Flexible Electricity Use for Heating in Markets with Renewable Energy

Using electricity for heating can contribute to decarbonization and provide flexibility to integrate variable renewable energy. We analyze the case of electric storage heaters in German 2030 scenarios with an open-source electricity sector model. Making customary night-time storage heaters temporally more flexible offers only moderate benefits because renewable availability during daytime is limited in the heating season. As storage heaters feature only short-term heat storage, they also cannot reconcile the seasonal mismatch of heat demand in winter and high renewable availability in summer. Generally, flexible electric heaters increase the use of generation technologies with low variable costs, which are not necessarily renewables.


Introduction
Mitigating climate change demands decarbonizing energy supply, and renewable electricity sources play an essential role (IPCC, 2018). In Germany, often considered a frontrunner in the transition to renewables, they supplied 36% of gross electricity demand in , up from 6% in 2000(BMWi, 2018a. For 2030, current legislation foresees a growth to at least 50%, and the 2018 government coalition agreement targets an even faster growth to 65%. 1 At the same time, decarbonization must go beyond current electricity use. By 2016, more than a quarter of gross energy consumption and 16% of greenhouse gas emissions stemmed from space heating (BMWi, 2018c). In Germany and many other countries, substantial efforts are required for reaching medium-and long-term climate policy goals. One option is the use of renewable electricity in the heating and transportation sectors, often referred to as sector coupling or electrification. In its latest report on limiting global warming to 1.5 degrees Celsius, the IPCC (2018) also puts an emphasis on such electrification of end energy use.
While electricity generation from wind and solar PV is largely carbon neutral, it comes with two peculiarities: its supply has virtually zero variable costs, and it cannot be dispatched at full discretion. Renewables' natural variability calls for flexibility within the electricity sector to efficiently use available low-cost renewables. One option is on the demand side of the electricity market: electricity demand, which has been largely inelastic in the past, could be shifted to hours with high renewable supply and avoid hours with scarce supply.
Against this background, this paper is motivated by the twin challenges of decarbonizing space heating supply and providing flexibility for the integration of renewable electricity.
Specifically, we apply an open-source electricity sector model to a German 2030 setting to analyze the system effects of flexibilizing electric heating in Germany. Current electric nighttime storage heaters demand electricity at night -when other demand and prices were, historically, low -and convert it to heat. This heat is stored and released again during the day to meet the households' space heat demand. An upgrade can render electric storage heaters more flexible, such that they can demand electricity not only at night-time, but at each point in time and thus respond more flexibly to variable renewable energy supply. Across a range of 2 scenarios, we analyze the effects on system costs, renewable energy integration, and emissions. In doing so, we also disentangle the drivers of cost savings.
Previous research has addressed various aspects of flexible electric heating in renewablesdominated electricity systems (Bloess et al., 2018). We contribute to the literature in several ways: first, we provide evidence on system effects of electric thermal storage heaters; past contributions were scarce and findings mixed. Second, previous papers largely refrain from explicitly disentangling drivers of cost savings; a point that we analyze in depth. Specifically, we explicitly compare model outcomes for different assumptions on the flexibility of electric heating technologies, while most analyses in the literature generally assume flexible operations. Third, we offer a comprehensive formulation for modeling a range of power-toheat technologies in an open-source framework. Finally, we provide evidence on the role of flexible electric heating in German future decarbonization scenarios.
Our analysis illustrates that additional power system flexibility related to electric heating generally increases the use of generation technologies with low variable costs, but not necessarily renewables. Results further show that overall cost savings of making customary night-time storage heaters more flexible are rather moderate. Accordingly, upgrades must come at very low costs to be economical. This is driven by mismatching patterns of heat demand and renewable supply in Germany, which serves as an example for temperate countries, and a lack of seasonal storage capabilities of electric heaters. During summer and spring, the value of additional flexibility is modest because absolute heat demand is low and thus cannot profit from high renewable electricity supply during daytime. During the heating season in winter and fall, the absolute value of additional flexibility is also modest because there is relatively low supply of low-cost renewable electricity during daytime. Even in case of substantially higher shares of renewable energy sources than today, flexible electric heaters would still mainly charge at night-time. Yet additional demand-side flexibility proves more valuable when the merit order is steeper, for instance in case of a coal phase-out or higher CO2 prices.
