Optimal strategies for a cost-effective and reliable 100% renewable electric grid

Climate change concerns and falling costs of renewable energy technologies are driving increased interest in clean and sustainable sources of energy.^1–5 Leveraging these trends, many U.S. states, cities, and municipalities are showing their commitment to reduce their environmental impact by developing plans to shift to 100% renewable energy sources.^6–10 Long-term societal benefits of this shift toward sustainability include decreased electricity costs, local job creation, cleaner air, and reduced medical costs related to pollution and other effects of climate change.¹¹ However, the most significant drawback of renewable sources is their inherent variability. Consequently, grid reliability is a major concern in an energy system where most of the electricity produced is from variable generation (VG) sources, such as wind and solar photovoltaics (PV).¹² 

Numerous studies have focused on understanding the role of energy storage in increasing grid reliability and balancing supply and demand in high VG penetration scenarios.^13–18 To date, there is no consensus on the required energy storage capacity for operating and maintaining a 100% renewable energy portfolio.^19–21 However, there is agreement among researchers that some energy storage is necessary to maintain a continuous power balance between a 100% VG supply and natural demand for electricity.²² Moreover, multiple energy storage solutions are likely to be required, with each system's unique characteristics being leveraged to address a specific grid challenge.²² For example, the fast response time of high-power flywheels and supercapacitors makes them inherently suited for regulating grid frequency. The higher energy densities of electrochemical storage well-position the technology for ramping and operating reserves. In contrast, larger-scale energy storage solutions, such as pumped hydro, compressed air, and hydrogen storage, will likely prove useful in addressing bulk energy management challenges given their economies of scale.^23,24

Current studies of VG penetration in power systems mainly focus on identifying strategies that minimize generation curtailment and maximize the economic value of renewable resources.^25–30 Denholm et al. investigated storage duration requirements for 55% VG penetration scenarios on the Electric Reliability Council of Texas (ERCOT) grid system and concluded that 4 h of storage reduces curtailment to 8%–10% of variable generation.²⁸ In a separate study, an 80% VG scenario on the ERCOT grid system was investigated, and results showed that storing or moving just 4-h of average system load could enable reliable operations while keeping renewable curtailment below 20%.²⁹ Another study investigated the storage needs for substituting fossil fuel plants with renewables in ERCOT and concluded that above 25%–30% renewable energy penetration, significant energy storage capacity is needed.³⁰ The primary objective function in this study was minimization of storage needs; hence, the minimization of the combined renewable and storage investment costs was not investigated. Moreover, these studies constrained the analysis to predefined curtailment limits; therefore, techno-economic tradeoffs between renewable curtailments and storage capacities were not considered. Finally, these studies do not consider the remaining 20% of renewable penetration needed to reach a 100% renewable target, which we show has the most significant impact on storage requirements and total investment costs to achieve the target.

Several studies have focused on the value of long-duration energy storage in scenarios with high adoption of renewable energy sources.^31–35 Shaner et al. investigated U.S. storage needs and concluded that above 80% renewable penetrations, seasonal misalignments in supply and demand would have to be overcome.³¹ Guerra et al. explored the value of seasonal storage for 83.5% renewable energy penetration in the western U.S. with an emphasis on power system operational benefits.³² The study concludes that 1-week of hydrogen storage could be cost-effective at US$1.8/kWh by 2025 [32]. Similar studies identified cost targets for long-duration energy storage technologies to compete against low-carbon sources, such as nuclear, and natural gas.^33,34 Sepulveda et al. conducted an analysis for Texas and New England and concluded that long-duration energy storage costs must be less than $1/kWh to fully displace firm low-carbon generation technologies.³⁴ It is important to note that the solution space in the mentioned studies is limited by their lack of consideration for supply-side strategies, such as excess generation capacity, and demand-side strategies, such as building load flexibility and permanent building energy efficiency investments. In addition, long-duration energy storage cost targets that compete against surplus renewable capacity and curtailment, in 100% renewable constrained formulations, are not identified in these studies.

Through recent efforts by Cebulla et al., an extensive synthesis of 17 country-wide storage expansion studies in the literature was conducted for Europe, Germany, and the U.S.³⁵ The study concludes that with increasing variable generation shares, energy storage power capacity requirements increase linearly, and the energy capacity increases exponentially. The study provides a good reference on general trends observed by recent research on the subject; however, their synthesis did not filter for energy storage requirements by imposed curtailment constraints, renewable generation mixes, or demand-side strategies. Moreover, their investigation did not account for U.S. regional implication on cost-effective 100% renewable power systems.

In a recent study, Perez et al. explored the impacts of overbuilding PV generation and concluded that proactive curtailment enables lowest cost solutions;³⁶ however, their analysis was constrained to PV curtailments only. In addition, their investigations are limited to a case study in the state of Minnesota. Through their investigations, they also consider supply side flexibility through a 5% gas generation allowance and show that this leads to major reductions in overbuilding PV.³⁶ However, their investigations do not include load flexibility strategies in strict 100% renewable scenarios.

The objective of this paper is to identify cost-optimal pathways to 100% renewable power systems for the U.S. building stock. Throughout the analysis, we focus on energy storage duration and capacity requirements that are necessary to achieve the target. In contrast to the current body of research, we consider regionally dependent opportunities and solutions that minimize total investment costs. In addition, our analysis removes renewable curtailment constraints that intend to maximize the economic value of VG resources. In doing so, we explore the tradeoffs of excess renewable generation capacity and associated curtailments on storage requirements and total investment costs. Furthermore, we consider readily available supply side and demand-side strategies that minimize total costs. Techno-economic investigations of demand-side strategies include building load flexibility and permanent building energy efficiency impacts. Building energy efficiency investments decrease the necessary renewable capacity, transmission capacity, and storage requirements; therefore, its impacts are threefold. We also consider the techno-economics of supply-side strategies such as oversizing VG sources and the diversification of renewable portfolios.

To summarize, the following list succinctly reiterates the novel elements of this research that have not been explored or identified in the literature:

1. We investigate a U.S. regional analysis of pathways to 100% renewable power at minimum total investment costs. In doing so, we identify cost-optimal and region-dependent strategies to reduce the otherwise dominant long-duration energy storage capacity requirements and associated costs.

2. We identify the optimum regional investment priorities and associated breakdowns by energy resource assets to achieve the target. Our analysis considers readily available supply-side and demand-side strategies, and energy assets.

3. We identify regionally dependent long-duration energy storage cost targets for emerging storage technologies. In contrast to published works, we identify long-duration energy storage cost targets needed to compete with oversizing of increasingly lower-cost renewable generation.

4. We reveal that a combination of (1) optimally mixed renewable resources, (2) oversized generation capacities, and (3) building energy efficiency investments can eliminate the need for long-duration energy storage in some U.S. regions. This is particularly important given that most long-duration storage technologies are either geologically constrained or still underdeveloped.²⁴ 

Our research also intends to demonstrate an overarching calculation methodology that can be leveraged by future site-specific studies of cities, states, municipalities, districts, and communities aiming to achieve cost-optimal 100% renewable status.

We begin our discussions in Sec. II by describing the methods used to develop the baseline model and for modeling generation, energy storage, building energy efficiency, and building load flexibility. Our results are presented in Sec. III, and in Sec. IV we highlight the limitations of our research and discuss opportunities for future work.

