# Flexible heat pumps: must-have or nice to have in a power sector with
renewables?

Alexander Roth111German Institute for Economic Research (DIW Berlin),
Mohrenstraße 58, 10117 Berlin, Germany 222Corresponding Author<EMAIL_ADDRESS>Dana Kirchem††footnotemark:  Carlos Gaete-Morales††footnotemark:  Wolf-Peter
Schill††footnotemark:

###### Abstract

Heat pumps are a key technology for reducing fossil fuel use in the heating
sector. However, the transition to heat pumps implies an increase in
electricity demand, especially in the cold winter months. Therefore, the
flexible operation of heat pumps will be of high importance to the power
sector. Using an open-source power sector model, we examine the power sector
impacts of three different expansion scenarios of decentralized heat pumps in
an interconnected Germany until 2030 and the role of buffer heat storage of
different sizes. We quantify the required additional investments in renewable
energy sources and the effects on firm capacity needs. If wind power expansion
potentials are limited, the rollout of heat pumps can also be accompanied by
solar PV with little additional costs. The expansion of heat pumps increases
the need for firm capacities and battery storage, but even small heat buffer
storage with an energy-to-power ratio of two hours can reduce these additional
capacities. We further show that increasing the number of heat pumps from 1.7
to 10 million saves around 180 TWh of natural gas and 35 million tonnes of
CO2_eq emissions per year.

##  1 Introduction

In light of the climate crisis, heat pumps are regarded as a central
technology to reduce greenhouse gas emissions in the heating sector [1]. When
powered with electricity from renewable energy sources (RES), heat pumps can
displace traditional heating technologies such as oil- and gas-fired heating
and thus mitigate greenhouse gas emissions. In addition, in the European
context, the Russian invasion of Ukraine has led to further political,
especially in Germany, to reduce the dependence on Russian natural gas
imports. In Germany, natural gas is currently still the dominant source of
residential heating. Therefore, the electrification of heating can be
considered a critical measure to reduce the use of natural gas.

In Germany, policymakers are working to accelerate the implementation of
decentralized heat pumps, with a declared target of six million heat pumps
installed by 2030 [2]. Given the current stock (2024) of around 1.7 million
heat pumps, such a transition implies an increase in the electricity demand.
So far, it is not yet fully understood how a larger heat pump stock affects
the power sector in detail, considering that the electricity needs for
mobility, hydrogen production, and other energy services will also rise. One
common concern is that heat pumps could add to existing load peaks due to
electricity load profiles coinciding with heat demand profiles and thus
increase the need for firm generation capacity or electricity storage.
Therefore, the potential benefits of flexible heat pump operations are of
central interest. Therefore, we explore the power sector effects of various
heat pump rollout scenarios in Germany. In particular, we focus on different
degrees of temporal flexibility in heat pump operations by varying the size of
the heat storage assumed to be attached to heat pumps. To do so, we use the
open-source capacity expansion model DIETER [3, 4, 5] to model the central
European power sector for various scenarios of 2030.

Previous studies have highlighted the important role of heat pumps in the
decarbonization of the heating sector. A recent study shows that deploying
heat pumps is one of the fastest strategies to reduce natural gas consumption
in the German heating sector [6]. Several studies investigate the potential of
heat pumps to facilitate the integration of renewable energy sources in the
power sector. For example, different analyses show that deploying additional
heat pumps aligns well with additional investments into wind power plants [7,
8]. Regarding the flexibility of heat pumps and optimal heat storage size, the
picture is inconclusive. Investigating various heat storage sizes, one study
finds that the optimal thermal energy capacity of heat pumps in Spain and the
UK lies between twelve and 14 hours [9] of maximum heat output. A previous
analysis of wind power deployment in Denmark finds that the flexible operation
of heat pumps provides only has moderate system benefits and that even
inflexible heat pumps enable a higher share of wind power energy [10]. In
another paper, heat pump flexibility is provided by the thermal inertia of
buildings [11]. A more recent study for Germany points out that the power
system cost savings from flexible electric heating with night storage in
Germany are moderate because renewable availability patterns do not align well
with heat demand profiles [12]. The seasonal demand pattern disadvantages
flexible electric heating compared to other sector coupling options without
this seasonality, such as electric vehicles. This finding is also supported by
another study [13] that identifies a larger potential for load shifting in
electric vehicles than in heat pumps. Another study focuses on the role of
flexible, large-scale, centralized heat pumps in district heating grids [14],
finding a correlation between RES expansion and the choice of heating
technologies. With higher deployment of RES, large heat pumps become more
competitive. Other studies focus on the competition of flexibility provided by
heat pumps with electricity storage units. In power systems with a share of
renewable electricity of 80% or higher, the flexible use of heat pumps reduces
the investment needs for short-term electricity storage significantly [15].
The substitutional nature between pumped hydro storage and thermal storage is
also highlighted in the literature [7].

Our paper adds to the existing body of literature by investigating the power
sector effects of decentralized heat pumps in detail, specifically accounting
for different amounts of temporal flexibility facilitated via heat storage. In
our analysis, we use an open-source capacity expansion model that considers
the hourly variability of renewable electricity generation and heat demand
over an entire year and accounts for additional loads related to electric
vehicles and the production of green hydrogen. To the best of our knowledge,
such an analysis has not been done so far. We investigate how different
rollout speeds of heat pumps in Germany, specifically in combination with
different heat storage capacities, impact the optimal capacity investment and
dispatch decisions in the power system. In addition, we also provide an ex-
post calculation to measure the associated natural gas usage, cost, and
emission savings. To check the robustness of our results, we further carry out
numerous sensitivity analyses with alternative assumptions on relevant input
parameters such as renewable availability, including an extended drought
period, different natural gas prices, and a German coal phase-out.

##  2 Methods

In the following, we describe the methodological approach as well as the
sectoral and geographical scope of the study. First, we introduce the power
sector model used in this analysis. Second, we provide details about the
modeling of the heating sector and, in particular, the assumptions regarding
the operation of heat pumps in our model. Third, we outline how other sector
coupling options are considered in the model, namely electric mobility and the
production of green hydrogen. Finally, we describe the geographical scope of
the model.

##### Power sector model

In this study, we use the power sector model DIETER (Dispatch and Investment
Evaluation Tool with Endogenous Renewables), which has already been used in
prior studies of energy storage and sector coupling [4, 12, 16, 17, 18].333The
model code can be accessed here: https://gitlab.com/diw-
evu/projects/heatpumps_2030. It is an open-source linear program that
determines the least-cost investment and dispatch decisions for a range of
electricity generation and storage technologies. The model minimizes total
system costs while considering all subsequent hours of a year to capture
renewable energy variability and storage use accurately. A detailed
description of the objective function and the most relevant constraints can be
found in [3]. The model covers the electricity sector and includes a detailed
space heating module, e-mobility, and flexible hydrogen production options.
Input data include time series of electric load, heat demand, electric vehicle
charging, hydrogen demand, and capacity factors of renewable energies. Cost
assumptions and technology investment constraints are further inputs. We are
following a brown-field approach, in which we consider exogenous bounds on
investments to account for existing plants and path dependencies. These are
aligned with the current renewable capacity expansion plans of the German
government and the currently installed fossil-fuel capacities. More detail on
the capacity bounds can be found in section 3.2 and Table SI.2.

##### Heating sector

The German space heating sector is characterized by twelve archetypes of
residential buildings categorized by two size classes (single-/two-family
homes and multifamily buildings) and six age classes, corresponding to varying
energy efficiency levels. While the building stock is described in detail in
[12], we provide a brief overview here. We model twelve different building
archetypes, which are distinguished by year of construction (six classes:
before 1957, four periods between 1958 and 2019, and after 2019) and housing
type (two classes: one -& two-family homes and multifamily homes). Depending
on the year of construction, the building archetypes are characterized by
different energy efficiency levels: younger buildings have a lower annual
heating requirement, and buildings constructed after 2020 are characterized as
passive houses. Table SI.1 depicts the building stock assumptions for 2030,
which are based on [12].

For each of the twelve building archetypes, an hourly heating demand time
series is generated using the open-source thermal building model TEASER (Tool
for Energy Analysis and Simulation for Efficient Retrofit, [19]) and the
publicly available AixLib Library [20]. The thermal building model considers
the physical components of all major building elements and their thermal
inertia to derive hourly heat flows inside the building and toward the
ambiance (conduction, convection, and radiation). We assume indoor temperature
requirements of 22∘C at daytime and a nighttime reduction to 18∘C between 10
p.m. and 5 a.m. Further, a test reference year approach is used to derive
heating demand, which is representative of historical weather data in central
Eastern Germany. Domestic hot water demand is modeled separately based on the
Swiss SIA 2024 standard [21]. A graphic representation of the resulting hourly
heat demand time series is provided in the Supplemental Information (Figure
SI.2).

We exogenously set the share of total space heating and hot water demand,
which has to be covered by two different types of heat pumps for each
scenario; hence, we implicitly only consider the part of the building stock
where heat pumps are installed. On an hourly basis, the heat pumps must
satisfy the demand for space heating and hot water, as determined by the
shares. We assume that heat pumps can be combined with buffer a heat storage
of different sizes, which vary between scenarios. Based on these inputs and
assumptions, the model optimizes the hourly electricity use by heat pumps.

Figure 1 depicts how heat pumps are modeled in DIETER. The electric energy
needed depends on the coefficient of performance (COP), which in turn depends
on the ambient temperature in the case of air-source heat pumps. Lower ambient
temperatures decrease the COP, so more electric energy is required to provide
the same amount of heating energy. For more information, see section SI.1.1.
How much heating energy is provided to the building depends on the heat
outflow from the buffer storage, which can neither exceed the total amount of
heating energy stored plus the storage inflow in the same hour nor the
installed heat output capacity of the heat pump. We only consider
decentralized heat pumps with decentralized thermal energy storage.
Centralized large heat pumps supplying district heating grids and centralized
seasonal heat storage are not part of the analysis.

