Domestic thermal energy storage applications: What parameters should they focus on?

Thermal energy storage (TES) is required to allow low-carbon heating to meet the mismatch in supply and demand from renewable generation, yet domestic TES has received low levels of adoption, mainly limited to hot water tanks. Current reviews and studies primarily focus on the comparison of storage materials neglecting the performances at a system level and analysis studies tend to solely look at hot water tanks, missing the key technology developments in thermal storage systems which are under development. Therefore, this paper in- vestigates performance and cost variations of TES from material-level to system-level analysis and assesses impacts of emerging heat storage technologies. By simulating different types of TES materials and varied system integration options, a significant reduction in energy densities and increase in specific costs of TES systems were found compared to the material-level analysis. Direct electrical heating has much greater potential to integrate with TES from its high operating temperature with TES compared to heat pumps or solar thermal which are constrained to lower temperatures. TES properties are simulated in various scenarios in a domestic heating techno-economic framework. It was found that for heat pumps there is economically-limited potential for TES, even if very high energy densities are possible. In addition, the priority for TES coupling with heat pumps is low capital cost, although current high tariff rates due to the energy-crisis do improve economic viability of TES. On the other hand, with direct electrical heating, high energy density is the most valuable parameter for TES, as it allows significant quantity of demand to be shifted to very low-tariff times, in particular for low demand dwellings where negligible amounts of peak electricity could be required for heating.


Background
Heating currently accounts for 37 % of worldwide greenhouse gas emissions mostly through burning fossil fuels, which needs to be reduced to meet countries' net zero targets [1]. Fossil fuel fired heating is also the major source of health damaging air pollution due to insufficient combustion. Globally, residential and commercial building energy use is the largest source that contributes nearly one-third of deaths related to air pollution [2]. In the UK, where burning wood is a very small proportion of the total heat source, domestic combustion emissions from heating has been increasing between 2005 and 2020 and is responsible for 20 % of the country's PM 2.5 and PM 10 (particulate matter less than or equal to an aerodynamic diameter of 2.5 or 10 μm respectively), larger than the transportation sector [3].
To reduce these heating emissions a shift towards alternative environmental-friendly heating such as electrified heating, of heat pumps or direct electrical heating (DEH), and solar thermal is required. DEH makes use of resistance heaters which have close to 100 % efficiency and can be flexible and fast responding with no or minimal moving parts and low capital expenditure (CapEx). Heat pumps use electrical energy as an input to make use of outdoor low-grade heat, allowing much higher efficiencies than DEH, but with higher CapEx requirements. Solar thermal collectors directly use the irradiation from the sun and therefore have no flexibility or control on when they generate heat. As electrified heating, heat pumps or DEH, needs to use high amounts of renewable generated electricity to reduce emissions, both electrified heating and solar thermal face the challenge of a mismatch in the supply of variable renewable energy against heating demands, from seasonal to diurnal timescales.
Thermal energy storage (TES) can help to play a key role in meeting this mismatch, by storing the energy at the time of generation and allowing it to be used at a time of demand. However, the transition to low-carbon heating technologies and TES has been slow in many regions due to various technical and economic challenges [4]. Both TES and lowcarbon heaters face challenges of high investment cost and space constraint challenges in retrofitting [4]. Currently, water tanks are the most used domestic TES technology, but water storage suffers from low energy density, so the storage usually only provides domestic hot water that is about 15 % of domestic heating demand [4]. The only other TES that has seen reasonable uptake is in lower demand dwellings that have historically been a popular choice for electrical storage heaters which use ceramic materials and so can reach elevated temperatures, although this technology differs to other TES as it is also acts as the radiator [5].
Previous studies of TES technologies typically focus on the material level analysis of the storage materials [6][7][8][9], which may not create feasible solutions to scale up to commercialisation and does not include economic parameters of investment and operational costs, and associated emissions, for consumers using these TES concepts. Analysis studies of TES alongside low-carbon heating technologies that have been completed typically focuses only on water tanks as TES storage material and give little comparison of TES technologies and parameters other than variation in sizes [10][11][12]. Yet new TES designs are emerging and entering the marketplace. Emerging TES technologies include the use of higher temperature sensible heat storage (SHS) which are smartly charged at off-peak times using modern tariffs and, have significantly higher storage capacities than the traditional electrical storage heaters [13,14]. In addition to SHS, latent heat storage (LHS) technologies have begun commercialisation by storing thermal energy from the phase change of salt hydrates without the need for higher temperatures [15].