The remainder of this paper is structured as follows: Section 2 gives an overview over the related literature. Section 3 presents the model. Section 4 exhibits data and scenarios. We describe and interpret results in Section 5. Section 6 sets our findings into perspective and outlines avenues for future research. The final Section 7 concludes.
Electronic copy available at: https://ssrn.com/abstract=3366910 3 2 Related literature The literature highlights a vital role for power-to-heat technologies to decarbonize energy systems beyond current electricity use. Based on a comprehensive model of a future German electricity and heating system , Palzer and Henning (2014) put forward that a complete renewable supply is not more costly than the existing energy system.
Comparing cost-effectiveness across sectors, Merkel et al. (2017) highlight that the heat sector plays a prominent role in efficient and ambitious German decarbonization pathways to 2050. Kiviluoma and Meibom (2010) provide a similar result for Finland, and Connolly et al. (2016) draw an analogous conclusion in their analysis of a complete decarbonization of the European energy system, comprising electricity, heat, and mobility. They identify a central role for heating electrification as low-cost option with a high impact for reducing emissions.
Yet such decarbonization requires that electricity for space heating is increasingly generated by renewable energy sources. In many countries, these are predominantly variable wind power and solar PV because potentials for hydro-or bio-energy are topologically or economically limited. Thus, the temporally flexible use of available renewable energy gains relevance. Systematically reviewing model-based studies, Bloess et al. (2018) provide a focused overview on flexibility potentials of power-to-heat technologies in energy systems.
Specifically for heat pumps, previous research yields rich evidence on the benefits of their flexible operation in power systems with high shares of renewable energy. In a stream of papers for a Belgian application, Patteeuw and co-authors identify reduced total system costs Arteconi et al., 2016), CO2 abatement costs, necessary peak load capacities (Patteeuw, Reynders et al. 2015), and curtailment (Arteconi et al., 2016, Patteeuw and compared to an inflexible heat pump operation, and reduced emissions compared to a baseline with natural gas-based heating . For Denmark, Hedegaard and Balyk (2013) conclude that flexible operation of residential heat pumps saves on system costs through both arbitrage gains from shifting power-to-heat electricity demand to low-price hours with high renewable supply and a reduced need for investments into peak generation capacity. In their analysis, heat storage plays a vital role. Kiviluoma and Meibom (2010) derive a comparable result for Finland while Hedegaard and Münster (2013) highlight the potential of flexible heat pumps to integrate 4 wind energy and thus reduce CO2 emissions and total system costs also without making use of flexibility from heat storages. The literature provides comparable evidence on the benefits of flexible heat pumps also for other countries such as China (Chen et al., 2014), Germany (Papaefthymiou et al., 2013), the UK ( Barton et al., 2013;Dodds, 2014), and the US (Waite and Modi, 2014).
Yet the role of other power-to-heat technologies, specifically electric (night-time) storage heaters, is less well understood. While Dodds (2014) highlights, for the UK, that electric nighttime storage heaters continue to play a role, evidence on power system effects is scarce and mixed. Barton et al. (2013) emphasize that their flexible operation can reduce electricity peak load and smooth the electricity demand profile. For China, Chen et al. (2014) conclude that they do not help to mitigate emissions to a great extent due to the relatively low efficiency compared to heat pumps; considerably, this result is based on the assumption of a high share of coal power in the electricity mix. For the PJM system in the US, Pensini et al. (2014) stress that flexible decentral electric storage heaters can greatly reduce curtailment, but centralized heat pumps with heat storage would be more cost effective. For the Finnish housing stock, Rasku and Kiviluoma (2019) find that electric storage heaters can become more beneficial than energy efficiency improvements from a system cost perspective when assuming very high shares of variable renewables; yet from a house owner's perspective, the opposite may be true.

