Development of a high-resolution top-down model to estimate actual household-level heat pump electricity consumption

Heat pumps can play an important part in decarbonizing the residential sector due to their use of electricity instead of fossil fuels, and their high efficiency, which often exceeds 100%. However, heat pump performance and energy savings vary with climate and individual household energy usage. Recent studies have used geospatial models to estimate potential heat pump energy consumption across the United States. Yet most studies use generic and oversimplified heat pump models. We contribute to this field with a geospatial model based on manufacturer data and measured test data for 16 different R410A, high efficiency, variable speed compressor heat pumps. Using linear regression, we estimate a market average of COP with respect to ambient temperature. From this, we can identify the variation in efficiency with temperature across this technology class. We also use linear regression to estimate demand for heating and cooling as a function of ambient temperature and household characteristics. We compare the performance of both the predicted energy demand and heat pump efficiency against measured data from a heat pump-equipped house in West Lafayette, Indiana, and find that the model predicts daily heat pump electricity consumption with 27.8% relative error, comparable to other building simulation models. By incorporating high-resolution geospatial data inputs, such top-down models can still maintain a large scope across technologies and diverse climates while increasing spatial and temporal resolution.


Introduction
The heating sector accounts for almost half of total global energy consumption, with only 1/10th of heat produced from renewables (International Energy Agency 2022). In the United States, residential energy consumption-largely attributed to space heating and cooling-emits 20% of greenhouse gases (Energy Information Administration 2022a, 2022b). Heat pumps are key to electrifying heating, expanding the use of decarbonized electricity for residential energy use, and minimizing energy expenses. Heat pumps use electricity to transfer-rather than generate-heat from a reservoir (usually air, water, or ground) to an indoor space. This energy transfer means heat pumps achieve efficiencies greater than 100%, which reduces primary energy consumption and can contribute to consumer cost savings. While 32% of households in the U.S. would already economically benefit from installing a heat pump today (Deetjen et al 2021), the cost savings and emissions reductions can vary based on climate, local energy prices, and individual household energy use. Different heat pump technologies will be better suited for different environments, and we need tools that can examine both the technical performance of heat pump technologies and geospatially analyze local trends and conditions to assist in technology selection.
Evaluating heat pump performance is dependent on the amount of heating or cooling households consume, and using this information to estimate how much electricity heat pumps will consume to provide those services. Methods for estimating energy demand are typically categorized as either top-down or bottom-up models (Swan andUgursal 2009, Kavgic et al 2010). Top-down models typically split energy demand by fuel type (electricity or residential fossil fuel consumption), and use predictors like GDP, household income, energy prices, and averaged weather data to estimate energy demand. The time horizon of these models can also vary, with economic variables serving as better predictors for energy demand in future years or decades. Meanwhile weather-related variables are better predictors for monthly or hourly energy demand predictions, especially for residential natural gas consumption (Soldo 2012, Liu et al 2021. In these cases, linear regression models using outdoor air temperatures have proven extremely effective at predicting natural gas demand, since most natural gas is used for space heating (Soldo et al 2014, Hribar et al 2019. Bottom-up models of energy demand can use statistical methods or engineering models to account for energy consumption by specific end uses. Like top-down models, statistical bottom-up models frequently use regression analysis of building characteristics, weather data, and energy consumption data (Min et al 2010). Engineering models will use representative building types and equipment specifications to estimate energy consumption (Rhodes et al 2015), and may try to extrapolate to explore impacts of building technology adoption of broader energy networks. This extrapolation also relies on using statistical information similar to bottom-up statistical models (Swan andUgursal 2009, Soldo 2012).
