Each building is unique, not just in terms of the physical construction and location, but also in its occupancy and use. This model follows the approach of segmenting the stock into building archetypes. Once building archetypes are defined, a transient thermal simulation is developed to calculate the hourly heat demand using historical weather data. The advantages of using a custom a thermal model for simulating buildings is that it allows the efficacy of interventions such as altering insulation to be evaluated and enables the use of custom weather data to simulate heat demand. While individual building will be simulated, results will be stored at an aggregated level (LSOA or MSOA) and diversity is achieved by statistically varying occupancy.
2.1. Domestic Archetype Segmentation
Most domestic archetypes used in modelling studies in the UK have extensively drawn on the English Housing Survey [
65]. The EHS splits domestic buildings into seven archetypes: end and mid terrace, semi-detached, detached, bungalow, converted flat, and purpose built flat. The ONS data per LSOA reports on dwelling types as detached, semi-detached, terraced, purpose built flat, converted flat, and others such as bungalow or caravan. The ONS categories do not directly correspond to the EHS ones.
This model combines end terrace and mid terrace to correspond to the ONS reporting. While the ONS reports on purpose built and converted flats, converted flats have wide variety in form and the construction information in the available literature is largely for purpose-built flats. Therefore, all flat varieties will be treated as purpose-built flats. The same archetype segmentation has also been used in other studies [
33,
66]. The observed distribution of the used dwelling types is shown in
Figure 1.
Each dwelling category is further split according to construction period. The VOA reports dwelling age in 12 build periods, from pre-1900 to post-2010, corresponding roughly to a decade in length while the EHS splits this into five build periods from pre-1919 to post-1990. The proportion of dwellings per age range has been applied to each dwelling type present in the LSOA. While it is likely that different dwelling types are built in different periods, the age variation per dwelling type is estimated from the overall distribution per LSOA as the data is provided per LSOA without further breakdown of age per dwelling type. This may be an issue with LSOA’s that have a diverse range of dwelling types and construction periods but in many smaller LSOA’s the construction type and age fall within a narrow range [
67]. The distribution of dwelling build-period is shown in
Figure 2.
The SAP assessment has 11 age bands that are often combined. Oikonomou et al. [
33] use five age bands with multiple variations, reducing these to the 15 most commonly found in their modelled area. Mata et al. [
58] combine six dwelling types with eight narrow and recent age bands, Cheng and Steemers [
27] use ten age bands that become progressively narrower while Buttita et al. [
69] use the EHS age bands but combine two of the periods.
Table 2 summarises the archetypes used in other studies.
2.2. Domestic Archetype Characterisation
The form and fabric data for each archetype is used to estimate a specific heat loss (SHL) and thermal mass (ThM) from construction and fabric assumption per archetype. Dwelling archetype geometry will be taken directly from the English Housing Survey [
70]. The specific heat loss will largely be derived from construction data from BREDEM 2012 [
15] and glazing ratio and performance data are taken from the BRE’s SAP 2016 [
71]. The thermal mass represents the heat capacity of a building or its ability to store heat. Construction and fabric play a large role in the thermal mass as do the internals of a dwelling. SAP gives thermal mass with a thermal mass parameter per unit floor area. It has three categories of light, medium, and heavy construction ranging from 100 to 450 kJ/m
2K. The TMP used are adapted from Stamp [
66] who provides estimates for the building archetypes used here and shows that older constructions tend to be heavier while newer constructions utilise modern lightweight construction methods and so have a lower TMP.
The power rating and efficiency of the heating system varies greatly between dwellings, and the power capacity determines to a large extent how it is operated. For the purposes of calibrating the heat load with gas consumption data, it is assumed that all buildings have a gas boiler with an average efficiency of 85% for heating and 75% for hot water [
71,
72]. The power ratings of the heating system per archetype are assumed from a conservative calculation of gas boiler power ratings using the domestic heating sizing method CE54 [
73].
Table 3 summarises the data sources drawn upon for domestic archetype parameters and
Table A1 in
Appendix A contains all the estimates and parameters used for domestic archetype characterisation.