Model
To analyze the electricity sector effects of electric storage heaters, we augment the opensource electricity sector model DIETER by a power-to-heat module. DIETER is a dispatch and investment model with a long-run equilibrium perspective that minimizes the total cost of electricity generation for one year in hourly resolution. See Zerrahn and Schill (2017) for an introduction to the basic model version.

DIETER
The model's objective function covers operational costs, consisting, among others, of fuel and CO2 emission costs, and annualized investment costs. A market clearing condition, also referred to as energy balance, ensures that electricity supply satisfies inelastic electricity Electronic copy available at: https://ssrn.com/abstract=3366910 demand in each hour. Generation technologies comprise thermal generators, such as coaland natural gas-fired plants, and the renewable technologies biomass, run-of-river hydro, onshore and offshore wind, and solar photovoltaics (PV). Flexibility options to temporally align supply and demand include different types of energy storage, several demand-side management (DSM) options, differentiated by load shedding and load shifting, as well the curtailment of renewables. Further constraints ensure that hourly generation by a technology does not exceed installed capacities and that installed capacities do not exceed the potential of a technology. Moreover, the model features intertemporal restrictions for storage and DSM operations as well as constraints related to the provision and activation of balancing reserves.
Model inputs comprise costs and availabilities of technologies as well as hourly demand and renewables feed-in profiles. Endogenous variables are investments into generation and flexibility technologies and their hourly use, including the provision of balancing reserves.
Model outputs cover the total cost of providing electricity, installed capacity, the hourly dispatch of all technologies, and various derived indicators on the utilization of different technologies.
The model version used here focuses on the German electricity sector and abstracts from an explicit spatial resolution as well as modeling interactions with neighboring countries. The model assumes perfect foresight and is solved once for an entire year. DIETER is implemented in the General Algebraic Modeling System (GAMS). Code, data, and a comprehensive model documentation are available open-source under a permissive license. 2 3.2 Representation of the residential power-to-heat segment in DIETER For this analysis, we augment the DIETER version presented by Zerrahn and Schill (2017) by a representation of the residential power-to-heat segment, featuring direct resistive heaters, electric storage heaters, and water-based heating systems. In the latter case, ground-sourced or air-sourced heat pumps, or fossil-fueled boilers with an auxiliary electric heating rod supply heat to a buffer storage. In this paper, our main focus in on electric storage heaters. For brevity, we denote them by NETS (night-time electric thermal storage heaters) for customary devices that charge electricity inflexibly during the night, and SETS (smart electric thermal 6 storage heaters) for upgraded devices that can charge flexibly around the clock. The residential heat module also features the provision of domestic hot water (DHW), either from the buffer storage, from a separate module complementing SETS, or from direct resistive heaters. All electric space heating and DHW technologies, except direct resistive heating, can also provide secondary and tertiary balancing reserves, both positive and negative.
In Appendix A.1, we present the model equations relating to residential heat. They interact with the overarching electricity sector model at three instances: first, electricity demand by heating technologies enters the electricity balance of DIETER; second, reserve provision by heating technologies enters the reserves balance of DIETER; and third, costs of fossil fuel consumption for hybrid heating technologies enter the objective function.

Data and scenarios
We carry out our analysis for the year 2030. The time horizon allows for different plausible scenarios on costs and availabilities of various technologies. At the same time, 2030 is still close enough to plausibly abstract from major uncertainties with respect to technology developments, breakthroughs of alternative sector couplings or costs.

Input data
Input data lean on the EU Reference Scenario 2016 (Capros et al., 2016;E3M Lab, 2016). For the power plant portfolio, we take the figures as given in the Reference Scenario whenever possible. For some technologies, we adopt further assumptions, preferably from other established studies, to align them with the technology types in our model. 3

Capacities of power plants and flexibility options
We adopt assumptions on lower capacity bounds for solar PV, wind power, and pumped hydro storage as well as assumptions on upper capacity bounds for fossil-fueled, biomass plants, and run-of-river hydro plants, guided by the Reference Scenario. Appendix A.2 provides further details on the derivation of the input data. Figure 1 shows the specific assumptions. 7

Figure 1: Assumptions on upper and lower bounds for the generation portfolio
Note: Dispatchable thermal and run-of-river generation capacity (black) can be installed up to the specified upper bound; in contrast, variable renewable and pumped hydro storage capacity (green) face a lower installation bound.
Concerning flexibility options, we assume 6.5 GW of pumped hydro storage power capacities, with an energy capacity of 45.5 GWh. This figure leans on the pumped hydro capacity installed in Germany in 2018. We assume no further flexibility options, such as batteries or demandside management (DSM). If a scenario allows for DSM, we base maximum capacities for three load shedding and five load shifting technologies to potentials derived by Frontier and Formaet (2014), Gils (2014), and Klobasa (2007).

Electricity demand and renewable generation time series
Time series inputs follow German data from the default base year 2016, taken from the Open Power System Data platform (OPSD, 2018;Wiese et al., 2019). For renewable infeed, we take hourly capacity factors, defined as actual hourly generation of onshore wind, offshore wind, and solar PV, divided by the historical capacity of the respective technology. Hourly load time series include electricity demand by existing night-time electric thermal storage heaters. Total annual demand is around 490 Terawatt hours (TWh) of which about 2.5%, or 11.5 TWh, accrue from NETS. For the SETS upgrade case, we construct a synthetic demand profile of NETS, subtract it from the demand time series, and allocate the 11.5 TWh of heating electricity demand to SETS. To this end, we transform the yearly space heating energy provided by existing night-time storage heaters to an electricity consumption pattern covering night-time hours between 10 p.m. and 6 a.m. Accordingly, the electricity consumed by NETS in any such night-time period equals the heating demand of the respective subsequent day. Within contiguous hours of each night, we assume a uniform distribution of heating energy.
Hourly demand for the provision of balancing reserves also follows German data from the base year, differentiated into primary, secondary, and tertiary reserves, each both positive and negative (regelleistung.net, 2018a). Likewise, hourly activation of secondary and tertiary reserves follows the actual German pattern from the base year (regelleistung.net, 2018b); for primary reserves, we assume a flat hourly activation of 5%.