The goal of this paper is to investigate the total storage requirements and quantify the relative impacts of various readily available supply side and demand-side strategies on reducing its capacity and associated costs in 100% renewable targets. The investigation is conducted through the development of regional baseline models that are representative of the U.S building stock. This study explores optimal design scenarios that minimize total asset investment costs, which can be used to inform future investment priorities and cost targets for emerging storage technologies. The trends and opportunities for reducing storage requirements, and minimizing total investment costs, are explored in climate regions that span the U.S.

In this study, we consider the stringent case in which the demand must be met by renewable energy sources at all times. Therefore, nonrenewable power cannot be relied upon for unmet loads. The load cover factor (LCF),³⁷ given by Eq. (1) below, is the primary metric utilized in our analysis to quantitatively define whether the 100% renewable target has been met by a particular design scenario. Investigated design scenarios may comprise some combination of building energy efficiency packages, a diversified portfolio of properly sized renewable generation sources, energy storage assets, and flexible building load capabilities. The LCF metric represents the fraction of the load covered by renewable generation on an hourly basis, and a 100% renewable target is considered achieved when the LCF metric is equal to 1,

In Eq. (1), L represents the hourly load profile, G is the hourly renewable generation profile, T is the total time under consideration (one year), $Δt$ is the simulation time step (1-h), and i represents a specific time step in the simulated year. Note that the lowest possible LCF value of 0 is reached when the load and generation are nonconcurrent at all instances of time. In contrast, a maximum LCF value of 1 is reached when the generation overlaps or surpasses the load at every time step. The LCF metric will not exceed a value of 1, even in cases where the generated electricity is several times greater than the load.

An LCF value of less than one indicates misalignments in load and generation, which may require reshaping their profiles to achieve an LCF of unity. Reshaping the load can be achieved through permanent building energy efficiency measures, dynamic building load flexibility methods, and through energy storage. Reshaping the generation profile can be achieved through the diversification of renewable portfolios and through oversizing generation capacities. This study optimizes the utilization of these strategies with the objective of minimizing the total investment costs to achieve a 100% renewable target. Through this study, we consider the current regional costs of generation and storage, and we show that the optimum solution leads to a substantial reduction in the otherwise significant storage capacities needed to achieve an LCF of 1 for the U.S building stock.

The need for energy storage and the methods for reducing its capacity are demonstrated in Fig. 1. The plots in Fig. 1 begin with a Typical Load & Solar Profile and progress from left to right to illustrate one sample pathway to maximize their overlap. The curves in the plot represent a sample load, in blue, and solar PV generation profile, in yellow. Excess solar power during the day is stored for times of day where solar is unavailable, as indicated by the gray shaded regions. Through energy efficiency, the load and required generation are reduced, as is the need for storage. Moreover, certain end-use loads can be shifted through thermal storage, flexible controls, and/or passive designs to times of available supply, therefore further reducing storage requirements.

Similarly, diversifying the renewable generation sources can lead to a reduction in storage requirements. Diversification has the effect of increasing the proportion of times that generation is available to meet loads, which can alleviate the need to shift energy use to times of abundant supply. In this study, we show that the optimal mixture of renewable sources can heavily depend on the demand, climate, and resource availability. Oversizing the generation can also reduce storage requirements by ensuring that loads are met during times of otherwise inadequate supply. This approach may require curtailing excess power during periods of abundant supply. We later show that oversizing generation can have substantial impacts on storage capacities, and in some cases potentially eliminating the need for storage.

The objective of this work is to identify total storage requirements and optimize the methods outlined in Fig. 1 based on a minimum total investment cost objective. Figure 2 illustrates the primary steps of the analysis workflow, variables, and objectives. First, regional baseline models and generation profiles were developed in addition to energy efficiency, energy storage, and building load flexibility models. This is followed by a regional parametric analysis, which considers demand-side and supply side variables, to explore designs of minimum total investment costs for 100% renewable targets. Impacts of load flexibility were considered separately in the parametric optimization, with an emphasis on the maximum technical potential to reduce storage requirements and associated costs. Finally, an uncertainty analysis is performed to understand impacts of storage and energy efficiency cost variations on the cost-optimal pathways to 100% renewable. The uncertainty analysis is also used to develop long-duration energy storage cost targets for emerging storage technologies.

In Secs. II B–II E, a description of the procedures used to develop the baseline model of regional U.S. building stock loads is presented. Subsequently, the methods used to simulate building energy efficiency savings, renewable generation profiles, and energy storage controls are presented and followed by a description of the energy storage and renewable generation sizing strategies. Finally, a definition of load flexibility, in the context of this analysis, and its modeling strategies are described.

The U.S Department of Energy's (DOE's) prototype building models³⁸ were used to simulate the demand of a collection of buildings that are representative of the U.S building stock. Survey data from the Energy Information Administration (EIA) were used to inform the aggregation of the prototype building model loads to match the characteristics of the U.S building stock. The DOE prototype building models are articulated using assumptions from the American Society of Heating, Refrigeration, and Air-Conditioning Engineers (ASHRAE) 90.1 building standards, and are distinguished by climate zones defined by the International Energy Conservation Code (IECC). In contrast, EIA survey data are categorized by DOE Building America (BA) program climate regions. Therefore, the reconciliation of the DOE prototype building models and EIA survey data was accomplished by dividing the baseline models into major U.S. climate zones as defined by the IECC and that are overlapped by the BA climate regions,³⁹ as shown in Fig. 3 The simulated collection of prototype building models considers climate locations and building vintages in its model articulation process. Data from EIA's most recent Commercial Building Energy Consumption Survey (CBECS) and Residential Energy Consumption Survey (RECS) were used to inform relative distributions of conditioned floorspace areas of the prototype building models, and their vintage assignments, that are representative of the U.S. building stock in each U.S. climate region.^40,41 The mapping of the EIA (RECS 2015 and CBECS 2012) building occupancy types to DOE prototype models and modeled IECC climate zone(s) that correspond to each BA climate region is summarized in Table I. Moreover, the DOE prototype models were mapped to EIA-reported vintages across each building sector (Table II). Resulting building floorspace area and vintage breakdowns, across building occupancy types and sectors, were used to inform the development of the baseline model.

A demonstration of the Climate Zone (CZ) 3B baseline model building occupancy types and vintage distributions by conditioned floorspace area is shown in Fig. 4. Each prototype building model load was scaled by floorspace area, while maintaining a constant annual energy-use intensity, to reflect the appropriate occupancy distributions from Table I. The prototype building model loads were further disaggregated into three separately scaled models spanning the pre-1980, 1980–2004, and 2010 vintage distributions.