Here, we examine emerging domestic TES technologies and concepts and their integration with renewable and electrification heater options while also exploring the impact of power system decarbonisation on emissions of future domestic heating. In particular, we focus on the trade-offs between costs and emissions that consumers face in selecting a low-carbon alternative. Although cost is not the sole influence on consumer purchasing decisions, low-carbon heating and TES will only achieve a dominant market share if they are affordable to most of the population. We address these issues by comprehensively examining TES technologies and concepts, covering all prominent options: SHS, LHS, and thermo-chemical storage (TCS). We take a step back from the existing thorough material analysis which focuses on how specific materials differ, instead focusing on the integration of the technologies at a system level and applying them to domestic heating applications from the consumer's perspective.
In this paper, we cover the range of technology readiness level from existing TES technologies of hot water storage tanks and electric storage heaters, emerging TES technologies such as high temperature SHS and LHS which are just starting the commercialisation process, and potential future technologies from theoretical improvements to determine what parameters are most valuable for TES. A hot water tank TES is added into a domestic heating simulation framework, where 0.1 to 0.5m 3 sizes are analysed. Additionally theoretical changes to TES parameters of energy densities, CapEx, storage temperature and insulation value are investigated. This enables an understanding of which aspects are useful for TES rather than examining specific materials/systems, which has already been done in existing TES studies. A default temperature of 51 • C is used for the TES storage temperature, but higher temperatures of up to 500 • C are considered in the simulations, and up to 1500 • C in initial material and system comparisons.
We evaluate cost and emission impacts of TES on domestic heating decarbonisation to answer the overarching questions: why TES has not seen more widespread adoption beyond basic hot water tanks, and what parameters are the most valuable for TES concepts to improve their economic viability? In addition to addressing these questions, we also find the use of TES in domestic heating systems can ensure heating security and provide benefits to wider energy system operations and decarbonisation, while changes in carbon emissions and costs vary greatly depending on heater and TES choices. The insights and choices identified in this study likely will be of interest to homeowners, manufacturers of heating systems, and policymakers in energy sectors.

Methodology
In order to decarbonise heating, the source of the energy needs to come from low-carbon sources. As this is generally considered to be from variable renewable energy generation, TES is required to meet this mismatch. TES needs to be able to store sufficient capacity of energy to allow a shift in demand, it also aims to do this in the most efficient way as possible to maximise use of renewable generation. There are various aspects to a TES round trip efficiency, as this includes charging efficiency, storage efficiency and discharging efficiencies, all of which need to be considered.

Analysis of TES applications: from materials to systems
First an analysis of existing and emerging TES materials and TES systems will be undertaken from a comprehensive review of the literature, covering the full spectrum SHS, LHS, and TCS. Comparisons of the TES will be made at a material level and system level to compare how this alters the position of the technologies, instead of purely focusing on the material level as current studies tends to. The system level analysis will include manufacturers data on traditional hot water tanks and electrical storage heaters as current TES technologies, as well as emerging commercial products that target high efficiency and storage densities that are using SHS at higher temperatures with high quality insulation [13,14], and LHS systems using salt as the phase change material designed for domestic heating application with melt temperatures setup to efficiently store energy around the domestic demand temperatures [15]. Analysis will also be broken down showing how the TES technologies alter in their performance depending on if they are coupled with the prominent low-carbon heating technology of an air source heat pump (ASHP) with its limited operating temperatures, or with the more flexible and lower CapEx DEH which is better suited to lower-demand dwellings and can achieve higher temperatures.

TES integration into domestic heating framework
The study will then go on to look at how TES can integrate into a domestic heating application with hourly simulations across a year for a dwellings demand met by TES that is heated with DEH or ASHP, comparing economics and environmental factors. This study will then look at how changing parameters of TES alters the system viability, to demonstrate which parameters are most valuable to reducing costs of TES. A consumer centric mathematical model to simulate domestic heating across the year at an hourly resolution is used as introduced in previous work [10,16].
