Hourly accounting of carbon emissions from electricity consumption

Carbon accounting is important for quantifying the sources of greenhouse gas (GHG) emissions that are driving climate change, and is increasingly being used to guide policy, investment, business, and regulatory decisions. The current practice for accounting emissions from consumed electricity, guided by standards like the GHG protocol, uses annual-average grid emission factors, although previous studies have shown that grid carbon intensity varies across seasons and hours of the day. Previous case studies have shown that annual-average carbon accounting can bias emission inventories, but none have shown that this bias is substantial or widespread. This study addresses this gap by calculating emission inventories for thousands of residential, commercial, industrial, and agricultural facilities across the US, and explores the magnitude and direction of this bias compared to hourly accounting of emissions. Our results show that annual-average accounting can over- or under-estimate carbon inventories as much as 35% in certain settings but result in effectively no bias in others. Bias will be greater in regions with high variation in carbon intensity, and for end-users with high variation in their electricity consumption across hours and seasons. As variation in carbon intensity continues to grow with growing shares of variable and intermittent renewable generation, these biases will only continue to worsen in the future. In most cases, using monthly-average emission factors does not substantially reduce bias compared to annual averages. Thus, the authors recommend that hourly accounting be adopted as the best practice for emissions inventories of consumed electricity.


Introduction
Greenhouse gas (GHG) emissions from electricity generation are a significant contributor to climate change and can comprise a large share of the carbon footprint of an individual activity, product, building, company, or city. Accounting and attributing these emissions to specific end-users of the electricity is a common practice and important tool to help understand the sources of climate-changing emissions and enable action to mitigate them. Once limited to academic life-cycle assessment studies and voluntary carbon disclosure initiatives, carbon accounting and disclosure is increasingly being used to guide financial investments, inform policymaking and business decisions, and measure compliance with regulations.
Current GHG accounting protocols account for 'scope 2' emissions (those associated with the consumption of grid electricity) by applying an annualaverage, attributional grid carbon intensity factor to all electricity consumed by an entity each year. This annual-level accounting represents the carbon intensity of grid-supplied electricity as a single, static value throughout the year. However, because the mix of generators supplying electricity to the grid is constantly changing, grid carbon intensity also varies across seasons and the hours of each day [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. While there are benefits to the simplicity of annuallevel accounting, ignoring this hourly heterogeneity may come at the cost of accuracy, which can have real effects both on academic analyses and the effectiveness of our policies in curbing climate change [16]. However, it is unclear from previous studies whether this potential bias is a substantial or widespread problem. Existing studies, primarily in the field of life-cycle assessment, focus on specific building GHG inventories as case studies, demonstrating that annual accounting may bias emission inventories anywhere between 0.2% and 26% when compared to hourly accounting, as summarized in table 1 [3, 5-8, 17, 21, 22] 4 .
To understand whether annual accounting leads to widespread bias in emission inventories, this study calculates scope 2 GHG emission inventories for approximately 113 000 simulated residential and commercial buildings in 52 grid balancing areas (BAs) across the United States, using annual-average, monthly-average, monthly time-of-day (TOD) average, and hourly grid emission factors. We also examine a specific case study of a high-renewable region in California, utilizing a dataset of actual metered load representing over 13 million residential, commercial, industrial, and agricultural facilities in the state. Our results suggest that the magnitude and direction of the bias introduced by annual accounting depend on when and how you consume electricity and where you are located: specifically, activities with more variable electric demand located in grids dominated by clean and renewable energy will see a larger relative bias from annual accounting than activities with flat demand in grids dominated by traditional fossil generation. We also find that these biases can only be meaningfully reduced by using emission factors that reflect both the seasonal and TOD variation in grid carbon intensity.