The 27 prototype building models reflected in Fig. 4 were simulated in 5 IECC climate zones spanning five major BA climate regions covering the U.S. The baseline model totals 135 annual building model simulations, on an hourly timescale: 27 building models for each of the 5 investigated climate zones. Typical meteorological year (TMY3) weather files of representative cities in each climate zone (Tampa, El Paso, New York, Denver, and International Falls corresponding to CZ's 2A, 3B, 4A, 5B, and 7, respectively) were used to drive the building model simulations.³⁸ The building models were simulated using DOE's physics-based, high-fidelity, OpenStudio energy modeling platform.⁴² 

The prototype building models leverage electricity as the primary fuel source that supplies most of their loads. However, some building loads, such as space heating and/or service hot water systems, are fueled by natural gas. Our analysis only considers the case where all loads are met by renewable sources of electricity; therefore, gas-powered loads were converted to their approximate electrical equivalent. To convert the energy consumption of gas to electricity, we post-processed the building simulations and converted the model's natural gas fueled space heating thermal efficiencies to air-source heat pump system equivalents with auxiliary, electric resistance, heating. An air-source heat pump rated coefficient of performance (COP_rated) of 3.3 (at T_oadb = 47 °F) with a performance curve as a function of outside air dry-bulb temperature was applied based on ASHRAE 90.1 building standards assumptions.⁴³ The energy input ratio (EIR) curve outlined in ASHRAE 90.1 was used to calculate the heat pump COP (COP = COP_rsted/EIR) at each hourly simulation time step. The air-source heat pump EIR curve is shown as follows:

Similarly, measured COP curves of heat pump water heaters with auxiliary heating from a laboratory performance evaluation study were leveraged in our analysis to model heat pump performance variations as a function of ambient inlet air conditions.⁴⁴ Based on the study, a rated COP of 2.77 (at T_wb = 57 °F, and T_wa = 120 °F) was assumed with a COP curve as a function of inlet air wet-bulb temperature and water tank temperature, as follows:

where C₁ = 0.982, C₂ = 0.05334, C₃ = −0.0002802, C₄ = −0.003073, C₅ = −0.0001384, C₆ = −0.0002897, and T_wa = 120 °F.

The aggregated annual electric consumption of the baseline models, by end-use, in each modeled climate zone is shown in Fig. 5. Monthly aggregated load profiles are provided in  Appendix A. The baseline model's energy consumption depicts an increase in heating consumption and decrease in cooling consumption from hotter to colder regions.

In our analysis, we consider wind and solar PV generation given that most 100% renewable plans consider these as their primary sources of renewable power.^6–10 Solar and wind profiles were created for representative cities in each climate zone (Tampa, El Paso, New York, Denver, and corresponding to CZ's 2A, 3B, 4A, 5B, and 7, respectively) using the System Advisor Model (SAM) tool.⁴⁵ SAM uses models developed by U.S. DOE's National Renewable Energy Laboratory and Sandia National Laboratory to calculate hourly energy production from solar PV and wind turbines, given system specifications and a typical meteorological year (TMY) weather file containing local hourly solar irradiance data. Default SAM assumptions were leveraged for PV and wind turbine systems. PV systems assume a 96% inverter efficiency and 1.1 DC to AC ratio. In addition, PV systems were assumed to be south-west facing (225-degree azimuth) with a fixed 20-deg tilt. Effects of snow on solar PV power output are considered where applicable (e.g., International Falls) using the approach developed by Marion et al. (2013).⁴⁵ To size the systems, SAM generated profiles were first normalized by their aggregated annual generated energy. Subsequently, the baseline renewable portfolio profiles were scaled to equate the annual energy consumption (annual energy generation = annual energy consumption) while preserving the hourly generation profile shape. This ensures adequate generation capacity to meet a 100% renewable target. The maximum annual output power is identified as the rated system capacity. The following equation exemplifies the process used to normalize and scale the SAM solar PV profiles to their proper size:

where $PSized_solar(h)$ is the properly sized solar power generation profile value at hour $h$⁠, $Psolar(h)$ is the SAM solar power generation value at hour $h$⁠, $Eload$ is the aggregated annual energy consumption of the baseline model, $Esolar$ is the aggregated annual energy generation of the SAM PV profile, and $fsolar$ is the fraction of annual renewable generation from solar PV (e.g., $fsolar=1$ if the renewable portfolio is composed of solar PV only). The $fsolar$ fractional value is later varied, while maintaining the equality shown in Eq. (5), to understand the optimal mix of PV and wind on minimizing storage requirements and total investment costs,

Finally, PF in Eq. (4) is the renewable energy production factor, defined as the ratio of the aggregate annual generated energy over the aggregate annual energy consumed. Throughout this analysis, PF has a minimum value of 1, which reflects the minimum generation requirement to meet a net zero 100% renewable target. However, this factor is varied later in the analysis to understand the impacts of oversizing, and curtailing, renewable generation (PF > 1) on the total energy storage requirements and total asset costs in real-time 100% renewable targets. A similar sizing method is used for wind power, as follows:

Regional costs of solar PV and wind power were considered in the analysis and are summarized in Table III.^46,47 Regional unit transmission capital costs associated with solar PV and wind generation were also considered in the analysis and are summarized in Table III.⁴⁸ The transmission costs in Table III reflect average historical unit capital costs from 1294 reports of actual solar and wind generation projects in addition to planned projects from two regional transmission operators (Pennsylvania-New Jersey-Maryland interconnection, and Midcontinent Independent System Operator) and U.S. EIA interconnection data.⁴⁸ The estimated average unit costs in Table III include bulk transmission, point of interconnection, and spur transmission costs.

Throughout this study, generality of the analysis results is attempted through normalizations by the total baseline model floorspace area, where appropriate.

The energy storage requirements are divided into two categories that are distinguished by their storage durations: (1) diurnal storage requirements that are intended to alleviate misalignments of supply and demand on the order of daily timescales and (2) long-duration storage requirements, which may address days to months of shifts in stored energy. Electrochemical lithium-ion batteries are investigated for improvements in diurnal alignments in supply and demand. Using the baseline model loads and renewable generation profiles (produced through Eqs. 4–6), batteries are sized to meet the annual average unmet energy load of a single day. The formula used to size the system is shown in Eq. (7), where $ηr,d$ is the round trip storage efficiency of the diurnal (Li-ion battery) storage system. Equation (7) also includes a constant factor, $α$⁠, of 0.7 to prolong battery capacity retention over numerous cycles.⁴⁹ The capacity factor, $α$⁠, oversizes the battery to avoid complete depletion during normal operations while also meeting storage capacity requirements. The battery is modeled to operate between 15% and 85% capacity range, which has been shown to aid in Li-ion battery capacity retention,⁴⁹ 

The storage system control strategy is demonstrated in Fig. 6, where curves of net load are shown for the CZ 2 A baseline loads and a solar PV portfolio (⁠$PF=1, fsolar=1$⁠), with and without a battery system. The net load is defined as the load minus the generation at each hourly time step, as depicted in the following equation:

As shown by the example summer days in Fig. 6, significant surplus power is generated in the baseline without the utilization of a battery system. The battery operates by storing excess generated power, without exceeding 75% of the total storage capacity, and discharges to supply the load during times of unmet demand. The battery performs its charge and discharge operations chronologically, without forecasts or knowledge of future load or generation. In the example scenario of Fig. 6, the battery charges through use of the surplus power and discharges during periods of positive net load (unmet load) until the batteries' state-of-charge (SOC) reaches the predefined minimum of 15%. As depicted by Fig. 6, the battery flattens and zeros the net load for a significant portion of the time relative to the baseline.

Although diurnal storage can aid the alignment of supply and demand by dampening daily net load variations, long-duration misalignments can remain unaddressed. In many cases, additional unexploited surplus power (i.e., in the spring, when solar generation is relatively high and space conditioning loads are low) must be stored over long-durations (i.e., weeks or months) and dispatched through extended periods of scarce supply (i.e., winter PV) for complete alignment of demand and supply over the course of a year. Figure 7 (top) is a demonstrative plot of the hourly net load of the baseline model in CZ 3B with a solar PV portfolio (⁠$PF=1, fsolar=1$⁠) over the course of the simulated year. In Fig. 7 (top), misalignments in supply and demand appear to reside on diurnal timescales. However, Fig. 7 (bottom) is a plot of the residual net load post-battery operation, where long duration supply and demand misalignments are revealed.

