Article
Reference
Geospatial global sensitivity analysis of a heat energy service decarbonisation model of the building stock
CHAMBERS, Jonathan, et al.
Abstract
Decarbonising energy used for space heating and hot water is critical for reaching emission targets. Modelling of thermal energy decarbonisation becomes increasingly complex as additional technology options are included. Spatial aspects become increasingly important when considering heat transport, for example using district heating. This study develops a model for heating energy decarbonisation that makes use of a techno-economic model applied to a large geographic area (Western Switzerland) at high spatial resolution. Global sensitivity analysis is applied to quantify the variance characteristics of the model. Heating energy services provided by retrofits, decentralised heat pumps, and thermal networks are considered. Final energy demand reductions ranges of 70–80% and emissions reductions of 90% were found with levelized costs of providing the heat service of 0.14–0.22CHF/kWh. High sensitivities were found with respect to efficiency parameters (retrofit potentials and seasonal performance factors). The spatial distribution of costs and sensitivities was shown to be highly variable, with a strong correlation with [...]
CHAMBERS, Jonathan, et al . Geospatial global sensitivity analysis of a heat energy service decarbonisation model of the building stock. Applied energy , 2021, vol. 302, p. 117592
DOI : 10.1016/j.apenergy.2021.117592
Available at:
http://archive-ouverte.unige.ch/unige:155125
Disclaimer: layout of this document may differ from the published version.
Applied Energy 302 (2021) 117592
0306-2619/© 2021 Published by Elsevier Ltd.
Geospatial global sensitivity analysis of a heat energy service decarbonisation model of the building stock
Jonathan Chambers
*, M.J.S. Zuberi , K.N. Streicher , Martin K. Patel
University of Geneva, Department F.-A. Forel for Environmental and Aquatic Sciences and Institute for Environmental Science, Energy Efficiency Group, Uni Carl-Vogt, 1205 Gen`eve, Switzerland
H I G H L I G H T S G R A P H I C A L A B S T R A C T
•Developed a geospatial model of cost optimal heat electrification in buildings.
•Global sensitivity analysis of variance as a function of space and model parameters.
•Potential final energy demand re- ductions of 70–80% were foun.
•Levelized costs of providing heat service of 0.14CHF/kWh − 0.22CHF/kWh ere found.
•Found higher sensitivity to efficiency parameters than to energy price.
•High spatial distribution sensitivity, with a strong dependence on building density.
A R T I C L E I N F O Keywords:
Geospatial Sensitivity analysis Heat
Decarbonisation Building stock Efficiency
A B S T R A C T
Decarbonising energy used for space heating and hot water is critical for reaching emission targets. Modelling of thermal energy decarbonisation becomes increasingly complex as additional technology options are included.
Spatial aspects become increasingly important when considering heat transport, for example using district heating. This study develops a model for heating energy decarbonisation that makes use of a techno-economic model applied to a large geographic area (Western Switzerland) at high spatial resolution. Global sensitivity analysis is applied to quantify the variance characteristics of the model. Heating energy services provided by retrofits, decentralised heat pumps, and thermal networks are considered. Final energy demand reductions ranges of 70–80% and emissions reductions of 90% were found with levelized costs of providing the heat service of 0.14–0.22CHF/kWh. High sensitivities were found with respect to efficiency parameters (retrofit potentials and seasonal performance factors). The spatial distribution of costs and sensitivities was shown to be highly variable, with a strong correlation with building density. This raises important questions, notably on equitable distribution of energy transition costs.
Abbreviations: ASHP, Air source heat pump; CO2eq, Carbon dioxide equivalent emissions; DH, District heating; ERA, Energy reference area; GHG, Greenhouse gas emissions; GSA, Global Sensitivity Analysis; HP, Heat pump; HTDH, High-temperature district heating; LTDH, Low-temperature district heating; LCOE, Levelized cost of energy; O&M, Operation and Maintenance; SA, Sensitivity Analysis; SPF, Seasonal performance factor.
* Corresponding author.
E-mail addresses: jonathan.chambers@unige.ch (J. Chambers), martin.patel@unige.ch (M.K. Patel).
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
https://doi.org/10.1016/j.apenergy.2021.117592
Received 7 June 2021; Received in revised form 19 July 2021; Accepted 7 August 2021
1. Introduction
Heating and cooling in buildings are currently responsible for over 50% of final energy consumption in the European Union (EU) [1].
Buildings account for 36% of greenhouse gas emissions [2] and are a high priority with a view to accelerating demand reduction and decar- bonisation through a ‘renovation wave’ [3,4]. Slow building renovation rates and urgent need for emissions reductions have highlighted the importance of taking a broader energy-system approach [5], that is, considering approaches to decarbonise heat energy services considering the urban or district scale as well as the building scale, and considering different technology combinations to decrease heat demand while also decarbonising the heat supply [4]. This can include building envelope renovations, electrified heating through heat pumps, as well as other options such as biomass. Indeed, the latest IEA Energy Roadmap envi- sions the complete elimination of fossil fuel heating [2], a process that has already been applied in some regions (e.g. Basel City has banned new fossil heating since 2017 [6]).