Figure 1: Heat module in DIETER

##### Other sector coupling options

As the electrification of other energy sectors is a policy target in Germany,
we also account for electric mobility and the production of green hydrogen.
The additional system load of electric vehicles enters the model as an
electricity demand time series. Cars are assumed to charge with a balanced,
yet not wholesale market price-driven time profile determined by the open-
source tool “emobpy” [5] (for further details, see SI.1.2). The model also has
to satisfy a given yearly demand for green hydrogen that has to be produced
with electrolysis. The hourly hydrogen production profile is endogenously
optimized, with given electrolysis capacity and assuming hydrogen storage at
no cost. We provide the equations that describe the straightforward hydrogen
model in Section SI.1.3 in the Supplemental Information.

##### Geographical scope

The study focuses on Germany, where an explicit heat pump rollout is modeled,
but also includes Denmark, Poland, Czechia, Austria, Switzerland, France,
Luxembourg, Belgium, the Netherlands, and Italy. To keep the model tractable
while still considering the effects of European interconnection, we optimize
investment decisions only in the German power sector while assuming (largely)
fixed power plant fleets for other countries. We also do not explicitly model
sector coupling for countries besides Germany. Section 3.2 discusses capacity
bounds for different countries.

##  3 Data and scenario assumptions

###  3.1 Input data sources

Time series data for the electric load, capacity factors for renewables, and
hydro inflow data for all countries are taken from the ENTSO-E Pan-European
Climate Database (PECD 2021.3) [22].444We use the target year 2030 and the
weather year 2008 Cost and technology parameters of electricity generation and
storage technologies are depicted in Table 3(b) in the Supplemental
Information. The relevant technical assumptions related to heating
technologies and gas-based electricity generation technologies for the ex-post
analysis of natural gas and emission saving are shown in Table 2 (more
information in Section 4.6).

###  3.2 Scenario assumptions

We refer to our main set of scenario assumptions as baseline. In the
following, we briefly sketch the most important features of this scenario.
Whenever we deviate from the baseline, for instance, when we present
sensitivity analyses, we make this explicit.

##### Heating sector

We distinguish between three policy scenarios of the overall heat pump stock
in 2030 which we compare to a reference scenario. In this reference scenario,
we assume 1.7 million decentralized heat pumps in 2030. This number reflects
the stock of heat pumps installed in Germany at the time of writing, meaning
no further pumps would be installed until 2030. In the slow rollout, the
number of heat pumps would reach three million by 2030. Additional heat pumps
would be exclusively installed in single- and two-family homes built between
1995 and 2009. This scenario largely corresponds to the current growth of heat
pump deployment in Germany.555See
https://openenergytracker.org/en/docs/germany/heat/ In the government rollout,
the stock of heat pumps would reach six million in 2030, reflecting the target
of the German government [23]. In this scenario, most single- and two-family
homes built after 1995 would be equipped with heat pumps. In the fast rollout,
heat pumps would installed in more single- and two-family homes, even old ones
built before 1979 with very low energy efficiency standards. In this scenario,
the total number of heat pumps would increase to ten million by 2030, and the
total annual heat provided by heat pumps increases substantially. Table 1
provides an overview of the different heat pump rollout scenarios. Table SI.1
provides additional information on how heat pumps are rolled out across
different building types. In the most ambitious scenario, decentralized heat
pumps provide around 40% of total space heating and domestic hot water needs
(Table 1). The electricity demand of heat pumps and other sectors in the
different scenarios is depicted in Figure 2.

Table 1: Heat pump data

|  | Reference | Slow | Government | Fast
---|---|---|---|---|---
Number of installed heat pumps | [million] | 1.7 | 3.0 | 6.0 | 10.0
Heat pump power rating | [GWe] | 8.7 | 14.5 | 27.5 | 52.6
Maximum thermal heat pump output | [GWth] | 19.6 | 32.7 | 61.9 | 118.5
Share of air-sourced heat pumps |  | 0.8 | 0.8 | 0.8 | 0.8
Share of ground-sourced heat pumps |  | 0.2 | 0.2 | 0.2 | 0.2
Yearly heat supplied by heat pumps | [TWhth] | 18.6 | 43.3 | 74.0 | 195.3

_Notes:_ Heat includes space heating and domestic hot water.

Across all building types, air-source heat pumps account for 80% of installed
heat pumps and ground-source heat pumps account for the remaining 20%. While
ground-source heat pumps are more energy-efficient, air-source heat pumps are
cheaper to install. We assume that all heat pumps can, in principle, be
combined with thermal energy storage. We conduct analyses with varying storage
energy capacities. The assumed energy storage size is expressed in energy-to-
power (E/P) ratios ranging from zero to 168 hours (zero, two, six, 24, and 168
hours). In this terminology, a heat storage with an E/P ratio of two hours has
a total heat storage capacity that equals two hours of maximum heat output of
the heat pump. Equipping heat pumps with a zero-hour storage means that heat
pumps have no attached heat storage and thus have to exactly follow the heat
demand profile in every hour. That means heat pumps are operated inflexibly.
With increasing heat storage, heat pumps can be operated with more
flexibility, allowing to decouple electricity consumption from heat provision.
Importantly, our modeling approach assumes that heat pumps are operated in a
system-friendly, i.e., cost-minimizing manner whenever possible. This could be
interpreted as if heat pump operators faced hourly wholesale prices and
operated their heat pumps to minimize overall system costs. As this is not the
case today, we discuss the consequences of this assumption in the conclusion.

##### Capacity bounds

In Germany, we limit the capacities of coal- and oil-fired power plants to
current levels. Capacities of gas-fired power plants, open-cycle (OCGT), and
combined-cycle (CCGT) - following current policy discussions - can be expanded
beyond current levels. In sensitivity analyses with a German coal phase-out,
we assume the upper capacity limit for hard coal and lignite to be zero.
Regarding wind energy, we align upper capacity bounds for on- and offshore
wind energy with the current German government targets of 115 GW for onshore
wind and 30 GW for offshore wind in the baseline scenarios. We use the
government target for wind power as an upper limit, as wind capacity expansion
in Germany is slow due to long assessment and permit processes, and limited by
land (and sea) availability. In this context, the government targets can be
considered ambitious. An even higher wind energy capacity expansion appears
unrealistic to achieve by 2030 [23]. In a sensitivity analysis, we remove
these upper bounds on wind power capacities. The capacities of solar PV do not
have any bounds. The electrolysis capacity is fixed at 10 GWe.

In other countries, renewable energy capacities are fixed based on the values
of Ten-Year Network Development Plan (TYNDP) [24] of ENTSO-E and set as upper
bounds for fossil generators. The reason for not fixing the fossil generators
in other countries is to avoid an unduly large power plant fleet that could
support the German heat pump rollout. Therefore, the model is free to choose
the smallest capacity needed. In all countries, we fix the capacities of all
hydropower technologies (run-of-river, reservoirs, and pumped-hydro) according
to the ERAA 2021 [22] and bioenergy under the assumption that their potential
for further capacity expansion is exhausted. Table SI.2 provides an overview
of all capacity bounds in all countries.

##### Sector coupling demand

In Germany, we consider electric loads related to electric mobility and
hydrogen production. To incorporate the impact of electric mobility, we
include a fleet of 15 million electric cars compatible with the government’s
goal of 2030 [23]. This fleet would require approximately 36 TWh of additional
electricity annually. Additionally, we account for 28 TWh_H_2 of hydrogen
demand in Germany produced by domestic electrolysis, resulting in an
additional electricity demand of around 39 TWh. This number is based on the
target set in the updated German National Hydrogen Strategy of 2023 to build
up an electrolysis capacity of 10 GW [25, 26] and assuming 4000 full-load
hours. This does not include hydrogen imports, which are expected to satisfy
50 to 70 % of the German hydrogen demand (95-130 TWh_H_2 in 2030) [25]. We
further assume that hydrogen can be stored without additional investment
costs, e.g., in existing cavern storage. This enables electrolyzers to operate
with a substantial degree of flexibility to produce hydrogen over the course
of the year. In countries besides Germany, additional loads related to sector
coupling are included in the electric load time series data provided by
ENTSO-E and thus assumed to be inflexible. Figure 2 provides an overview of
the electricity demand of the different sector coupling options.

_Notes:_ The figure shows the electricity demand in the scenario where heat
pumps do not have heat storage and are operated inflexibly.

Figure 2: Electricity demand Germany

##### Renewable energy constraint

In all scenarios, 80% of the yearly electricity consumption in Germany
(including the consumption of electric vehicles and electrolysis) has to be
covered by renewable energy sources. That is in line with the goal of the
current German government coalition. In addition, the electricity demand by
heat pumps has to be entirely met by additional renewable energy sources over
the course of a year (but not in every single hour). In other countries, we do
not assume any renewable energy targets.

##### Fuel and carbon prices

Our fuel price assumptions are summarized in Table 3(b). In our baseline
assumptions, we set the wholesale price of natural gas to 50 Euro per MWh. We
further assume a carbon emission cost of 130 Euro per ton of CO2 in 2030 [27].
This cost is associated with the emission factor of fossil-based heating and
electricity generation technologies and is considered a variable generating
cost, along with fuel expenses.