While numerous types of large-capacity, long-duration storage systems have been proposed and investigated in the literature, including compressed air storage and thermal storage ,^50–52 hydrogen storage has received much attention as a promising seasonal energy storage resource.^38,51 Therefore, this analysis considers the use of hydrogen energy storage (electrolysis hydrogen production coupled with fuel-cell electric generation) for meeting long-duration, large-scale, energy storage needs.

Figure 8 is a demonstrative example of the long-duration storage operation and sizing strategy for the CZ 3B baseline load with a solar PV portfolio. The system is sized by modeling an “accumulator,” where surplus power is stored and accumulated over the course of the year and unmet load is fulfilled by dispatching the stored energy when demanded. The long-duration storage system acts on the residual net load following diurnal battery operations. The accumulator model is repeated over the course of a two-year period, without modifications to the load or generation profiles, to consider interactions across winter months (i.e., December to February). Portions of the accumulator curve with a positive slope indicate an increase in storage charge, and a negative slope indicates regions when storage must be discharged to meet the load. The storage system is sized by determining the largest discharge (drop in SOC) over the course of 2-years.

As a reminder, this study only considers scenarios where the annual generated energy is sized to equate or exceed the annual energy demand (⁠$PF≥1$⁠), which ensures adequate generation capacity to meet a 100% renewable target. In scenarios where $PF=1$ (i.e., annual generating = annual load, and no generation curtailment), the accumulator SOC reaches zero at the end of the year (by definition). Therefore, the minimum storage capacity can be determined by calculating the largest discharge (drop in SOC), as shown in Figure (8) and Eq. (9). In Eq. (9), $ηr,l$ is the round trip efficiency of the long-duration energy storage system,

In contrast, scenarios where $PF>1$ (i.e., annual generation > annual load, and curtailment is leveraged) lead to accumulator SOC's greater than zero at the end of the simulated year. As a result, the approach of sizing the minimum required long-duration storage capacity by determining the largest discharge (drop in SOC) is also valid for all values of $PF>1$⁠, but requires an alternative to Eq. (9). Instead, an algorithm was developed to identify the maximum drop in SOC as outlined by the following steps:

1. Smooth the accumulator curve (SOC) using a Savitsky–Golay filter to remove diurnal-scale variations in local minima and maxima, which are found in the next step. This step reduces computation time without compromising accuracy of the results.

2. Identify local maxima and minima in the accumulator curve by calculating dSOC/dt = 0 and identifying regions where d²SOC/dt² < 0 and d²SOC/dt² > 0, respectively

3. Determine the largest drop in SOC between each identified local maxima and future local minima.

4. The largest energy drop calculated in step 3 is identified as the minimum required storage capacity.

Figure 8 demonstrates the long-duration storage SOC curves for PF = 1, PF = 1.1, and PF = 1.2. As depicted by the PF = 1 curve, the bulk of the charge process occurs in the early spring months, and the charge must be held through summer and fall months prior to the bulk winter season discharge. The size of the storage system must meet the maximum drop in storage (1.05 kWh/ft²). Increasing the production factors to values above unity (PF > 1) results in curtailed generation during the spring and potentially summer and fall seasons, depending on the extent of overproduction. This is depicted in Fig. 8 by the zero SOC values in the PF = 1.1, 1.2 curves during the spring-fall seasons. The benefit of oversizing and curtailing generation is illustrated by the lower requirements in storage capacities and durations. As shown in Fig. 8, increasing the PF to 1.1 results in a reduced storage capacity requirement of 0.7 kWh/ft². In addition, the bulk charge process can instead occur during the fall months and discharged during the winter months. Also note that the summer loads are met with negligible storage as indicated by the zero and/or positive SOC slopes during this period. Increasing the production factor by 20% further reduces the storage size by 53%, and the storage duration, as indicated by the PF = 1.2 curve.

The diurnal and long-duration energy storage system types, round trip efficiencies, and cost assumptions are summarized in Table IV. U.S. DOE has identified low, moderate, and high range estimates of 2020 and projected 2030 hydrogen energy storage capital costs.⁷¹ We begin our analysis by considering DOE's projected, and moderate, 2030 total installed capital cost of bi-directional fuel-cell hydrogen energy storage, shown in Table IV. The installed capital cost encompasses the hydrogen electrolyzer, rectifier, compressor, cavern storage, fuel cell, controls, and grid integration costs. A detailed breakdown of the hydrogen energy storage system costs by component is provided in  Appendix B. In Sec. III C, we conduct a sensitivity analysis to understand impacts of storage cost variations on the results. In addition, we also compare our sensitivity analysis results with DOE's 2020 storage cost reports and projected 2030 low-cost estimates.⁷¹ 

It is important to note that the generation profiles are initially sized, using Eqs. (4)–(6), to equate or exceed the annual load. Equations (4)–(6) do not consider generated energy that is lost through round trip storage efficiencies. Therefore, in  Appendix C, we outline the corrective factors used to properly size generation capacities while considering lost energy through round trip storage efficiencies.

There are numerous commercially available building energy efficiency measures that span building end-uses, including heating, ventilation, and air conditioning (HVAC), refrigeration, lighting, equipment, envelope, building supervisory controls, etc., where each end-use further contains numerous component and sub-component measures. For example, within HVAC alone, improvements can include upgrades to fan motors, fan belts, evaporative pre-cooling retrofits, economizer controls, demand-controlled ventilation, variable supply air volume controls, and cooling capacity controls, among many others.

To avoid excessive computation time associated with modeling specific building energy efficiency measures, energy efficiency upgrades were approximated through scaling's of the hourly baseline model demand profile in discrete, time-continuous, annual percent energy reductions while preserving the load shape. While this approach does not consider interactive effects associated with multiple building energy efficiency retrofits, nor their temporal energy impacts, the general influence on the energy storage requirements associated with load reductions are still preserved. However, the authors encourage a comprehensive analysis of specific efficiency measures in future site-specific studies. In Sec. IV (Limitations and Future Work) of this paper, we further elaborate on the limitations of our modeled assumptions, present future research opportunities, and describe the expected impacts of our assumptions on the results.

An extensive literature search was conducted to gather real-world case study datapoints of building energy efficiency retrofit investment costs and associated annual whole-building energy savings. A scatterplot of 63 case studies spanning several climate zones is shown in Fig. 9,^55–66 with an exponential curve fit providing the highest coefficient of determination (R² = 0.5864) compared with other trendline forms including linear, logarithmic, power, and polynomial trends. In this study, energy efficiency investments costs are approximated by the trendline of Fig. 5, also shown in the following equation:

The relation between building energy efficiency investment costs and energy savings is highly dependent on the state of the baseline building; therefore, variances are expected given the numerous possible opportunities of unique building energy savings. Hence, the energy efficiency cost trendline in Eq. (10) is leveraged as a starting point but approached with caution. We later show a sensitivity analysis to illustrate the impact of energy efficiency investment cost uncertainties on the results.