Cost assumptions, fuel and CO2 prices
Assumptions on fuel prices follow the Ten Year Network Development Plan (TYNDP) 2016 (ENTSO-E, 2015a,b), scenario "Vision 3" ( Table 1). The CO2 price of 33.33 Euro per ton follows the EU Reference Scenario. Additionally, we explore a scenario with a high CO2 price of 71

Power-to-heat technologies
We assume that a large share of the presently existing fleet of customary night-time electric thermal storage heaters devices is still present in Germany by 2030. Turning these NETS into more flexible SETS requires respective control and communication interfaces. According to figures provided by a leading manufacturer, we make the following default assumptions: 270 Euro per SETS unit for a communication module plus 140 Euro per flat for a gateway. 4 We further assume an average flat size of 150 square meters and 32 kWh storage capacity per SETS device. With a ten years depreciation period and an interest rate of 4%, the upgrade cost annuity amounts to about 1.13 Euro per kWh.
With respect to SETS dimensioning, we assume their maximum hourly heat output per square meter to cover the hour with the highest heating load of the year, i.e., we do not assume backup heating options. SETS' electric power rating per square meter is then set to be twice as high, and SETS' energy storage capacity in turn is eight times the maximum hourly electric power consumption. That is, SETS have a storage capacity of eight hours. These parameter choices are guided by technical data sheets of typical SETS devices sold in Germany by 2018. 5 We further assume a static heat release of 2.5% of stored heating energy per hour. SETS domestic hot water devices (SETS-DHW) are also parameterized such that their maximum hot water output covers the hour with the highest demand of the year. Electric power rating of SETS-DHW devices is equal to maximum hourly DHW output, and energy storage capacity covers 2.2 hours of the maximum hourly electric power consumption.
Ground-sourced or air-sourced heat pumps supply heat to a buffer storage, covering three hours of maximum hourly heating load. We set the maximum hourly heat output capacity to cover the hour with the highest heating load of the year, including domestic hot water. We 4 Information provided by the manusfacturer GlenDimplex in the context of the EU Horizon 2020 project RealValue. 5 Specifically, the parameter choices are guided by the device "Quantum heater" by the manufacturer GlenDimplex as well as additional information provided in the context of the EU Horizon 2020 project RealValue. Also compare the manufacturer's product website https://www.glendimplexireland.com/brands/dimplex/domestic-heating-systems/quantum-off-peak-heaters (accessed November 17, 2018) 10 also take into account the coefficient of performance (COP) such that the respective electric power rating is accordingly lower. 6

Heat demand
To adequately represent the German residential building stock, we assume twelve building archetypes: six for one-family homes and six for multi-family buildings, differentiated by building age and corresponding energy efficiency levels. The archetypes are defined by RWTH Aachen University, based on the findings of two research projects. 7 A thermal simulation model calculates the annual energy demand per square meter. Taking into account the German targets for energy efficiency improvements of the building stock, we next determine a projection of the total square meters, and thus total annual energy demand, for each building archetype in 2030. We assume that the share of electric storage heaters in total 11 square meters of the respective building archetypes does not change by 2030. Beyond SETS, we assume a certain share of the residential floor area to be equipped with heat pumps, with an equal split between ground-sourced and air-sourced devices. This share is present in all scenarios. Table 2 shows the central parameters.
Hourly heat demand profiles for each archetype are based on a building simulation model, taking into account the behavior of residents and inner loads. 8 Figure 2 exemplarily shows hourly space heating demand profiles for a full year for three one-family home archetypes.
The typical heating period is clearly visible.