##  4 Results

###  4.1 Heat pump rollout triggers investments in electricity generation and
storage

In the following, we show the results of the baseline scenarios in which we
assume expansion limits of 115 GW for onshore wind power and 30 GW for
offshore wind power, have no regulated phase-out of coal-fired power plants,
and assume a natural gas price of 50 Euro per MWh. Figure 3 shows the power
plant capacities needed to cover the required electricity needs of heat pumps
and the impact of heat storage.

Expanding the stock of heat pumps requires additional investments into
electricity generation infrastructure. Looking first at inflexible heat pumps,
we find that in the reference rollout, the cost-optimal capacity mix for
reaching 80% renewable energy in Germany entails so (Figure 3, panel A).
Further, ten GW of hard coal and 47 GW of gas-fired power plants are present.
A rollout beyond the reference scenario requires higher generation capacity
additions. The total additional generation capacities are around five GW and
20 GW (panel B) in the scenarios slow and government. For the slow rollout,
two GW of offshore wind power and less than one GW of PV capacities are added,
while around three GW combined of gas-fired power plants and lithium-ion
batteries are added. For the government rollout, these numbers increase to
seven GW of additional gas-fired power plants and eight GW of additional solar
PV, driven partly by the fact that offshore wind capacities have reached their
upper bounds and can only be expanded by an additional four GW. In the
scenario fast with the highest rollout of ten million heat pumps, 57 GW of
solar PV capacity is added.

In parallel to this large expansion of solar PV capacities, firm capacities in
the form of gas-fired power plants increase by 18 GW to ensure the coverage of
peak loads, while also nine GW of lithium-ion battery storage are added. The
optimal storage energy capacity of batteries increases by three, eight, and 49
GWh in the three respective rollout scenarios (Figure SI.3).

_Notes:_ The figure shows optimal capacity investments in the reference
scenario (panel A) and changes induced by the rollout of heat pumps (panel B)
in the case of inflexible heat pumps. Panel C and D show capacity changes to
the respective references for different heat storage sizes in the government
rollout (panel C) and fast rollout (panel D). The changes shown in panels C &
D are to their respective references with different heat storage sizes.
Reference results (panel A) are almost identically for different heat pump
storage sizes; hence, for better visibility, only one reference rollout is
shown. Please note the different y-axis ranges of the different panels. The
complete set of results, including those for storage energy, is shown in
Figure SI.3.

Figure 3: Capacity investments under baseline assumptions with different heat
pump rollouts and heat storage sizes

###  4.2 Heat storage reduces capacity needs for electricity generation and
storage

Equipping heat pumps with heat storage reduces the need for additional
electricity generation and storage capacities (Figure 3, panels C & D).
Introducing heat storage with an E/P-ratio of two hours reduces the need for
additional solar PV capacities (e.g., six GW instead of an additional eight GW
in the government rollout) compared to the reference. In addition, the need
for battery storage is reduced by around seven GW compared to the case without
heat storage, and even by two GW compared to the reference. This effect can be
explained as lithium-ion batteries and heat storage of heat pumps are both
short-duration storage technologies and, therefore, serve as complements,
especially when taking up daily PV surplus generation peaks. Expanding the
heat storage of heat pumps beyond an E/P ratio of two hours, even lower
additional solar PV capacities are needed, but especially additional
capacities of gas-fired power plants are reduced. If combined with heat
storage larger than six hours in the government rollout (panel C) or larger
than 24 hours in the fast rollout (panel D), the introduction of heat pumps
even reduces the overall need for gas-fired power plants as compared to the
reference. Qualitative results are largely similar between the government and
fast rollout.

We find a substitution between lithium-ion batteries and heat storage not only
for storage power but also for storage energy capacities (Figure SI.3). While
the deployment of heat pumps leads to additional lithium-ion energy capacities
in all three rollouts, the introduction of a two-hour heat energy storage does
not only reduce the additional need for storage energy capacities but even
turns it negative: hence the introduction of heat pumps in combination with
two-hour heat storage is reducing the overall need for lithium-ion energy
capacities. For larger heat storage capacities of 24 and 168 hours, this
absolute reversal cannot be detected, yet additional energy capacities are
still strongly below the case of inflexible heat pumps.

Due to the interconnection with its neighboring countries, the heat pump
expansion in Germany could be partly supported by non-German generation and
storage capacities. To avoid unintended support of German heat pumps by
foreign power plants, we also co-optimize the power plant portfolios of
neighboring countries, assuming an upper limit for fossil-fuel power plants
outside Germany. Therefore, we ensure that German heat pumps in the model do
not unduly benefit from an oversized exogenous power plant fleet outside
Germany. Figure SI.5 (in the Supplemental Information) confirms that
aggregated generation capacities in all countries except Germany barely change
after the introduction of heat pumps in Germany.

###  4.3 Heat storage helps to integrate renewable electricity

The rollout of heat pumps affects optimal generation and storage discharge
(Figure 4) similarly to optimal capacities. The additional electricity needed
for heat pumps is primarily generated by offshore wind power and solar PV. The
latter plays a more significant role in the fast rollout due to the upper
capacity bound of offshore wind power. As the profiles of solar PV generation
and heat pump load only align to some extent, the expansion of heat pumps
triggers additional generation by gas-fired power plants. Battery storage is
also used more in the case of inflexible heat pumps but less if heat storage
is available. If no heat storage is available, the rollout of heat pumps is
also accompanied by additional generation from bio energy, which is another
flexible generation technology, but comes with relatively high variable costs.
Accordingly, bio energy use decreases (or turns even negative in the
government rollout) if heat storage is available. Net imports of electricity
slightly decrease with the rollout of heat pumps, especially when they do not
come with heat storage, i.e., are operated inflexibly. That is due to more
exports of renewable energy surpluses triggered by additional renewable energy
capacities needed for the additional heat pumps.

_Notes:_ The figure shows optimal dispatch in the reference scenario (panel A)
and changes induced by the rollout of heat pumps (panel B) in the case of
inflexible heat pumps. Panel C and D show changes to the respective reference
scenarios for different heat storage sizes in the government rollout (panel C)
and fast rollout (panel D). The changes shown in panels C & D are to their
respective reference scenarios with different heat storage sizes. The results
for the different reference scenarios (panel A) are almost identically for
different heat pump storage sizes; hence, for better visibility, only one
reference rollout is shown. Please note the different y-axis ranges of the
different panels. The complete set of results is shown in Figure SI.4.

Figure 4: Yearly electricity generation by source under baseline assumptions

While the capacity and dispatch results already show that heat storage can
help integrate renewable energy into the energy system, this effect is
highlighted in Figure 5. It provides an illustration of hourly electricity
generation and heat pump operation in combination with additional heat pumps.
The figure depicts two exemplary weeks under baseline assumptions with a
government rollout and two hours of heat storage. The diurnal fluctuations of
solar PV generation are clearly visible, especially in the autumn week. In
contrast, wind power generation has less regular yet longer variability
patterns. In hours of low wind and solar PV generation, gas-fired power plants
and imports cover the remaining residual load. Even with only two hours of
heat storage capacity, heat pumps can align a substantial part of their
electricity consumption with PV peak generation periods. This indicates that
even small heat storage capacities already improve the integration of heat
pumps into the system. Hours of electricity exports, storage charging, and
heat pump use often coincide, which are also hours with relatively low prices.
Conversely, heat pumps largely avoid drawing electricity from the grid during
hours when imports take place, which often coincides with hours of low
renewable generation and relatively high prices.

_Notes:_ Two exemplary weeks are shown for the government rollout of heat
pumps with heat storage of two hours.

Figure 5: Exemplary weeks of electricity generation, heat pump operation, and
wholesale prices

In our model, heat pumps are operated in a way that minimizes system cost,
which can be interpreted as if they are following wholesale market price
signals. The presence of heat storage enables and increases their potential to
do so. As visible in Figure 6, there is a strong alignment of heat pump
electricity intake and relatively low residual load levels when heat pumps are
equipped with heat storage. Heat pumps with no heat storage are inflexible
electricity consumers, which directly follow the hourly heat demand profile.
In Figure 6 that is visible by the parallel movement of heat output (gray
line, right y-axis) and the electricity demand in case of no heat storage (red
line, left y-axis). This changes when heat storage is added. Even small two-
hour heat storage makes heat pumps sufficiently flexible that they can adjust
their demand to the overall system conditions to a considerable extent. If
heat storage is expanded further, heat output and electricity intake are even
less correlated.

_Notes:_ The figure shows the residual load, the heat output of heat pumps,
and their electricity demand for different heat storage sizes in the baseline
setting with a government rollout.

Figure 6: Heat output, heat pump electric load with different storage sizes,
and residual load

The shifting of electric loads through heat storage is also depicted in Figure
7. The figure shows the electricity demand of heat pumps depending on the size
of the heat storage over the course of an entire year. Panel 0 in Figure 7
shows the electricity demand of heat pumps without heat storage, which mirrors
the heat demand (also shown in Figure SI.2). We see that in the winter months,
hence on the bottom and top of every panel, demand is higher than in the
summer months. In all days of the year, heat demand during the first hours of
the day is assumed to be zero. Moving from panel 0 to the right, we see that
the electric load patterns change when heat pumps are operated more flexibly.
Already with heat storage of two hours, heat pumps are used to integrate
excess solar energy from the middle of the day. Furthermore, due to the
flexibility enabled by heat storage, heat pumps can draw electricity in hours
of no heat demand, such as at night, and hence smooth heat consumption peaks
in morning hours. For larger heat storage sizes, such as 24 and 168 hours, the
electric load of heat pumps increasingly resembles the charging of a longer-
duration storage asset, sometimes consuming excess electricity for extended
periods and avoiding consumption later. While this mode of operation may not
be realistic for small, decentralized heat pumps due to limited potential for
low-cost heat storage installations, such operational patterns appear more
plausible for centralized heating solutions with larger and lower-cost heat
storage options.

