Regionalised heat demand and power-to-heat capacities in Germany – An open dataset for assessing renewable energy integration

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Regionalised heat demand and power-to-heat capacities in Germany – An open dataset for assessing renewable energy integration Wilko Heitkoetter, Wided Medjroubi, Thomas Vogt, Carsten Agert DLR Institute of Networked Energy Systems, Carl-von-Ossietzky-Str. 15, Oldenburg, Germany

HIGHLIGHTS

GRAPHICAL ABSTRACT

heat demand calculated • Residential for each administrative district in Germany.

of heat demand share • Determination covered by electric heating technologies.

building categories defined from a • 729 special evaluation of census data. classes of heating types and in• Five stalled heating capacity considered. data and developed source • Resulting code provided under open source licenses.

ARTICLE INFO

ABSTRACT

Keywords: Regionalised heat demand Power-to-heat capacities Open data Open source Census special evaluation Heating capacity classes

Higher shares of fluctuating generation from renewable energy sources in the power system lead to an increase in grid balancing demand. One approach for avoiding curtailment of renewable energies is to use excess electricity feed-in for heating applications. To assess in which regions power-to-heat technologies can contribute to renewable energy integration, detailed data on the spatial distribution of the heat demand are needed. We determine the overall heat load in the residential building sector and the share covered by electric heating technologies for each administrative district in Germany, with a temporal resolution of 15 min. Using a special evaluation of German census data, we defined 729 building categories and assigned individual heat demand values. Furthermore, heating types and different classes of installed heating capacity were defined. Our analysis showed that the share of small-scale single-storey heating and large-scale central heating is higher in cities, whereas there is more medium-scale central heating in rural areas. This results from the different shares of single and multi-family houses in the respective regions. To determine the electrically-covered heat demand, we took into account heat pumps and resistive heating technologies. All results, as well as the developed code, are published under open source licenses and can thus also be used by other researchers for the assessment of powerto-heat for renewable energy integration.

1. Introduction The expansion of renewable energy sources (RES) is considered a main instrument for reducing global CO2 emissions and mitigating climate change [1]. In Germany, the share of RES in power production increased tenfold, from 3% in 1990 up to 32% in 2016 [2]. In the heating

and cooling sectors, the RES share is still significantly lower, accounting only for 13% in 2016 [3]. Amongst different options for increasing the RES share in the heating sector [4], one approach is to convert power that has been fed into the grid by wind and solar power plants into heat [5]. The most used power-to-heat (PtH) technologies are resistive heaters and heat

E-mail address: [email protected] (W. Heitkoetter). https://doi.org/10.1016/j.apenergy.2019.114161 Received 14 June 2019; Received in revised form 17 October 2019; Accepted 12 November 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: Wilko Heitkoetter, et al., Applied Energy, https://doi.org/10.1016/j.apenergy.2019.114161

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Nomenclature

Thl Q QDHW QSH q qDHW

Selected abbreviations A/V DHW SH

surface area-to-volume ratio domestic hot water space heating

Qinst Q (Ta ) t flh h nhdd

Variables A nres Ta

floor area [m2 ] number of residents [–] ambient temperature [°C]

pumps [6]. As resistive heaters directly convert electricity into heat, the resulting ratio of heat output per power input, called the coefficient of performance (COP), is approximately COP = 1. Heat pumps convert thermal energy from the surroundings, e.g., the ambient air or the ground, into utilisable heat. They can reach values of COP > 3, depending on several influencing factors, e.g., the heat source temperature [6]. Due to this high COP value, the specific CO2 emissions of heat supplied from heat pumps can be lower than those from conventional gas or oil heating systems, even if fossil fuel-based power plants contribute a significant share of electricity generation [7]. On the one hand, PtH expansion leads to a higher electricity demand and increases grid loading [8]. On the other hand, PtH can contribute to the reduction of RES curtailment, in cases of excess electricity feed-in [9]. For this purpose, scheduled PtH load is shifted from time periods of low RES power generation to periods with high generation. As the actual heat demand of the users does not change temporally, thermal storage is required, which can thus be regarded as an equivalent electricity storage. In most cases, heating systems are equipped with heat storage to buffer peak demand. Furthermore, a building’s structure has a significant storage capacity [10]. When using existing thermal storage as equivalent electricity storage, costs can be saved, e.g. in comparison to installing a new battery storage. However, the optimal future mix of energy storage types depends on multiple influencing factors, as well as political objectives, and is addressed in [11]. Besides the storage capacity, there are other constraints that limit the amount of PtH load that can be shifted, e.g., the economic viability of equipping PtH devices with information and communication technology (ICT) or user acceptance [12]. In this paper, we do not take these constraints into account and determine the heating capacity of electrically-driven heating devices that are currently installed and will be installed in future, henceforth abbreviated as “PtH capacity”. We consider only the residential building sector and disregard the commercial as well as the industrial sector. To assess how PtH can contribute to the successful integration of RES in Germany, it is not sufficient to calculate one PtH capacity value for the entire country. The curtailment of renewable power plants due to a surplus feed-in and limited grid transport capacity is often a local phenomenon, depending on the installed capacity and energy demand in the respective region, as well as on the power flow from or to other regions [13]. Therefore, PtH capacity data for every grid region is required. A main driver for the PtH capacity within a region is the corresponding heat demand. Throughout this paper we will refer to the process of allocating data to regions of a territory as “regionalisation”. Top-down regionalisation approaches decompose the overall heat demand of a country or continent into its associated regions by using distribution keys, such as the number of inhabitants per region. Bottomup approaches determine the heat demand of individual consumption units, e.g., buildings, and aggregate the demand of all units associated

heating limit temperature [°C] annual heat demand [kWh/a] annual heat demand for domestic hot water [kWh/a] annual heat demand for space heating [kWh/a] annual area-specific heat demand [kWh/m2/a ] annual domestic hot water demand per resident [kWh/ cap/a] installed heating capacity [kW] heat load [kW] full load hours [h] temperature and area-specific heat load [kW/K/m2 ] heating degree days [K·d ]

with a region. Also, the number of building characteristics that are taken into account for the regionalisation varies between the different approaches. Another important driver of the PtH capacity in a region is the share of the heat demand that is covered by PtH technologies. It is possible to distinguish between decentralised PtH in individual buildings and centralised PtH in district heating grids. Heat demand regionalisation and the determination of PtH capacities are covered by several studies with different geographical and technological focuses, as summarised in Table 1.1 Gils [14] developed a top-down approach for the regionalisation of heat demand on a European scale, taking into account residential and commercial buildings. The demand data were extracted from national energy balances and scenarios. They were then allocated according to land use and population density using a raster of approximately 0.5 km2 pixel size. Furthermore, it was assumed that multi-family buildings have a 20% lower heat demand than single-family buildings. Persson et al. [15] account for more building characteristics, using a complex bottom-up approach to create the Pan-European Thermal Atlas. This considers residential buildings as well as the service sector and has a resolution of 100 × 100 m. The authors used input data from the Danish National Building Register, census data, Corine land cover data and the European settlement map. The data were processed in a floor area regression model and a heat and cooling demand density model. PtH capacities for the entirety of Europe were determined, but the PtH technology was not the focus of the study. The results can be visually depicted on an online map2 but the underlying data are not publicly available. Due to the high degree of model complexity, the results are difficult to reproduce. The Institute for Housing and Environment (IWU) developed a comprehensive topology of the German building stock [16]. The BadenWuerttemberg State Institute for the Environment (LUBW) used these data to regionalise the heat demand of the German State of BadenWuerttemberg into its associated administrative districts [17], taking into account multiple building properties that influence the heat demand: floor area, year of construction and building type. The resulting dataset is publicly available,3 but no source code used for the modelling is provided. Corradini et al. [18] determined the residential heat demand for each municipality in Germany. The authors combined multiple statistics for the year of construction of the buildings, settlement type, number of flats per building and floor area. Due to the usage of different data sources for the respective attributes, assumptions needed to be made, e.g., that the distribution of the buildings within the year of construction is independent of the building type. The results of [18] are further used in [19], where a merit order of energy storage for the 2030 1