Domestic Occupancy
Mean occupancy has been adapted from the SAP methodology based on floor area [
71]. Measured hourly gas consumption profiles have been used as a proxy for active occupancy profile and heating system operation for all dwelling archetypes. Average domestic heat load profiles in UK households exhibit a double peak pattern, with morning and evening peaks. From surveys on how dwellings are heated with various heating systems including gas boilers and heat pumps, it appears that dwellings are predominantly heating this way regardless of heating system and mixed work patterns [
37,
74,
75]. Yao and Steemers [
34] showed that the load profile is same across dwelling types, with the magnitude of peaks corresponding to the size of dwelling archetype. A normalised domestic load profile has been adapted from Wang et al. [
76] to represent the probability of active occupancy and operation of heating as shown in
Figure 3.
2.3. Nondomestic Archetype Segmentation
The nondomestic archetypes are based on the CaRB2 activity classifications which expand on the four VOA bulk classes: retail, office, industry, warehouse [
38,
59]. The primary source of data for nondomestic counts and floorspace as previously discussed is the VOA taxation database. The available data from CaRB2 contains activity classification and aggregated floor area per postcode which were combined to LSOA level by matching postcodes to output area without detail on activity type (due to data protection). While floor area has made available, this data is deemed inaccurate due to the method of taxation data collection where some classes (such as schools, hotels, and hospitals) do not have floor area records [
77]. The CaRB2 activity classifications, count and floor areas are shown in
Figure 4. For the purpose of urban load modelling, the five most important categories are office and shops (retail), followed by factories, warehouse, and hospitality. It was not possible to obtain localised Scottish nondomestic figures as the VOA database covers only England and Wales. Instead the overall count of each archetype in Scotland was scaled to each IZ using annual gas consumption data [
63].
After filtering the data for only those in urban area, several categories were omitted or combined. These categories and relative proportions in modelled urban areas is shown in
Figure 5.
Figure 6 shows the classification share for Scotland.
2.4. Nondomestic Archetype Characterisation
The occupancy and use of nondomestic buildings shows a large variation even within the same classification and there can be many different sizes and floor plans [
78]. While classifications such as “offices” or “education” are generally occupied during normal working hours, the occupancy and usage can often vary with occupancy in the evenings and weekends.
The archetypes were adapted from analysis of the CaRB2 data by Barrett [
79]. The mean floor areas for each category were calculated from the total gross internal area and archetype form was inferred from prior surveys of the nondomestic building stock [
80,
81,
82]. A medium-weight construction TMP of 250 kJ/m
2K was applied to all archetypes to derive a thermal mass. Benchmark guidelines were followed for the sizing of the heating system and determining internal heat gains in the various archetype activity classifications [
83,
84]. Where data and benchmarks for the archetype were not found, the figures were estimated from other archetypes.
Nondomestic internal gains are estimated from benchmark figures from CIBSE [
84] Guide A. Offices and schools are well represented in other literature [
85,
86], but where the archetype data is unavailable, such as the case for industrial buildings, this has been estimated based on CIBSE Guide A. A summary of the nondomestic archetype parameters is shown in
Table A2.
Nondomestic Occupancy
Building occupancy and use was determined mainly from analysis of hourly gas consumption data for 37 buildings provided by Sustainable Energy Limited [
87]. Normalised profiles were extracted for each activity class available in the dataset as shown in
Figure A2 and
Figure A3. This was further supplemented through secondary studies on occupancy in offices, shops, health and educational buildings but for non-UK based buildings [
88,
89]. There are three categories where there is a lack of available data on occupancy: factory, warehouse, and transport. Factories and warehouses constitute 19% of the modelled stock and both are very diverse in their activity types. The factory classification can range from a food processing factory to newspaper print works while it is unclear to what extent warehouses are heated due the large floor area they occupy. Transport buildings are similarly diverse, from a train station to a petrol station. A 24-hour occupancy with higher daytime usage has been estimated for these categories as in shown in
Figure A1.
2.5. Spatial Disaggregation
The highest level of spatial disaggregation is to the LSOA level. All GB domestic stock has been mapped to this spatial resolution. While the nondomestic activity classifications in the CaRB2 database were available per postcode in England and Wales, these were also mapped to the LSOA level. In Scotland, nondomestic stock counts were only available at the national aggregated scale, these were distributed per MSOA, weighted by MSOA nondomestic gas consumption.
Due to computing capacity and storage limitations, only selected MSOAs have been modelled. The gas demand per square kilometer has been estimated per MSOA using Standard Area Measurements, then ranked by gas consumption density. The top 20% cumulatively were chosen as representative of urban heat demand. A further 10% of largest absolute gas consumption were included to include a more representative consumption profile to scale to national level. The results for each LSOA and MSOA are stored in a table within an SQL database. Each hour or row of data contains roughly 1600 bytes of data. Six years of results for 10,226 individual LSOAs and MSOAs results in just over 40 GB of stored results.