_Notes:_ The figure shows values from the baseline scenario with government
rollout.

Figure 7: Heatmap of the electricity demand of heat pumps for different heat
storage sizes

###  4.4 Heat storage reduces electricity sector costs

Our analysis focuses on additional electricity sector costs caused by the heat
pump expansion. We relate these costs to the additional heating energy
provided (Figure 8). More heat pumps lead to additional costs for the
electricity sector due to additional investment into generation and storage
capacities and higher variable costs. We find that electricity sector costs
increase by around four ct/kWh of additional heating energy provided in the
government rollout scenario with inflexible heat pumps.

This cost effect decreases with larger heat storage sizes. The relative
decline in additional costs is the largest when moving from no storage to a
two-hour storage. With larger heat storage sizes, the decreases become smaller
and are minimal between a day (24 hours) and a week of heat storage (168
hours). This means that the additional value of long-duration storage compared
to shorter-duration storage is relatively small in the modeled setting with an
80% renewable share in Germany. In other words, the marginal electricity
sector cost savings decrease with larger heat storage. The cost effects shown
in Figure 8 do not include the installation costs of heat pumps and heat
storage, but only the costs related to the electricity sector, such as
investment and operational expenses of generation and electricity storage
capacities. Therefore, we can interpret these figures as opportunity costs of
heat storage.

We calculate the break-even overnight investment costs of heat storage that
would be required to deliver overall system cost savings. We do so by relating
the power sector cost differences between scenarios with different heat
storage sizes to the respective storage capacity and deriving annualized
overnight investment costs. For the latter, we assume that heat storage
installations have a lifetime of 20 years, face an interest rate of four
percent, and do not incur any variable or fixed operation and maintenance
costs. As the marginal power sector cost savings decrease with larger heat
storage capacities, the specific break-even costs of heat storage decrease
even faster. For example, specific heat storage investment costs have to be
below around 80 Euro/kWh_th in the government rollout with two hours of heat
storage. This break-even cost decreases to 40 Euro/kWh_th in the case with six
hours of storage and sharply declines to only about two Euro/kWh_th for a heat
storage size of one week. In other words, long-duration heat storage would
have to be very cheap. Results are qualitatively similar for the slow and
government rollouts. In the latter, break-even costs are slightly higher at
around 94 Euro/kWh_th in the two-hour case, as the additional PV generation in
this scenario increases the value of temporal flexibility. While the real-
world costs of short-duration heat storage technologies are likely well below
the range of two-hour break-even costs determined here, we consider it
implausible that storage sizes of a day or more could be realized in
combination with decentralized heat pumps at the required costs. Low-cost,
long-duration heat storage appears much more plausible in combination with
district heating networks and large-scale, centralized heat pumps, which is
beyond the scope of our analysis.

_Notes:_ For different rollout scenarios, the gray bars depict the additional
costs in ct/kWh_th of additional heating energy provided for different rollout
scenarios and heat storage sizes (compared to the respective reference, left
y-axis). The red lines show the break-even investment costs in Euro/kWh_th of
heat storage (compared to the respective scenario without heat storage, right
y-axis).

Figure 8: Additional electricity sector costs and break-even investment costs
of heat storage

###  4.5 Qualitative results also hold in sensitivity analyses

In addition to our scenario runs under baseline assumptions in which we vary
the rollout speed of heat pumps and heat storage duration, we conduct several
sensitivity analyses. Those help us judge how strongly our results hinge on
certain fundamental model assumptions. We alter the assumptions on the upper
bounds of wind power expansion, the level of natural gas prices, and the
possibility of electricity generation from coal. We also introduce a week of a
stylized “renewable energy drought” with zero wind and solar availability.
Table SI.5 provides an overview of all sensitivity analyses.

In the following, we summarize the principal takeaways of these sensitivity
analyses. An extensive description and discussion of the results of the
sensitivity analyses, including additional figures, are found in section
SI.3.2.

_Notes:_ The figure shows the optimal dispatch in the reference rollout for
different scenario assumptions in case of a two-hour and zero-hour heat
storage (panel A). Changes to the respective reference for a government
rollout are shown in panel B. Please note the different y-axis ranges of the
different panels.

Figure 9: Yearly electricity generation in different sensitivity analyses

In the baseline scenarios, we assume an upper limit for on- and offshore wind
power capacity expansion in Germany of 115 GW and 30 GW, respectively. This
appears to be realistic and policy-relevant from a 2030 perspective.
Considering real-world constraints related to regulation, land availability,
and public acceptance, unbounded wind power capacity expansion seems
implausible. Still, removing these limits (scenario no wind cap), generates
complementary insights into a less constrained equilibrium setting. Results
show an increase in wind onshore capacities at the expense of offshore wind
and a slight reduction in PV capacity. This leads to higher onshore wind
generation and less offshore wind dispatch (Figure 9). The seasonality of
heating demand aligns well with wind power and additional system costs due to
heating decrease slightly compared to the baseline.

Scenarios with higher gas prices (gas100 and gas150) show fewer gas-fired
power plants and more solar PV capacities in the reference and different
rollout scenarios. Especially in gas150, additional capacities are mostly
solar PV as offshore wind is already at its limit in the reference. In
parallel, dispatch sees reduced gas-fired generation both in the reference and
the rollout scenario (Figure 9). The system costs per heating unit increase
significantly due to more expensive natural gas (Figure SI.9).

Without coal-fired power plants (coal phase-out), gas-fired generation and
electricity imports increase in the reference rollout. Yet, the dispatch
effects of a heat pump rollout do not substantially differ from the baseline
setting. Combining coal phase-out with higher gas prices leads to similar
effects like in the scenarios gas100 and gas150.

As the share of variable renewable energy increases, the security of supply
during prolonged periods with low renewable energy supply becomes an
increasing concern [28, 29]. Therefore, we assess how a week of a severe
renewable energy drought in Europe would affect our results. To simulate an
extreme case of such a week, we artificially set wind and solar PV capacity
factors to zero in all modeled countries during one winter week. Such a week-
long renewable energy drought (scenario RE drought) requires substantially
more firm capacity, which is provided by gas-fired power plants in the
reference (Figure SI.8). The effects of a heat pump rollout on electricity
generation and storage technologies is also higher than in the baseline, and
we see higher cost increases. Yet, the overall yearly dispatch in the
reference, and also the dispatch effects of a heat pump rollout, hardly change
as compared to the baseline.

Overall, our sensitivity analyses indicate that the key insights and results
from the baseline scenarios hold true under varying assumptions. The addition
of heat pumps, depending on the rollout speed, requires additional investments
in wind offshore, solar PV, gas-fired plants, and short-duration storage to
meet renewable energy constraints. Unlimited wind power expansion offers some
benefits, but overall cost reductions are modest.

###  4.6 An ambitious rollout of heat pumps leads to large savings of overall
system cost, natural gas use, and carbon emissions

Based on the power sector optimization results, we also examine the effects of
different rollout speeds of heat pumps on natural gas usage and carbon
emissions. We compare the reference rollout of 1.7 million heat pumps with 4.3
million additional heat pumps in the government rollout scenario and 8.3
million additional heat pumps in the fast rollout scenario. The underlying
assumptions for the calculation of gas and emission savings are stated in
Table 2. Table 3 summarizes the results.

Table 2: Cost and technical parameters for savings calculation Parameter | Value
---|---
Overnight investment costs [EUR/kWth] |
Air-sourced heat pumps | 850
Ground-sourced heat pumps | 1400
Gas boilers | 296
Efficiencies |
Open-cycle gas turbine | 0.4
Combined-cycle gas turbine | 0.542
Gas boilers | 0.9
Technical lifetime of heat pumps [Years] | 20
Interest rate | 0.04
Emission factor [t CO2_eq / MWhth] | 0.2

Under the assumption that each heat pump replaces one gas boiler with a
thermal efficiency of 0.9666A thermal efficiency of 0.9 means that 1 kWh of
natural gas will be transformed to 0.9 kWh of heat., additional heat pumps
displace around 61 TWhth of natural gas in case of a government rollout and
196 TWhth with a fast rollout (Table 3 and Table SI.4), compared to the
reference rollout. At the same time, natural gas usage for electricity
generation slightly increases in both scenarios, but this is by far
overcompensated by natural gas savings in the heating sector, leading to total
savings of around 178 TWhth in the fast rollout compared to the reference
rollout. For the more moderate government rollout with lower gas prices,
overall natural gas savings still amount to around 59 TWh. To put these
numbers into perspective, 59 (178) TWh of natural gas corresponds to around
seven (21) percent of Germany’s overall natural gas consumption in 2022, or
around a fifth (three-fifths) of private and commercial natural gas demand. In
the scenarios with higher natural gas prices of 100 Euro or 150 Euro per
MWhth, we find largely similar effects on overall natural gas usage.

We observe an increase in overall system cost savings with an increasing
number of heat pumps and increasing gas prices. In this calculation, overall
system cost effects include the increase in power sector costs due to higher
electricity demand, the total annualized overnight investment costs of the
additional heat pumps, the savings in natural gas expenditures, savings of CO2
emission cost of gas heaters, as well as investment costs of replaced natural
gas boilers. As the investment- and installation costs of heat pumps might
even fall below our cited values to the technical progress, our costs saving
numbers can be interpreted as a lower bound. Overall system cost savings are
between 1.0 and 4.6 billion Euro in the government or fast rollout scenarios
for a conservative natural gas price assumption of 50 Euro per MWh. Savings
increase substantially with higher gas prices, up to 22.2 billion Euro per
year in the fast rollout scenario with a gas price of 150 Euro per MWh.