For a comprehensive literature review on the topic of PtH, refer to [6]. For more information visit: http://stratego-project.eu/pan-europeanthermal-atlas/. 3 For more information visit: https://www.lubw.baden-wuerttemberg.de. 2

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Table 1 Overview of selected studies taking into account heat demand regionalisation and determination of installed PtH capacities. Study

Spatial scope

Spatial resolution

Regionalisation Method

Building details

Demand sectors: residential/ commercial/ industrial

Openness and reproducibility

Centralised/ decentralised PtH capacities

Gils [14]

Europe

0.5 km2

top-down

+

✓/✓/−

grey box

−/−

0.01 km2 municipality municipality municipality admin. district admin. district

bottom-up bottom-up bottom-up bottom-up bottom-up

++ ++ +++ +++ +++

✓/−/− ✓/✓/✓ ✓/−/− ✓/−/− ✓/−/−

grey box grey box grey box white box grey box

−/− ✓/✓ −/✓ ✓/✓ −/−

Persson [15,62]

Corradini [18] Pellinger [19] Kotzur [20] present study LUBW/ IWU [17]

Europe

Germany Germany Germany Germany German fed. state

bottom-up

++

✓/✓/−

grey box

✓/✓

Annotation: − = not considered; ✓ = considered; + = limited; ++ = medium; +++ = high; white box = applied equations, source code and data are publicly available; grey box = significant part of applied equations, source code or data remains undisclosed.

• What are the effects of the regionalisation parameters on the ob-

horizon is modelled. Also centralised and decentralised PtH as an equivalent energy storage are investigated. Kotzur [20] developed an algorithm to aggregate archetype buildings and determine the residential heat demand per municipality in Germany. Building attributes on the form, envelope, heating system and operation as well as the ownership are considered. The main data source is the census enumeration and in the study 200 archetype buildings are used. The results of [18–20] are not provided as open data. In the listed studies, data on regionalised heat demand and PtH capacities are determined and are, to some extent, suitable for the investigation of how PtH can contribute to avoiding RES curtailment and grid congestion. However, the studies do not consider several aspects that are covered in this paper, as described in the following paragraphs. In contrast to the mentioned studies, we provide all input data and the results of this paper as open data and publish the developed code as open source.4 The open source and open data approach has been chosen by the authors, because it allows for an external evaluation of the models, the assumptions used, as well as the obtained results [21]. Moreover, publishing data and models enables their use by other researchers and helps reduce duplication in data collection. Some of the listed studies already took into account more than one building characteristic to regionalise the residential building stock. Therefore input data from multiple statistics has been combined, which may lead to inaccuracies and hamper the reproducibility of the results. To avoid this, we ordered a special evaluation of the German census enumeration results at the Research Data Centre of the German Federal Statistical Office. The resulting dataset contains a cross combination of six residential building attributes that influence the heat demand. After assigning the heat demand to the regionalised building stock and calculating the electrically-covered share of the heat load, the above-listed studies provide aggregated demand values per region. To our knowledge, this paper is the first that further categorises the heat demand in a region according to the size of the installed heating capacity in the individual buildings. This categorisation allows for the estimation of size-specific costs more precisely for equipping PtH devices with information and communication technology (ICT), required for a time-flexible operation. In particular, this paper will examine the following research questions:

tained heat demand?

The remaining sections of this paper proceed as follows. Section 2 describes the methods and data used to derive the regionalised heat demand and PtH capacity data. In Section 3 the results are presented and validated against values from the literature. We highlight the main conclusions of the study and give an outlook in Section 4. 2. Methods In this section, our seven-step approach for determining the regionalised heat demand and PtH capacity is introduced. As shown in Fig. 1, the process consists of spatial and temporal heat demand modelling, as well as determination of the electrically-covered heat load (PtH capacity) and definition of future scenarios. The implementation of the process is described in B. 2.1. Spatial modelling of the residential heat demand The heat demand spatial modelling process can be summarised as follows. First, we defined building categories and obtained the number of buildings per category for each administrative district from a special evaluation of the German census data. Then, for each building category, the respective heat demand was assigned, also yielding the overall heat demand per administrative district. Finally, we divided the buildings into classes according to the size of the required heating capacity. In the next paragraphs, these three steps of the spatial heat demand modelling will be elaborated upon. 2.1.1. STEP 1: Building categories and regionalisation In the first step of the spatial modelling, residential building categories were defined and the number of buildings per category was assigned to each administrative district. We used data from the census enumeration5 to model the German building stock. Amongst others, the following attributes6 are surveyed in the census enumeration that influence the thermal energy demand: type of building, number of flats per building, year of construction, floor area, heating type and number of residents per building. We ordered a special evaluation7 of the census data at the Research Data Centre of the German Federal Statistical Office and Statistical Offices of the Länder [23]. As shown in Fig. 2, the dataset contains three possible types for each of the six building attributes, relevant for the heat demand. For example, the attribute “year of construction” has the

• What are the residential heat demand and PtH capacities at the •

administrative district level (NUTS-3) in Germany? What installed capacity can be expected in the future in Germany? How are the heat demand and its electrically-covered share broken down on heating capacity size classes in the different regions?

5

For more information visit https://www.zensus2011.de. A comprehensive description of the surveyed attributes is provided in [22]. 7 For more information visit https://www.forschungsdatenzentrum.de. 6

4

For data and source code refer to Appendix A (Supplementary Material). 3

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2.1.2. STEP 2: area-specific annual heat demand In the second step of the spatial modelling, we determined the floor area-specific heat demand of the different building categories. As shown in Fig. 3, we accounted for the attributes: year of construction, number of flats per building and building type. The utilised input data were the 729 building categories defined in the prior step, heat demand measurement data and data regarding the surface area-to-volume ratio ( A/ V ratio) of buildings. To model the influence of the building attributes, “year of construction” and “number of flats per building” on the annual area-specific heat demand q , we used data of the German Energy Agency (DENA) [25]. The data are based on measurements of the final energy consumption for both space heating and domestic hot water (DHW), obtained from energy performance certificates10 of more than 50000 residential buildings. The influence of retrofits is included in the data, as the energy consumption measurement values are the result of the energy efficiency of the building present at the issue date of the energy performance certificate. The numerical values are given in the supplementary material11 and as shown in Fig. 4, the data categorisation is the same as for the used census data. The area-specific heat demand of the buildings with the oldest year of construction (<1979 ) is about two times the demand of the buildings with the newest year of construction (>2000 ), which is caused by the different quality of insulation used. For the buildings built before 1979, the energy demand drops significantly with higher number of flats per building. The reason for this is that buildings with multiple flats have a lower ratio of surface area to building volume and thus a relatively lower area for heat transfer. For newer buildings, the number of flats has a lower influence on the heat demand, due to more efficient insulation. Also, the attribute of “building type” influences the A/V ratio and thus the area-specific heat demand. In Fig. 5, the three considered building types are assigned to their respective A/V ratio, using data provided in [26]. The influence of the A/V ratio on the heat demand can be calculated by Eq. (1), which is given in [27]:

Fig. 1. Overview of the process for deriving the regionalised heat demand and PtH capacity.

q (A/V ) = 50, 94 + 75, 29· A/V + 2600/(100 + A).