Models that account for how heat pumps will influence energy demand predictions are less common than energy demand models that assume continued use of conventional space heating technologies. Yet many have used both top-down and bottom-up modeling frameworks. Previous top-down models have considered changes to national energy consumption in the U.K. if residential heating were provided by electricity, using a scenario analysis of fixed heat pump coefficients of performance (COP) (Wilson et al 2013). A similar analysis for the U.S. disaggregated energy consumption by census tract to estimate how an increase in heat pump adoption would impact peak electricity demand, using three different U.S. Department of Energy heat pump performance targets that vary with temperature (Waite and Modi 2020). Others have used breakeven analysis to identify a fixed COP at which heat pumps would reduce each U.S. state's emissions or energy costs, explicitly ignoring how heat pump performance varies with temperature due to differences between heat pump models (Walker et al 2022). In each case, there was relatively little differentiation or specification of the type of air source heat pump chosen, which can have significant impacts on overall electricity consumption.
Bottom-up engineering studies that use building simulations allow for more examination of how individual heat pumps use energy. Studies have examined how heat pump control systems and priorities for space and water heating impact the demand response services heat pumps can provide (Clauß and Georges 2019). Other bottom-up models will use building simulation models of representative homes to examine the energy consumed by heat pumps generally, and the climate impacts of the transition from fossil fuels to electric heating systems (Vaishnav and Fatimah 2020). Some have focused on different heat pump configurations, including specific refrigerants and compressor configurations, for a variety of locations throughout the U.S. (Lu and Ziviani 2022). Other models have combined building simulation models with controlled operation of real heat pumps. One model compared a simulated building and measured performance ground source heat pump, where the setpoint temperature was both fixed and known, as were additional characteristics about the building, resulting in a difference of 0.01% and 2.7% between the modeled and measured data (Rad et al 2013). While each of these building simulation studies is helpful for examining the performance of specific technologies, they still rely on statistical information to extrapolate the impacts to electricity grids or other macro energy systems. This leads to reduced prediction accuracy for out-of-scope households. Bottom-up models that rely on statistical methods to predict end-use heat pump energy consumption are more limited, with one study aiming to use economic variables and other technology diffusion models to estimate changes in energy consumption (Eggimann et al 2019). This study used aggregated empirical data to extrapolate an average electricity consumption profile for air source and ground source heat pumps in the U.K.
Here we explore a hybrid model to estimate demand for heating and cooling and then determine how heat pumps can meet that demand. Similar to most top-down heat pump energy consumption models, we utilize weather, housing, and energy consumption data. However, we disaggregate this data into the smallest resolutions possible: at the census tract level for housing characteristics and weather, and at the state level for energy consumption. The combination of weather and energy consumption data allows us to separate heating and cooling energy use from other energy uses. We supplement this statistical information with a model of heat pump efficiency that varies with temperature based on both measured and reported performance. To test the accuracy of our model, we conducted a case study of the model to predict energy consumption for a house in West Lafayette, Indiana, and compare the estimated heat pump energy consumption against measured data for this household. By constructing a hybrid model using top-down methods and high resolution data, our model achieves a large geographical and temporal scope while maintaining high spatial and temporal resolution results. While our household-level case study shows high-resolution spatial results, we are also capable of expanding our model scope to the state and national level, and can incorporate new heat pump technologies as the market continues to evolve. Preserving technological and spatial detail is extremely important to provide insight to how technology differences influence the overall impact of heat pump adoption at scales necessary to achieve decarbonization targets.
The rest of the paper will proceed as follows: the second section will go over the data and methods used to construct energy demand models and a heat pump model. Then, we will present our results-model outputs and case study findings-followed by conclusions.

Methods
Our model consists of an energy demand model based on publicly available residential energy consumption data, local air temperatures, and housing characteristic data. This energy consumption data is then used to estimate the actual thermal energy demand, using information about residential heating and cooling equipment efficiencies. Finally, we model how different heat pumps perform at different temperatures, and use this performance data to estimate the electricity necessary for a heat pump to provide the same thermal comfort energy as current systems. We compare this estimated electricity consumption to measured energy consumption for a comparable heat pump using data from the Nanogrid House. Figure 1 shows our overall workflow with yellow signifying input data, blue signifying our models, and green signifying model outputs.