Our overall system cost calculations depend on the assumption that every new
heat pump substitutes a new gas boiler, which would otherwise have to be
installed. We do not consider retiring existing gas boilers before the end of
their lifetime. The extent to which an accelerated heat pump rollout would
lead to a replacement of existing gas boilers, which have not yet reached the
end of their lifetime, is unclear due to a lack of data on the age of existing
gas boilers in the buildings modeled here. We calculate a counterfactual
extreme case that assumes that the gas boilers replaced by heat pumps could
have been used for another 20 years, which means we do not consider their
investment costs in the calculation. This leads to smaller, but still
positive, overall system cost savings below 0.1 billion Euro in the government
rollout and 2.5 billion Euro in the fast rollout.

The reduced consumption of natural gas correspondingly leads to lower
greenhouse gas emissions. In a fast rollout scenario of heat pumps, emission
savings in the range of 35-37 million tons CO2_eq can be expected under
different gas price assumptions. For the government rollout, we can expect
emission savings of around 11-12 million tons CO2_eq. The latter corresponds
to around 13% of German households’ carbon emissions from buildings in 2022.
Hence, an ambitious heat pump rollout, as described in this paper, could make
a significant contribution to Germany’s carbon emission reductions. A further
expansion of heat pumps beyond 2030 would lead to even higher reductions in
carbon emissions. Note that the assumed emission factor of natural gas of 0.2
tCO2_eq/MW_th appears to be a conservative estimate, as it does not take
methane leakage within the natural gas supply chain into consideration. Thus,
the emission savings from switching to heat pumps presented here can be
considered a lower bound and might be substantially higher because of methane
leakage.

Table 3: Yearly saving of natural gas, CO2_eq emissions, and costs related to
heat pumps

Gas price | Euro/MWh | 50 | 100 | 150
---|---|---|---|---
Heat pump rollout |  | Gov. | Fast | Gov. | Fast | Gov. | Fast
Natural gas displaced by additional heat pumps | TWhth | -61.49 | -196.31 | -61.49 | -196.31 | -61.49 | -196.31
Additional gas usage for electricity generation | TWhth | +2.58 | +18.01 | +1.92 | +12.75 | +4.90 | +20.35
Total gas savings | TWhth | -58.91 | -178.30 | -59.57 | -183.56 | -56.59 | -175.96
Total emissions savings | Mio t CO2_eq | -11.78 | -35.66 | -11.91 | -36.71 | -11.32 | -35.19
Change in overall system costs | Billion EUR | -0.96 | -4.63 | -3.68 | -13.32 | -6.56 | -22.20

_Notes:_ Changes and savings are shown relative to the respective reference
scenario. Gov. refers to the government rollout scenario of heat pumps.

##  5 Discussion and conclusion

As heat pumps are considered a key technology in the heating transition, their
potential future impact on the electricity sector is of interest. We determine
the effects of different rollout paths of decentralized heat pumps in Germany,
combined with heat storage of different sizes, on the power sector. Under
baseline assumptions, we find that the expansion of the German heat pump stock
from 1.7 to ten million would require additional investments of around 54-57
GW of solar PV capacity in a least-cost solution, depending on how much heat
storage is available. These results are driven by the assumption that the
additional electricity consumption of heat pumps has to be covered by
additional renewable electricity on an annual basis and that the expansion of
wind power is limited to 115 GW (onshore) and 30 GW (offshore), respectively.
For a slower rollout speed, which still achieves the German government’s
target of 6 million heat pumps by 2030, additional PV capacities of around 4-8
GW are needed.

Our results suggest a moderate need for additional firm capacity in the form
of gas-fired power plants and lithium-ion batteries in most rollout scenarios,
particularly in the fast rollout scenario. More flexible heat pump operations
facilitated by heat storage can partially relieve these additional capacity
needs, which is in line with previous studies [30, 7]. The European
interconnection also helps to integrate heat pumps into the power sector and
to limit additional capacity needs. This is in line with other findings [14],
which also highlight the importance of interconnection, as large-scale heat
pumps become more competitive if they can make use of renewable surpluses in
other countries.

Already small buffer heat storage with an energy capacity of two hours enables
heat pumps to better align electricity consumption with the residual load.
This results in power system cost savings of up to 0.9 ct per kWh of provided
heat (or around 20%) compared to a case with inflexible heat pumps. Costs
further decrease with increasing heat storage, yet the marginal cost savings
strongly decline with larger heat storage size. This hints at the fact that
heat storage mainly serves to smooth daily renewable energy fluctuations. For
two-hour storage, it appears plausible that the costs of installing heat
storage remain below the power sector benefits determined here. In contrast,
long-duration heat storage would have to be very cheap to break even, which
appears more plausible for large-scale thermal storage in district heating
systems.

Sensitivity analyses show that results are generally robust against changes in
key scenario assumptions. Assuming unconstrained expansion potentials for wind
power substantially reduces solar PV capacity deployment since wind energy
aligns better with heat demand [7], yet barely changes power sector costs. A
complete coal phase-out in the electricity sector also does not have major
effects on the impacts of accelerated heat pump rollouts on power sector
capacities, dispatch, or costs. Higher natural gas prices have more
substantial effects and, in particular, lead to higher additional power sector
costs of additional heat pumps. Considering a week-long, pan-European
renewable energy drought requires overall more firm capacities, and the
rollout of heat pumps is accompanied by substantially higher solar PV
investments in this case.

We further find that an accelerated replacement of gas boilers with heat pumps
can bring yearly natural gas savings between around 57 and 184 TWhth,
depending on the rollout speed and gas prices, and already accounting for
increased gas usage in the electricity sector. For instance, in a fast rollout
to ten million units in 2030, the additional heat pumps could save more than
half of the private and commercial natural gas demand in Germany, which
corroborates related findings [6]. Overall yearly system cost savings depend,
among other factors, on the natural gas price and range from around 1 to 22
billion Euro for different natural gas price assumptions. CO2 emissions
decrease by around 11-37 million tons per year, corresponding to around 13-43%
of German households’ carbon emissions from buildings in 2022.

As with any model-based analysis, our study has limitations. For example, we
implicitly assume perfect distribution and transmission grids within countries
that neglect any kind of grid congestion caused by heat pumps. In some
distribution grid settings, the effect of heat pumps on grid congestion may be
more severe than the impacts on system-wide generation capacities and dispatch
modeled here. We also note that the hourly heat demand profiles used in our
study are smoother than empirically measured heat pump operation patterns from
the U.K. [31, 32]. A more “peaky” future heat demand could, in fact,
potentially lead to higher load peaks and smaller flexibility potentials of
heat pumps, which merits further investigation in future work. In addition,
our heat demand time series follow a synthetic test reference year approach,
while the renewable electricity generation profiles and ambient temperatures
come from actual weather years. This may lead to underestimating the system
challenges in case of situations where very low renewable availability
coincides with very low ambient temperatures and, accordingly, high heat
demand. Therefore, it is advisable to use consistent electric and heat load
data from the same weather years for future work. In addition, our approach of
exogenously fixing the bioenergy capacity may lead to an underestimation of
its flexibility potential. Without increasing the overall use of bioenergy,
its conversion into electricity could become more concentrated in fewer hours
to better complement variable wind and solar power. This would require a
higher installed generation capacity (with lower full-load hours), as well as
appropriate storage of biomass or biogas.

Furthermore, Germany is not the only country pushing for an accelerated
rollout of heat pumps. While we assume inflexible heat pumps outside Germany,
future work could analyze rollouts in the whole of Europe in more detail to
obtain more comprehensive insights into a wider European heating transition.
Finally, our assumption of balanced charging for electric vehicles may not
reflect reality. As the electric vehicle market evolves and charging
infrastructure develops, there may be significant changes in charging behavior
and the adoption of smart and bidirectional charging technologies, which may
decrease the value of flexibility provided by heat storage. Future research
should explore more detailed modeling approaches that account for such
potential changes. Likewise, smartly charged electric trucks could also be
considered in future work [18].

Our results show that even relatively small heat storage capacities may
already have substantially positive power system effects. While in this
analysis, heat pumps were either operated totally inflexibly with no heat
storage or perfectly system-oriented with heat storage, future research could
analyze the effects of other, and potentially more realistic, operating
behaviors. Further, flexibly operating heat pumps requires the right
incentives for consumers. Hence, from a policy perspective, it is important to
make sure that electricity consumption can be measured and controlled on a
continuous basis (sometimes referred to as “smart metering”) and that
consumers have the possibility to choose electricity tariffs that reflect the
dynamics of wholesale electricity markets. While very large heat storage sizes
appear not to be realistic for decentralized heat pumps, our results still
serve as an indication of how larger, centralized heating systems with long-
duration heat storage could operate.

In summary, we find the power sector impacts of an accelerated heat pump
rollout in Germany to be moderate and manageable, even under the assumption
that the electric load from heat pumps has to be met by a corresponding yearly
increase in renewable electricity generation. If wind energy expansion is
restricted, additional solar PV capacity can be deployed instead without
substantially increasing the overall system costs, facilitated by the European
interconnection. In general, operating heat pumps in a temporally flexible
manner entails substantial power sector benefits. Even relatively small heat
storage already helps to reduce the additional needs for firm capacities or
electricity storage induced by heat pumps and lowers power sector costs. To
sum up, operating heat pumps in a temporally flexible manner is not strictly a
“must-have” in the power sector modeled here, but it emerges as a desirable
feature of the energy transition.