(1)

We inserted the individual values for A and A/ V of the building categories (as defined in Section 2.1.1) into Eq. (1). Fig. 5 shows the resulting curve for an exemplary floor area value of A = 150 m2 . By this procedure, the heat demand was disaggregated on the different building categories depending on the building type. More details are given in C. 2.1.3. STEP 3: absolute heat demand and capacity classes In the third step of the spatial modelling, we calculated the absolute annual heat demand of the building categories as well as the overall heat demand of the administrative districts and introduced classes of installed heating capacity. Fig. 6 shows the input data and the performed substeps, which are further elaborated upon in the following paragraphs. To get the absolute annual heat demand, Q, of the building categories, we multiplied the area-specific heat demand that was obtained in the prior step with the average floor area, Q = q · A. The floor area values that were used are presented in the supplementary material.12 Subsequently, we regarded the influence of the attribute “number of residents per flat” on the DHW demand. In the data from DENA [25] that was used to calculate the area-specific heat demand in the prior

Fig. 2. The cross-combination of six building characteristics obtained from a special census evaluation.

types “<1979 ”, “1979 2000 ” and “>2000 ”. This results in 36 = 729 possible combinations of the three types of all six attributes. Each such combination represents one building category. In the resulting table of the special evaluation of the census data, the number of buildings per building category is given for all German administrative districts. The table can be found in the supplementary materials section.8 We chose the administrative district level, as it has the highest possible spatial resolution of the data, without having a significant influence of the SAFE algorithm.9

10 For buildings on sale or new constructions energy performance certificates need to be issued in Germany by registered experts. For more information visit: https://www.febs.de. 11 Supplementary material/other input data/heat demand according to year of construction and number flats per building.xls. 12 Supplementary material/other input data/floor area.xls.

8

Supplementary material/census special evaluation data. The SAFE algorithm is applied to the census data by the German Federal Statistical Office for privacy reasons [24]. 9

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Fig. 3. Overview of the process to determine the floor area-specific annual heat demand.

Fig. 6. Overview of the process to derive the absolute heat demand and classes of installed heating capacity.

QDHW , was subtracted from the overall heat demand, yielding the space heating demand of the building, QSH = Q QDHW . For more details, refer to the supplementary material.13 From the absolute annual heat demand, the installed heating capacity Qinst could also be approximated:

Qinst =

Q , t flh

(2)

using the full load hours parameter, t flh [kWh/kW], which represents the relation of the annual final energy demand for space heating plus DHW and the installed heating capacity. The better a heating system fits to the demand pattern, the higher are the full load hours [30]. Improved insulation of a building leads to shorter heating periods and thus to lower full load hours [31]. No dataset was available that allowed for plausibly integrating these influences into the full load hours and assigning individual full load hour values for each defined building category. We therefore adopted a value of t flh = 1900 h from [31] as full load hours for all heating systems, as it represents an intermediate value between the minimum value of 1350 h [32] found in the literature and the maximum value of 2300 h [30]. Next, we took into account the attribute “heating type”. We grouped the buildings according to the three types, i.e., single-storey heating, central heating and district heating. For the central heating technology, we further distinguished between three classes of installed capacity, Qinst < 12.5 kWth, 12.5 kWth < Qinst < 25 kWth and 25 kWth < Qinst . 14 In the case of district heating, we summed the heating load of all buildings per administrative district with this heating type. The resulting value is a measure for the aggregated capacity of the heat transfer units from the heat grid to the connected buildings. The installed capacity of thermal power plants may significantly differ from this aggregated capacity value, as we did not assign the load to individual, existing district heating networks. Furthermore the assumed number of full load hours would need to be adjusted according to the size of the thermal power plant. Steps one, two and three of the spatial modelling result in the determination of the installed heating load for each administrative district in Germany. In order to use the results of the present study for investigating the coupling of the heat sector with the power sector, the data on administrative district level may be assigned to the respective electricity grid districts.

Fig. 4. Annual floor area-specific final energy consumption for space heating and DHW, following [25].

Fig. 5. A/V ratio of building types [26] and influence on heat demand, normalised by the heat demand of the terraced house building type.

step, the energy demand for both space heating and DHW heating was aggregated. To disaggregate these two energy demand types, we derived an average annual DHW heating demand per resident. To do so, we divided the overall final energy demand for DHW in the German residential building sector, 90.12 TWh , in 2010 [28], by the number of inhabitants in Germany, 80.21·106 inhabitants according to the census 2011 [29], which yielded qDHW = 1123 kWh/cap/a . This value was then multiplied by the average number of residents per flat and the number of flats per building. The resulting absolute DHW demand per building,

2.2. Temporal modelling of the residential heat demand In this section, the temporal modelling of the heat demand is 13

Supplementary material/other input data/number of residents per flat.xls. The size classes are defined such that they each contain a similar number of buildings. 14

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described, and comprises step four and five of the overall modelling process. In step four, we calculated the daily load profile of the heat demand for different weekdays with a resolution of 15 min. These intraday load profiles are dominated by the usage patterns of the residents and the control settings of the heating system. In step five, the time series of the heat demand in the course of the year was considered. First, a yearly load profile with a resolution of one day was determined, which is dominated by the daily average ambient temperature. Then, the daily average load values were multiplied with the normalised intraday load profiles that were calculated in step four, thus yielding a yearly load profile with a resolution of 15 min. 2.2.1. STEP 4: daily load profiles For modelling the intraday resolution of the space heating and DHW load, we used measurements that were carried out by the DLR Institute of Networked Energy Systems as part of the NOVAREF project [33] for 12 residential buildings. These buildings are single-family, detached houses located in northern Germany and were constructed between 1974 and 2015. The residents are families without children, families with up to three children and senior citizens. The measurements were performed for at least one year for each building, with a time resolution of two seconds. We used the NOVAREF data, as they were obtained measuring the heat flow and return at the heat exchangers and thus represent the actual demand of the residents. Yet it has to be considered that demand patterns measured in other geographical regions, building types or time periods may differ. We aggregated the NOVAREF time series of each building from a two second resolution into 15-min average values < Q15min >. The resulting yearly time series of each building with a 15-min resolution was then cut into 365 one-day-interval time series. Furthermore, the daily load profiles were normalised by dividing the 15-min average load values by the daily average load | < Q15min > | = < Q15min > / < Q24h >. The normalised load profiles were grouped by working days, Saturdays and Sundays and for each of the obtained groups all associated daily load profiles were averaged. This averaging reduces load peaks and is required, because the scope of this paper is to analyse the statistical demand time series of multiple thousands of buildings, e.g., in one administrative district. Such aggregated load profiles are smoother than those of individual buildings on one specific day.

Fig. 7. Overview of the process for determining the yearly load profile.

flat” and “floor area”. The values of the specific heat load, h, and heating limit temperature Thl are not yet defined. We therefore derived functions for h and Thl that are dependent on the annual heat demand for space heating QSH . As we defined QSH depending on the building category attributes, as described above, h and Thl are also indirectly dependent of these. We began the derivation of the functions for h and Thl by defining QSH , not from measurement values as in Section 2.1.1, but by integrating the space heating load (first summand from Eq. (4)) over time:

QSH =

= h ·A·

h=

Ta < Thl: Q (Ta) = h· A·(Thl

Ta) + qDHW · nres.

(Thl

Ta (t )) dt

Ta (t )) dt

QSH , A· nhdd

(5) (6) (7) (8)

where tstart and tend are the time limits of the heating period. As h and A are constants, they can be extracted from the integral (Eq. (6)). The remaining integral part yields the so-called heating degree days nhdd [K ·d ] (Eq. (7)) [35], which in turn depend on the heating limit temperature and location of the building. Using an Excel tool15 developed by the Institute for Housing and Environment [36], we calculated the number of heating degree days for three different heating limit temperatures, averaged over all weather stations in Germany. For each station, the average number of heating degree days of all years was used that were measured at the respective station. The results are listed in Table 2. We interpolated the average heating degree day values using the following linear function:

nhdd =

(3)

Thl: Q (Ta ) = qDHW ·nres ,

tend tstart

h·A·(Thl

= h ·A· nhdd,

2.2.2. STEP 5: yearly load profiles In step five, we determined the yearly load profiles for every building category considered and the aggregated heat load for each administrative district. An overview of this process is shown in Fig. 7 and more details are described in the following paragraphs. To model the dependency of the heat load Q (Ta ) on the ambient temperature for each building category, we introduced a bilinear load profile that is also used in several standards [34]. The profile is plotted in Fig. 8 and is defined by Eq. (3) and (4):

Ta

tend tstart

1087.3 + 232.28·Thl.