Scenarios
The capacity bounds of the generation portfolio shown in Figure 1 serve as a reference for the it is unlikely that SETS are installed in buildings in which a water-based heating system already exists, taking into account installation and operating costs as well as thermal comfort. If existing water-based heating systems, powered by fossil-fueled boilers in 2018, were to be replaced by power-to-heat options, it appears more likely that they will be converted to heat pumps, which require considerably less electricity. For the same reason, third, new future dwellings are also more likely to be equipped with heat pumps or some centralized heating system.
In all scenarios, we abstract from endogenous investments into SETS or other electricity-based heating systems. Instead, we vary their presence exogenously while their hourly use is determined endogenously in the model. 9 This allows to readily identify effects of more flexible electric heaters and their drivers within the electricity sector. Thus, assumptions on future investment or upgrade costs for various heating systems in different building types, which are both uncertain and idiosyncratic, are not required. Accordingly, such costs are also not part of 13 the objective function. Nonetheless, we consider the costs for upgrading NETS to SETS when comparing overall model results. Table 3 lists our central scenarios. Beyond the central SETS upgrade scenario, two scenarios explore the effect of competing flexibility or power-to-heat options: demand-side management and a greater share of heat pumps. Three additional scenarios implement more ambitious environmental policies: a higher CO2 price, a higher share of renewables in electricity generation, and a coal phase-out. The coal phase-out scenario is in line with the generation capacity reduction path discussed in Germany by the time of writing. 10 The additional natural gas OCGT capacities reflect the backup capacities currently contracted in the German "grid reserve" between 2018 and 2021.

Results
We examine how a more flexible use of electricity for heating affects costs, investments into different generation capacities, their dispatch, CO2 emissions, the provision of balancing reserves, and wholesale electricity prices. In doing so, we also investigate important drivers of different effects.

Electricity sector costs and total system costs
Total system costs are calculated as overall costs of providing electricity within one year, consisting of investment and dispatch costs. They are given as the sum of electricity sector costs, i.e., the value of the objective function, and SETS investment costs. 11  Accordingly, more flexible electricity demand can gain a somewhat larger advantage of directing demand to hours with low-cost generation. Fourth, improving the charging patterns of night-time storage heaters through upgrading them to SETS does not necessarily lead to overall efficiency gains, depending on the configuration of the electricity sector. 12 To capture uncertainty in future cost developments, we vary the default cost assumption for upgrading NETS to SETS by halving or doubling it. Except for the heat pump breakthrough scenario, total system costs decrease at least slightly if SETS upgrade costs are only half the default assumption ( Figure 4). Conversely, the costs of respective investments exceed the electricity sector benefits in all scenarios under the assumption of double upgrade costs.
Therefore, low upgrade costs are a vital condition for enabling total system costs savings from making electric storage heaters more flexible. demand-driven, low electricity prices occurred at night. In the future, rising shares of variable wind and solar PV energy add supply-driven price variability, not necessary related to the time of day. However, this shows that the general pattern of low night-time electricity prices remains relevant during the heating season.

Investment, dispatch, and CO2 emissions
Next, we investigate investment and dispatch effects as drivers of system cost changes.
Flexibilizing NETS leads to only minor adjustments in the power plant fleet in the central SETS upgrade scenario. Notably, the additional flexibility related to SETS allows reducing the electrical storage capacity in the system by 250 MW (Figure 5). A similar finding holds also for the other scenarios. 14 Sizeable additional renewable investments are only triggered if we assume a high CO2 price. Under higher carbon prices, SETS flexibility allows integrating additional 3.1 GW of photovoltaics and 0.8 GW of wind power, which goes along with an increasing share of renewables.

Figure 5: Differences in installed generation and storage capacities compared to the respective NETS baselines
14 This is an instance of a more general finding: additional flexibility can strongly mitigate electrical storage requirements, as long as the share of variable renewable energy sources is well below 100% (for a more generic analysis, see Zerrahn et al. 2018).  share accordingly increases from 57.8% to 58.7% in this scenario. Thus, the shape of the merit order determines which technologies benefit from additional flexibility. With a high CO2 price, the absolute advantage in marginal costs of renewables compared to fossil-fueled technologies is greater, and it is optimal to invest into additional renewables that can be more easily integrated by flexibility from SETS, despite higher fixed costs. For the default CO2 price, the absolute advantage of renewables in marginal costs hardly justifies further investments into renewables, even though more flexibility from SETS is available.

Figure 7: CO2 emissions in the NETS baseline and SETS upgrade cases in the central scenarios
The changing dispatch pattern has implications for CO2 emissions. Independent of SETS, emissions are lowest in the high CO2 price and coal phase-out scenarios (Figure 7). In all scenarios with baseline assumptions on the CO2 price, SETS trigger additional electricity generation from coal, and CO2 emissions of the electricity sector accordingly increase. In the

Drivers of system cost savings
To disentangle dispatch and investment effects on the reduction of system costs, we devise a "waterfall" separation of the system cost effects of SETS. We first run the baseline specification with NETS, fix all generation capacities to their optimal values, and then re-run the model in a pure dispatch mode with SETS to isolate the system value of SETS arbitrage.
Next, we allow reserves provision by SETS to pin down the reserves value. Finally, we carry out the full-fledged investment run to infer the capacity-related value of SETS. The latter reflects the value of an adjusted power plant portfolio, which also includes additional dispatch changes. 16 Figure 8 shows the results.   18 Finally, around one quarter of the electricity sector cost savings stems from the capacity, or portfolio, value attributable to SETS.