Background
The carbon intensity of the grid can vary continuously in response to changes in generation at the minute or second timescale. Thus, even hourly emission factors may not capture the full variability in grid carbon intensity. Indeed, some previous studies evaluating the variability of grid carbon intensity have utilized half-hourly or quarter-hourly emission factors [10][11][12]22]. However, in this study, we use hourly-average carbon intensities as the baseline rather than sub-hourly values, first because hourly grid data is more widely available than sub-hourly data, and second due to the relatively low variation 4 A separate body of literature has focused on comparing the accuracy of using of average, attributional emission factors to marginal, consequential emission factors for quantifying the avoided emissions of grid interventions. However, it is important to note that marginal emission factors are not appropriate for use in attributional carbon footprinting and are thus not relevant to this paper. in grid carbon intensity within a single hour. Previous studies note that the variability of wind and solar power, which contribute to the variability of grid carbon intensity, is much less at the hour or shorter timescale than it is across several hours or days [23]. We confirmed this by analyzing a dataset of 5 min resolution carbon emissions data published by the California independent system operator (ISO), finding that even in this renewable-heavy region, the mean coefficient of variation of grid carbon intensity within a single hour was only 2.4%, compared to 31% across the entire year.
Because we calculate actual carbon emissions as the product of hourly energy demand (D h ) and the hourly regional carbon intensity (C r,h ), the bias resulting from using an averaged carbon intensity value (C r,h,l ) at some aggregation level l is the product of the hourly energy demand and the residual carbon intensity (µ r,h,l =C r,h,l − C r,h ). Thus, the expected bias introduced into an annual inventory by using an averaged carbon intensity value can also be expressed as the following equation (see the supplementary information [SI] for a full derivation available online at stacks.iop.org/ERL/17/044073/mmedia): In this equation, σ D is the standard deviation of hourly energy demand, σ µ is the standard deviation of the residual hourly carbon intensity, and ρ D,µ is the correlation coefficient between hourly energy demand and the residual hourly carbon intensity. This relationship suggests that the magnitude and direction of bias is driven by the variability in both carbon intensity and energy demand, as well as the correlation between demand and carbon intensity, and it has three important implications. First, in regions with substantial variation in hourly emissions rates (high σ µ ), there is a potential for larger bias, and vice versa. Second, end-uses of electricity with sizable hourly variation in energy demand (high σ D ) would expect to see larger biases than an end-use with flat energy demand. Finally, the sign of the bias (whether the inventory is over-or under-estimated) will depend on the sign of the correlation coefficient between demand and the residual carbon intensity (ρ D,µ ). An end-use whose demand is correlated with times of high carbon intensity (and is thus negatively correlated with the residual carbon intensity), will have their emissions under-estimated by using an averaged carbon intensity value.
As shown in figure 1, hourly consumption-based carbon intensities in certain regions can be highly variable throughout the year, depending on the fuel mix of generated and imported electricity consumed in the region. While production-based carbon intensities only reflect emissions from generators that operate within each region, consumption-based carbon  intensities reflect emissions from electricity imported into a region as well. Because imported electricity represents a substantial portion of consumed electricity in many regions and can have a carbon intensity that differs from that of in-region generation, this paper focuses on consumption-based carbon intensity throughout.

Data and methods
This study examines carbon inventories for thousands of building load profiles across the United States at different temporal resolutions. To demonstrate the impact that the intra-regional variability in carbon intensity has on the magnitude and direction of the bias resulting from annual-average accounting, this study first examines annual and hourly inventories for approximately 113 000 simulated residential and commercial buildings across different climate zones in 52 different grid regions in the US. Then, to demonstrate the impact that variability in electricity demand profiles has on this bias, this study examines inventories for thousands of residential, commercial, industrial, and agricultural building profiles located within the California Independent System Operator (CAISO). Finally, we explore how well the use of monthly and monthly TOD average carbon intensity values mitigates the inventory bias compared to using an annual average.

Hourly building demand data
Although as of 2019, over 60% of all electric meters nationwide included advanced metering infrastructure (AMI), which collect hourly or sub-hourly electricity demand data, wide-scale hourly demand datasets are not publicly available due to privacy concerns [24,25]. However, the National Renewable Energy Laboratory (NREL) recently published a dataset of approximately 900 000 simulated end-use load profiles which have been calibrated and validated using actual meter data and statistically represent the US residential and commercial building stock [26,27]. Each of the 14 unique commercial building types and nine unique residential building types (summarized in the SI) are represented by individual building variants with different combinations of physical and operational characteristics that affect the load profile. To keep the volume of data computationally manageable while representing the diversity of actual load profiles that would be found in each grid region, we select a stratified random sample of 10% of the buildings of each type located in each climate zone in each grid region, resulting in a sample of 112 717 unique load profiles.
However, the NREL dataset does not include load profiles for agricultural, industrial, and certain common commercial (e.g. data center) end uses. Thus, for our California ISO case study that examines the impact of different building load profiles on bias, we utilize a dataset from Lawrence Berkeley National Lab (LBNL). This LBNL dataset contains actual hourly AMI data representing over 13.1 million individual residential, commercial, industrial, and agricultural electricity customers (aggregated into 2766 building profiles) across the three major investor-owned utility territories in the California ISO territory (see SI for details) [28]. The choice of CAISO as a case study is also useful because the region is on the vanguard of renewable energy deployment and may be more representative of the carbon intensity variability of more and more grids as the energy transition continues.