Energy demand model
As a test case, we estimate energy demand for West Lafayette, Indiana. To do so we first obtained hourly temperature data from NASA's Modern-Era Retrospective analysis for Research and Applications Version 2 (MERRA-2) dataset (Global Modeling and Assimilation Office (GMAO) 2015). NASA satellites and data assimilation provide MERRA-2 data on a uniform grid of resolution 0.5 • × 0.625 • . We used distance calculations between centroids to attribute the MERRA-2 dataset temperatures to each census tract. Information about heating fuels used in each Indiana census tract was gathered from the U.S. Census Bureau, and census-tract level housing area data from the Federal Emergency Management Agency's Hazus software and database (Federal Emergency Management Agency 2021, US Census Bureau 2022). The Hazus database relies on 2010 census data, limiting the other variables of our training data to the year 2010. We took state-level, monthly energy consumption data from the U.S. (Energy Information Administration (EIA) 2020, 2021, 2022c). Our residential heating and cooling demand models use a linear least squares regression to estimate energy consumption by fuel type per square foot for each census tract. One model estimates electricity consumption and the other, fossil fuel consumption. Both models contain a temperature-independent term and temperature-dependent terms based on the difference between observed ambient temperatures and a reference temperature. Linear regression models with outdoor air temperatures as a predictive variable have proven to be effective for estimating energy demand for space heating and cooling (Hribar et al 2019, Liu et al 2021. We assume that the temperature independent term represents non-heating and non-cooling energy demand, such as cooking or home appliance usage, and use similar data to disaggregate demand by census tracts and time steps as previous studies (Waite and Modi 2020). Equation (1) shows the fossil fuel consumption model Here, Y FF, i, t is estimated fossil fuel consumption in each census tract i at time t in hours, A is household square footage for each census tract, p FF, i is the percentage of households using fossil fuel for heating in each census tract, w 0, FF, s represents the fossil fuel consumption of the state s independent of temperature (i.e. cooking, clothes dryers), and w H, FF, s is the relationship between fuel consumption and heating for state s. In our case study, we examine statewide energy consumption data for Indiana. T amb, i, t is the ambient temperature in each census tract i at time t in hours, and T ref is the reference temperature. The plus sign next to the temperature differences in parentheses denotes that any negative temperature difference values are set to zero. There exists one of these equations for Y FF, i, t for each census tract i at each hourly timestep t.
The reference temperature is defined as the outdoor temperature at which heating (or cooling) equipment turns on. Common practice also suggests setting the reference temperature conservatively at 65 • F (18.3 • C) (Alberini et al 2011, Waite andModi 2020). In addition, the fossil fuel consumption model assumes that fossil fuel is used only for heating and not cooling.
Similarly, we build an electricity consumption model shown in equation (2). Here, Y elec, i, t is estimated electricity consumption in each census tract i at time t in hours, p elec, i is the percentage of households using electricity as heating fuel in each census tract, p AC, i is the percentage of households using electricity for cooling in each census tract, w 0, elec, s represents a state's electricity consumption independent of temperature, w H, elec, s is the relationship between the state's electricity consumption and heating, and w C, elec, s is the relationship between state electricity consumption and cooling. The negative sign next to the temperature differences in parentheses denotes that any positive temperature difference values are set to zero To find the percentage of homes with air-conditioning, we fit a curve based on the relationship between cooling degree days and percentage of homes with air conditioning in U.S metropolitan areas (Waite and Modi 2020, National Oceanic and Atmospheric Administration 2021, US Census Bureau 2021). The curve is then used to estimate the percentage of homes with air conditioning for each census tract.
We then minimize the residual sum of squares to solve for w 0 , w H , and w C for equation (1) and equation (2). Due to the difference in spatial and temporal resolution for consumption and temperature data, this minimization involves summation of our consumption estimates over the time and space dimensions as shown below for fossil fuel consumption. The model was also constructed using 2010 data due to the use of 2010 data by the FEMA housing area database Here, RSS FF,s is the residual sum of squares for the fossil fuel consumption model for state s-in our case Indiana. The variable m denotes month and Y (2010) FF is the actual state-level fossil fuel consumption in 2010. From this we obtain w 0, FF, s and w H, FF, s . We minimize RSS elec,s in the same way to obtain w 0, elec, s , w H, elec, s , and w C, elec, s .