The framework holistically considers each combination of heating technologies, ancillary solar and TES sizes, and tariffs. The CapEx and the single years' operating expenditure (OpEx) are then used to calculate the 20-year Net Present Cost (NPC). A time period, t, of one year and a discount rate, r d , of 0.035 are used for the NPC Eq. (1). The OpEx, CapEx, NPC, and emissions values are used for technology comparisons. Emissions include operational emissions and embodied emissions, to give an equivalent annual emission. Inputs to the model are: dwelling location; number of occupants; desired thermostat temperature; dwelling floor area, and annual space heating demand, the latter two can be found on the dwelling's energy performance certificate in many countries. To demonstrate the sensitivity of TES parameters a case study is complete in the UK for multiple scenarios.
The heating model is described in detail in previous work [10], where the thermal efficiency of the dwelling is back-calculated from the input data, then a higher resolution space heating demand can be calculated using calculations and assumptions from SAP [17] and BREDEM [18] and using location specific reanalysis weather dataset from Renewable Ninja for the year 2019 [19]. Heat pumps are set to operate at a constant indoor temperature throughout the day, due to their low thermal power, and other heating devices set the target thermostat temperature from 07:00 to 22:00. The key heating demand equations are shown in Table 1.
Where Q hl i is the heat loss from the dwelling at that time interval in kWh, A d is the heated floor area of the dwelling in m 2 , U d is the overall dwelling thermal efficiency relative to its floor area in W/m 2 • C, and T in i and T out i are the inside and outside temperature of the dwelling in • C. C d is the heat capacity of the dwelling in kWh/ • C, using the average specific heat capacity of UK dwellings at 250 kJ/m 2 • C [18]. The previous hour's indoor temperature T in i− 1 in • C is used to calculate the current hour's temperature with the dwelling's heat loss, solar gains G s i and metabolic gains G m both in kWh, and the dwelling's heat capacity. The space heating demand Q sh i in kWh is then calculated relative to the T d i desired indoor temperature in • C (thermostat setpoint for that time). Hot water daily volumetric demand, V t in litres, is determined from BREDEM assumptions relative to the amount of residents in the dwelling [18]. Geographical monthly cold water temperatures T cw, m in • C and hourly ratios of daily demand R dhw, h i from Energy Saving Trust are used alongside BREDEM monthly ratios in daily hot water demands R dhw, m [18,20]. Combining these parameters gives the hourly hot water demand Q dhw i in kWh. Heating demands are met by either the baseline natural gas boiler using an efficiency of 90 %, DEH with an efficiency of 100 % or ASHP which has varying Coefficient of Performance (COP) as shown in Eq. (7). TES is simulated as stratified hot water tanks at sizes from 0.1 to 0.5m 3 in 0.1m 3 steps, but with the ability for its parameters to be changed to test their sensitivities on the TES integrated systems performance. The TES maximum thermal energy capacity Q tes i in kWh is calculated depending on the TES volume in that simulation V tes in m 3 , and the TES specific heat capacity C p in kJ/kg • C which is nominally set to 4.18 for water unless stated otherwise, and relative to a minimum useful temperature of 40 • C. The TES is simulated as stratified hot water tanks with upper and lower heat losses Q tes, up i and Q tes, lower i in kWh, respectively above and below the thermocline height h t, c i at that time, which is a ratio of the TES height h tes in m. TES losses are also relative to its temperatures T tes, up i and T tes, low i in • C above and below the thermocline respectively, the radius of the TES r TES in m, and the thermal efficiency of the TES U tes in W/m 2 • C that is nominally set to 1.3 unless stated otherwise ( Table 2).
The CapEx for each of the technologies are shown in Table 3. The framework created offers the ability to be easily adopted for any home and set of personal demands, by adjusting the dwelling inputs and locations for heating demands and in scaling the typical baseload electricity and transport demands. Case studies are used in the paper to demonstrate the functionality of the framework using an average, low and high demand UK dwellings are considered at a central England location of Coventry (3717 heating degree days), with two occupants, using a thermostat temperature of 20.0 • C, and a maximum TES size of 0.5m 3 considered. All dwellings use an average thermal efficiency of 1.85 W/m 2 K, then dwelling size is adjusted to match different percentiles of UK homes heating demands. Resulting in the average demand dwelling set to 87m 2 , lower 10th percentile demand to 31m 2 , lower 25th percentile demand to 52m 2 , and high 75th percentile demand at 114m 2 as determined in previous work [10]. Emissions are also taken from previous work [10].