Wholesale electricity prices
If NETS are upgraded to SETS, this has an impact on wholesale electricity prices. In the model, they are given as the marginal on the electricity market balance. In the NETS baseline, the unweighted mean electricity price is around 60 Euro per MWh (Figure 9). The mean price for NETS electricity is about 53 Euro per MWh, around 12% below the system mean price. The mean price for SETS electricity in the central SETS upgrade scenario is about 48 Euro per MWh, 20% below the system mean price. This reflects the greater flexibility of SETS to better schedule consumption to low-price hours, i.e., hours with higher availability of generation technologies with low marginal costs. In line with that, the mean electricity price for inflexible direct resistive heating in the counterfactual baseline is markedly higher, at 71 Euro per MWh, more than 18% above the system mean price.
If competing flexibility options are available, average prices for SETS electricity demand are slightly higher. This "cannibalization" increases the mean price for SETS to around 49 Euro per MWh in the DSM breakthrough scenario. Conversely, the electricity price advantage of SETS is more pronounced in the 65% renewables and coal phase-out scenarios, both in absolute and relative terms. With more renewables, the temporal flexibility of SETS allows to make better use of low-price periods compared to the respective NETS baselines.
The price advantage of SETS is also reflected in the annual heating electricity bill of households, which can be obtained by summing up all hourly electricity payments for residential space heating and DHW and subtracting revenues from the provision of balancing 22 reserves. 19 In the central SETS upgrade scenario, the annual heating electricity bill for SETS is 9.35 euros per square meter, compared to 10.21 euros per square meter in the NETS baseline.
Analogous to the mean heating electricity prices, the reduction in the electricity bill is lower if there is more competing flexibility in the electricity sector, and it is larger if the share of renewable energy sources increases. While SETS flexibility helps making use of cheaper generation resources, overall system cost effects are not necessarily beneficial, but in any case rather moderate. This is due to the temporal pattern of electricity demand for heating. Figure 10 Figure 11). 20 Therefore, SETS have an incentive to mainly charge at night and their flexibility does not offer a substantial price advantage compared to NETS. Conversely, PV feed-in is highest at summer and spring days around noon, and prices are lower than at night-time.
However, only about 20% of heating demand falls into that seasons, and SETS heat storage capacity does not allow for seasonal storage. These special characteristics of electricity demand for heat render benefits rather moderate. 21 20 For a better exposition, we removed some peak price hours for the calculation of mean prices in Figure 11 and Figure  If the renewable share rises to 65%, daily price patterns change ( Figure 12). While average prices are still absolutely lowest at night, the PV dip is more pronounced also in winter.
Accordingly, more charging occurs during daytime and the temporal flexibility of SETS proves more valuable to the electricity sector. The model we use in this paper is subject to several limitations relevant for interpreting results. First, we analyze the German electricity sector in isolation without explicitly taking into account exchange with neighboring countries. Spatial balancing could provide flexibility to the electricity sector. Moreover, we do not incorporate further potential flexibility options such as electric vehicles or power-to-x, for instance hydrogen. If these technologies are sufficiently flexible, we tend to under-estimate the supply of flexibility and thus over-estimate its value. 22 The results of the DSM and heat pump breakthrough scenarios point into this direction. This conclusion is not unanimous though. It is also conceivable that a future electric vehicle fleet charges predominantly in a user-driven fashion and thus inflexibly. Likewise, power-to-X could operate in a rather inflexible base load mode in order to achieve high fullload hours of electrolyzers. Future research is needed to assess the interplay between several more or less flexible sector coupling technologies.
Second, we do not incorporate the electricity network and thus network congestion. Especially in regions with high demand or high renewable supply, temporal demand-side flexibility could prove more valuable to the electricity sector, irrespective whether of electricity prices reflect congestion or not. In this regard, our results could under-estimate the local demand for flexibility and thus its spatial value. However, in a study on heat pumps, Felten et al. (2018) conclude that locally differentiated prices only have a modest beneficial effect on the electricity system while entailing large distributional repercussions. Future research could assess the spatial dimension of temporal (demand-side) flexibility in an explicit manner. 23 Third, we do not take into account all conceivable power-to-heat options. Based on this analysis, specifically those technologies that potentially come with large long-term heat storage are likely to provide a greater benefit to the electricity sector. They are better able to align the mismatching temporal long-term patterns of renewable electricity supply and heat demand. Such long-term heat storage could be realized either in centralized heat supply systems such as district heating, but potentially also in a more decentralized form for a smaller 22 See Zerrahn et al. (2018) for an illustration of power system effects of a flexible generic power-to-x technology. 23 Runge et al. (2019) devise an analysis for different electric fuels that sheds some light on the impact of locally differentiated prices on electricity demand of this sector coupling option. 26 group of buildings or a residential neighbourhood. Whether and under which conditions the electricity sector benefit exceeds their respective investment requires further research.
