*3.2. Energy Systems Optimisation Modelling (ESOM)*

A heat pump diffusion model has been developed to explore the potential uptake of heat pumps and quantify the impact on the electrical load at the dwelling and island level for Orkney to help assess the transition from fossil fuels to electricity. The model considers different building archetypes (detached, semi-detached, end-terraced and mid-terraced), building specifications (unrefurbished, refurbished, new building), heat pump sizes (8.5 kW, 11.2 kW, 14.0 kW), TES tank sizes (250 L, 500 L, 750 L, 1000 L), flow temperatures (35 ◦C, 45 ◦C, 55 ◦C), backup heater settings (gas boiler as a backup heater, no backup heater), and electricity tariffs (Standard, Economy7, Comfy Heat, Economy12, Economy20), each of them being modelled as in [29]. We assume the heat pumps have a variable operation pattern, where variable load curves are used for the analysis. The model calculates hourly heat pump electricity loads, so an electricity load profile study is conducted to investigate the Orkney grid level.

The time resolution of weather data (outside temperature and solar radiation) has been scaled to hourly for a high temporal resolution. Thermal bridging, internal gains, thermal mass, and standing loss for TES tank calculations are included in the model. Heat pump specifications for different sizes and flow temperatures are taken from the manufacturer's website. Hourly heat pump maximum, medium, and minimum capacities and COP curves are calculated based on outside temperature and flow temperature.

Hourly outdoor temperature and solar irradiation data have been collected from Renewables.ninja to calculate heat gains and losses [30]. The internal thermostat set point temperature is specified as 21 ◦C based on recommendations from the World Health Organization [31] and Public Health England [32]. A number of archetypes have been identified to represent the housing stock ('detached', 'semi-detached', 'end-terrace' and 'mid-terrace') based on BSM results. These archetypes are used to analyse the variation of heating technologies' performance with different physical properties.

EPC data [28] were used for information about the gross floor area of the houses, the number of storeys, room height and occupancy. Glazing ratio information and building thermal properties data were taken from The Building Regulations Approved Document Part L1A [33]. The houses are named into three categories 'refurbished', 'unrefurbished' and 'new building'. Data on domestic hot water (DHW) consumption, distribution of DHW throughout the day, and heating patterns were taken from Energy Saving Trust's report [34]. The Government's SAP for Energy Rating of Dwellings [35] was used for generic values (plan aspect ratio, floor thickness, etc.).

Electricity and gas tariff data were collected for 6 different tariffs. Standard and Economy7 tariff was gathered from ScottishPower [36] to analyse Orkney electricity prices. Moreover, tariffs which are not yet available on Orkney such as Economy12 [37], Economy20 and Comfy Heat [38] also analysed to investigate different options. The peak time prices for Economy7, Comfy Heat, Economy12, and Economy20 tariffs are identified as 20.8 p, 15.7 p, 20.7 p, and 16.3 p. Off-peak tariffs are identified as 9.0 p, 8.6 p, 8.6 p, and 11.4 p, respectively. Standing charges are also identified as 23.9 p, 20.3 p, 18.0 p, and 46.9 p, respectively. Standard electricity tariff and gas prices are identified as 16.5 p and 3.2 p for unit prices and 23.8 p and 23.3 p for standing charges (Appendix B, Table A1).

The distribution of off-peak and peak hours during the day was identified according to tariff options. Standard tariff assumes that there is no peak time pricing so standard pricing is assumed as an off-peak tariff. Economy7 tariff assumes 7 h of off-peak time during the night. The number of off-peak hours is very similar in the Comfy Heat tariff with 8 h, but they are distributed throughout the day with 4 h during the night and 4 h during the day. Economy12 and Economy20 tariffs have 12- and 20-h off-peak time with 2 h during the day and the remaining during the night (Appendix B, Table A1).

TES tanks store energy in required times and help to avoid overpricing in peak times. Therefore, four different sizes of TES tanks (250 L, 500 L, 750 L, and 1000 L) are tested in the model to explore lower peak time heating costs. Standing losses are calculated based on SAP document [35] and Hot Water Association [39] methodologies. In terms of the backup heater, both electricity and natural gas-fired heaters are tested. It has been assumed that a condensing gas boiler has a 15 kW size capacity with 90% efficiency, and the electric heater has an 8.5 kW size capacity. In scenario analysis, the performance of the heat pump is tested with and without these backup heaters in operation.