Addressing this significant challenge means moving beyond the traditional focus on individual building interventions (e.g. single building renovations) to consider the radical transformation of the building stock. In addition to introducing new questions as to the optimal technology mix at the stock level, this also introduces a geo- spatial aspect due to heterogeneity in building typology distributions as well as the introduction of spatial constraints if district heating (DH) networks are to be considered as a technology option. The suitability of DH depends on the local characteristics of the built environment (building densities, energy intensities, etc.) [7]. In addition, the acceptability of energy transitions is being increasingly recognised as an important topic, notably the regional distribution of technologies and the costs and benefits that accrue to a region as a result [8]. These can include the direct financial burdens or rewards, as well as other impacts such as the visual impact of new installations.
Previous projects have mapped heat demands and resources (such as industrial excess heat) at high spatial resolution over large areas (single or multiple countries) including the Heat Roadmap Europe [9,10],
Hotmaps [11], and several projects within FEEB&D1 [7,12,13]. How- ever, these works did not attempt to model the economic optimal mix of technologies over the areas studied. At smaller geographic scales (e.g. a city district), existing thermal energy system models optimise heat supply and thermal network layout [14,15], and heat flows for districts have been created [16,17]. However, these models do not readily scale to large areas due to their computational complexity. Models of district heating must consider pairwise building interconnection options and therefore have a computational complexity that grows with the square of the number of buildings [18]. Furthermore, modelling of energy systems, including the context of thermal energy decarbonisation, quickly becomes complex as additional technology options are included.
Finally, a particular challenge for modelling the thermal energy in buildings is that, unlike many other energy uses (such as for home ap- pliances), there are extremely large ranges for the final energy needed to provide a given energy service level (i.e. providing suitable thermal comfort). This is reflected in order-of-magnitude reductions in energy intensity between best and worst performing buildings (e.g. in Switzerland this drops from 300kWh.m−2 to 40kWh.m−2 from the worst to best building energy certificate label [19,20]). Therefore, unlike electricity system models which tend to take energy demand as an exogenous parameter [21], modelling of thermal energy must aim to model the provision of energy services by considering both demand reduction and low carbon supply. The trade-offs between demand reduction and sizing of clean heat supplies, especially heat pumps (HP), must be determined. Note that in the past, it has often been assumed that demand reduction and HP installation always go together, this is being increasingly questioned [19,22].
It has been shown in the context of electricity supply modelling that uncertainties can result in large changes in model results and lead to significant divergence from the real world [23,24]. Understanding the behaviour of models as a function of variation and uncertainty in input Nomenclature
α Heat pump cost curve coefficient 1 (–) β Heat pump cost curve coefficient 2 (–) δCRetrofit Retrofit cost uncertainty factor (–) δCHP Heat pump cost uncertainty factor (–)
δCDH District heat network cost uncertainty factor (–) a Annuity factor (–)
C1 Heat network construction cost constant 1. (CHF.m−1) C2 Heat network construction cost constant 2. (CHF.m−2) CSAVINGS Retrofit model total investment cost for given savings.
(CHF)
CO2eq Current CO2eq emissions from heating. (kg.y-1) d Mean pipe diameter
ERA Energy Reference Area (ERA) of the given archetype contained within the pixel. (m2)
E Current final energy demand for heat. (kWh.y-1) fERA,Retrofit Fraction of ERA retrofit (–)
fQ,Retrofit Fraction of heat service provided by retrofit (–) fQ,HP Fraction of heat service provided by decentralised heat
pumps. Includes heat service in pixels which are partially served by thermal networks (–)
HD Linear heat density. (kWh. m−1.y-1)
HDmin,HTDH Minimum linear heat density for HTDH. (kWh. m−1.y-1) HDmin,LTDH Minimum linear heat density for LTDH. (kWh. m−1.y-1) LDH System lifetime for district heating. (years)
LHP System lifetime for heat pump. (years)
LCOHe Levelized cost of heat service equivalent. (CHF.kWh−1) OMHP Heat pump operation and maintenance cost (CHF. y-1) OMDH District heat network operation and maintenance. (CHF. y-
1)
Pmax Peak useful power demand for heating and domestic hot water. (kW)
pelec Electricity price. (CHF.kWh−1) Q Current useful heat demand. (kWh.y-1)
q Current useful heat demand per unit area. (kWh.m−2.y-1) qSAVINGS Retrofit model savings per unit area. (kWh.m−2.y-1) qmin,HTDH Minimum building heat demand intensity per unit area for
HTDH to be feasible. (kWh. m−2.y-1)
qmax,HTDH Maximum building heat demand intensity per unit area for HTDH to be feasible. (kWh. m−2.y-1)
ql,HTDH Network thermal loss fraction, HTDH (–)
qmin,LTDH Minimum building heat demand intensity per unit area for LTDH to be feasible. (kWh. m−2.y-1)
qmax,LTDH Maximum building heat demand intensity per unit area for LTDH to be feasible. (kWh. m−2.y-1)
ql,LTDH Network thermal loss fraction, LTDH (–)
SPFHP Decentralised heat pump Seaonal Performance Factor (–) SPFHTDH High temperature thermal network heat pump Seasonal
Performance Factor (–)
SPFLTDH Low temperature thermal network heat pump Seasonal Performance Factor (–)
1 Future Energy Efficiency in Buildings and Districts project of the Swiss Competence Centre for Energy Research
data as well as across the spatial dimensions has therefore been recog- nised as an important issue [25]. Sensitivity analysis (SA) allows to understand the effects of uncertainty in models; in particular global sensitivity analysis (GSA) is an accepted standard for the evaluation of the impact and interactions of uncertain inputs in complex models [26].