We also assume that the demand side faces wholesale real-time electricity prices and thus abstract from a range of regulatory price components. Residential retail prices normally include a range of taxes and surcharges, for instance, to finance the electricity network or renewable support schemes. However, this common simplification helps to isolate relevant tradeoffs within a power sector optimum. Future research could identify how incentives and behavior on the demand side depend on the design of regulated price components, for instance whether they are energy-based or capacity-based. This could also incur a specific focus on prosumage, that is, the self-consumption of solar electricity. 24 Finally, and related, while arbitrage benefits are possible, we tacitly assume that households are able and willing to behave accordingly. As Boait et al. (2017) and Darby (2018) conclude from field trials with smart electric thermal storage devices in several countries, critical success factors for a demand-response system comprise a well-designed interface and effective user activation. One obstacle for the realization of system-friendly behavior by households may be their concern about data protection and security (Michaels and Parag, 2016). Broberg and Persson (2016) and Wilson et al. (2017) and raise concerns about the unwillingness of households to cede autonomy and accept more remote control of parts of their electricity use. However, both large-scale empirical evidence on acceptance and the incorporation of such "soft" factors into numerical models is missing Second, temporal flexibility on the demand side is agnostic about the electricity it helps to integrate. It benefits generation technologies with low marginal costs. This is also the main channel for the (moderate) electricity sector benefits from upgrading electric storage heaters; the benefit from adjustments in the generation portfolio is lower, the benefit from providing reserves negligible. Which technologies benefit from additional demand-side flexibility depends on the shape of the merit order. Beyond renewables, this may be also coal versus natural gas. For flexibility options to trigger the further expansion of renewables, other measures may be required, like for instance higher CO2 prices.
Third, overall cost savings are moderate because the temporal patterns of renewable availability and heat demand are not well aligned in Germany, which serves as an example of temperate climate countries. During the heating season in fall and winter, when energy demand is high, electricity wholesale prices are likely to be lowest at night-time, even for a renewables penetration above 50%. Accordingly, more flexible electric heaters do not gain a large advantage compared to customary night-time storage heaters. Only if the share of renewables increases to 65%, low-price phases more frequently occur at daytime, and flexible electricity demand for heating gains a larger advantage. Thus, temporal flexibility for electric heating appliances could prove to be less valuable to the power system in the medium run than other demand-side flexibility options such as electric vehicles or industrial or commercial demand-side management. Those may provide flexibility also during periods of the year in which renewables have a more dominant part, for instance during summertime with high PV supply. Alternatively, power-to-heat technologies with a long-term heat storage may help to exploit high availability of renewables outside the heating season. 28 Electric storage heaters entail several further drawbacks not explicitly analyzed in this paper.
Compared to heat pumps, they come with a relatively low electrical efficiency. Especially in the long run, the level of electricity consumption is likely to become a more critical factor when it comes to a comprehensive decarbonization of energy supply based renewable energy sources. In this respect, accelerated building retrofitting toward greater energy efficiency and heat pumps appear as a more promising option. However, if upgrades can be realized at low costs, electric storage heaters may play a beneficial yet small role in decarbonizing the energy system. 35 The specific proportion of the floor area of a building type equipped with the respective heating technology follows an exogenous assumption. It is contained in the hourly heat demand parameters that are derived separately for all building type-heating technology combinations at hand. On that note, a proportion of a building type can be equipped with one heating technology, and another proportion of the same building type with another heating technology.