To promote the shifting of energy to consumers, which is the main function of TES and other energy storage, variable rate tariffs are used as these create low electricity rates at times of lower demand. A range of different tariffs are considered, the flat rate tariff is the only tariff which does not promote shifting demands due to a constant rate across the day. Night off-peak tariff is a traditional two rate tariff, with 7 h of low-cost electricity at typical low demand times in the night, but a higher day rate than the flat tariff. A more modern version of this is the EV off-peak tariff, which has a shorter four-hour window of very low rates. Finally, a variable, day ahead, time of use tariff is also considered, which has a different rate for each hour of the day and changes every day depending on supply and demands. As the tariffs used in this study are existing tariffs available to customers, they all include sufficient costs to cover demand/distribution charges, energy generators and supplier costs and profits, and any other associated costs with purchasing electricity from a national electrical network. This paper then also considers the comparison of these tariffs at the pre-energy crisis low rates from 2020 to the current high costs tariffs from 2022 to determine how the tariff changes alter the position of TES, as shown in Table 4. The tariffs selected are the lowest rate tariffs of that structure available across the year 2020 and 2022, as any consumer is likely to select the lowest rate tariff available to them. Apart from the variable time of use tariff which uses data with the changing rate for each half hour across the two years.
For this study variable GB electricity grid emissions are used from the year 2020, which averaged 181gCO2e/kWh across the year [30]. Where reduced grid emissions scenarios were input into the framework this was completed by subtracting or adding a fixed value, in 25gCO2e/kWh increments, to each hourly value. Values were limited to a minimum value of zero emissions at each time step. The electrified technologies coupled with TES are compared against the baseline of natural gas boilers where natural gas emissions are 181gCO 2 e/kWh and costs use low 2020 tariffs of 2.1 p/kWh and 17.85p/day and high 2022 tariffs of 8.34p/kWh and 26.1p/day [28,31].
For SHS the upper material temperature limit is used to calculate the values, importantly these high potential temperatures allow relatively good densities and specific costs for SHS, but do not emphasise that with the higher temperatures comes more storage losses (with the same insulation). SHS materials are also grouped by their sub-categories and some of the best performing materials for energy density and specific costs of key sub-categories are labelled. For SHS oils and salts, there are only small differences in densities within their groups, cost also remain similar, with the exception of vegetable oils which give comparable costs to the salt group but at lower densities. The metals and earth materials groups have varied performance across their groups, with some materials able to withstand very high temperatures and high densities. This results in some of the best energy densities, and, due to their low cost, they are the clear preferred TES materials for these parameters.
LHS data focuses on potential energy storage available from phase changing: the materials can achieve reasonable densities just relying on the latent heat from the phase change. Although LHS can allow further improvements in energy densities if the materials continue to be elevated up to their maximum workable temperatures, this also comes with the downside of more heat loss and lower storage efficiencies as with SHS. In addition, the larger temperature change alongside the phase change may cause further degradation of the LHS materials. For the LHS sub-categories, the paraffins, fatty acids, alcohols, and salt hydrates all have comparable energy densities, but with vast ranges in costs depending on the abundance of the material. Hydroxides in LHS improve on energy densities, but not as significantly as some metals and other salt materials.
As TCS is at the development stages, mass production costs are unclear, the potential range of production costs and energy densities of TCS are shown by the transparent green box using data gathered from the thorough literature review, and TCS technologies are positioned at the upper cost value of this due to not being commercially available. The energy density for TCS is shown using the energy from the material's chemical reaction. The materials under consideration from the literature are predominantly using adsorption reactions instead of absorption reactions. This has very varied results for TCS but does have many options with very high energy densities. The additional benefit of LHS and TCS, not show, being lower temperatures and therefore higher storage efficiencies than some of the high SHS. With temperature constraints, and disadvantages, removed it becomes clear that SHS generally is the most cost and space effective compromise.
In addition to higher operating temperatures of TES materials making high storage efficiencies more challenging, they also restrict the type of heater used, which is pertinent for decarbonising heating. Fig. 1(b) shows how the potential low-carbon heaters perform depending on their output temperature, with thermal power on the left axis with solid lines and efficiency on the right axis with dashed lines. Solar thermal and ASHP show decreases in efficiency and therefore thermal power output with higher sink temperatures. Although DEH has a relative low efficiency at lower sink temperatures compared to the heat pumps, it remains nearly 100 % efficient at higher temperatures. Making DEH the only suitable method to couple with the higher temperatures required by some TES.