Grid carbon intensity data
We source hourly average, consumption-based emission factors for each grid BA in the US from Carbonara, a carbon analytics platform developed by Singularity Energy [29]. This study utilizes carbon intensity values for 53 of the 75 grid BAs in the United States, which represent a spatial resolution that reflect actual power system boundaries and operations [30,31]. To calculate its production-based emission estimates, Singularity uses data on hourly net generation by fuel type for each BA from the U.S. Energy Information Administration's (EIA) Form 930, and multiplies it by the fuel-specific, annual-average, adjusted CO 2 output emission rate for that BA, from the U.S. Environmental Protection Agency's (EPA) eGRID2019 database [32]. To calculate consumption-based emissions, which account for imports and exports of electricity between BAs, they solve a multi-region inputoutput model which utilizes hourly BA-to-BA net interchange data from EIA-930 [16]. Using these hourly values, we then calculate annual, monthly, and monthly TOD averages.

Carbon inventory methodology
A carbon inventory I for each building b in each grid region r is calculated by summing the product of the building's hourly electricity demand D and the actual hourly grid carbon intensity C at each temporal aggregation level for each hour h in year: An estimated carbon inventoryĪ is then calculated in the same manner, but using an averaged grid carbon intensityC, which can have one of three levels of temporal aggregation l (annual, monthly, or monthly TOD): The relative carbon inventory bias from using averaged carbon intensity values is calculated as the percentage error compared to the hourly inventory:

Regional differences in carbon inventory bias
The results of the 112 717 carbon inventories that we calculated for residential and commercial buildings around the country reveal that the use of annualaverage carbon accounting can result in an overestimation up to 33% and underestimation up to 22% when compared to hourly-average accounting, although most bias falls in the range of ±5%. Importantly, as figure 2 demonstrates, the magnitude and direction of this bias depends on where you are located and who you are.
In certain regions, clustered near the center of figure 2, annual accounting introduces negligible bias for all inventories. Referring to figure 1, we can see that these low-bias regions tend to rely more heavily on fossil fuel generation and have low standard deviations in their hourly carbon intensity, which confirms what we would expect to see based on equation (1). In a region like Duke Energy Florida, which is supplied mostly by methane gas and has a small standard deviation in carbon intensity, we see a correspondingly low amount of bias, within the range of ±0.7%.
In contrast, in regions where the variability in hourly carbon intensity is higher, annual-average accounting results in higher inventory bias, although the magnitude and direction of the bias depends on the variability of the building load, and how highly correlated that load is with periods of high or low carbon intensity on the grid, both on a seasonal and daily basis. If building energy demand tends to peak during seasons or times of day that coincide with peaks in grid carbon intensity, annual accounting will tend to underestimate emissions. For example, in the New York ISO, where emissions peak seasonally in the summer and daily during daylight hours, annual accounting underestimates commercial building emissions because commercial building load follows a similar seasonal and daily pattern.
Because residential building demand profiles can peak at different times than commercial buildings, we see that in some regions annual-average accounting underestimates residential emissions while at the same time overestimating commercial building emissions. This can again be explained using equation (1), since we identified that the direction of the bias Figure 2. The relative bias that annual-average carbon accounting introduces compared to hourly accounting, for both residential and commercial buildings in each grid region. Each box plot shows the distribution of these biases for all building inventories in each region. The regions are ordered from lowest to highest median bias for all buildings in a region. The results for two regions were omitted from this figure (but can be found in the SI) for the readability of the results, as their relative biases ranged from −29% to +182%.
is driven by the sign of the correlation coefficient between demand and the residual carbon intensity.
Re-framing these results in terms of the regional energy supply mix, regions with higher bias tend to have higher shares of renewables, as renewables introduce more variability into the hourly carbon intensity. Additionally, emissions from buildings whose demand is positively correlated with the timing of generation from the predominant renewable energy source in the region will be over-estimated using annual-average accounting. For example, for buildings that consume energy more heavily during the day, annual average accounting will over-estimate emissions in solar-dominated regions and underestimate emissions in wind-heavy regions where wind tends to be stronger at night.