## Acknowledgments

We thank our colleague Adeline Guéret for supporting the calculations
described in section 4.6. We further thank various colleagues of the Ariadne
project for feedback on an earlier draft. We thank the participants of the
IAEE 2023 Conference Milano, the Smart Energy Systems - International
conference 2023 Copenhagen, and the Strommarkttreffen 2024/01 Cologne for
their constructive feedback. We gratefully acknowledge financial support from
the German Federal Ministry of Education and Research (BMBF) via the
Kopernikus project Ariadne (FKZ 03SFK5N0, FKZ 03SFK5N0-2), as well as from the
Federal Ministry of Labour and Social Affairs (BMAS) via the project FIS
(FIS.03.00016.21).

## Author contributions

Conceptualization: AR, WS; Methodology: AR, CG, DK, WS; Software: AR, CG;
Formal analysis: AR, DK, WS; Investigation: AR; Data Curation: AR, CG, DK, WS;
Writing - Original Draft: AR, DK; Writing - Review & Editing: WS;
Visualization: AR; Supervision: WS; Funding acquisition: WS

## Data availability

All input and results data used in this paper can be accessed here:
https://gitlab.com/diw-evu/projects/heatpumps_2030

## Code availability

The model and analysis code used in this paper can be accessed here:
https://gitlab.com/diw-evu/projects/heatpumps_2030

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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##  Appendix SI Supplemental Information

###  SI.1 Additional information on the model

This section provides additional information regarding the model we use for
our analysis.

####  SI.1.1 Heat pumps

Following [12], we model the coefficient of performance (COP) of heat pumps as
follows:

$\text{COP}^{hp}_{h}=\eta^{\text{hp}}\frac{{\text{temp}^{\text{sink}}+273.15^{\circ}\text{C}}}{{\text{temp}^{\text{sink}}-\text{temp}_{h}^{\text{source}}}}$
(1)

We generally assume a sink temperature of 50∘C. For ground-source heat pumps,
we assume a constant source temperature $\text{temp}_{h}^{\text{source}}$ of
10∘C for all hours. Assuming a dynamic efficiency parameter
$\eta^{\text{ground}}$ of $0.45$, this renders a COP of 3.64 for ground-
sourced heat pumps. For air-source heat pumps, the source temperature varies
with the hourly ambient temperature. Using an efficiency parameter
$\eta^{\text{air}}$ of $0.35$, this renders a COP of 2.83 in hours with an
ambient temperature of 10∘C, and a COP of 2.26 at 0∘C. Compared to state-of-
the-art heat pumps, these values may be considered conservative, resulting in
inflated electricity consumption of heat pumps. Yet, we assume that heat pumps
are also installed in older buildings where heating systems may require higher
sink temperatures, which would decrease the COP, especially in the fast
rollout scenario. As we assume a constant sink temperature of 50∘C in all
building types, this makes our COP assumptions appear less conservative.

####  SI.1.2 Electric vehicles

The analysis includes battery electric vehicle (BEV) time series using the
emobpy tool [5]. The dataset [33] used has been created utilizing data from
the “Mobilität in Deutschland” survey, distinguishing between commuter and
spontaneous drivers and incorporating various factors such as trip
frequencies, distances, trip duration, departure times, charging station
availability, and charging strategies, as well as the use of popular BEV
models. The dataset encompasses multiple charging strategies. For this
research, we have selected the “immediate-balanced” approach to reflect the
electricity drawn from the grid. Under this charging strategy, the vehicles’
batteries are charged upon arriving at charging stations, with a constant and
often lower power rating than the charging station. This approach ensured that
the BEV reached a 100% state of charge just before commencing the next trip.
The selected time series are scaled to represent the demand for 15 million
battery electric vehicles, with an annual electricity demand of 36 TWh. Figure
SI.1 depicts the electricity demand of BEV in an exemplary week. For more
information regarding the construction of the BEV demand time series, we refer
to previous work [33, 5].

Figure SI.1: Hourly average electricity demand of 15 million BEV for a
representative week.

####  SI.1.3 Green hydrogen

In the analysis, the production of green hydrogen is only foreseen in Germany
and modeled following the approach described in [34]. We assume that a given
hydrogen demand $h2^{demand}$ of 28 TWh has to be covered by electrolysis over
the course of a year (Equation 2). We assume a temporally flexible hydrogen
demand and unlimited hydrogen storage. The electrolysis capacity is
exogenously set to 10 GW in Germany (Equation 4). The conversion factor of
electrolysis is 71%; hence, one kilowatt-hour (kWh) of electricity is
transformed into 0.71 kWh of hydrogen.

$\displaystyle h2^{demand}=\sum^{h}H2^{prod}_{h}$ (2) $\displaystyle
H2^{prod}_{h}=H2^{elec}_{h}\times 0.71$ (3) $\displaystyle H2^{elec}_{h}\leq
INV^{H2}$ (4)

###  SI.2 Additional information on input data

In this section, we present the input data to our model in more detail. Table
SI.1 provides information on the different building archetypes and their
respective heating energy demand.

Table SI.1: Building archetypes and heating energy demand assumptions for
Germany in 2030

|  | Total number | Annual |  | Shares of heat pumps [%]
---|---|---|---|---|---
Type | Year construction | of buildings | heating energy | Floor area | Reference | Slow | Government | Fast
|  | [million] |  demand [kWh/m2] | [million m2] | air | ground | air | ground | air | ground | air | ground
| One- & two-family houses |  |  |  |  |  |  |  |  |  |  |
1 |  Before 1957 | 1.41 | 276 | 247 | 0.008 | 0.002 | 0.008 | 0.002 | 0.008 | 0.002 | 0.2768 | 0.0692
3 |  1958-1978 | 2.46 | 203 | 431 | 0.008 | 0.002 | 0.008 | 0.002 | 0.008 | 0.002 | 0.2768 | 0.0692
5 |  1979-1994 | 2.55 | 153 | 446 | 0.0136 | 0.0034 | 0.0136 | 0.0034 | 0.0136 | 0.0034 | 0.72 | 0.18
6 |  1995-2009 | 3.02 | 112 | 528 | 0.0488 | 0.0122 | 0.38288 | 0.09572 | 0.60048 | 0.15012 | 0.72 | 0.18
7 |  2010-2019 | 1.75 | 66 | 306 | 0.272 | 0.068 | 0.272 | 0.068 | 0.72 | 0.18 | 0.72 | 0.18
9 |  After 2019 | 2.15 | 15 | 375 | 0.272 | 0.068 | 0.272 | 0.068 | 0.72 | 0.18 | 0.72 | 0.18
| Multifamily houses |  |  |  |  |  |  |  |  |  |  |
2 |  Before 1957 | 0.34 | 223 | 170 | 0.0104 | 0.0026 | 0.0104 | 0.0026 | 0.0104 | 0.0026 | 0.0104 | 0.0026
4 |  1958-1978 | 0.64 | 164 | 322 | 0.0104 | 0.0026 | 0.0104 | 0.0026 | 0.0104 | 0.0026 | 0.0104 | 0.0026
6 |  1979-1994 | 0.46 | 130 | 230 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0
8 |  1995-2009 | 0.47 | 103 | 239 | 0.0112 | 0.0028 | 0.0112 | 0.0028 | 0.0112 | 0.0028 | 0.0112 | 0.0028
10 |  2010-2019 | 0.36 | 51 | 181 | 0.128 | 0.032 | 0.128 | 0.032 | 0.128 | 0.032 | 0.128 | 0.032
12 |  After 2019 | 0.46 | 11 | 232 | 0.128 | 0.032 | 0.128 | 0.032 | 0.128 | 0.032 | 0.128 | 0.032

Figure SI.2 depicts the heat demand in kWh/m2 for different housing classes,
depending on the hour of the day and the day of the year.

_Notes:_ The number above every panel refers to the building archetypes, as
defined in table SI.1.

Figure SI.2: Space heating demand

Table SI.2 provides an overview of the capacity assumptions and bounds of the
different technologies in all countries.

Table SI.2: Assumptions on capacity bounds [GW]