Many current studies on TES focus on the potential of the materials, at their upper temperature limits showing what is possible for different TES materials and how the different categories of SHS, LHS and TCS typically differ, as shown in Fig. 1(a), however by considering the limitations of the low-carbon heaters gives a more complete picture. This temperature constraint from heat pumps and solar thermal collectors restrains the performance of the TES, making it an important aspect to consider when analysing TES applied to domestic heating.
By adapting the data in Fig. 1(a) to show how TES materials can perform when restricted to sensible upper values for ASHP and solar thermal of 70 • C Fig. 1(c) is created. SHS now has significantly lower values as the upper temperatures are limited, reducing the capacity and energy densities of these systems. LHS and TCS removes any material that melts/reacts above the 70 • C limit, significantly reducing the number of options, leaving much lower energy densities for LHS and with the remaining TCS now significantly higher energy densities than other thermal storage materials. With this limit also imposed, Li-ion batteries become much more favourable forms of energy storage, especially if considering being coupled with ASHP that operate at higher efficiencies.
As prior studies tend to focus on TES materials, they can miss the performance changes that occur when considering the full thermal storage system. Fig. 2 shows how different TES systems can perform against each other using thermal store data from manufacturers, with (a) using the maximum TES system operating temperature and (b) limiting temperatures to 70 • C. The system level data analysis is taken from manufacturers, shown in Appendix A, when including their whole installation, not simply just the storage material. This higher level differs from the material level as the upper temperatures of the system may be limited lower than the maximum possible temperature achievable by the material. It also includes the increase in volume and cost requirements from the heat exchangers, insulation, and other ancillary parts, which lowers the energy densities and increases the specific costs compared to at the material level.
These are important factors as this is not the same fixed values for all types of TES i.e., higher storage temperatures require more advanced insulation materials. As discussed, getting the maximum performance from many of the TES systems as shown in Fig. 2(a) is only possible with DEH. At the maximum TES system temperature scenario, as found in the material level, SHS remains the most advantageous technology, but with a reduced cost benefit compared to at the material level. At the system level the cost benefit of water for storage is limited as it is comparative to storage radiators and is only slightly lower specific cost than new high temperature SHS technologies which all come with higher energy densities. LHS has acceptable energy densities put at higher costs, but not as high as batteries, as shown in Fig. 2. However, batteries are positioned using their stored electrical energy to calculate both energy density and specific costs, unlike the TES technologies which are used in thermal energy. The thermal equivalent of energy storage for batteries depends on which heater it is coupled with: if this is coupled with DEH this is near identical to the electrical values shown as DEH efficiency is close to 100 %. If electrical batteries are coupled with ASHP the battery performance would be 3.5 times better with a typical ASHP COP of 3.5, making it the second lowest specific cost in Fig. 2(b) after hot water tanks but with an energy density over seven times better than any TES. Fig. 2(b) using the limited temperatures causes a few key changes to energy storage system landscape. SHS energy densities and costs are reduced, so much so that water tanks are the only feasible option as the high temperature SHS technologies are limited when coupled with ASHP or solar thermal. The reduction in performance of SHS makes LHS and batteries much more competitive, with LHS only slightly higher specific costs but with good energy density improvements over water tanks.
These new insights show how important it is to consider the system level for domestic TES, where consumers have limited space, capital to invest, and TES may be coupled with different types of heaters. As the system level shows the significant increase in specific costs and decrease in energy densities compared to the material level. It highlights that if the commonly favoured low-carbon heater of ASHP is to be used, that The shaded green box shows the range of potential commercial costs and energy densities of TSC materials due to many uncertainties at mass production, the TCS technologies are positioned on the upper cost value of this estimate as they are currently not in production. Lead and lithium-ion electrical battery materials shown for comparison. (b) Shows low-carbon heater thermal power output and efficiencies against increasing output temperature. With heater power in solid lines on the left axis and efficiencies in dashed lines on the right axis of the same colours. Using fixed electrical input, 10 • C ambient conditions and 1000 W/m 2 solar irradiance. ASHP COP calculated from [23]. Solar thermal collectors efficiencies calculated from [17,44]. Data in Appendix A. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) the simple hot water tank remains competitive although LHS can have a strong future in this market if costs can reduce, therefore integrating the right technologies for the specific application is important.