California ISO case study
While the national results primarily demonstrate how regional carbon intensity characteristics affect the bias introduced by annual-average carbon accounting, it also showed how the bias can differ for different building types with different energy demand profiles. To further explore these demanddriven impacts for a more complete set of electricity end users (including industrial and agricultural loads), this section focuses on a case study located within the California ISO, using a demand dataset representing millions of actual buildings in the state.
From the results presented in figure 3, we can see that the heterogeneity in the energy demand profiles of individual buildings within a single category of buildings means that it is not always possible to generalize conclusions about the magnitude and direction of bias of annual-average accounting. Commercial office buildings, for example, may have their inventories overestimated as much as 15% or underestimated as much as 10%. For data centers in California, we could conclude that annual-average carbon accounting overestimates emissions, although the magnitude of this bias ranges anywhere from 0.5% to 8% for an individual data center.
In the California ISO, which has a high penetration of solar generation, the carbon intensity tends to dip during the mid-day, which shapes the bias trends that we see in figure 3. Most commercial buildings, whose energy demand also peaks during the day, will have their emissions overestimated by annual-average accounting.
Industrial facilities, which can have larger swings in energy consumption between on-shift and off-shift times, and thus larger variability in energy demand (σ D ), tend to have higher emissions inventory bias resulting from annual-average accounting than commercial buildings. The exception is industrial processes which consume energy on a relatively continuous, 24/7 basis, like petroleum refining, for which the inventory bias is much closer to zero. For energy demand that is more intermittent or seasonal in nature, like agricultural water pumping and irrigation, annual-average carbon accounting can introduce much larger biases, in the range of ±30%, especially if the carbon intensity during the seasons or times of day when the pumping is occurring do not reflect the annual average, leading to a high correlation between demand and residual emissions (ρ D,µ ).

Inventory bias at different temporal resolutions
While hourly accounting using 8760 unique emission factors for each hour of the year will more precisely quantify the emissions attributable to each end user, it also introduces greater data management complexity for accounting practitioners. Thus, this study also examines whether the use of 12 monthly average emissions factors, which reflect annual seasonality, or 288 monthly TOD average emission factors, which reflect both annual and daily seasonality, could improve accuracy while limiting complexity. From a practical standpoint, monthly-average carbon accounting would be convenient because most endusers of electricity are billed monthly and thus have easy access to monthly electricity consumption data. Figure 4 plots the absolute percentage bias resulting from the use of annual average emission factors versus the absolute bias resulting from using 12 monthly average or 288 (12 × 24) month-by-hourof-day average emission factors for each end-user in each grid region. Panel (a) shows that monthlyaverage accounting can reduce bias by over 50% on average for residential buildings, while having no substantial impact on the bias for commercial . Each plot compares the absolute percentage bias for inventories calculated using monthly-average carbon intensities (top row) and monthly-TOD-average carbon intensities (bottom row) compared to the bias from using annual-average carbon intensities for both the national results (left column, N = 112 717) and the California case study (right column, N = 2766). Any points below the 45 • line in each plot mean that the higher resolution carbon intensity decreased bias compared to the annual resolution, and vice versa. For the California ISO case study (right column), the results are broken out by residential loads, commercial and industrial (C&I) loads, and agricultural and water pumping loads.
buildings. Monthly-average accounting does not, however, lead to a systematic reduction in bias: approximately one-quarter of buildings showed no improvement or even an increase in bias when using monthly-average accounting. In panel (b), we can also see that for facilities with highly seasonal energy demands, such as water pumping and irrigation, monthly-average accounting may substantially reduce inventory bias compared to annual-average accounting, because these monthly averages reflect the predominant seasonality of the energy demand. These results suggest that monthly-average accounting could be beneficial for certain types of buildings in certain regions, but it does not represent a substantial improvement on a systematic basis.
The bottom panels of figure 4 demonstrate that monthly TOD average accounting substantially reduce, though do not eliminate, carbon inventory bias compared to annual-average accounting for all building types. This is because monthly TOD averages reflect both seasonal and daily patterns which are present in most energy demand profiles. These results suggest that the use of monthly TOD average emissions factors for accounting may strike a reasonable balance between simplicity and accuracy. However, in practice, monthly TOD average data may not be that much simpler to use than hourly emissions factors, because hourly energy demand data would still need to be collected and analyzed to use these emission factors.

Recommendations
Accuracy is one of the fundamental GHG accounting and reporting principles described by The GHG Protocol. As noted in the Protocol's Corporate Accounting and Reporting Standard, 'data should be sufficiently precise to enable intended users to make decisions with reasonable assurance that the reported information is credible. GHG measurements, estimates, or calculations should be systemically neither over nor under the actual emissions value, as far as can be judged, and that uncertainties are reduced as far as practicable' [33].
As explained through equation (1), the results illustrate how the bias in carbon inventories is based on a combination of factors including the variability in hourly building demand, the variability in hourly carbon intensity, and the correlation between building demand and grid carbon intensity. If any one of these factors is small (close to zero), whether because building demand is relatively flat, grid carbon intensity is relatively flat, or the variation in either is mostly random and uncorrelated with the other, then the bias introduced by using annual accounting will be small.
However, the results of this study make clear that in today's electricity system, annual-average emissions accounting yields imprecise emission inventories in most regions and for most end-users. In addition, this study shows that monthly average emission factors do not reliably or substantially address this bias. Thus, we recommend that hourly or sub-hourly accounting be adopted as the best practice for attributional GHG accounting of grid-consumed electricity and for location-based scope 2 GHG inventories.