Heat energy balance
The heating energy balance (1) prescribes that, for each hour, heat output by the respective technologies installed in the building archetypes must satisfy residential heat demand.

Direct resistive heaters
Alternatively to SETS, residential heat may be provided by direct resistive heaters. Their heat output is part of the heat energy balance (1) above. Their electricity input enters the energy balance of the electricity sector in the same hour (not shown here).

Water-based storage heating: heat pumps
Heat pumps convert electricity input, , ℎ,ℎ ℎ , to heat output to the water storage tank, , ℎ,ℎ ℎ . This conversion is subject to the coefficient of performance (COP).
, ℎ,ℎ ≡ ℎ , The COP relates the sink temperature, , ℎ , to the source temperature, , ℎ,ℎ , both in degrees Celsius. It is augmented by the efficiency of the heat pump, ℎ , . For ground-sourced heat pumps, we assume a time-constant source temperature, and a timevarying source temperature for air-sourced heat pumps. The time series of the air temperature enters the model as data. As for SETS, the electricity demand is netted by the activation of balancing reserves.
Heat pump electricity demand is restricted by the electrical power rating, , ℎ ℎ , , (3c) as well as a required minimum scheduled electricity demand in case of positive reserve provision (3d). To differentiate between lignite and hard coal, we assume a split as the 2030 scenario Vision 3 ("National Green Transition") of the Ten Year Network Development Plan (TYNDP) 2016 (ENTSO-E, 2015a,b). We attribute natural gas-fired capacities evenly to combined cycle gas turbines (CCGT) and open cycle gas turbines (OCGT). For the split between onshore and offshore wind, we assume about 18% offshore and about 82% onshore. This follows the most recent proposal for the central scenario B from the German Network Development Plan for 2030 (50Hertz Transmission et al., 2018). Lastly, we summarize the remaining, minor technologies "other renewables", "hydrogen plants", and "geothermal heat" as the type "other" for our model application.

A.3 More information on heating demand
Hourly time series of space heat and DHW demand per square meter enter the model as data, differentiated between twelve building archetypes. Further exogenous inputs comprise the electric power rating of heating technologies, their storage energy capacity, the heat output capacity, and the static and dynamic efficiency, which is given as the coefficient of performance (COP) for heat pumps. For ground-sourced heat pumps, the COP is constant; for air-sourced heat pumps, it varies hourly over the year, depending on the outdoor air temperature, which also enters the model as input data in line with the test reference year assumptions of the heating profiles.
Hourly outputs comprise the electricity demand of residential power-to-heat options, their heat and DHW output, the provision and activation of balancing reserves, and the heating electricity price. Derived indicators encompass, among others, yearly heating costs, average electricity prices as well as revenues from providing reserves. Domestic hot water demand in buildings is generally not correlated with the building's size, year of construction or standard of energy efficiency. Therefore, DHW demand was modeled separately, depending on the assumed number of residents in each apartment or building. Its hourly profile was also derived from the Swiss SIA 2024 standard (SIA 2006 Table 4 gives an overview. If only a part of the current NETS fleet is upgraded to SETS, electricity sector costs, i.e., not accounting for SETS investments, decrease with a diminishing marginal rate: if SETS replace 25% of the current NETS capacity, they are lower by 0.045%; if SETS replace 50% of NETS, they are lower by 0.083%; by 0.116% for 75%, and and by 0.145% for 100% NETS upgrades. Figure   13 plots this convex curve against a hypothetical linear decrease (dotted line). If we increase the share of the residential floor area heated by SETS beyond upgrading the existing NETS fleet, electricity sector costs no longer decrease (as in the basic SETS upgrade scenario), but rise by around 1.5% ( Figure 14). This is driven by additional electricity demand of storage heaters, which is here twice as large as for the initial NETS fleet. Accounting for SETS investments, the effect of total system costs would be more pronounced. To allow for better comparison, we assume that the additional SETS replace natural gas-based heating systems and include according fuel cost savings in the calculation. Even then, the overall cost effect is still positive. This finding is in line with our assumption that SETS are unlikely to become a widespread heating option beyond the NETS replacement market. Lastly, if we assume that natural gas hybrid electric heating systems or heat pumps replace NETS, electricity sector costs decrease by a greater extent than if NETS are upgraded to SETS.
This cost advantage is particularly pronounced in the heat pump substitution scenario with a cost decrease of -1.0%, reflecting the more efficient electricity use of heat pumps compared to SETS. In the hybrid substitution scenario, the pure electricity sector cost effect is even larger, but savings drop to -0.3% if we also consider additional natural gas expenditures for hybrid heating systems.
While these sensitivities provide complementary insights, more detailed calculations on relative advantages of specific heating technologies, which would also have to consider the full costs of respective installations, are out of the scope of this work and are left for future research.
-0.15% Cost difference to baseline also considering natural gas expenditures