Integration to domestic heating analysis framework
To better understand how TES operates in domestic applications and which TES parameters are most effective to improving its performance, various TES and heating demand scenarios are simulated at an hourly resolution across the year in framework introduced in previous work and explained in the methodology [10,16]. With multiple tariffs available for consumers considered in the framework it is worth stating that, other than flat tariffs, the tariffs that have varying costs across the day generally have lower costs at the times when the associated emissions from grid generated electricity is also lower, as demonstrated in Fig. 3. This highlights that if TES is targeting reducing consumers OpEx by shifting demand to off-peak times of the day with electrified heating this has the added benefit of reducing emissions and improving utilisation of variable renewable energy generation. The positive effect of TES to reduce emission will be enhanced with the progress of the power system decarbonisation.
ASHP and DEH are simulated alongside the commonly used domestic TES of hot water tanks and variations for representing other TES scenarios, the heater parameters are detailed in Appendix A. Then, the results are compared to the fossil fuel baseline of natural gas boilers in Fig. 4 in their systems OpEx and 20-year NPC. Tariffs considered are from 2020 (pre-energy crisis) and results shown use the EV style tariff, with 4 h of very low cost electricity in the night, as this tariff structure is shown to be the most beneficial for energy storage viability [16].
With the electrified heaters different TES scenarios are presented, a minimal 0.1m 3 TES, a large 0.5m 3 TES, a 0.5m 3 TES with high (×10) and low (÷10) specific heat capacities/energy densities to simulate how significant improvements to energy densities would alter TES viability, compared to the current technologies which can approach 2.5 times hot water tank energy densities shown in Fig. 2. Scenarios are also included for a 0.5m 3 TES with high (×10) and low (÷10) TES CapEx, where high CapEx is comparable with more recent TES technologies and low CapEx could be an ideal scenario. These hypothetical changes to key parameters can help identify what direction domestic TES should develop.
Firstly, looking at Fig. 4(a) for the average UK dwelling heating demand, the ASHP is more viable across the 20-years over DEH, although neither can compete with the gas boiler economically. With the ASHP the addition of larger TES and changing TES parameters has a small impact over an ASHP with a minimal TES, other than high CapEx TES which significantly increases the NPC of the system. This is primarily due to the lower OpEx from using an ASHP, meaning any improvements in reducing its OpEx using TES make a small absolute different and therefore do not payback the increased CapEx of TES over its lifetime. In addition, the most cost-effective charging time for TES is using the nighttime off-peak times, which is accompanied by cooler temperatures and therefore lower ASHP efficiencies, which typically give ASHP lower charging power than DEH. Showing TES struggles to improve the economics of the relatively lower OpEx ASHP, and that lower CapEx TES is the most useful direction for TES coupled with and ASHP.
However, alongside DEH the potential for TES is much greater. Although low CapEx TES has similar overall advantages as with ASHP, the higher energy density has a much stronger impact. The high energy storage capacity of the high energy densities scenarios with the large 0.5m 3 TES coupled with the faster charging DEH, can better take advantage of off-peak electricity rates, and make a larger absolute Manufacturers data for TES system energy densities against specific system energy costs (a) using their maximum system operating temperatures (b) only heating up to 70 • C to remain suitable for heat pumps and solar thermal technologies. Electrical wall battery system shown for comparison. Data provided in Appendix A [13,15,33,42,[45][46][47][48][49][50] .   Fig. 3. Variation in British electrical grid emissions compared to a variable time of use tariff, for the first four days of 2020 [29,30]. difference due to the nominally higher OpEx of DEH compared to ASHP. Although this best-case scenario for DEH can result in similar peak electricity usage and NPC to ASHP, the lower efficiency of DEH still results in over double the equivalent annual emissions to the ASHP system. Fig. 4(b) introduces a higher demand dwelling which has been correlated to the upper 75th percentile UK dwelling heating demand. The scene remains similar for the high demand dwelling as with the average demand dwelling, but with further increase in DEH relative to ASHP due to the higher OpEx representing more of the overall NPC than the CapEx, where ASHP CapEx is higher than DEH.