For the purposes of this paper, the term load flexibility includes all strategies that could be used to shape building demand profiles to match renewable supply, excluding batteries (electrochemical storage, such as Li-ion batteries) and other electrical storage systems. Load flexibility can be categorized into the following:

1. Dedicated thermal storage (e.g., stand-alone ice storage)

2. Inherent thermal storage (e.g., thermal mass in architecture features, sometimes called virtual storage)

3. Flexible controls (e.g., equipment, HVAC setpoint, and lighting).

In this analysis, we explore load flexibility associated with dedicated building-level thermal storage only (item 1 above). Load flexibility considerations are not the central focus of our investigation. However, the aim of our work is to provide early insights to the maximum technical potential for shifting space heating, space cooling, and water heating loads through available technologies, such as ice storage for cooling, high-temperature ceramic brick for space heating, and insulated hot water tanks for service water heating. Therefore, we investigate the maximum potential of dedicated thermal storage options for shaping loads to match renewable generation, which can reduce the capacity requirements of batteries, and potentially long-duration energy storage capacity needs. We take a conservative approach of limiting the shifting of thermal building loads to a maximum of 24 h. We remain general and agnostic of the thermal storage type by post-processing the modeled end-use consumption to quantify the necessary shifts in thermal loads that maximize the alignment with, and utilization of, renewable power. Space heating, space cooling, and water heating are primary end-uses for most buildings and therefore emphasis is placed on them.

Figure 10 provides a demonstration of the shifted space heating, cooling, and water heating loads, and their impacts on the net load shape for several example summer days. The dedicated thermal storage systems charge during periods of surplus power in anticipation of thermal loads 24 h ahead. The model assumes perfect prediction of future load and generation. The thermal storage system discharges to meet the heating and cooling loads during periods of inadequate supply, thereby decreasing the net load by an amount equal to the end-use load.

A demonstrative plot of the aggregated baseline monthly load and generation profiles for the hot-mixed BA climate zone (CZ 4 A) is provided in Fig. 11. Figure 11 (left) is the aggregated monthly load and regional solar PV generation profile, while Fig. 11 (right) is the aggregated monthly load and regional wind generation profile. In both plots, the production factor is assumed to be 1 (PF = 1 → annual generation = annual load) for demonstration purposes. These plots are provided to illustrate the exacerbated seasonal misalignments associated with supply and demand when only one renewable source is relied on. Nonetheless, Fig. 11 also demonstrates the potential opportunity, through some linear combination of both wind and solar PV sources, to maximize the long-duration alignments in supply and demand, hence leading to a reduction in storage requirements.

To quantify the impacts of renewable portfolio diversification on the total energy storage and renewable power investment costs, the renewable source factor [$fsolar$⁠, in Eqs. (4)–(6)] is varied and the normalized total investment costs are plotted as shown in Fig. 12. Each curve in Fig. 12 is associated with a constant total annual generated energy, which is defined by the production factor value [PF, in Eq. (4)]. In addition, each curve in Fig. 12 begins with a 100% wind portfolio (left end of curve) and ends with a 100% solar PV portfolio (right end of curve). Curves are plotted in Fig. 12 for discrete production factor values to demonstrate the impacts of oversizing generation on (1) the total storage and renewable asset costs and (2) the optimal mixture of renewable sources corresponding to minimum total investment costs. Oversizing generation allows for more power to be available during periods of inherently lower supply (i.e., winter solar PV generation), resulting in fewer shifts in energy that are needed to meet the demand. However, overgeneration (PF > 1) will require curtailing the renewable sources during periods of excess generation (i.e., spring solar PV generation). With total investments being dominated by energy storage costs, coupled with the relatively cheaper costs of renewables, some degree of oversizing generation always results in lower total investment costs, as illustrated in Fig. 12.

For each climate, a clear and unique optimum renewable portfolio exists that minimizes total investment costs. The cost-optimal mix of renewables reflects the minimization of expensive long-duration energy storage costs through maximization of alignments in supply and demand. For each region, the extremities of associated heating and cooling demands align with an optimum mixture of inherent resource variability that minimizes storage. For example, in the hot-humid BA climate (CZ 2A), an optimum portfolio is composed primarily of solar PV, where solar power availability aligns best with the extreme summer demands. In contrast, the very cold BA climate region (CZ 7) exhibits an optimum portfolio that is composed mostly of wind resources, where wind power aligns best with the extreme winter heating demands. The near optimum portfolio mixtures that lead to minimum asset costs, for each climate regions and across several discrete production factors, are outlined in Fig. 12. Regional trends depicted by Fig. 12 indicate that increasing the allocation of solar PV in hotter climates generally decreases total investment costs, and vice versa. It is also important to note that while the optimal mix of renewable sources can vary with the production factor, the sensitivity is relatively small and is nearly constant in most regions, as shown by the curves in Fig. 12. This observation is used in Sec. III B to understand the cost-optimal production factor (extent of oversizing) and energy efficiency penetration in each climate region.

While this study only considers 100% renewable scenarios, defined by a load cover factor of unity (LCF = 1), it is important to note that the required energy storage capacity increases non-linearly toward a 100% renewable target. To demonstrate this, regional curves of the total storage capacity as a function of the load cover factor [Eq. (1)] are shown in Fig. 13. Moreover, the regional cost-optimal renewable mixes are considered in these curves to demonstrate the significant increase in capacity requirements despite the optimal diversity in generation mix. As indicated in Fig. 13, the load cover factor ranges from 0.48 to 0.642, depending on the region, without any storage capacity. Meaning, 48%–64.2% of supply and natural demand overlap is achieved by leveraging the optimal mix of renewable profiles. Moreover, relatively little storage is needed to achieve an LCF of 75%–90%. However, a substantial increase in storage capacity is needed for the remaining ∼10%–25% of load coverage, with a difference that spans at least one order of magnitude as shown by Fig. 13.

At LCF = 100%, over 92% of the total storage capacity is associated with long-duration storage that mitigates seasonal misalignments in supply and demand. In Sec. III B, the optimal mix of renewable resources is used in conjunction with optimal production factors (extent of overgeneration) and energy efficiency penetrations to arrive at regional minimum total investment cost solutions. It will be demonstrated that the resulting cost-optimal solutions lead to further reductions in long-duration storage capacities.

While the optimum renewable portfolio, which is driven by minimizing storage requirements, can be identified for each climate region through Fig. 12, the extent of oversizing renewable generation (the production factor value) and its associated cost-optimal value requires further investigation. Along with oversizing renewables, we simultaneously explore the impacts of permanent building energy efficiency savings on the total asset costs to quantify potential design tradeoffs. In addition, we identify an optimum solution corresponding to minimum total energy efficiency, energy storage, and renewable generation investments. Figure 14 shows the regional contour plots of constant total investment cost savings as a function of energy efficiency penetration and the renewable production factor, which defines the extent of overgeneration. The total installed capital expenditure cost savings, in Fig. 14, are quantified relative to total costs at a production factor of unity (no overgeneration or curtailment of renewable power) and zero energy efficiency investments. The design of a region is confined to a point on this map, and operations that approach maximum cumulative cost savings in energy storage, energy efficiency, and transmission and renewable generation will follow the direction of the total cost savings gradient, as annotated on the contour cost map for CZ 4 A in Fig. 14.