| Germany | Austria | Belgium | Switzerland | Czech Republic | Denmark | France | Italy | Luxembourg | Netherlands | Poland
---|---|---|---|---|---|---|---|---|---|---|---
Run-of-river hydro | 3.93 | 6.38 | 0.15 | 4.22 | 0.43 | 0.00 | 13.60 | 7.03 | 0.04 | 0.04 | 0.37
Nuclear | 0.00 | 0.00 | 0.00 | 1.19 | 4.04 | 0.00 | 58.21 | 0.00 | 0.00 | 0.49 | 0.00
Lignite | 0.00-9.30 (0.00) | 0.00 | 0.00 | 0.00 | 0.00-3.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00-6.32
Hard coal | 0.00-9.80 (0.00) | 0.00 | 0.00-0.62 | 0.00 | 0.00-0.37 | 0.00-0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00-9.88
Natural gas (CCGT) | 0.00-$\infty$ | 0.00-2.82 | 0.00-7.61 | 0.00 | 0.00-1.35 | 0.00 | 0.00-6.55 | 0.00-38.67 | 0.00 | 0.00-8.65 | 0.00-5.00
Natural gas (OCGT) | 0.00-$\infty$ | 0.00-0.59 | 0.00-1.08 | 0.00 | 0.00 | 0.00 | 0.00-0.88 | 0.00-5.40 | 0.00 | 0.00-0.64 | 0.00
Oil | 0.00-1.20 | 0.00-0.17 | 0.00 | 0.00 | 0.00-0.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00
Other | 0.00-4.10 | 0.95 | 1.32 | 0.89 | 1.23 | 0.24 | 1.87 | 5.99 | 0.03 | 3.77 | 6.82
Bio energy | 6.00 | 0.60 | 0.21 | 1.20 | 1.06 | 0.67 | 2.56 | 4.93 | 0.05 | 0.54 | 1.41
Onshore wind | 56.00-115.00 ($\infty$) | 10.00 | 5.93 | 1.25 | 3.00 | 5.48 | 44.11 | 19.05 | 0.35 | 8.30 | 11.28
Offshore wind | 7.77-30.00 ($\infty$) | 0.00 | 4.30 | 0.00 | 0.00 | 4.78 | 3.00 | 0.60 | 0.00 | 6.72 | 0.90
Solar PV | 59.00-$\infty$ | 15.00 | 13.92 | 11.00 | 10.50 | 4.75 | 42.63 | 49.33 | 0.25 | 15.46 | 12.19
Lithium-ion batteries |  |  |  |  |  |  |  |  |  |  |
… power in/out | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$
… energy [GWh] | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$
Power-to-gas-to-power |  |  |  |  |  |  |  |  |  |  |
… power in/out | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$ | 0-$\infty$/0-$\infty$
… energy [GWh] | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$ | 0-$\infty$
Open pumped hydro storage |  |  |  |  |  |  |  |  |  |  |
… power in/out | 1.86/2.14 | 5.33/5.61 | 0.00/0.00 | 1.89/2.46 | 0.60/0.65 | 0.00/0.00 | 1.85/1.85 | 2.22/3.62 | 0.00/0.00 | 0.00/0.00 | 0.17/0.22
… energy [GWh] | 471.23 | 1746.66 | 0.00 | 1194.00 | 2.95 | 0.00 | 90 | 289.99 | 0.00 | 0.00 | 1.31
Closed pumped hydro storage |  |  |  |  |  |  |  |  |  |  |
… power in/out | 7.17/7.01 | 0.45/0.45 | 1.23/1.31 | 1.90/1.90 | 0.64/0.69 | 0.00/0.00 | 1.95/1.95 | 4.17/4.17 | 0.00/0.00 | 0.00/0.00 | 1.49/1.33
… energy [GWh] | 391.59 | 3.60 | 5.80 | 56.00 | 3.70 | 0.00 | 10.00 | 61.20 | 0 | 0 | 6.35
Reservoirs |  |  |  |  |  |  |  |  |  |  |
… power out | 0.82 | 2.80 | 0.00 | 8.53 | 0.52 | 0.00 | 9.8 | 8.77 | 0.00 | 0.00 | 0.42
… energy [TWh] | 0.24 | 0.77 | 0.00 | 7.91 | 0.01 | 0.00 | 10.00 | 5.57 | 0.00 | 0.00 | 0.001
Electrolysis | 10.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00

_Notes:_ Based on Bundesnetzagentur [35] and ENTSO-E [24]. If two numbers are
connected with a hyphen, the model can choose endogenously in that range;
otherwise, the value is fixed. All values refer to the baseline assumption. In
brackets, numbers are provided for sensitivity analyses. All numbers are
provided in GW except for storage energy, which is provided in GWh or TWh.

Table 3(b) provides an overview of the cost assumptions of the model.

Table SI.3: Cost and technology parameters

(a) Electricity storage | Interest | Lifetime | Availability | Overnight costs | Efficiency | Marginal costs |
---|---|---|---|---|---|---|---
Technology | rates |  |  | energy | charging power | discharging power | charging | discharging | charging | discharging |
|  | [years] |  | [1000 EUR] | [1000 EUR] | [1000 EUR] |  |  | [EUR] | [EUR] |
Li-ion battery | 0.04 | 20 | 0.98 | 142 | 80 | 80 | 0.96 | 0.96 | 0.5 | 0.5 |
Pumped hydro | 80 | 0.89 | 10 | 550 | 550 | 0.97 | 0.91 | 0.5 | 0.5 |
Power-to-gas-to-power | 25 | 0.95 | 2 | 550 | 435 | 0.73 | 0.42 | 0.5 | 0.5 |

(b) Electricity generation Technology | Interest rates | Lifetime | Availability | Overnight costs | Fixed costs | Efficiency | Carbon content | Fuel costs
---|---|---|---|---|---|---|---|---
|  | [years] |  | [1000 EUR] | [1000 EUR] |  | [t/MWh] | [EUR/MWh]
Run-of-river | 0.04 | 50 | 1.00 | 3,000 | 30 | 0.90 | 0.00 | 0
Nuclear | 40 | 0.91 | 6,000 | 30 | 0.34 | 0.00 | 3.4
Lignite | 35 | 0.95 | 1,500 | 30 | 0.38 | 0.40 | 5.5
Hard coal | 35 | 0.96 | 1,300 | 30 | 0.43 | 0.34 | 8.3
CCGT | 25 | 0.96 | 800 | 20 | 0.54 | 0.20 | 30.0
OCGT | 25 | 0.95 | 400 | 15 | 0.40 | 0.20 | 30.0
Oil | 25 | 0.90 | 400 | 6.7 | 0.35 | 0.27 | 29.0
Other | 30 | 0.90 | 1,500 | 30 | 0.35 | 0.35 | 18.1
Bioenergy | 30 | 1.00 | 1,951 | 100 | 0.49 | 0.00 | 32.5
Wind onshore | 25 | 1.00 | 1,182 | 35 | 1.00 | 0.00 | 0
Wind offshore | 25 | 1.00 | 2,506 | 100 | 1.00 | 0.00 | 0
Solar photovoltaic | 25 | 1.00 | 400 | 25 | 1.00 | 0.00 | 0

###  SI.3 Additional results

####  SI.3.1 Baseline

In the following, we show further results of our baseline scenario runs.

Figure SI.3 shows the complete optimal capacity choices of the model. The
effects of additional heat storage of heat pumps on optimal battery storage
energy capacities (lower row of panels, Figure SI.3) are pronounced.
Inflexible heat pumps lead to an increased need for storage energy; battery
energy storage increases by eight GWh in the government rollout (panel G) by
and 49 GWh in the fast rollout (panel H). With a two hour heat storage, this
finding reverses and the optimal energy capacity of batteries decreases by 17
GWh or 25 GWh, respectively. Beyond a two hour heat storage, effects are
smaller. The results presented in Figure SI.3 show that especially short-
duration electricity storage and heat buffer storage are substitutes.

_Notes:_ Absolute values in the reference scenarios (panels A and E) and
changes to the respective reference scenarios depending on the rollout
scenario and the size of heat pump storage. Values for Germany are depicted.

Figure SI.3: Capacity investments under baseline assumptions

Figure SI.4 depicts the complete dispatch results from Germany, including all
references and renewable curtailment.

_Notes:_ Absolute values in the reference scenarios (panels A, E, and I) and
changes to the respective reference scenarios depending on the rollout
scenario and the size of heat pump storage. Values for Germany are depicted.

Figure SI.4: Total electricity generation under baseline assumptions

Figure SI.5 depicts the aggregated capacities and other countries and how they
change with a heat pump rollout in Germany. The introduction of heat pumps in
Germany does not affect the aggregated power plant and storage portfolio of
other countries on a large scale. In terms of power (discharge) capacities
(upper row of Figure SI.5), the introduction leads only to minor changes, even
to reductions in battery discharge capacities for some heat storage sizes.
Regarding storage energy, we see capacity decreases and increases, especially
for long-duration storage; however, there is no consistent pattern that would
mean that the expansion of heat pumps in Germany is mainly supported by
generation and storage capacities outside Germany.

_Notes:_ Results are shown for the scenario under baseline assumptions with a
fast rollout.

Figure SI.5: Capacity changes in other countries due to an introduction of
heat pumps in Germany

Figure SI.6 shows the profiles of heat output and electricity demand of heat
pumps (for different heat storage sizes) and the residual load. The decoupling
of heat output/demand and electricity consumption of heat pumps can be seen
easily, even for small heat storage sizes. The heat pumps aim to align their
consumption to the hours of lowest residual demand, i.e., often around midday
with high generation of electricity from PV.

_Notes:_ The figure shows the residual load, the heat output of heat pumps,
and their electricity demand for different heat storage sizes in the baseline
setting with a fast rollout.

Figure SI.6: Heat output, heat pump electric load with different storage
sizes, and residual load

Figure SI.7 shows the impact of additional heat pumps on residual load
duration curves and how heat storage changes these. The peak load-increasing
effects of heat pumps can be clearly seen moving from the reference rollout to
more ambitious rollouts. The peak load-reducing effect of heat storage is
especially pronounced in the government and fast rollout scenarios.

_Notes:_ The figure shows residual load duration curves in Germany, depending
on the rollout speed of heat pumps (columns) and their heat storage size
(color). A residual load duration curve depicts hourly residual loads (load
minus generation of renewable energies), sorted in descending order.

Figure SI.7: Residual load duration curves (first 50 hours)

Table SI.4 provides an overview of the full results of natural gas and
emissions savings.

Table SI.4: Full results of natural gas and emissions savings

Gas price | Euro | 50 Euro | 100 Euro | 150 Euro
---|---|---|---|---
Heat pump rollout |  | Gov. | Fast | Gov. | Fast | Gov. | Fast
Total gas displaced by heat pumps | TWhth | -82.18 | -217.00 | -82.18 | -217.00 | -82.18 | -217.00
Change in gas displaced by heat pumps | TWhth | -61.49 | -196.31 | -61.49 | -196.31 | -61.49 | -196.31
Total electricity produced from gas | TWh | 219.59 | 227.87 | 76.88 | 82.86 | 70.72 | 78.97
Change in electricity produced from gas | TWh | +1.33 | +9.61 | +1.00 | +6.97 | +0.00 | +10.81
Total gas use for electricity generation | TWhth | 407.44 | 422.86 | 145.27 | 156.10 | 131.44 | 146.89
Change in gas use for electricity | TWhth | +2.58 | +18.01 | +1.92 | +12.75 | +4.90 | +20.35
Gas savings | TWhth | -58.91 | -178.30 | -59.57 | -183.56 | -56.59 | -175.96
Emission savings | Mio tCO2eq | -11.78 | -35.66 | -11.91 | -36.71 | -11.32 | -35.19
Cost savings | billion Euro | -0.96 | -4.63 | -3.68 | -13.32 | -6.56 | -22.20

_Notes:_ The changes shown in the table are calculated with respect to the
corresponding reference scenario (with the same natural gas price).

