseline. For each of the DR types, the calculation is performed for a range of calculation periods from 10 to 60 years with a 10-year step interval. In addition, price development for electricity and district heating are applied individually and in combination for each DR type and calculation period. OAT analysis for DR types and specific PD were applied only to the baseline model that utilizes district heating as the main supply for heating and DHW. This was performed to quantify the difference between applied DR, PD, and for variation of calculation period. Given that the building is owned by a social-housing association and provided that for this type of client (public), one must follow the Ministry of Finance [32], the DR can be considered a deterministic model input. This is because the discount rate is determined by the standard, meaning that a designer is obligated to apply a specific value. Boundary conditions are thus variated by OAT only, with the purpose of quantifying possible output variation for the different DR types, price developments, and calculation periods. The second step in the OAT approach consists of variating model input parameters related to the specific building renovation. In this case, this entails the input parameters that make up the baseline. Two variations for each parameter are performed--one with the lower and one with the upper value of uncertainty, defined in Table 1.  
Evidently, the ranges for different parameters in Table 1 are obtained from different sources. Costs related to energy supply and renewable systems are obtained by the two Technology Data Catalogues (TDC) published by the Danish Energy Agency (DEA) [34; 35]. Costs related to renovation works and energy efficiency improvements originate from the MOLIO database [36], whereas the applied ranges are assumed due to a lack of a better source. Lastly, the cost for the operation of the building stems from the DEA's historical energy price database from 2018 [33]. The unit cost for energy types used in the baseline and variation ranges applied in the OAT calculations are determined as follows:  
* District heating (DH)--the unit price for district heating is available for 392 DH plants across Denmark. There is great variation in the cost of delivered heat across Denmark. Therefore, cost data in [38] are given as annual values for 2018--found in the 392 different DH plants and not as historical values--for electricity and gas. The average price for 2018 from the different stations is 525 DKK/MWh and varies significantly from one DH plant to the next (\(\pm\)135 DKK/kWh). The range for OAT calculations is determined by the minimum and maximum value, accessible in the database. * Electricity--the unit cost of electricity is a quite complex and uncertain parameter. The final unit cost depends on the \"raw\" energy price and several other factors influencing the price. Some of the main factors are governmental fees and taxes, provider subscription expenses, network maintenance, and fees.