Lower heating demand dwellings are shown in Fig. 4(c) and (d) representing the lower 10th and 25th percentile respectively. In lower demand, with lower OpEx, DEH becomes more favourable, and with the high energy density TES, DEH is even the optimum cost overall lowcarbon solution. However, although this is now the optimum solution the benefit of high energy density reduces compared to low CapEx TES alongside reduced demand. The ability of DEH with high-capacity TES in the low demand dwelling shows great flexibility potential for being able to shift demands, as only £2 of the £331 annual bill is from peak electricity usage (98 % reduction compared to £91 a year was from the fixed daily standing charge).
In comparing the emissions of the key combinations of heaters and TES parameters in Fig. 4 reveals similar trends to OpEx, as Fig. 3 highlights the link between tariff rates and electrical grid emissions. Emissions fall in-line with demand, so reducing heating demands is one of the largest ways to reduce associated emissions. The difference between ASHP and DEH efficiencies (typically 3.5) is greater than the variation in electrical grid emissions and therefore concludes ASHP has lower associated emissions than DEH in all TES scenarios, even if ASHP use electricity at times of higher emissions. Increasing the energy density and therefore capacity of the TES allows a decrease in emissions, however this is less than the OpEx reduction as the variation in the EV tariff peak vs off-peak rates is greater than the variation in electrical grid emissions.
A key factor to domestic energy technologies viability is the tariff rates, to understand how the increased cost of energy from the energy crisis has altered the position of the heating systems, Fig. 5 uses the same tariff styles but from 2022 for (a) 10th percentile and (b) 25th percentile dwellings again. As found with the higher demand dwellings, the higher OpEx, now from higher tariff rates, benefits the more efficient ASHP over DEH. However, as the demand remains low a high percentage of the electricity used can be from off-peak times for the high energy density TES with the fast-charging DEH, keeping the high energy density TES with DEH as the overall optimum NPC solution. Although gas and electricity costs have both increased, the ratio between gas and electricity has reduced. On top of this, the off-peak electricity rate for the EV tariff only has a small absolute increase of 2.5p/kWh. Combining these points gives a significant economic improvement in electrified technologies relative to gas boilers, but gas remains the lowest NPC and very competitive on OpEx. ASHP having similar OpEx to gas and DEH with high density TES a very strong potential using large quantities of the off-peak electricity.
As discussed, the high energy density can bring benefits to the OpEx of electrified heating systems, so far in framework this has been considered by using a theoretical material with higher specific heat capacities. As introduced in Section 3, high energy densities can also be achieved by SHS operating at higher temperatures. Although this makes storage efficiency more challenging as heat is lost through from the TES. Fig. 6 looks at how the thermal storage efficiency of the TES (the U value), which is of particular importance when operating at the higher temperatures to retain the stored energy, alters the system performance. Now shifting the focus to the environmental aspects of the system for an average demand dwelling, showing how the input variables can impact the equivalent annual emissions, even if both OpEx and emissions benefit in the same way of being able to shift demands from peak times to off-peak times efficiently. This plots the equivalent annual emissions from the system at different TES U values and different average grid emissions, all grid emissions used the varying hourly profile based on 2020 data as explained in the methodology section. The default value in the framework had average 2020 electrical grid emissions at 181gCO2e/ kWh and a TES U value of 1.3 W/m 2 K. Fig. 6 uses a large, 0.5m 3 , hot water tank with (a) using DEH and an upper (hypothetical) TES limit of 500 • C to simulate values close to new commercial SHS technologies considered in Section 3 which are well suited to low-demand dwellings  and (b) remains at the 51 • C temperature and is coupled with an ASHP which is economically a preferred solution for the average demand dwelling. Unsurprisingly, as grid emissions are reduced the equivalent heating emissions from electrified technologies reduce proportionately. Because the difference of energy efficiency for heating between DEH and ASHP, heating emissions vary significantly as shown in Fig. 6. For example, with the average grid emission of 150 gCO2e/kWh, the heating emission of DEH can be three times of the emission of TES coupled ASHP. However, if electrical grid is deeply decarbonised (average emission lower than 25 gCO2e/kWh), both DEH and ASHP (coupled with TES) can deliver low-carbon heating at a similar emission level (i.e., <30 gCO2e/ kWh).
