*3.1. Building Stock Modelling (BSM)*

Energy Performance Certificates (EPC) assess the energy efficiency of a building and include information about recommended improvements [27] showing the current and potential energy rating of a property named as Standard Assessment Procedure (SAP). The overall EPC rating is comprised of walls, roof, floor, windows, hot water, lighting and heating efficiencies, and has 7 bands ranging from A to G with a certain amount of SAP points out of 100 points as a maximum [27].

EPCs provided by Scottish Government Statistics [28] have been used to explore Orkney housing stock in terms of archetype, age and efficiency. Orkney has 11,228 dwellings and the majority of them are detached houses with 59.8% of the total followed by semidetached, terraced, and flats with 22.1%, 11.1%, and 6.9%. The EPC dataset has 1740 dwellings representing 15% of the total housing stock but the share of detached houses in this dataset is around 75% which is greater than real data. The EPC dataset has been used for archetype characteristics and specifications.

Some elements of the EPC calculated by SAP are directly linked to the heating demand such as walls, roof, floor, and windows efficiencies. Therefore, these categories are investigated to understand the heat loss condition in the housing stock. The dataset has five efficiency categories as 'very poor', 'poor', 'average', 'good', and 'very good'. These categories are represented with numeric values (1, 2, 3, 4, and 5 respectively) to calculate the average efficiency score of the construction element and the overall efficiency score of the housing stock.

The average efficiencies of individual construction elements (walls, roof, floor, and windows) are calculated and illustrated in three categories based on their scores (1.0–3.5, 3.5–4.5, 4.5–5.0) to represent 'unrefurbished', 'refurbished', and 'new building' categories used in energy modelling. However, the impact of individual construction elements varies in different archetypes and building specifications. Therefore, while calculating the overall efficiency score of the house, the weight of the construction element has been altered as in the following equation:

$$E\_{\text{overall}} = (E\_{\text{wall}} \times \mathcal{W}\_{\text{wall}}) + (E\_{\text{window}} \times \mathcal{W}\_{\text{window}}) + (E\_{\text{roof}} \times \mathcal{W}\_{\text{roof}}) + (E\_{f\text{lvar}} \times \mathcal{W}\_{f\text{lvar}}) \tag{1}$$

where *E* refers to efficiency and *W* is the weight of the construction element in different house archetypes which is calculated in the energy model and illustrated in Section 4.1.