In addition, fuel consumption data from the U.S. EIA is based on information from fuel suppliers, which means that fuel oil, kerosene, and propane data is based on amounts of fuel stored but not immediately used. Natural gas data is reported as actual monthly usage. We assume that total actual fossil fuel usage by month scales with natural gas usage, as shown in equation (4) Y Here, Y (2010) NG, s, m is the state-level natural gas consumption in 2010 for a given month, Y (2010) FOK, s is the state-level annual fuel oil and kerosene usage, and Y (2010) prop, s is the state-level annual propane usage.

Thermal comfort energy demand
We then convert the energy demand estimates to thermal comfort energy demand. We define thermal comfort energy demand as the energy (or heat) added or removed to a space that the household experiences as opposed to the actual energy consumed by the heating or cooling equipment. Thermal comfort delivered differs from the equipment energy consumption because of the efficiencies of the heating and cooling equipment. The efficiencies of furnaces and air conditioners are based on energy efficiency standards. Furnaces have been required to have an annual fuel utilization efficiency (AFUE) of at least 78% since 1987 (National Appliance Energy Conservation Act of 1987Act of , 1987. In 2007, ENERGY STAR standards for furnaces increased to an AFUE of 90% (ENERGY STAR ® 2006). We calculated a weighted average AFUE using ENERGY STAR furnace purchase data until 2010 (Energy Information Administration 2013a, 2018a, ENERGY STAR ® 2021). In 2009, less than 5% of Indiana and Ohio homes were heated with heat pumps, so we assumed that electric heat was provided via resistance heaters with 100% efficiency (Department of Energy 2013, Energy Information Administration 2013a), and all cooling is provided via electric air conditioners. We base the efficiency for these air conditioners on a weighted average of the seasonal energy efficiency ratio (SEER)-an industry rating of seasonal cooling energy output to electricity input, and age of air conditioning equipment (Energy Information Administration 2013b, 2018b). Before 2006, the minimum standard cooling efficiency of air conditioners was 10 SEER, and after 2006 the standard was increased to 13 SEER (Energy Information Administration 2019).
Here, TCED i, t is thermal comfort energy demand in each census tract i at time t in hours, η FF is fossil fuel heating equipment efficiency, η H, elec is electric heating equipment efficiency, and η C,elec is air conditioning efficiency.

Heat pump model
We then convert the thermal comfort energy demand into an estimate of heat pump electricity consumption by multiplying the hourly thermal comfort energy demand by a heat pump technology's COP. The COP is highly dependent on temperature, with peak efficiencies observed at temperatures closest to the reference temperature.
We obtained most heat pump data from openly accessible engineering manuals from original equipment manufacturers (OEMs). Out of the 16 HP models studied (shown in table 1 of the supplementary information) only the data for '25VNA' was acquired from lab testing (Dhillon et al 2022). The heat pump models were chosen with regard to three main criteria: a high SEER value of 20 and over, a variable speed compressor technology, and R410A as the refrigerant. Currently, R410A refrigerant is the most commonly used refrigerant for heat pumps in the U.S. market, and most available OEM data is for systems with this refrigerant. We chose high SEER units with more efficient variable speed compressors to represent technologies that may be adopted by households in the near future. These units were also found to be efficient when considering their heating performance, with heating seasonal performance factors (HSPF, a ratio of the seasonal heat delivered over to the electricity consumed) of up to at least 9 (a rating of 8.2 is sufficient for an EPA Energy Star rating).