Weather Data
Weather data is divided into GB regions (the highest tier of sub-national division). Weather stations were selected per region based on proximity to population centers and completeness of data, covering at least the period 2010–2016. The regional stations from which data is drawn upon is shown in
Table 4.
Met office data was compiled ensuring that each station has been active since at least the beginning of 2010. Missing temperature (wet bulb) values were linearly interpolated unless large gaps of more than 12 h were found. Missing wind speeds were forward filled for a maximum of 2 h, otherwise they were interpolated to the next available wind value unless large gaps of more than 12 h were found. Missing solar observation data was first linearly interpolated if less than three consecutive hours were missing, otherwise values were shifted from the previous 24 h unless large gaps of more than 24 h were found. In cases where large sections of data were missing these were filled using data from the closes available weather station.
2.6. Thermal Model Development
Thermal simulations of the building stock are conducted on a per LSOA bases, applying the compiled data on the numbers of each domestic and nondomestic archetype to the LSOA. Each building is assigned a set-point temperature, T
set, which is normally distributed about a mean of 20 °C with limits of 15–25 °C based on reported domestic set-point temperatures [
90]. There is also evidence that nondomestic archetypes such as offices and schools fall within this range albeit skewed to the higher limit [
85,
86].
The simulation procedure calculates the temperature change of the building thermal mass per hourly time step. The thermal model simplifies the representation of the buildings as cuboids with heat transfer through four walls and assumes the temperature of the building thermal mass and internal wall surface to be same as the internal air temperature, Tint. The net heat flows from the buildings are the sum of gains and losses and calculated dynamically to update the temperature of the thermal mass.
The ambient temperature, T
amb, is given by the hourly weather data. To calculate conduction through the wall, we first need to estimate the external wall temperature from convective heat transfer to the air. Calculating wind induced convection is complicated due to geometry, orientation, and other factors such as roughness and protection from surroundings such as trees or larger buildings. Heat transfer theory suggests a power law model for heat loss from an object but a linear form has been found to fit the data well in the ranges often experienced by dwellings (although this may not hold for very tall tower blocks) [
91]. A linear form equation to estimate the wind convection coefficient for each surface, h
c,s, with wind speed, v
w, has been suggested [
92]. With the assumption that wind forced convection acts on one side only, the convection transfer is given by Equation (2), setting v
w = 0 in Equation (1) for the remaining surfaces:
Conduction heat transfer through each surface, Q
cond,s, can be calculated from:
Under the assumption of steady-state, conduction through each wall is equal to the convection from the wall, Qconv,s = Qcond,s. Using Equations (2) and (3) we can estimate Text for each wall and from this, Qcond,s through each wall.
Infiltration is based on the air changes per hour, ach, and building volume, V
b:
Domestic internal gains, Q
gain, are estimated from the mean hourly occupancy, P
h, and floor area, A
f assuming 54 W per person, 0.1 W/m
2 for lighting and small appliances, 105 W per dwelling for large appliances (e.g., fridges) [
93].
Nondomestic internal gains are calculated from the intensity factors in
Table A2 multiplied by normalised occupancy in
Figure A1 and
Figure A2. The sum of the heat transfers, Q
tot, can now be calculated from:
The internal temperature change, ∆T
int, is then updated by:
For a large set of buildings, the CIBSE [
94] code of practice for heat networks suggests the use of an 80% diversity factor for peak space heat load. This diversity factor is multiplied by the normalised occupancy profile value to give the hourly probability of heating system operation and determined randomly for each building.
If internal temperature is lower than setpoint temperature and the building is actively occupied, then the heat demand is the heat required to raise the temperature of the thermal mass to the setpoint temperature up to the power capacity of the heating system. If heat is supplied to the building, then internal temperature is updated using Equation (8).
Hot Water Demand
There have been a range of models produced to calculate hot water demand, mostly for domestic buildings [
95]. These have generally been compiled from high resolution sampling of water consumption and are suitable to apply in an individual building analysis such as the BREDEM estimation of hot water. The building model presented here does not have sufficient detail to calculate high resolution hot water demand per building. As we are not concerned with the heat performance of an individual building but a demand at an aggregated level, it is thus appropriate here to simplify the approach to hot water demand.