(9)

The heating limit temperature in Eq. (9) is not yet defined. According to [36], the average heating limit temperature for low-energy houses is 12 °C and 15 °C for buildings with a weak heat insulation. Therefore, we assigned Thl = 12 °C to the building category (according to the definition in Section 2.1.1) with the lowest annual area-specific heat energy demand (67.29 kWh/m2/a ) and Thl = 15 °C to the category with the highest area-specific annual heat energy demand (198.41 kWh/m2/a ). To determine the heating limit temperature values for the other building categories, depending on their annual area-specific heat demand QSH /A , we interpolated the maximum and minimum of the heating limit temperature values by using a linear function, as follows:

(4)

When the ambient temperature Ta is greater than or equal to the heating limit temperature Thl , which depends on the attributes of the building, no space heating is required, only DHW heating. The DHW heat load per resident qDHW is assumed to be independent of the ambient temperature. Dividing the annual DHW heating demand per resident, introduced in Section 2.1.1, by the number of hours per year, 8760 h , yields a value of qDHW = 0.128 kWth . Then, qDHW is multiplied by the number of residents per building nres . In the case of Ta < Thl , the space heating load rises linearly with the difference of Thl and Ta . The slope of the space heating curve is the temperature and area-specific heat load, h, multiplied by the floor area A. Eqs. (3) and (4) show that the heat load Q (Ta ) directly depends on the values of the building category attributes, “number of residents per

15 For more information concerning the tool “Gradtagszahlen-Deutschland. xls” (engl.: “Heating Degree Days Germany”) visit: https://iwu.de.

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Fig. 8. Heat load dependency on ambient temperature. Table 2 Heating degree days for different heating limit temperatures [36] averaged over all weather stations in Germany. Thl [°C]

nhdd [K·d ]

10 12 15

1254.78 1667.90 2409.75

15 Thl = 12 + 198.41 = 10.46 + 0.0229·

12 Q ·( SH 67.29 A

67.29)

Fig. 9. Heat load of the different building categories in the heating limit temperature region. One line represents one building type. Dark colour: low heating limit temperature; bright colour: high heating limit temperature. For improved clarity, not all of the 729 load curves shown.

We applied the second approach to account for day-to-day temperature variability and used the daily average ambient temperatures from 2011 as a case study, measured at the closest weather station to the respective administrative district.19 Due to the thermal inertia of the building mass, the temperatures of previous days influence the daily heat load. According to [37], the ambient temperature Ti, ref on day i, used as a reference temperature for the heat load calculation, can be appropriately modelled by a geometric series, taking the three previous days (i 1, i 2, i 3) into account:

(10)

QSH . A

(11)

Inserting Eqs. (9) and (11) into Eq. (8) yields:

h=

QSH A·24·( 1087.3 + 232.28·(10.46 + 0.0229·

= 0.00783324

1.97679 Q 252.359· SH A

QSH )) A

(12)

Ti, ref =

.

(13)

1·Ti + 0.5·Ti 1 + 0.25· Ti 2 + 0.125· Ti 1 + 0.5 + 0.25 + 0.125

3

.

(14)

Then, in a next step, we inserted the resulting daily ambient temperatures from both approaches into Eq. (4) for all building categories that have been defined in Section 2.1.1. This yielded the respective daily average space heating and DHW load, where the first dataset was based on long-term average temperatures and the second was based on the daily average temperatures from 2011. The daily average loads were then multiplied with the normalised intraday load profile with a 15-min resolution for the respective day category (i.e., working days, Saturdays and Sundays).

A factor of 24 had to be added in the denominator in order to convert days into hours. More details on the derivation of Eqs. (9)–(12) are provided in the supplementary material.16 After deriving the functions for the heating limit temperature, Thl , and the specific heat load, h, we evaluated Eqs. (3) and (4) for all building categories that have been defined in Section 2.1.1. An excerpt of the resulting curves for the heat load over the ambient temperature is presented in Fig. 9, showing the region of the heating limit temperature in detail. There are three groups of curves with a vertical offset between each other, which is caused by the different number of residents in the building categories,13 which influence the DHW demand. The curves in Fig. 9 have varying heating limit temperatures and different slopes, which is due to the differing years of construction, building type, floor area and number of flats per building. To define the ambient temperature during the course of the year, we assigned the administrative districts each to the closest of the 44 weather stations in Germany [36]. For each weather station, we determined daily average temperatures, applying two approaches: The first approach was used to derive long-term average heat load data. Therefore, the monthly average temperatures since the start of measurements at the weather stations were obtained from [36].17 The related data are provided in the supplementary material.18 We assigned the monthly average temperature to each fifteenth day of the month. The temperatures for the other days were linearly interpolated.

2.3. STEP 6: Power-to-heat capacity After modelling the spatial and temporal distribution of the heat demand in the previous steps, we continued by determining the share of the heat load that is covered by an electric source in Step 6. We took into account the heat pump technology, for which we summed up the numbers of the air- and ground-sourced systems. Moreover, we took the resistive space heating and resistive DHW heating technologies into account. For more information on the functionality of these technologies, refer to [6]. There are no datasets available in which the numbers of installed electric heating systems are divided up into all of the census enumeration attributes, used to define the building categories in Section 2.1.1, but the two attributes, “number of flats per building” and “year of construction” are covered. Table 3 shows the number of buildings equipped with heat pumps [31], broken down according to the number of flats per building.

16

. In [36] the temperature data were obtained from the German Meteorological Service. 18 Supplementary material/other input data/administrative districts closest weather station average temperatures.xls. 17

19 The daily measured average temperatures for 2011 were obtained directly from the website of the German Meteorological Service: https://cdc.dwd.de/ portal/.

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defined, with differences in the development between the administrative districts being disregarded. Furthermore, we approximated the demand for DHW stays as a constant until 2030. For the development of the overall space heating demand of the German residential building stock, we adopted a scenario from [42], according to which the demand decreases by 22.5% from 2011 to 2030. As detailed in F, the input data for the scenario are building retrofit and reconstruction rates and the achieved heat demand reduction. For the expansion of PtH until 2030, we defined three scenarios with different expansion rates of decentralised heat pumps and resistive heaters, as well as centralised PtH in district heating. As far as was possible, the assumptions were based on literature values and are listed in Table 5.

Table 3 Number of installed heat pumps in Germany (2011) listed according to the number of flats per building [31]. Category: flats per building

Installed heat pumps per category [–]

1 2–6 >6

195000 123000 55000

Table 4 Flats with resistive heating in Germany (2010) listed according to the number of flats per building and the year of construction [38]. PtH technology

Category: flats per building

Number of flats with this PtH technology

2.4.1. Moderate PtH Expansion Scenario (PtHmod) The PtHmod Scenario assumes a moderate expansion of PtH technologies. We adopted the number of 1.7 million installed heat pumps from [31] (Business As Usual Scenario) in 2030, which assumes an approximately 3% increase in heat pump sales rates per year.22 Resistive space heaters are mostly implemented as night storage heaters, allowing customers to purchase excess power from fossil or nuclear power plants [44] at reduced prices. The energy transition and phase out of large-scale power plants is expected to cause a reduction in the number of installed night storage heaters. At the same time, the need to balance renewable energy feed-in may lead to an increase in the numbers of resistive heaters [45]. Following [46], we assumed that both effects will compensate each other, yielding a number of 1.1 million installed resistive heaters that remains constant until 2030. The number of resistive DHW heaters is assumed to stay constant in all scenarios. The advantages of such boilers, as e.g., the low required space for installation will also be relevant in future. A possible use of DHW boilers for load shifting is expected to not have an increasing effect on the high number of installed devices. For centralised PtH in district heating systems, no differentiation was considered between the future development of heat pumps and resistive heaters. This was mainly because of the lack of scenario data. In the time period between 2011 and 2017, centralised resistive heaters with an overall capacity of 0.61 GW were installed in Germany [40]. In the Scenario PtHmod, this growth is linearly extrapolated, leading to a capacity of 1.9 GW in 2030, also including possible installations of large-scale heat pumps in district heating grids.