Each heat pump was studied individually using the manufacturers' data. For each, the COPs at different ambient temperatures were calculated using the given heat (Q) and electricity consumption (W) values in OEM heat pump model specification sheets with equation (6). Heat output and electricity consumption values for each technology were averaged over all given heat pump capacities, chosen at the lowest given airflow, and chosen at the indoor dry and wet bulb temperatures closest to the reference temperature The COP values were plotted as a function of temperature, and we fit a linear regression model to estimate the relationship between COP and temperature. While we explored polynomial models, the low R 2 values generated and high error in operating temperature of polynomial models at the studied temperatures favored the use of two discontinuous linear regression models (one for heating mode and one for cooling mode). Finally, we average these linear regression models together, to estimate a market average relationship between temperature and COP.

Heat pump COP model
In figure 2, we plot the linear regression estimates of COP based on all OEM data and our set of actual test data. The COPs are discontinuous at the preset reference temperature (18.3 • C), signaling a shift from heating to cooling mode. This shift represents a simplification of U.S. market heat pumps' performance shifts with climate. Even within one operational mode, there is substantial variation in COP at the reference temperature. For heating, COPs range from approximately 3 to 5. At that range, the higher COP means that approximately 40% more thermal comfort energy could be provided for the same input electrical energy. Similarly, the range from approximately 4 to 6.5 for cooling equates to more than 60% of thermal comfort energy removal possible for the same input electricity.
For all of the heat pumps, we notice large reductions in COP as temperatures become more extreme. The variation in COP with temperature also differs by specific model, despite the fact that these heat pumps each have similar design characteristics. For some heat pumps at very low temperatures, they underperform even an electric resistance heater, which would have a COP of 1.
In figure 2, we also see that the model based on actual test data tends to have the lowest COP compared to the rest of the models (all based on OEM data). This result shows how OEM performance metrics can overestimate actual COP (Dhillon et al 2022).
We then averaged the slopes and intercepts of each of the temperature-dependent linear regression lines to find the market-wide average model. The resulting average models for both heating and cooling are shown in equations (7) and (8) respectively where T denotes the ambient temperature in degrees Celsius COP Heating = T * 0.0634 + 3.283 (7) COP cooling = T * − 0.1004 + 7.151.
We also quantified the error and uncertainty of the average heat pump model in equations (7) and (8) in comparison to OEM and measured heat pump data. The relative root mean squared error (RRMSE, calculated using equation (9) for the heating mode model was 38.2% while the RRMSE for the cooling mode model was 16.8%. This is consistent with the data shown in figure 2, which shows there is less variation in COP amongst the heat pump models considered when operated in cooling mode than in heating mode. The 95% confidence intervals for the slope and intercept of equation (7) were [0.0607, 0.0661] and [3.246, 3.319], respectively. The 95% confidence intervals for the slope and intercept of equation (8)  (9) Figure 3 shows the hourly average energy consumption by month from January 2020 to December 2022 for both the business-as-usual combination of heating and cooling equipment, and the average R410A heat pump. The business-as-usual scenario represents current average heating and cooling equipment in Indiana-largely furnaces, electric resistance heaters, and air conditioners. We see the minimum point of energy consumption near the set reference temperature. Since we calculate average energy consumption, this minimum point is not exactly at our reference temperature 18.3 • C. At temperatures less than the minimum point temperature, the equipment is in heating mode. At temperatures greater than the minimum point temperature, we see the equipment is in cooling mode. The figure shows that the business-as-usual case always consumes more energy than the heat pump model, especially during heating mode. In cooling mode, the two scenarios show closer energy consumption levels due to current air conditioners exhibiting similar-but still less efficient-performance compared to the average R410A heat pump. In short, the figure shows that this market average heat pump can save more energy in heating mode than in cooling mode, at least for West Lafayette, IN.

