## 3 Methodology
### Annual Energy Consumption and CO\({}_{2}\) Emissions  
The total annual energy consumption per property was calculated which included all items contained within the SAP model, _i.e._, Primary space and water heating, secondary resistive heating (e.g., fan heater), central heating pumps, lights and appliances. Total annual CO\({}_{2}\) emissions per property were calculated using the total energy consumption and the CO\({}_{2}\) emissions intensity values of the national electricity and gas grids [24], also shown in Table 2. It should be noted that the projected electricity grid emission factor for 2030, though consistent with UK Government projections, is subject to considerable uncertainty given possible future scenarios relating to political, social and techno-economic factors [25]. Importantly, these include risks and uncertainties related to the development of the UK's proposed fleet of new nuclear generation facilities.  
\begin{table}
\begin{tabular}{l c} \hline
**Energy Source** & **Emissions Factor (kg CO\({}_{2}\) per kWh)** \\ \hline Electricity Grid—Present & 0.55 \\ Mains Gas Grid—Present & 0.19 \\ LPG—Present & 0.21 \\ Oil—Present & 0.27 \\ Electricity Grid—2030 & 0.05 \\ \hline \end{tabular}
\end{table}
Table 2: Energy source emissions factors.  
Figure 3: Gas boiler MC performance input distribution.  
Figure 2: Heat pumps Monte Carlo (MC) performance input distribution.  
Probability and cumulative distributions of total annual property energy consumption and CO\({}_{2}\) emissions were produced in order to illustrate how heat pump technologies performed when compared with traditional gas boiler central heating and electrical resistive heating. A cumulative distribution was also produced to illustrate the performance that could be expected of the majority of properties.  
In order to ascertain how the variability of performance of heat pumps may affect emissions with penetration levels of 55% and 75% (equivalent to 12.1 million and 16.5 million installations respectively) and the planned decarbonisation of the electricity grid, the mean energy consumption for the 16,000 EHCS properties was extrapolated to cover the entire English housing stock of 22 million properties. By 2030 it is expected that the English housing stock will have grown to 27 million properties; however with the forthcoming tightening of building regulations in 2016 [26], the extra 5 million properties are assumed to be zero carbon, _i.e._, no CO\({}_{2}\) emissions [27]. As a result of this assumption, all the comparison scenarios consider the 22 million properties in the current housing stock only and then project their emissions performance to 2030.  
A baseline measure was used that represents the current housing stock; based upon the EHCS (16,000 properties), there is broadly a split of 85% gas central heating and 15% non-central resistive electric heating [12,28], along with other heating types such as oil or LPG boilers and district heating. However, these are of a sufficiently small penetration (<3%) to be disregarded in this case. Furthermore, the total average heating efficiency across the housing stock is cited as being 74% [28], which is broadly consistent with the current UK gas boiler efficiency benchmark, and the emission factors for LPG and oil (the other non-gas grid yet centrally heated heating sources), Table 2, are close to that for natural gas.