Year of construction of building 1918–1979 1979–2000 >2000 Resistive space heating

1 >1

223000 691000

44000 119000

8670 10340

Resistive DHW heating

1 >1

1296000 4531000

21300 707000

46000 70000

The number of flats with resistive space heating and resistive DHW heating systems are shown in Table 4, following [38], where the data are separated according to buildings with one flat and buildings with more than one flat. Furthermore, three different categories for the attribute year of construction of the building are distinguished. Additionally, we assumed that resistive space heating is only used in flats with single-storey heating. Then, the number of flats equipped with heat pumps and resistive heating technologies was divided by the total number of flats in each category. The resulting shares were multiplied by the total installed heating capacity in the respective category, which yielded the installed electrically-covered heat load. For more details on the number of flats equipped with PtH technologies, refer to the supplementary material.20 We used the data sources [31,38] for the number of installed heat pumps and resistive heating devices for the years 2010/2011, because the developed model for the heat demand is also based on data from 2011, when the last census enumeration was conducted in Germany.21 The numbers listed in Table 3 and 4 refer to the installed heat pumps and resistive heaters in the entirety of Germany. In order to account for regional differences, we introduced a scaling factor for each German federal state. This factor specifies whether, in the respective federal state, the electrically-covered share of the heat load is higher or lower than in the other federal states. The scaling factor of each federal state is multiplied with the electrically-covered heat load share in all administrative districts associated with the state in question. More information on the calculation of the scaling factor is given in D. The thermal capacities of power-to-heat facilities in district heating systems in Germany are listed in [40] (Note E for heat storage in district heating systems). In this paper, we assigned these capacities to the centroids of the respective administrative districts and plotted the resulting data in Fig. 11. The numerical values are also listed in the supplementary material.20.

2.4.2. Low PtH expansion scenario (PtHlow) In Scenario PtHlow, the PtH expansion is reduced in comparison to Scenario PtHmod. The sales rates of heat pumps remain constant at the level of 2018 [47], which yields a total of 1.4 million installed heat pumps in 2030.23 The number of resistive heaters decreases by 0.7% per year, as stated in [48], but is not compensated by opposing effects as in Scenario PtHmod. This leads to a reduction in the number of installed resistive heaters to 0.952 million in 2030. The limited economic viability of PtH in district heating [40] does not improve and no additional PtH plants are installed. Thus the installed PtH load in district heating remains at 0.613 GW [40]. 2.4.3. High PtH Expansion Scenario (PtHhigh) In the Scenario PtHhigh, the PtH expansion is increased in comparison to Scenario PtHmod. The number of installed heat pumps rises to 2.3 million in 2030, adopting the number from the optimistic expansion scenario in [31]. Additionally, in this scenario the increasing effects on the number of resistive space heaters (as described in

2.4. STEP 7: future scenarios As the coupling of the heat and power sectors may become more relevant with the future expansion of RES [41], we provide an outlook for the development of the heat demand and PtH deployment until 2030. Therein, a generalised perspective for the entirety of Germany is

22 The scenarios in [31] use data from [43] and consider the influence of the policy framework, technical requirements and energy price trends. 23 For the time period 2011–2018, we used actual heat pump installation numbers according to [47]

20

Supplementary material/other input data/electric heating factors. 21 For more recent numbers of the installed electric heating devices refer to [39] and www.waermepumpe.de. 8

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Table 5 Number of decentralised heat pumps and resistive space heaters and installed heating capacity of PtH in district heating systems in the defined 2030 scenarios.

Heat pumps [million] Resistive space heaters [million] PtH in district heating [GW]

PtHlow

PtHmod

PtHhigh

1.4 0.95 0.61

1.7 1.1 1.9

2.3 2.2 4.5

Scenario PtHmod) overcompensate the decreasing effects. It is assumed that this will cause a doubling of the number of resistive space heaters, to 2.2 million, in 2030. In the PtHhigh Scenario, the installed load of centralised PtH in district heating grids is assumed to be 4.5 GW. This number was derived in [49] by a comparison with the currently installed PtH capacity in Denmark, which the authors consider to be a front runner to centralised PtH. 3. Results and discussion In this section, we present the modelling results for the regionalised heat demand and PtH capacities of the administrative districts in Germany. First, the findings for the installed heating capacity are described, considering different technologies and capacity sizes. Next, the temporal resolution and future development of the heat load and PtH capacities are addressed. Finally, a validation of the results is conducted for both the heat demand values of the entirety of Germany and individual administrative districts.

Fig. 10. Installed heating capacity and heating technology distribution in the city of Berlin and surrounding rural districts (bar charts: absolute values; pie charts: relative values).

3.1.2. Structure of the installed heating capacity in different major cities The distribution of the heat load in different major German cities, normalised by the total installed heating capacity in the respective city, is shown in Fig. 12. Such was the case in Berlin, where district heating and large-scale central heating cover a significant percentage of the heat demand in the cities of Hamburg and Munich. The share of the medium-scale central heating (12.5kWth < Qinst < 25kWth ) in Hamburg and Munich is more than twice that in Berlin. This may be explained by the lower number of single-family houses in Berlin due to a different housing policy in the former German Democratic Republic than in Western Germany [51].

3.1. Installed heating capacity In the following subsections, we show the results obtained from the modelling of the installed heating capacity in the German administrative districts. Differences between municipal and rural districts, as well as between different major cities, are especially highlighted. The electrically-covered heat load and shares of the different technologies are also presented. In the supplementary material,24 the numerical results for all German administrative districts can be found.

3.1.3. Share of electric heating technologies covering the heat load As described in Section 2.3, we next multiplied the installed heating capacity with the electrically-covered share, considering different technologies. This yields the PtH capacity that could potentially be used for load shifting in order to balance fluctuating renewable energy feedin. The results are depicted in Fig. 13a, using the example of the city of Berlin. The share of the electrically-covered load is relatively low, with a maximum of 0.25GWth from a 1.8GWth total heat load for the singlestorey heating category, which corresponds to 13%. Fig. 13b shows, how the electrically-covered load is split up into different technologies. The largest part is covered by resistive DHW heating, followed by resistive space heating. Heat pumps still play a minor role. Currently, there is one 6MWth resistive heater installed in the district heating system in Berlin. Compared to the total load electrically-covered by single-storey heating systems, it is of a much lower value. In Fig. 11, the PtH facilities in district heating systems in Germany are presented. The smallest, situated in the Spree-Neisse district, has a power of 0.55MWth , while the largest one, situated in the city of Heilbronn, has a power of 100MWth . According to the data provided in [40], only resistive heaters are installed in the district heating systems in Germany, unlike Denmark, where large-scale heat pumps are used [52].

3.1.1. Structure of the installed heating capacity in municipal and rural districts We begin by demonstrating the differences in the installed heating capacity and heating technology distribution with the example of the city of Berlin ( populationdensity = 4000 inhabitants/km2 ) and the surrounding fairly rural25 administrative districts ( populationdensity < 150 inhabitants/km ). As shown in Fig. 10, in Berlin, a high share of the residential heat load is covered by the district heating system. Single-storey and large-scale central heating systems (25kWth < Qinst ) also represent a large share of the heating technologies used. This is mainly the result of the high number of multi-family houses. In rural districts such as Havelland, the highest share of the heat load is covered by small- and medium-scale central heating systems (Qinst < 25kWth ). The reason for this is that there are mostly single-family houses in the rural districts. The installed heating capacities for all districts in Germany, divided into the same size classes as for those in the Berlin region, are shown in Fig. 11. This demonstrates that also for all of Germany, single-storey heating, large-scale central heating and district heating predominate in cities. Meanwhile, small- and medium-scale central heating systems dominate in rural areas. 24

Supplementary material/results. All administrative districts shown in Fig. 10, apart from Berlin and Potsdam, have a population density lower than 150 inhabitants/km2 , which can be considered rural, according to the definition in [50].