Regional designs with higher production factors result in increased installed renewable expenditures. However, the added renewable costs from overgeneration are considerably outweighed by steep reductions in storage capacities, and associated costs. The optimum level of oversizing generation, which maximizes the total asset cost savings, can be quantified through a production factor value in the range of 1.4–3.2, depending on the climate region as shown in the plots of Fig. 14. Optimum overgeneration is illustrated in Fig. 14 by the change in the total investment saving slope that occurs along the direction of increasing production factors for all climate regions. Hence, the total cost savings associated with oversizing generation eventually passes through a maximum since additional times of renewable supply eventually plateau and impacts of oversizing generation on reducing storage requirement begin to diminish. Comparing the cost maps in different climate zones shows that regions with higher wind power portfolios typically exhibit larger potentials for cost savings through higher overgeneration factors. This is because wind power generally exhibits greater times of generation as compared with the relatively narrower solar generation time windows.

As illustrated in Fig. 14, load reductions offered through permanent energy efficiency savings can further contribute to total cost savings. Energy efficiency investments decrease the necessary renewable capacity, storage requirements, and transmission capacity; therefore, its impacts are threefold. However, energy efficiency penetrations eventually reach a point of diminishing return as added savings become more costly compared with associated cost reductions in generation and storage. The cost-optimal energy efficiency penetrations for each climate region are shown in Fig. 14. In addition, Fig. 14 reveals the global cost-optimal solutions corresponding to specific overproduction and energy efficiency penetrations in each climate region. It is important to note that while overproduction can have substantial impacts on total cost savings, global cost-optimal solutions that maximize total cost savings cannot be reached without incremental investments in efficiency, further substantiating the importance and relevance for permanent building energy efficiency measures.

A summary of the regional cost-optimal energy efficiency penetrations, production factors, and renewable mixes is provided in Table V. In addition, Table V outlines the regional storage capacity requirements and the calculated total investment costs that achieve the 100% renewable target.

It is important to note that the maps in Fig. 14 are of total cost savings associated with energy efficiency and renewable oversizing at the optimum renewable mix outlined in Table V. Therefore, the cost maps in Fig. 14 do not include added savings associated with shifts to an optimal renewable mix. As a result, a baseline renewable portfolio scenario was chosen to match current distributions of solar PV and wind power from regional independent system operators and utilities.^67–70 This baseline scenario is used to compare the cost savings associated with shifts to an optimal renewable mix in addition to the optimal energy efficiency and renewable generation capacities. A summary of the baseline energy efficiency penetration, renewable production factors, and renewable distribution assumptions, per region, is provided in Table VI. Note the drastic reduction in long-duration storage capacities and total investment costs between the baseline and the cost-optimal solution.

Figure 15(a) shows the total asset costs of the baseline, defined by Table VI, with no energy efficiency savings and no overproduction (PF = 1), and with renewable portfolios based on current distributions of regional independent system operators and utilities. In addition, Fig. 15(a) shows the cost-optimal designs, with production factors, energy efficiency savings, and shifts to renewable portfolios, per region, that are defined by Table V. Figure 15(a) demonstrates the substantial reductions in total asset costs that are particularly a result of reduced long-duration storage capacities. In particular, at least one order of magnitude of total asset costs can be reduced by investments in energy efficiency combined with oversizing and diversifying renewable generation. The asset costs, as a percent of total costs, are shown in Fig. 15(b). As depicted by Fig. 15(b), the baseline storage requirements and costs are primarily attributed to misaligned long-duration generation and demand. Figure 15(b) suggests a specific breakdown and prioritization of investments with significant impacts on total investment costs associated with real-time 100% renewable targets. Moreover, the outcomes from Figs. 14 and 15 emphasize the consideration of avoided energy storage costs in search of cost-optimal 100% renewable energy scenarios and the significant opportunity associated with readily available methods for reducing the otherwise substantial energy storage needs.

As a reminder, the analysis results in Sec. III B were produced assuming a $161/kWh hydrogen storage cost based on U.S. DOE's 2030 moderate cost projection.⁷¹ Therefore, the results in Table V show drastic reductions in optimal long-duration storage capacities even in optimistic long-duration storage cost assumptions. In this section, we present a long-duration energy storage cost sensitivity analysis to illustrate the impacts of storage cost variations on the cost-optimal solution results. In addition, we compare our findings with U.S. DOE's 2020 and projected 2030 low-cost estimates for hydrogen energy storage.⁷¹ 

Figure 16 shows curves of optimum long-duration storage capacities, by region, as a function of long-duration storage costs. As illustrated by Fig. 16, the optimal storage capacities decrease with increasing long-duration storage costs. As the storage cost increases, the economical solution shifts toward an increase in production factors (overgeneration and curtailment) as the alternative method for alleviating misalignments in supply and demand. This trade-off is illustrated in Fig. 16-right, where curves of associated production factors as a function of long-duration storage costs are plotted.

In this study, we assume long-duration storage capacities to be defined by storage volumes exceeding 2-days (>48 h) of average daily load. The distinction between long-duration and short-duration storage capacities is highlighted in Fig. 16-left. The results in Fig. 16-left suggest that it is theoretically feasible, and in some scenarios the most economical, to eliminate long-duration storage assets while still meeting a 100% renewable target.

The sensitivity analysis presented in Fig. 16-left suggests regional cost cutoff point, where further increases in long-duration storage costs would deem storage uneconomical. This cutoff point could also be interpreted as a long-duration energy storage cost target for emerging technologies. Storage technologies above this cost target would compete against designs with higher production factors (and curtailment) of readily available renewable resources. As depicted in Fig. 16-left, regions defined by CZ 2 A, CZ 3B, and CZ 5B have long-duration energy storage cost cutoff points, or targets, of $43/kWh, $30/kWh, and $73/kWh, respectively. Therefore, long-duration storage is an economical solution only if its installed capital costs are less than these targets. For CZ 4A and CZ 7, higher storage costs would still deem multi-day storage economical given the associated pronounced misalignment challenges in these regions. Nevertheless, the storage durations and capacities for CZ 7 and CZ 4A reduce from the order of seasons to multi-day capacities at costs above $40/kWh. To provide context to these results, we compare our findings with a comprehensive study conducted by U.S. DOE of 2020 and projected 2030 hydrogen energy storage cost estimates.⁷¹ U.S. DOE shows that installed 2020 bi-directional hydrogen storage installed costs are $312/kWh, while projected 2030 lower range costs are $144/kWh. As a result, 2020 and optimistic 2030 hydrogen storage costs are not economically competitive to serve long-duration storage needs in CZ 2A, 3B, and 5B compared with excess renewable generation capacities. Moreover, our identified cost targets are lower than the U.S. DOE's projected 2030 grid-scale cost estimates for electro-chemical storage (li-ion, lead-acid, and vanadium redox flow batteries at $270/kWh-$480/kWh) and pumped hydro ($220/kWh-$262/kWh). Meaning these grid-scale storage technologies are projected to remain uneconomical for meeting long-duration storage needs through 2030.

Similarly, a sensitivity analysis was conducted to understand the impacts of variations in the building energy efficiency investment costs on the cost-optimal energy efficiency penetrations by region. The sensitivity analysis results are shown in Fig. 17, where the optimum energy efficiency penetration levels are plotted against a percentage increase in the energy efficiency costs from the baseline. The baseline energy efficiency costs in Fig. 17 are defined by Eq. (10). As shown by Fig. 17, a 100% increase in the energy efficiency costs result in a 10% average reduction in the optimum energy efficiency penetration level. Hence, a reduction in the optimal energy efficiency penetration can be expected at higher energy efficiency costs. However, the results are relatively insensitive given that changes in the optimum are within ±5% of the results for ±50% changes in the input cost assumptions.