For DEH although the high temperature allows high energy storage densities, at the higher U values there are more losses and so there is little benefit until around 0.8 W/m 2 K, below this point the heat can better be retained to more efficiently use off-peak low emissions grid electricity. As the average grid emissions reduce although the percentage of heating emissions still reduces with the U value, the absolute difference decreases, however this is very dependent to how future grid emissions vary on an hour-by-hour basis. On the other hand, TES coupled with ASHP shows that the U value makes very little difference to heating emissions, due to the lower temperature limits of ASHP making TES capacity low and losses remain very low even at higher U values compared to overall heating demands.
To better visualise the greater system benefits of TES coupled with electrified heating systems Fig. 7 shows the first two days of the simulation for DEH in the lower 25th percentile home, which has previously been found to have a good potential for shifting demand and reducing peak electricity usage. Fig. 7(a) without any TES and (b) with a 0.5m 3 hot water tank TES. Without the TES the heating supply must instantaneously follow the heating demand to balance out building heating losses, domestic hot water demands, and increases in desired thermostat temperatures. Any following of off-peak electricity use here is purely coincidental as the system has little control. In reality DEH is likely to struggle to meet instantaneous heating demands without some TES. When then including TES, although similar trends occur of following increasing thermostat set points, the TES can significantly reduce peak electricity use and recharge when prices reduce again while still meeting the household demands. This affect is stronger with the lower demand dwelling as even with current TES technologies the capacity is significant enough to have an impact for low demand dwellings.
This study focuses on the system-level integration of different TES technologies into domestic heating, in contradiction to most previous TES studies which complete material level analysis. However, the study has its limitations as it only investigates in detail some of the important TES parameters. Future work needs to be done at a system level to include variations in charging and discharging efficiencies alongside other TES parameter changings which occur within the material subcategories.

Conclusion
The data and simulations shown in this study demonstrate the benefits of TES and importantly which areas of improvement can result in improved economic and environmental viability of TES in domestic applications, and therefore increase its adoption by consumers. TES can bring wider system benefits from shifting of demand, leading to reduction in peak electricity use which eases the burden along the electrical network and generation demands. This flexibility can also allow the increased utilisation of variable renewable energy generation, whether regionally or decentralised at the dwelling, allowing further reduction in emissions.
An important comparison of TES at a system level is considered as well as at a material level, which emphasis why system approach needs to be considered as the addition of ancillary parts alongside the storage material significantly alters the specific costs and energy densities. The study also quantifies how TES requirements change from DEH to ASHP. Giving clear conclusions that ASHP and solar thermal low-carbon heating technologies with limited output temperatures can benefit well alongside LHS that have a suitable melting temperature around 50 • C to provide useful heat to the home while maintaining high heater efficiencies. On the other hand, DEH, which maintains its efficiency at higher temperatures and has high charging power couples best with high temperature SHS.
Various scenarios simulated in the heating framework allow a clear clarification of what parameters are the most valuable for TES concepts to improve their economic viability, finding low CapEx is the most important factor for domestic TES, as also found in a review by Alva et al. [6]. The study specifies low CapEx TES is a much more dominant factor for ASHP compared to DEH. Our work further concludes that at the pre-energy crisis low tariffs, larger TES does not reduce its OpEx sufficiently enough over its lifetime to payback the additional CapEx alongside ASHP, but with the current high tariffs larger TES has now become cost effective. The low CapEx requirement for TES viability is why the simpler hot water tanks, with their competitive costs are the dominate technology, as other technologies are more expensive at a system level in £/kWh. For DEH, although low CapEx is found to be valuable for TES, the most valuable parameter for TES coupled with DEH is high energy densities, allowing greater use of off-peak electricity. This can be achieved at low CapEx by using low-cost materials that are capable of withstanding higher temperatures. It is found that for high temperature TES alongside DEH that the U value needs to be <0.8 W/m 2 K to reap the advantageous of the higher temperatures. Space availability for TES in homes can be a restricting factor, hence why this study focuses on energy densities as high energy densities can allow sufficient energy storage capacities in smaller spaces. With smaller dwellings there is likely a smaller area available for TES and ASHP, alongside this the smaller the dwelling the lower the demand (with a fixed dwelling thermal efficiency), therefore in lower demand dwellings it was found high-capacity TES has more potential, these points together highlight a real benefit of high energy density TES with DEH in low demand dwellings.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.