3.2. Temporally resolved heat loads

25

In this section, we present the results for the temporally resolved 9

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Fig. 11. Installed overall heating capacity (red colour scale) as well as centralised PtH and thermal storage in district heating systems (bars) in the German administrative districts (NUTS-3).

heat load. First, the intraday load profile for different weekdays is described. Then these profiles are superimposed with the ambient temperature dominated load profile in the course of the year.

3.2.1. Intraday load profile As described in Section 2.2.1, the intraday thermal load profiles have been derived from measurements that were carried out as part of 10

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Fig. 12. Normalised distribution of the installed heating capacity in major German cities.

Fig. 15. Normalised space heating intraday load profile; for constant load case: norm. load = 1.

probably, that most people come home after work in the evening hours and use DHW, but the level of simultaneity is lower than in the morning hours. The DHW average load profile for Saturdays and Sundays also shows a morning and evening peak, which are flatter and span a longer time than that for working days. This is due to the fact that weekends are non-working days and the load rather depends on the individual behaviour, leading to a lower level of simultaneity. The load profile for space heating is shown in Fig. 15. There is also a morning peak in the average load profile from 05:00 to 08:00 on working days, as well as from 05:30 until 12:00 on Saturdays and Sundays. The load at these peaks is approximately twice as high as for the constant load case. However, no significant evening peak can be recognised. Note also that, between 22:00 and 05:30, the load is about half the constant load case for all of the three load profiles. The coloured profiles for the individual building show significant ramps, e.g., in the morning. This leads to the assumption that the space heating profiles are only indirectly coupled to the demand of the residents. The profiles tend to be mainly dominated by the controller settings, e.g., starting the space heating at a specific time each morning. The numerical values of the average daily load time series for space heating and DHW can be found in the supplementary material.26

ff

Fig. 13. Installed heating capacity covered by electric heating technologies in the city of Berlin (subdivisions for central heating: small=Qinst < 12.5kWth ; medium=12.5kWth < Qinst < 25kWth ; large= 25kWth < Qinst ).

3.2.2. Yearly load profile The space heating and DHW load across an entire year with a 15min resolution for the example of Berlin is shown in Fig. 16, based on long-term monthly average ambient temperature data. In January, the space heating load reaches its maximum and its value then drops, until the ambient temperature reaches the heating limit temperature in May. During summer, only power for DHW is needed. After the ambient temperature drops again below the heating limit temperature in September, the space heating load rises until January. During spring and autumn, the DHW load peaks are on the same order of magnitude as the average space heating load. The numerical values for the yearly load profiles of all administrative districts in Germany can be found in the supplementary material.26. Fig. 17 shows the yearly heat load for Berlin with a 15-min resolution based on daily average ambient temperatures measurements in 2011. The peak load of space heating, 17.6 GW, is higher in comparison to the heat load curve based on long-term average ambient temperatures in Fig. 17. Furthermore, the day-to-day average heat load variability is stronger, i.e. it drops from 6.5 GW at the start of February to 2 GW and then increases again to 7.5 GW at the end of February. The overall installed capacity of all heating types in Berlin totals

Fig. 14. Normalised DHW intraday load profile; for constant load case: norm. load = 1.

the NOVAREF project [33]. The results for DHW are shown in Fig. 14, where one coloured line corresponds to the average daily load profile of one building. The solid black line represents the average of the daily load profiles for all 12 buildings for which measurements were carried out. The dashed black line shows the reference case of a constant load, where the DHW demand is equally distributed across the entire day (| < Q15min > | = 1). On working days between 06:00 and 07:00, the average thermal load is six times higher than the constant load case. This is due to DHW being used by the citizens for morning bathing and breakfast preparation with a high level of simultaneity. There is a second, flatter load peak between 18:30 and 20:00, where the average load value is about two times higher than in the constant load case. The reason for this is

26

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Fig. 18. Future scenarios for the installed heating capacity in Berlin.

a value for the excess electricity feed-in from RES of 450 GWh in 2013 for the Lausitz-Spreewald region and expects an increase to approximately 2000 GWh for 2030. This corresponds to an average excess power of 0.05 GW in 2011 and 0.23 GW in 2030, when dividing the annual value by 8760 h. According to Fig. 18b, this average excess feedin could be covered by the neighbouring city of Berlin, considering only the installed PtH capacity.27 However, a further investigation of feed-in peaks, the power grid loading and the maximum shifting horizons of the heat demand is required.

Fig. 16. Space heating and DHW load in the course of the year, calculated for the city of Berlin, based on long-term monthly average ambient temperature data.

3.4. Validation In this section, we compare the results of this study with those found in the literature. First, the total heat demand of all German administrative districts is addressed. Then, we compare different regionalisation methods and finally consider the installed PtH capacity of different technologies. Fig. 17. Space heating and DHW load in the course of the year, calculated for the city of Berlin, based on daily average ambient temperature measurements in 2011.

3.5. Yearly heat demand for total Germany and major cities In this study, we validate the results for the yearly space heating and DHW final energy demand for all of Germany with the data drawn from [55], as depicted in Fig. 19. The DHW demand stays roughly constant from 2011 until 2030, with approximately 90 TWh in the present study and 70 TWh in [55]. The discrepancy between these two values can be explained by different assumptions for the DHW usage of the German population. The annual DHW demand value per individual used in this work, of 1123 kWh/cap/a, corresponds to a range of DHW demand measurement values, of 707–1635 kWh/cap/a, provided in [56]. The status quo space heating demand for Germany amounts to 520 TWh in this paper and to 475 TWh in [55]. This difference of 9% probably arises, because we used long-term average ambient temperatures to calculate the heat demand and in [55] data for 2011 were used. In both studies, the yearly demand for space heating decreases by approximately 20% from 2011 to 2030. To validate the calculated heat demand of the residential buildings in the cities of Berlin and Hamburg, we used energy balance data from the State Statistical Offices of Berlin [57] and Hamburg [58]. As shown in Fig. 20, the annual demand for space heating and DHW calculated in the present study for the city of Berlin, at a value of 21.3 TWh, is 4% higher than the value of 20.4 TWh from [57]. For the city of Hamburg the value in this study, at 11.1 TWh, is 13% higher than 9.8 TWh in [58]. These differences may arise due to different data sources used for modelling the residential building stock.

11.2 GW. Several peak loads in Fig. 17 exceed this installed capacity value. An explanation for this may be that the intraday load profiles of space heating (see Fig. 15) refer to the actual demand of the residents. The highest load peaks in the intraday load profile of space heating last for less than 0.5 h and may thus be covered by thermal buffer storage [53] rather than the actual heating device. A further improvement of the model would also be to average the used intraday load profiles with profiles from other literature sources and thus achieve a higher sample number of the regarded buildings and probably lower peak loads. 3.3. Future scenarios The future development of the total installed heating capacity in Berlin and the electrically-covered share based on the values considered in Section 2.4 is shown in Fig. 18a. Due to the expected increase of energy efficiency, the total installed thermal load is predicted to drop by 22.5% until 2030. At the same time, the share of the electricallycovered load increases from 5% in 2011 to 8% in the 2030 PtHlow Scenario, 11% in the PtHmod Scenario and 17% in the PtHhigh Scenario. The future development of the technology shares in the electricallycovered heat load is shown in Fig. 18b. As described in Section 2.4, we assumed that the overall installed load of resistive DHW boilers would remain constant. For both the 2030 PtHlow and PtHmod scenarios, the resistive DHW heating keeps the highest share in the electrically-covered load, being overtaken by centralised PtH in district heating in the 2030 PtHhigh Scenario. Decentralised heat pumps have a higher installed load in all 2030 scenarios than decentralised resistive heating. The determined PtH capacity values can be further used for the assessment of RES integration. Although this is not in the focus of this study, we briefly consider the city of Berlin and the neighbouring region in the southeast, Lausitz-Spreewald, as an example. Plenz [54] provides

3.6. Monofactorial and multifactorial regionalisation In this paragraph, we compare the results presented in this study 27 The values from Fig. 18b for the installed thermal heating capacities need to be divided by a COP value to convert them into electric capacities, e.g., COP = 2.89 for heat pumps and COP = 1 for resistive heaters [19].