Commercially available load flexibility measures have the potential of improving the diurnal alignment of demand with generation, further reducing the storage requirements and potential investment costs. Space heating, space cooling, and water heating end-uses were shifted to periods of surplus generation to understand the maximum technical potential associated with commercially available, dedicated, thermal storage systems, as described in the methodology section. Figure 18 shows the battery capacity impacts associated with shifted water heating, space heating, and space cooling end-uses that maximize real-time renewable power utilization. Across all climate regions, load flexibility associated with these end-uses has the technical potential of reducing daily storage requirements by 37.5%–81.3%. Contributions from each end-use, in Fig. 18, are added incrementally in the bar chart corresponding to each climate zone. Assuming a linear correlation between capacity and cost, the percentage reductions can also be interpreted as associated diurnal, or battery, storage cost reductions. As shown in Fig. 18, cooling load flexibility demonstrates a higher potential for decreasing battery capacities and costs in hotter climates, given the higher cooling demands. Similarly, heating load flexibility has a higher potential for decreasing battery requirements in colder climates, given the higher heating demands. In general, hotter climates typically exhibit a larger potential for load flexibility. The is because hotter climates, with an optimum portfolio primarily composed of solar PV, have cooling demands that are relatively more misaligned to generation when compared with heating demands, in colder climates, to wind power availability.

This paper demonstrates an overarching calculation methodology that can be leveraged in future site-specific 100% renewable studies. While our analysis captures a range of representative U.S. building stock scenarios, energy efficiency opportunities, transmission costs, and renewable resources, we encourage future studies to include further comprehensive consideration that capture the existing circumstances of their investigated site. Site-specific circumstances may include constrained land area availability for renewable resources, and electric transmission and distribution infrastructure constraints. Nonetheless, the overarching trends and conclusions of our results are anticipated to remain the same. The list below highlights our research limitations and/or opportunities for future work:

• Our research is limited to the building sector; therefore, transportation and industrial sector loads were not considered in the analysis. However, considering buildings are responsible for 74% of the total electricity consumption,⁷² our analysis focus represents a critical sector for maintaining a continuous power balance in 100% renewable scenarios. In addition, it is imperative to note that monthly energy consumption profiles for the transportation and industrial sectors are historically flat throughout the year compared with monthly building loads.⁷² To demonstrate, U.S. EIA monthly energy consumption profiles for the transportation, industrial, and building sectors are plotted for the past decade (January 2009–2019) and shown in Fig. 19. Figure 19 also demonstrates that the total U.S. energy consumption profile shape is driven by building sector loads, as illustrated by the coincident peaks and troughs of the building sector and total energy consumption curves.

  Electrification of industrial and transportation sectors will require expanded renewable supply and, depending on electric vehicle controls and charge rates, may increase capacity requirements associated with diurnal storage. Given that industrial and transportation loads are largely driven by behavioral usage patterns, the current body of literature is centered around electrification impacts on their diurnal load profiles and associated challenges of accompanying higher grid peak demands.^73–75 While recent studies have indicated deviations in electric vehicle battery charge and discharge rates as a function of ambient temperatures,^74,75 the authors have not identified literature, suggesting a significant departure of electrified transportation and industrial energy load profile shapes from flat historical trends over longer timescales (e.g., monthly, and seasonal). As a result, minimization of long-duration storage through our identified strategies is anticipated to remain critical for maintaining a cost-optimal path to 100% renewable, even in electrified industrial and transportation scenarios, given the influence of building loads on the total consumption profile shape over long timescales. However, it is also imperative to note that even in situations where electrified transportation loads significantly deviate their monthly load profile shapes from flat historical trends, current research indirectly points to a potential increase in loads only at extreme seasonal temperatures.⁷⁵ This potential outcome would exacerbate the misalignments (increases peaks in the total consumption curve in Fig. 19) in long-duration supply and demand, and would further substantiate the need to minimize long-duration storage through our identified strategies. In any case, the authors encourage future work to consider electrified industrial and transportation loads for added comprehensiveness and to understand the impacts of electrification of these two sectors using our methodology.

• Our study also does not consider renewable energy land requirements and costs, or site-specific electric infrastructure constraints. While our analysis does consider average regional unit transmission costs based on a large number of reported solar and wind generation expansions, and interconnection projects, additional work is required to account for site-specific electric transmission and distribution infrastructure constraints. The authors encourage further considerations and comprehensiveness surrounding land and infrastructure needs using our methodology for future site-specific studies. However, the authors believe that the overarching conclusions presented in our research will remain the same given the dominant long-duration energy storage requirements and costs that were demonstrated for 100% renewable targets.

• Moreover, energy efficiency penetrations are modeled by continuous load reductions while preserving the load profile shapes. Therefore, we do not consider interactive effects associated with multiple building energy efficiency retrofits, nor their temporal energy impacts. While this can impact the results, it is critical to note that optimal efficiency penetrations were observed to be high (48%–65%). As a result, measures spanning multiple building end-uses will likely be required, which is prone to reduce the timeseries loads relatively evenly throughout the year. Therefore, our modeled assumptions are expected to have minimal impacts on our overarching analysis findings. In addition, while our assumed building energy efficiency costs capture a range of representative retrofit scenarios, additional work is required to model site-specific circumstances, anticipated performances, and costs. We mitigated the uncertainty by illustrating a low sensitivity of our results to energy efficiency cost variations; however, additional comprehensiveness is encouraged for future work of site-specific studies given the numerous possibilities for unique efficiency opportunities depending on the state of the baseline buildings.

• Our load flexibility analysis assumes perfect predictions of space heating, water heating, and space cooling loads over a 24-h period. In addition, our analysis does not consider penalties associated with charging and discharging thermal storage and their indirect impacts on load profiles. Our load flexibility assessment aims to quantify the maximum technical potential for shifting building thermal loads, based on our models predicted end-use load profiles, to quantify the associated impacts on diurnal energy storage capacity requirements. Our load flexibility analysis and associated thermal storage models are inherently assumed to alleviate misalignments on the order of diurnal timescales. Therefore, our overarching analysis conclusions regarding long-duration misalignments, and associated cost-optimal strategies that address this dominant challenge, are not expected to change with added thermal storage modeling fidelity. Nonetheless, we encourage future work to analyze specific thermal storage technologies of interest while considering the dynamics of these systems for robust technology-specific impact assessments. Our maximum technical potential results for load flexibility aim to provide future researchers with a performance upper bound to compare against during their evaluations of specific thermal storage technologies.

• Our modeled solar PV systems assume south-west facing (225-deg azimuth) panels at a fixed 20-deg tilt in all scenarios. We encourage future studies to leverage our methodology while considering site-specific configuration constraints (i.e., rooftop slopes) and the likely diversity in installed panel azimuth and tilt angles. Nonetheless, marginal variability in panel directions is not anticipated to deviate generation trends on seasonal and monthly timescales, therefore the overarching trends and conclusions of our results are not anticipated to change.

• Our diurnal battery model performs its charge and discharge operations chronologically, without forecasts or knowledge of future load or generation. While this assumption does not impact the battery energy capacity [Eq. (7)], long-duration energy storage capacity [Eq. (9)], or generation capacity requirements [Eqs. (4)–(6)] and associated costs, future investigations could consider load and generation forecasts to alleviate required power capacity limits for storage.