####  SI.3.2 Sensitivity analyses

In addition to our baseline scenario runs in which we vary the rollout speed
of heat pumps and heat storage duration, we conduct several sensitivity
analyses. Those help us judge how strongly our results hinge on certain
fundamental model assumptions. Table SI.5 provides an overview of all
sensitivity analyses conducted.

Table SI.5: Overview of sensitivity analyses | Scenario acronym | Description
---|---|---
1 | no wind cap | No upper bound on on- and offshore wind capacities in Germany.
2 | gas100 | Natural gas price at 100 Euro per MWh.
3 | gas150 | Natural gas price at 150 Euro per MWh.
4 | coal phase-out | No coal-fired plants allowed in Germany.
5 | coal phase-out + gas100 | Combination of 2 and 4.
6 | coal phase-out + gas150 | Combination of 3 and 4.
7 | RE drought | All renewable energy capacity factors of all countries set to zero in one winter week.
8 | RE drought + coal phase-out | Combination of 4 and 7.

In the following, we briefly present the different sensitivity analyses and
discuss their results in terms of capacity investments (Figure SI.8), dispatch
(Figure 9), and additional system costs of heating provided (Figure SI.9).

_Notes:_ The figure shows optimal capacities in the reference rollout for
different scenario assumptions in the case of flexible heat pumps (with two-
hour storage) and inflexible heat pumps (with no storage) (panel A). Changes
to the respective reference for a government rollout are shown in panel B.
Panels C and D illustrate the respective results for storage energy. Please
note the different y-axis ranges of the different panels.

Figure SI.8: Capacity investments in different sensitivity analyses

##### No capacity expansion limit of wind energy (no wind cap)

In the baseline scenarios, we assume an upper limit for on- and offshore wind
power capacity expansion in Germany of 115 GW and 30 GW, respectively. This
appears to be realistic and policy-relevant for 2030. Assuming unbounded wind
power capacity expansion, considering real-world constraints related to
regulation, land availability, and public acceptance, seems not feasible.
However, in a sensitivity analysis, we drop this upper limit so that expansion
of on- and offshore wind power capacities are unconstrained, and we assess
what a less constrained optimal solution looks like.

The removal of the upper bound for wind power leads to overall higher wind
capacities and slightly lower PV capacity expansion, already in the reference
rollout scenario (Figure SI.8, panel A). In particular, offshore wind is
substituted by onshore wind due to lower costs. These changes correspond with
a higher yearly generation of onshore wind energy in the reference rollout
scenario (Figure 9, panel A) compared to the baseline scenario. Given this
reference, an additional rollout of heat pumps leads to a substantial
expansion of wind onshore capacities, yet far fewer additional PV capacities
(Figure SI.8, panel B) than in the baseline. In consequence, additional
dispatch consists mainly of onshore wind energy instead of offshore (Figure 9,
panel B). These results confirm that the availability of wind power aligns
well with the seasonality of the heating demand. Optimal storage energy
installation rarely changes in comparison to the baseline (Figure SI.8, panels
C and D). Despite the relatively large shift between different generation
technologies, additional system costs do not change much compared to the
baseline setting (Figure SI.9). This implies that a rollout of heat pumps can
also be combined with different solar PV capacity expansions in case of
binding wind power capacity limits with little additional costs.

##### Sustained high gas prices (gas100 and gas150)

Due to the Russian invasion of Ukraine, the natural gas supply structure of
Europe was fundamentally changed. In the foreseeable future, Germany will not
import any more Russian gas but will rely on more costly imports of liquefied
natural gas (LNG) from other regions. Although wholesale gas prices have been
falling strongly since their peak levels of over 300 Euro per MWh in August
2022 and range by the time of writing between 30-40 Euro per MWh, it remains
possible that new spikes could arise in the future. In our set of baseline
scenarios, we assume a natural gas price of 50 Euro per MWh. We introduce two
alternative scenarios, gas100 and gas150, in which we assume natural gas
prices of 100 or 150 Euro per MWh.

Higher gas prices barely alter the optimal capacity expansion in the reference
rollout. Even a fast heat pump rollout leads to very similar capacity
installations compared to baseline assumptions, with increased solar PV and
reduced gas power plant capacities for a gas price of 150 Euro per MWh (Figure
SI.8, panel B). For the gas150 scenario, we see that a considerable amount of
long-duration storage is deployed, serving as a substitute. Introducing heat
pumps reduces slightly these capacities. Regarding yearly energy generation,
higher gas prices lead, not surprisingly, to lower electricity generation by
gas-fired power plants - in the reference rollout but also in more ambitious
rollouts. Noteworthy is that the additional electricity generated due to the
heat pumps comes in the scenario gas150 mainly from PV, as already the
capacity results suggest. This outcome can be explained by the capacity limits
of offshore wind power that is already reached in the reference rollout.
Additional power system costs per heating unit increase substantially compared
to the baseline because of more expensive natural gas SI.9, suggesting that
the model cannot fully substitute gas-fired power plants. Overall, we do not
observe substantial changes compared to our scenarios under baseline
assumptions with a lower gas price.

_Notes:_ The figure shows the additional system costs per heating energy
provided (in ct/kWh) in different sensitivity scenarios for a government and
fast rollout (with heat storage sizes of zero and two hours).

Figure SI.9: Additional power system costs of heating energy provided in
different sensitivity analyses

##### Coal phase-out (coal phase-out)

In the baseline scenarios, we allow coal-fired power plants to generate
electricity in 2030, in accordance with the currently planned German coal
phase-out by 2038. However, the current governmental coalition agreed to
“ideally bring forward” the coal phase-out to 2030. Although this agreement
has not yet been translated into binding law, we aim to analyze the power
sector consequences of an earlier coal phase-out combined with a faster heat
pump rollout.

In the reference rollout, coal-fired power plants that are present in the
baseline scenario are mainly replaced by gas-fired plants (Figure SI.8, panel
A), but hardly differ otherwise. The additional capacities due to heat pump
rollout are very similar to our baseline scenarios (Figure SI.8, panel B). In
terms of dispatch, generation by coal-fired power plants in the reference
rollout is mainly compensated by gas-fired (CCGT) plants, as well as by
increased net imports. Expanding heat pumps leads to largely similar dispatch
effects as in the baseline (Figure 9). Additional power system costs due to
heat pumps are very similar to the baseline (Figure SI.9).

We also combine the coal phase-out with higher gas prices (scenarios coal
phase-out + gas100 and coal phase-out + gas150). In consequence, we see
slightly higher solar PV capacity installations in the reference rollout.
Additional capacities in the government rollout are similar to those of coal
phase-out and gas150: either they are very similar to the baseline scenarios,
or more PV capacities are triggered in case of high gas prices (coal phase-out
+ gas150). Like in scenario gas150, offshore wind power is already at its
upper bound in scenario coal phase-out + gas150; hence, additional capacities
are mainly PV. Like in gas150, long-duration storage is installed. In terms of
dispatch, results do not differ too much from the baseline, either. For the
reference rollout, the missing coal-fired generation is partly displaced by
electricity net imports. Yet, these net imports diminish with additional heat
pumps in the fast rollout. For scenario coal phase-out + gas150, following the
capacity results, additional generation is mainly PV. Overall, additional
dispatch does not vary strongly between these sensitivity scenarios and the
baseline. Yet, the combination of a coal phase-out and higher gas prices leads
to considerably higher power system costs because of the higher production
costs of gas-fired power plants.

##### A week of a renewable energy drought (RE drought)

As the share of variable renewable energy increases, the security of supply
during prolonged periods with low renewable energy supply becomes an
increasing concern. To simulate an extreme case of such a week, we
artificially set wind and solar PV capacity factors to zero in all modeled
countries during one winter week (scenario RE drought). As a consequence,
substantially more gas-fired power plants are installed in the reference
(Figure SI.8, panel A). Adding more heat pumps does not change the optimal
capacities much compared to the baseline setting. We can see a capacity-
reducing effects of heat storage, when comparing the results of the scenarios
with flexible and inflexible heat pumps. The results regarding generation
(Figure 9) also do not differ much compared to the baseline. Additional system
costs per heat provided (Figure SI.9) are increased, and heat storage also
reduces power sector costs in this scenario. Combining this sensitivity with a
coal phase-out (scenario RE drought + coal phase-out) does not alter the
results substantially. The principal difference is that coal-fired power
plants are replaced by gas-fired power plants. Note that long-duration
electricity storage does not play much of a role in the renewable energy
drought modeled here, as it would be more expensive than providing a backup
capacity of OCGT plants. This would change in case of substantially higher
natural gas prices (compare sensitivity gas150), or if the potential to build
new gas-fired power plants was restricted, or if long-duration electricity
storage became substantially cheaper than assumed here.

Figure SI.10 shows the electricity consumption pattern in a week of a
renewable energy drought. Despite a consistent positive residual load, we see
stark differences in heat pump electricity demand depending on their heat
storage size. Comparable to a regular week, heat pumps shift their consumption
to the periods with the lowest residual load. That is even done for the
smallest heat storage size to the largest extent possible.

_Notes:_ The figure shows the residual load, the heat output of heat pumps,
and their electricity demand for different heat storage sizes in the RE
drought setting with a fast rollout.

Figure SI.10: Heat output, heat pump electric load with different storage
sizes, and residual load