There are various heat pump types. ASHP has been selected in the modelling for its wide range of use and less space requirement during installation. Mitsubishi Ecodan PUZ series are selected because of using R32 (low GWP and Ozon Depletion potential) to explore various heating performances [40]. However, the PUHZ series is also investigated to test the impact of using a different refrigerant (R410) on energy performance. To select the correct size of the heat pump, three different sizes are explored, namely 8.5 kW (PUZ85), 11.2 kW (PUZ112), and 14.0 kW (PUZ140). COP and capacity data under different outdoor temperature conditions and water outlet temperatures (35 ◦C, 45 ◦C, and 55 ◦C) are calculated hourly in the model. These figures illustrate that the PUZ series provide higher capacities and COP values under the same flow temperatures. Moreover, the PUZ series has an R32 type of refrigerant, which has a lower environmental impact. Therefore, the PUZ series are selected for scenario analysis.

A heat pump diffusion model [41] quantifying the impact of installing ASHPs on the electrical load curves at the dwelling and UK levels was integrated into this research. Data for Orkney electricity system load were taken from Scottish and Southern Electricity Networks [42]. Average household level hourly electricity load structures were taken from a study conducted by Intertek [43] for various types of household settings including with/without electricity heating. Heating-related loads were taken from the total values so the impact on dwelling and grid level load curves are calculated. The loads are calculated for the coldest winter workday and holiday to investigate.

The model calculates heat gains and losses to analyze the performance of the dwelling. Fabric heat loss, ventilation heat loss, thermal bridging, solar gains, internal gains, and thermal mass properties are calculated based on SAP methodology (Appendix A—Equations (A1)–(A16)). TES tank temperature is calculated as in the following equations:

$$
\sum DDHW = V\_W \times 4.18 \times T \tag{2}
$$

$$H\_R = \sum Ltotal\\_- - \sum Gtotal\\_+ + \sum DDHW\tag{3}$$

$$\begin{aligned} \text{if } T\_{TS} &> 5 + T\_{\varepsilon} & T\_{TE} &= T\_{TS} - \frac{\sum H\_R}{V\_T \times 4.18} - \frac{\sum H\_P}{V\_T \times 4.18} - L\_S\\ \text{if } T\_{TS} &\le 5 + T\_{\varepsilon} & T\_{Ts} &= T\_{\varepsilon} \end{aligned} \tag{4}$$

where *DDHW* is DHW demand, *VW* is the volume of the water (litre), *T* is required water outlet temperature (◦C), *HR* is required heat, *Ltotal* is total losses (W), *Gtotal* is total gains (W), *TTE* is tank end temperature, *TTS* is tank starting temperature, *Te* is external temperature, *HP* is provided heat with heat pump and backup heater, *VT* is tank size (litre), and *LS* is standing loss (◦C) of the tank. Standing loss is calculated as in the following equations:

$$L\_S = f\_V \times f\_T \times f\_C \times V\_C \tag{5}$$

$$f\_V = (120/V\_C)^{\frac{1}{3}} \tag{6}$$

$$f\_{\mathbb{C}} = (0.005 + 0.55/(t+4))\tag{7}$$

where *LS* is the standing loss of the cylinder tank, *fV* is the volume factor, *fT* is the temperature factor, *fC* is the cylinder loss factor, *VC* is cylinder tank volume (litre), and *t* is insulation thickness (mm). The heating schedule is decided as maximizing heat pump operation during off-peak times and avoiding gas boiler usage, and then minimizing heat pump operation during peak times and covering the remaining demand with a backup heater. The model calculated heat pump and backup heater capacities as in the following equations:

In peak times;

$$\begin{array}{lll}\text{if }\mathbb{C}\_{\text{MIN}} \ge H\_R & & E\_P = \mathbb{C}\_{\text{MIN}}\\\text{if }\mathbb{C}\_{\text{MIN}} < H\_R & & E\_P = \mathbb{C}\_{\text{MIN}}\end{array} \tag{8}$$

$$\text{if } T\_E < T\_L \tag{9}$$

$$\text{HP} \ge \text{ON} \tag{9}$$

In off-peak times;

$$E\_P = \mathbb{C}\_{MAX} \tag{10}$$

$$\text{if } T\_E > T\_H \tag{1}$$

$$\text{HP} \ge \text{OFF} \tag{11}$$

At all times;

$$\text{if } T\_E < T\_B \tag{12}$$

where *CMIN*, *CMID*, and *CMAX* are minimum, medium, and maximum heat pump capacities, *HR* is required heat demand, *EP* is provided energy, *TE* is the end temperature of the tank, *TL* is the lower threshold temperature, *TH* is the higher threshold temperature, and *TB* is the backup temperature.