• Our analysis does not consider potential added costs associated with frequency response controls in 100% renewable scenarios. While added variable generation reduces grid stability associated with conventional rotating generator inertia, recent research has demonstrated that increased penetration of these resources decreases the amount of inertia needed for stability.⁷⁶ This is because the frequency response times of variable generation are much faster than conventional generators. Nonetheless, grid stability must be addressed in any 100% renewable scenario. Given that our analysis is constrained to 100% renewable, potential added inverter-based (or similar) grid stability asset costs will remain relatively constant across all investigated scenarios. Therefore, our overarching findings regarding the minimization of long-duration storage are not anticipated to change with added frequency response measure costs. Nonetheless, we encourage future work to consider grid stability capabilities and added costs.

• Our investigation does not explicitly account for contingency or added resiliency considerations and associated costs. However, our key findings suggest investments in excess generation capacities and premeditated curtailments to achieve a cost-optimal 100% renewable grid. Therefore, in scenarios where supplementary power is required, excess generation that is otherwise planned for curtailment could be treated as contingency to address unanticipated power demands. Given that generation curtailments typically reside during the spring/summer months, our findings suggest that accompanying winter contingency shortcomings could benefit from building designs that prioritize winter energy efficiency measures and building-level resiliency capabilities. For example, building facades with higher solar heat gain coefficients could be leveraged to prioritize reductions in heating loads during the winter while trading off the associated increase in cooling loads during the spring/summer months. We encourage future work to account for contingency considerations and associated costs, in addition to exploring opportunities for building resiliency during periods of inherent vulnerability using our methodology.

The primary focus of this study was to understand cost-optimal pathways to 100% renewable power systems for the U.S. building stock. The U.S. DOE prototype building models and U.S. EIA survey data were used to simulate the demand of a collection of buildings that are representative of the U.S. building stock. Several climate zones spanning the U.S. were investigated to demonstrate regional trends and opportunities. Our analysis shows that the last 75%–100% of renewable penetration results in significant increases in long-duration energy storage capacities and costs. Through the analysis, we identified region-dependent supply-side and demand -side strategies that reduce, and in some cases eliminate, the otherwise dominant long-duration energy storage capacity requirements and associated costs. We show that for each U.S. region, a clear and unique optimum renewable portfolio exists that minimizes storage needs and total costs. The optimum renewable mix generally favors higher wind power allocations in colder climates and higher solar PV allocations in hotter climates. Our results reveal that cost-optimal renewable production factor range from 1.4 to 3.2, and optimal energy efficiency penetrations range from 52% to 68% savings, depending on the climate region. Therefore, the benefits of excess generation capacities and building energy efficiency measures are outweighed by their incremental investments. The cost-optimal renewable production factors and energy efficiency penetrations typically increases from hotter to colder regions.

A long-duration energy storage cost sensitivity analysis was presented which identifies regionally dependent storage cost targets for emerging technologies. In contrast to published works, we identify long-duration energy storage cost targets needed to compete with oversizing of increasingly lower-cost renewable generation. Our results indicate that U.S. regions defined by CZ 2A, CZ 3B, and CZ 5B have long-duration energy storage installed capital cost targets of $43, $30, and $73/kWh, respectively. For CZ 4A and CZ 7, higher costs would still deem multi-day storage economical, given the pronounced misalignment challenges in colder climates. We reveal that a combination of (1) optimally mixed renewable portfolios, (2) oversized generation capacities, and (3) building energy efficiency investments can eliminate the need for long-duration energy storage for U.S. regions defined by CZ 2A, CZ 3B, and CZ 5B. The findings of this research are particularly important given that most long-duration storage technologies are currently either uneconomical, geologically constrained, or still underdeveloped.

The authors have no conflicts to disclose.

The authors would like to thank Andrew Burr for supporting the project and Amy Allen, Marlena Praprost, and Jose Vazquez-Canteli for their early efforts on the initial body of work. Thanks to Adam Hirsch and Chuck Kutscher for reviewing the manuscript and providing their insights for improvement and Marjorie Schott for providing graphics support. The authors would also like to thank the journal editor and peer reviewers for their constructive comments and feedback which helped improve the quality of the paper. This work was authored in part by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding was provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Building Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. By accepting the article for publication, the publisher acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

ASHRAE

American Society of Heating Refrigeration and Air Conditioning Engineers

BA

Building America

COP

Coefficient of Performance

CZ

Climate Zone

DOE

U.S. Department of Energy

$Eload$

Annual Load Energy Consumption

$Esolar$

Annual Solar PV Energy Generation

$Ewind$

Annual Wind Energy Generation

EIA

U.S. Energy Information Administration

EIR

Energy Input Ratio

$fsolar$

Fraction of Renewable Portfolio from Solar PV

$fwind$

Fraction of Renewable Portfolio from Wind Power

G

Hourly Generation Profile

h

Hour

L

Hourly Electric Load Profile

LCF

Load Cover Factor

$Psolar$

Hourly Solar PV Power Profile

$Pwind$

Hourly Wind Power Profile

PF

Renewable Energy Production Factor (Annual Generated Energy /Annual Load)

SAM

System Advisory Model

SOC

State-of-Charge

Sqft

Square feet (ft²)

$T$

Simulation Time Period (1-year)

T_oadb

Outside Air Dry-bulb Temperature

T_wa

Average Hot Water Tank Temperature

T_wb

Wet-bulb Temperature

VG

Variable Generation

W

Watts

α

Battery Capacity Factor

$Δt$

Simulation Timestep (1-hr)

$ηr,d$

Roundtrip Efficiency of the Diurnal Energy Storage System

$ηr,l$

Roundtrip Efficiency of the Long-Duration Energy Storage System

The aggregated monthly electric consumption of the baseline models, by end-use, in each modeled climate zone is shown in Fig. 20. The plots in Fig. 20 depict high cooling loads in the summer months of hotter climates and high heating loads in the winter months of colder climates.

Table VII shows DOE's breakdown of the total installed capital cost estimates for hydrogen energy storage by system component.

The generation profiles are initially sized, using Eqs. (4)–(6), to equate or exceed the annual load. Equations (4)–(6) do not consider generated energy that is lost through round trip energy storage efficiencies. For example, consider an extreme scenario where a generation profile is misaligned with the load at all times of the year (LCF = 0), and an energy storage system with a round trip efficiency of 50% is used to shift the generated energy to meet the load profile. In this scenario, the annual generated energy must double the load in contrast to an ideal generation profile that would equate the annual load. Figure 21 illustrates this through a hypothetical example considering one energy storage system, while outlining the key dependent variables at play.

The generation capacity determined through Eqs. (4) and (6) is multiplied by a corrective factor, presented in Eq. (C1), that considers the round trip energy storage efficiencies and alignment of supply and demand post-battery and hydrogen storage operations,

where

and

In Eqs. (C1)–(C3), $LCFbase$ is the load cover factor of the baseline load and generation profile, $LCFd$ is the load cover factor of the residual load post diurnal (battery) storage operation, $ηr,d$ is the round trip efficiency of the battery, and $ηr,l$ is the round trip efficiency of the long-duration energy storage system (hydrogen storage). Note that if $LCFbase=1$⁠, then Eq. (C1) yields a factor of 1 and results in the ideal generation size. If $LCFbase≠1$⁠, the shifted load through each energy storage stage (represented by $ΔLCFd$⁠, and $ΔLCFl$⁠) is taxed by the respective round trip storage efficiencies (⁠$ηr,d$⁠, and $ηr,l$⁠).