Nanogrid House case study
To test the validity of our heat pump electricity consumption models, we compared them to collected heat pump energy consumption data from the DC Nanogrid House (figure 4). The Nanogrid House is a two-story 1920's era home located in West Lafayette, Indiana which houses three graduate students. The house includes 208 m 2 of floor space and works towards an implementation of a house-level nanogrid. Due to the nature of  this work, the house utilizes multiple data acquisition (DAQ) systems and a network of Internet of things devices to gauge the performance of their various household appliances and systems (Ore 2021). The heat pump used at the house is an 18 SEER, 10 HSPF, variable speed unit from TRANE. At the time of the data collection for this case study, the heat pump system was still operating on AC power. Since our  study focuses on highly efficient heat pumps with variable speed compressors, we found the used heat pump at the Nanogrid House sufficient for the case study. The electricity consumption of the house's heat pump was obtained through one of their DAQ systems, The Energy Detective (TED ® ) Pro Home. TED collected daily energy consumption for the operation of the heat pump's compressor, fan, and any additional heating associated with it. Summing those categories, we obtained the heat pumps total daily energy use. Figure 5 compares the daily Nanogrid House heating and cooling energy consumption data from 25 August 2020 to 2 March 2022 with our model, which uses the averaged heat pump model from equations (7) and (8). For the averaged heat pump model, the RRMSE on daily electricity consumption was 27.8%.
Our model estimates the heating period of the data better than the cooling period, as seen in figure 5 where the Nanogrid House cooling energy consumption is lower than the modeled energy consumption. Some possible sources of error include our inability to account for decreasing efficiency of air conditioning equipment over time, leading to an overprediction in thermal comfort cooling energy demand, or user behavior in operating the air conditioning at the Nanogrid House. Compared to bottom-up engineering or building simulation models with additional information about the building characteristics and setpoint temperatures, the error between the observed energy consumption and modeled energy consumption is relatively high. However, considering the model estimates energy consumption at a very high spatial resolution (in this case for a single household), our prediction accuracy is relatively good, and is comparable to individual household variation found within a study by Rhodes et al, without the use of a detailed building simulation model (Rhodes et al 2015). Furthermore, as the relative error decreases as the time horizon increases, we obtain a weekly RRMSE of 21.7%, and a relative difference of 10.3% (or an RRMSE of 1.07%) over the first year of our dataset.

Conclusions
A significant amount of literature exists concerning the potential benefits of various heat pump technologies. Such literature includes heat pump modeling but often on a single or several building-level. While such models can provide high prediction accuracy and high levels of technical detail, a smaller field of geospatial heat pump analysis has grown to assess heat pumps' effects on entire regions and countries.
Our model's scope falls in the latter category but also incorporates data from a specific heat pump technology-variable speed compressor and R410A refrigerant. We construct our model first with an energy demand model to estimate fossil fuel and electricity consumption at a census tract, hourly resolution. Using linear regression, we incorporate predictors of temperature to split estimates into heating and cooling. We also weight the estimates using housing area and percentage of homes using the heating fuel. Next, we use assumed current heating equipment and efficiencies to calculate thermal comfort energy demand. After building individual linear regression models for each variant of our chosen heat pump technology with respect to temperature, we averaged the models. We then divide the thermal comfort energy demand at each hour by the respective COP, giving the estimated heat pump electricity consumption. We then perform a case study comparing our estimates to energy consumption data from an operating heat pump in the Nanogrid House.
The main conclusions of this research are as follows: • Our hybrid top-down, high resolution model achieves a RRMSE of 27.8% for daily household-level heat pump electricity consumption. • Heat pump model performance estimates vary with respect to OEM data and measured heat pump test data incorporation. • In West Lafayette, Indiana, the business-as-usual case always results in higher energy consumption than the heat pump adoption case, especially during heating mode.
Our research compares the applicability of top-down models for individual homes with real-world heat pump data. With high resolution data inputs, such models can still maintain a large scope while increasing spatial and temporal resolution. These traits are extremely important to provide insight to technology impacts and implementation.

Data availability statement
Most of the data and code that support the findings of this study are openly available at the following URL: https://github.com/kbisco/Comparing-Top-Down-Heat-Pump-Energy-Consumption-with-Measured-Data. The data for the Nanogrid House heat pump energy consumption is available upon reasonable request from the authors.