12

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Fig. 19. Validation of the results for the yearly heat demand of all of Germany with the data from [55].

Fig. 21. Normalised heat demand per resident for all administrative districts of Germany (GER) and the federal state of Baden-Wuerttemberg (BW).

then multiplied by the number of inhabitants of each district to yield the heat demand per district. The subsequent normalisation yields a heat demand per resident of |qres, i | = 1 for every district. However, the literature agrees that the influence of the floor area on the heat demand is significantly higher than that of the number of inhabitants [59]. So if statistical data on the floor area per district are available, another monofactorial regionalisation can be conducted, as indicated by the dashed line in Fig. 21. The annual heat demand of Germany28 is divided by the country’s total floor area,30 which yields 161 kWh/m2/a . This factor is then multiplied by the total floor area per district. Fig. 21 shows that for the district with the lowest floor area per resident in Germany, the floor area-specific regionalisation leads to a roughly 20% lower heat energy demand than the resident specific regionalisation. For the district with the highest floor area per resident, the floor area-specific regionalisation leads to an approximately 25% greater energy demand than the resident specific regionalisation. Due to these large deviations, we do not recommend using the resident specific regionalisation. It may only be used in cases when no other statistical data are available than the number of residents per district. In this study, more factors influencing the heat demand in addition to the floor area and number of residents were considered: the building type, number of flats per building, year of construction and heating type. We thus denote this approach as “multifactorial regionalisation”. As shown in Fig. 21, in this study the normalised heat demand per resident of the administrative districts also generally increases with the average floor area per resident. This indicates that the floor area is the main driver of the heat demand. Due to the additionally considered building properties, the results reported here differ from those of the floor area-specific regionalisation by a maximum of + 9% and a minimum of 13% . The Baden-Wuerttemberg State Institute for the Environment (LUBW) regionalised the heat demand of the German state of Baden-Wuerttemberg to its associated administrative districts31 [17]. Also, in [17], multiple factors that influence the heat demand were taken into account: floor area, year of construction and building type. Fig. 21 shows that the results of [17] generally correspond to those of the present study for Baden-Wuerttemberg, with a Pearson Correlation Coefficient [60] of R = 0.95. Furthermore, we subtracted the results of the monofactorial floor area-specific regionalisation approach from the results of both of the multifactorial regionalisation approaches, the present study and [17] taking into account all of the administrative districts of Baden-Wuerttemberg. The two resulting sets of deviations are plotted against each other in Fig. G.24 (see G). The Pearson correlation coefficient of the deviations is R = 0.55, which indicates a moderate correlation. This

Fig. 20. Validation of the results for the annual heat demand of the cities Berlin and Hamburg with data from the State Statistical Offices of Berlin (SOB) [57] and Hamburg (SOH) [58].

with other methods to regionalise heat demand. We use Germany as well as the state of Baden-Wuerttemberg as an example, and split up the total heat demand into single demand values for the associated administrative districts. For a better comparison of the methods, the results of the regionalisation were normalised. As is shown in Eq. (15), we first divided the annual heat demand value, Qi , of each administrative district, i, by the number of residents per district, nres, i . Second, we divided the resulting value, qres, i , by the average heat demand per resident of all administrative districts < qres >:

|qres, i | =

qres, i Qi = . nres, i · < qres > < qres >

(15)

In Fig. 21, the normalised annual heat demand per resident of the administrative districts |qres, i | is plotted against the average floor area per resident. One dot represents one administrative district. Thus the dots on the left side of the figure represent districts containing large cities, where a high share of the population lives in comparatively small flats. The dots on the right side by contrast represent rural areas, where many inhabitants live in fairly large single-family houses. The number of residents is a statistical parameter for which data are available in most cases, even for smaller regions [29]. Regionalisation, using only the number of residents per region, is denoted by the solid black line in Fig. 21. We henceforth denote this kind of approach as “monofactorial regionalisation”, as only one statistical parameter is used. In this method, the annual heat demand of Germany28 is divided by the number of inhabitants,29 yielding 7650 kWh/cap/a. This constant is 28 29

30

We used the result from this study of 610 TWh. We used 80.21·106inhabitants , as per www.zensus2011.de.

31

13

We used 3.78·109 m2 , in accordance with https://www.zensus2011.de. For more information see: https://www.lubw.baden-wuerttemberg.de.

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curtailment of renewable energy sources, one option is to use excess feed-in locally for heating applications. In this paper, as a first step to assessing the potential of converting excess power into heat, we determined the overall heat demand and the electrically-covered share in the residential building sector. To account for regional differences, the data were spatially resolved at the administrative district level. In contrast to the other studies in this field, we provide all results as open data and take a larger number of building attributes into account for the regionalisation of the building stock. For this purpose, a special evaluation of the census enumeration data was ordered at the Research Data Centre of the German Federal Statistical Office, with a cross combination of six building attributes that influence the heat demand. Using these data, 729 building categories were generated and the number of buildings per category for each administrative district was determined. For each building category, heat demand values, as well as daily and yearly load profiles, were generated from measurement values. We distinguished between different heating technologies and three classes of installed heating capacity per building. For urban districts, this yielded a high installed heating capacity of small-scale and singlestorey heating, as well as large central heating systems. Both are due to the high share of multi-family houses in cities. In rural areas, there are more small-scale and medium-scale central heating systems because of the high number of single family houses. Most district heating networks were found in large cities, but a noteworthy share was also identified in fairly rural administrative districts. For the electrically-covered heat load, we took into account decentralised heat pumps, resistive space heating and resistive domestic hot water heating. Centralised resistive heating facilities in district heating systems were also considered. Thus, the distribution of the installed capacity across the different power-to-heat technologies in the administrative districts could be determined. The overall heat demand of German building stock was assumed to decrease by 22.5% from 2011 to 2030. Three future scenarios for the expansion of power-to-heat technologies were defined, in which the share of the electrically-covered heat load increases from 5% in 2011 to 8%, 11% and 17% in 2030. Moreover, different approaches to regionalising the overall heat demand of Germany down to its respective administrative districts were compared. Taking only one factor for the regionalisation into account, e.g., the population density, results in differences up to 25% from the present study. We therefore recommend considering multiple building attributes for the regionalisation of building stock and heat demand. The regionalised heat demand and power-to-heat capacities determined in this paper are valuable input data for future research. As the results are provided as open data, they can be used by other researchers for assessing the contribution of the power-to-heat technology to renewable energy integration. When investigating the flexible operation of power-to-heat devices, the heating capacity classes that were introduced in this study are beneficial. The specific costs for heat storage and equipping the power-to-heat devices with controllers generally drop with larger installed heating capacity, which may influence their economic viability. In this work, a general full load hour value was assumed for all heating systems. This value could be further differentiated by the heating type and size of the installed heating capacity. The derived intraday load profiles show significant load peaks and are based on measurements in a limited number of buildings in northern Germany. Combining these data with load profiles from other literature sources would lead to a smoother profile, which might be better suited to modelling the aggregated load of all buildings in an administrative district.