Implications and urgency
These results have broad implications for many fields including voluntary climate disclosure, building performance regulations, carbon pricing, communityscale climate action planning, climate-based investing, and general business decisions. As emissions accounting is increasingly incorporated into regulations, carbon pricing, and business decisions, the bias from annual-average carbon accounting could have real-world legal and financial implications. For example, New York City's Local Law 97 set a carbon emissions cap (enforced with a substantial fine of $268 ton −1 in exceedance) for 50 000 buildings in the city and will go into effect in 2024. If this law were to use annual-average grid emissions factors for accounting, the results of this study suggest that the emissions for commercial buildings located in the New York ISO could be underestimated by up to 7%, eroding the efficiency and effectiveness of this law.
These findings are also relevant to crafting effective transportation policies, especially those that require accurately quantifying air pollution related to charging electric vehicles (EVs) relative to pollution from internal combustion engines. For example, California's low carbon fuel standard, which is designed to decrease the carbon intensity of the state's transportation fuels, currently calculates its base EV charging credits based on annual-average grid carbon intensity, which may be eroding the efficiency of this credit market [34,35].
This research has several important implications for the academic research community, especially in the fields of lifecycle assessment (LCA), energy and climate policy research, and transportation research. Due to the ubiquity of electricity as an input to the manufacturing and use phase of many products, our findings suggest that hourly emissions factors should be used whenever possible for conducting attributional LCAs, especially when evaluating emissions from individual plug loads or end uses whose demand profile can be more variable than those of entire buildings. Although this study focused on the bias introduced in carbon inventories, future research should evaluate whether these biases also translate to other criteria pollutants (such as NO x , SO x , and particulate matter), which are also relevant to many LCAs.
Beyond the implications of this bias on scope 2 emissions inventories, these results also have implications for the accuracy of an organization's scope 3 inventory, which focus on upstream sources of emissions, such as the emissions of raw materials or products. Especially for organizations who rely on energy-intensive raw materials such as aluminum, annual-average accounting could lead to inaccurate calculations of the lifecycle emissions associated with those inputs into their products.
Although this study focused on carbon inventories for individual buildings, and thus do not tell us about the annual accounting bias for communityscale or company-wide emissions inventories (which include buildings of many different types, possibly across many grid regions for a company with a national or international footprint), it nonetheless has important implications for how emissions are allocated within the inventory. For example, a community-scale inventory may seek to identify whether residential or commercial buildings represent a larger share of emissions, or a corporate-wide inventory may seek to identify which business region is responsible for the most emissions, so that funding and resources can be allocated to mitigate the largest sources of emissions. These results suggest that the bias introduced by annual accounting could potentially mis-allocate emissions between building sectors or regions, thus mis-informing these types of prioritization efforts.
Annual accounting can also limit effective decision-making about individual carbon-mitigation efforts, such as energy efficiency investments. Using annual-average accounting would lead a decision-maker to believe that whichever project reduces the greatest number of kWh will reduce the organization's carbon footprint most effectively. However, using hourly accounting might reveal that if that project mostly reduces energy consumption when grid emissions are low, then the value proposition of that project would be undermined compared to a project that reduces consumption during hours of high carbon intensity.
The findings of this paper, and in particular the drivers of bias explained through equation (1), lead us to believe that these annual accounting biases will only get worse, based on current trends in building energy demand and grid carbon intensity. As grids continue to integrate more variable and intermittent renewable energy sources to meet state Renewable Portfolio Standards and other climate goals, the variability in hourly carbon intensity will likely increase, increasing σ µ and inventory bias [12,22,36]. On the demand side, as more and more large end-use loads are electrified, such as vehicle charging, water heating, and space conditioning, building the total facility load profiles may become spikier and more variable, increasing σ D and inventory bias [3]. Furthermore, efforts such as time-of-use rates, managed charging, and carbon-aware demand response, which seek to shape and shift load to better match the times when carbon-free resources are available, may strengthen the magnitude of the correlation between energy demand and grid carbon intensity (ρ D,µ ), also increasing inventory bias. These three trends in combination, suggest that the continued use of annual carbon accounting will lead to inventories that become increasingly biased in the future.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://zenodo.org/badge/latestdoi/461343198.