The average hot water consumption in UK dwelling is reported between 3–5 kWh per day [
96,
97]. The heat network code of practice [
94] states that the Danish standard DS439 for peak domestic hot water demand is widely used in the design of district heating in the UK. The peak hot water value, Q
hw,max (kW), for N
b number of domestic buildings has been estimated from the Danish standard DS439.
The peak heat load is then applied to a daily load profile. The daily domestic water load profiles have been adapted from a study for DEFRA [
96] and a design guide for hot water in district heating networks [
98]. From the literature a weekday, Saturday and Sunday load profile are given as well as a weekday/weekend variation factor,
fh, shown in
Figure 7. There were minor differences between the Saturday and Sunday load profile but an average of the two is used as a weekend load profile and the adjustment factor was applied to the weekend profile. A further adjustment,
fm, given in
Table 5. for the monthly or seasonal variation is applied as per Burzynski et al. [
99] which is based on BREDEM. Aggregated hourly domestic hot water demand can then be estimated from Equation (10).
Nondomestic hot water (and other low temperature heat) demand is more challenging, especially given the lack of absolute consumption and measured demand profiles. Fuentes et al. [
95] reviewed hot water load profiles in various building uses which showed a pattern that largely corresponded to occupancy.
BEIS [
100] has published estimates of nondomestic hot water energy consumption based on their Building Energy Efficiency Survey [
39]. The nondomestic hot water energy consumption in the UK was estimated to be around 14,900 GWh in 2015 and comprises 8% of the national nondomestic gas consumption. Compared to heating, hot water consumption has less variation between years, so the 2015 numbers were assumed to be representative of all years. Given that hot water account for 10% of nondomestic heat demand and around 3% of overall space and hot water heat demand in the UK. Further, it is unclear how the activity classifications produce hot water. In the case of larger hospitality buildings for example, it is possible that hot water is constantly produced and used in short term storage tanks. Given this, a simplified approach of assuming 8% of nondomestic gas consumption is for hot water, produced by gas boilers (at 75% efficiency) distributed evenly over all hours and it is assumed that large hot water production has been from gas.
2.7. Model Calibration
The annual domestic heat demand is then compared and calibrated to domestic LSOA gas consumption for LSOAs that had at least 50% of dwellings connected to the gas grid using an average boiler efficiency of 85% [
72]. An assumption is made that the dwellings connected to the gas grid are evenly distributed per dwelling type. This may not necessarily hold true in all areas; for example, all flats in a particular LSOA could be disconnected from the gas grid while all other dwelling have a connection, but this level of detail is currently unobtainable. For areas that had a lower percentage of gas connection, the average regional adjustment was applied across all years.
Nondomestic modelled heat loads have been adjusted using the mean regional domestic adjustment factor shown in
Table 6. The number of nondomestic gas connections do not correspond to nondomestic premise count from CaRB2 and neither is there data on the number of nondomestic premises without a gas connection similar to the domestic ‘non-gas’ data. In the nondomestic sector, multiple premises can share a single gas meter in one building, or across multiple buildings or may have an unconnected supply point. Analysis of the nondomestic gas consumption data shows that around 6% of this fall into the unallocated category. Also, the designation of a nondomestic gas meter is arbitrary and based on a 73,200 kWh cut-off applied by BEIS [
62], therefore some smaller nondomestic premises fall incorrectly into domestic consumption and vice versa.
Parameter Sensitivity
The sensitivity of the input parameters to the thermal model was tested. Each parameter in
Figure 8 was tested one at a time by scaling the parameter and observing the percentage change in total heat load for the entire six-year period. The sensitivity was conducted on 1000 domestic buildings, comprising of each domestic archetype in the ratios given in
Figure 1 using London meteorology data.
The most sensitive parameters observed in advanced building simulation models are the wall U-values, ventilation rate, and setpoint temperature [
101]. Linear responses to the inputs are observed with the window transmissibility and SHL. Increasing the transmissibility value results in larger thermal gains and thus reduced heat load. The SHL values encompasses both fabric U-values and air change losses. The most sensitive input parameter to the model is the internal setpoint temperature. Reducing the setpoint causes a rapid reduction in heat load, but the same is not observed with increasing setpoint. A limitation of this model is with the method in which the model infers occupancy and the power capacity of the heating system which both limit the maximum heat demand of a simulated building. Heating systems are normally sized according to the heat load requirements of a building. For the purposes of this sensitivity analysis, the power of the modelled heating system was not adjusted when changing SHL. If it were, then we would see a larger response to changing SHL as in this analysis the maximum heat load was limited by the capacity of the heating system.