Fig. 22. Validation of the results for the PtH capacities in all of Germany with FFE [19], ∗data from [19] converted as described in the text.

means that the results of the multifactorial regionalisation methods (the present study and [17]) do not only differ randomly, but systematically from the monofactorial regionalisation method. 3.7. Installed PtH capacity of different technologies To validate the installed heating capacity of different PtH technologies, we compared the results of the present study with those obtained in [19]. As the data in [19] were given as installed electrical capacity, we converted it to thermal capacities. The electric capacities of heat pumps were multiplied with an annual coefficient of performance of 2.89, which was also given in [19]. Regarding the resistive heating technologies used for space heating, DHW heating and district heating systems, we assumed as an approximation that the thermal capacity is equal to the electrical capacity. Furthermore, in [19], the authors distinguish between the amount of PtH capacity that can be additionally activated at a certain point in time and that which can be deactivated. We selected the respective maximum of these values to compare with the installed heat load determined in this study. As shown in Fig. 22, the installed thermal capacity of heat pumps for the status quo is comparable, with 3.5 GW in the present study and 2.89 GW in [19]. The capacity will increase to 7 GW in [19] and 13 GW in the PtHlow Scenario of this study. In the PtHmod and PtHhigh Scenario of the present study, it even further increases to 16 GW and 22 GW, respectively. Also, the load of resistive space heaters is lower in [19] for 2030 than in all scenarios presented in this study. A reason for these discrepancies may be that in [19], the additional category ancillary resistive heaters is introduced, to which the authors assign a capacity of up to 100 GW by 2030. Heat pumps may be smaller dimensioned when equipped with the ancillary heaters and the number of conventional resistive heaters is reduced. The installed resistive DHW heating capacity amounts to 8.2 GW in the present study and 7.4 GW in [19]. In both studies the capacity remains constant until 2030. For the status quo, the capacity of resistive heating in district heating is also approximately equal in both studies, at a value of 0.6 GW. Regarding the 2030 horizon, the PtH capacity will increase to 2.6 GW in [19], to 1.9 GW in the PtHmod Scenario of the present study and 4.5 GW in the PtHhigh Scenario. As the future expansion of this PtH technology strongly depends on single large-scale investments of district heating operators, it is difficult to predict. 4. Conclusion and outlook

Declaration of Competing Interest

With the expansion of renewable energy technologies in Germany, imminent grid congestion events occur more often. In order to avoid the

None. 14

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Acknowledgements

scholarship. The authors would also like to thank Marco Zobel, Michael Lange, Peter Klement, Christoph Schillings, Alaa Alhamwi and Joseph Ranalli for the fruitful discussions.

The first author gratefully acknowledges the financial support provided by the Foundation of German Business (sdw) through a PhD Appendix A. Supplementary Material

The residential heat demand and power-to-heat capacity data for all administrative districts in Germany (NUTS-3) determined in this study, as well as the input data used and the developed source code, are provided in the supplementary material of this paper under open source licenses. The Data can be found on the Zenodo repository at: https://doi.org/10.5281/zenodo.3404147. Appendix B. Implementation of the heat demand and PtH capacity determination The determination of the regionalised heat demand and PtH capacities is implemented in PostgreSQL. The code was executed under a Debian GNU/ Linux 9 environment, using PostgreSQL 9.4.18. As shown in Fig. B.23, the process is divided into multiple SQL files that are called by the bash script main.sh. First, the required SQL tables are created and input data are imported. In the file assign_non_regionalised_data.sql, the heat demand values are assigned to the building categories. The heat demand is then regionalised to the administrative districts with the execution of the file assign_regionalised_data.sql. Finally, different classes of installed heating capacity are introduced and the PtH capacities are assigned by running the files categorise_heat_demand_power_classes.sql and assign_power_to_heat_potential_data.sql. The developed source code and a more comprehensive flowchart of the sub-processes are provided in the supplementary material.32

Fig. B.23. The bash script main.sh calls the sub-processes for determining the regionalised heat demand and PtH capacities.

Appendix C. Influence of building type on heat demand By Eq. (1) it can be calculated how the building type influences the heat demand of buildings. When disaggregating the demand values, obtained from [25], according to the building type, it must be ensured that the overall heat demand of all building type categories does not change. This is expressed by the following equation: (C.1)

q ·(Adet + Asd + Ater ) = qdet · Adet + qsd · Asd + qter ·Ater ,

where q″ stands for the aggregated area-specific heat demand value of all building types, qdet for the disaggregated area-specific heat demand value of

32

Supplementary material/code. 15

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all detached buildings, qsd for the demand of the semi-detached buildings and qter for the demand of the terraced buildings. Adet stands for the accumulated floor area of all detached buildings, Asd for the area of the semi-detached buildings and Ater for the area of the terraced buildings. Eq. (C.1) is then transformed to get the ratios of the disaggregated demand values to the aggregated values, as follows,

qdet q qsd q qter q

=

Adet + Asd + Ater , Adet + Asd · qsd / qdet + Ater · qter /qdet

(C.2)

=

Adet + Asd + Ater , Adet ·qdet /qsd + Asd + Ater ·qter / qsd

(C.3)

=

Adet + Asd + Ater . Adet · qdet / qter + Asd · qsd /qter + Ater

(C.4)

The denominator of the Eqs. C.2, C.3 and C.4 contains the ratios of the disaggregated heat demands of different building types. We calculated these ratios by applying Eq. (1) for the respective building types and dividing the results by each other. The results of the Eqs. (C.2), (C.3) and (C.4) were then each multiplied by the nine area-specific heat demand values obtained from [25], depending on the year of construction and number of flats per building, which yields 27 disaggregated values that also depend additionally on the building type. The numerical values for the process described here can be found in the supplementary material.33 Appendix D. PtH technology scaling factor for German states The scaling factor x ij is defined for each of the technologies i = 1…3 (heat pump, resistive space heating and resistive DHW heating) and for all German states j, as:

x ij =

ndevices, ij / nbuildings, j ndevices, Germany, i /nbuildings, Germany

ndevices, Germany, i =

,

(D.1)

ndevices, ij ,

(D.2)

j = 1 … 16

nbuildings, Germany =

nbuildings, j.

(D.3)

j = 1 … 16

Therein ndevices, ij is the number of installed PtH devices per state (data from [61] for heat pumps and from [38] for resistive space heating and resistive DHW heating), nbuildings, j is the number of buildings per state [23], ndevices, Germany, i is the number of installed PtH devices for Germany and nbuildings, Germany is the number of buildings for Germany. The numerical values of the scaling factors are provided in the supplementary material.34 Appendix E. Heat storages in district heating systems Heat storage is not in the focus of this paper. However, the data on thermal storage capacities in district heating systems, listed in [40], may be very useful for researchers, investigating the time shifting of PtH operation. We therefore also assigned these capacity data to the respective administrative districts and added them to Fig. 11. The numerical values are provided in the supplementary material.34 For several heat storage facilities, no thermal storage capacity was given in [40] We therefore calculated an average volume specific capacity of all the storages, for which data are given. This yielded 0.04MWhth / m3 for both the atmospheric and the 2-zone storage type and 0.07MWhth / m3 for the pressurised heat storage. We multiplied these average values with the volume of the storages for which no thermal capacity data were given. Appendix F. Heat demand scenario input data Table F.6. Table F.6 Input data for the heat demand scenario provided in [42], regarding residential buildings in Germany; Values for the years between 2010, 2020 and 2030 are linearly interpolated.

building retrofit rate relative specific heat demand of buildings undergoing retrofit (relative to average) demand reduction achieved by retrofit demolition/reconstruction rate (relative to stock) final space heating energy demand in new buildings

[kWh/m2] relative specific heat demand of buildings undergoing demolition (relative to average)

33 34

2010

2020

2030

1% 1.2

2% 1.2

2% 1.2

35% 0.5% 60

50% 0.5% 15

50% 0.5% 9

1.3

1.3

1.3

Supplementary material/other input data/heat demand according to building type year of construction and number of flats per building. Supplementary material/other input data/electric heating factors. 16

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Appendix G. Deviation of the monofactorial regionalisation from different multifactorial regionalisation methods Fig. G.24.

Fig. G.24. Deviation of the normalised heat demand of the administrative districts calculated by the monofactorial floor area-specific regionalisation from the multifactorial regionalisation methods (x-axis: present study, y-axis: LUBW/IWU [17]).

Appendix H. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.apenergy.2019.114161.

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