Understanding broad trends in energy model uncertainty requires the ability to perform many model iterations over a representative fraction of the building stock, as well as over a sufficiently large geographic area in order to also understand the spatial variability – this has been a gap in the literature to-date. In particular, there is high uncertainty in the current and future costs as well as physical parameters (e.g. the real performance of heat pumps) of technologies that underpin the thermal energy transition. By building a simplified energy transition model and performing a GSA, the most important parameters in determining the technology choices can be identified, and the stability of the optimal technology mix options with respect to model parameters quantified, together with cost ranges and their spatial variation.
1.1. Aim
This study therefore develops a model for heating energy decar- bonisation that makes use of a simplified technology model applied to a large geographic area at high spatial resolution, thereby offering a trade- off between computational complexity and sufficient number of model iterations to be conducted for a spatial GSA. This model considers heating energy service provided by i) retrofits ii) decentralised heat pumps and iii) thermal networks. It builds on the authors’ previous works on data-driven spatiotemporal modelling of heating technologies.
These models’ algorithms were explicitly developed to be efficient in order to apply to large datasets and/or applied for large numbers of it- erations in the context of Monte Carlo simulations and SA. These include: a cost model for building retrofits (which studies individual building envelope improvements [27]), studies of the potentials and costs for different heat supplies in Switzerland [28,29], and algorithms for mapping the potential for thermal networks in Switzerland [7] as well as the integration of energy sources into these networks accounting for spatiotemporal constraints [30].
This work highlights which parameters must be most carefully specified when developing future models. It provides a first analysis of the spatial variability of costs for the thermal energy transition, which points to further questions around the equitability of this transition.
1.2. Scope
Given the mathematical and computational complexity of perform- ing GSA on highly detailed energy models, this work uses a simplified model of a full overhaul of the provision of heating and domestic hot water to buildings (including both residential and service sector build- ings). We develop such a model on a raster (pixel) geospatial basis, i.e.
which both uses raster data as input (e.g. maps of building density per pixel) and also produces raster data as outputs. We consider as
technology options:
• Thermal retrofit of building envelopes
• Decentralised air source heat pumps
• High temperature district heating networks fed by heat pumps
• Low temperature district heating networks fed by low temperature lift heat pumps (with correspondingly higher seasonal performance factor (SPF)).
We model a complete transformation of the energy system, wherein all fossil fuel heating is replaced. Although this choice is made initially to simplify the modelling process, it is also most likely necessary to perform such a comprehensive change to reach the most recent climate policy targets [28]. We do not consider the time dimension of the transformation i.e. the rates of replacement over time are not considered.
The model is applied to an area of Switzerland corresponding to the bounding box of the Geneva and Vaud cantons in French-speaking Switzerland. This region is chosen for several reasons including:
• Readily available data on the technologies resulting from previous work of the several authors, notably that in [31] which studied the potential application of district heating and cooling with shallow geothermal energy sources in the same region.
• A sufficiently large area to include a mix of urban and rural areas that is representative of Switzerland as a whole and, through Switzer- land’s situation at the confluence of western, central, and southern Europe, of other European regions as well.
• In Switzerland for residential buildings alone the current targets imply final energy consumption to be reduced by 46% and CO2 emissions by 77% by 2050 compared to current levels, therefore it is important to study the decarbonisation pathway [20].
1.3. Contribution
This work focuses on energy system transformation modelling for heating, which is a field that has received relatively little attention compared to the electricity sector. This work furthermore contributes a novel spatially resolved GSA, in comparison to past work that has studied aggregate sensitivities of thermal energy system models [32].
The model developed also provides a basis for future work integrating a wider range of thermal resources and energy transformation technologies.
2. Method 2.1. Model overview
A model for the decarbonisation of building space heating was developed based on building archetype characteristics (allowing to model the building stock based on a reduced set of characteristics for typical buildings). This was applied to data aggregated into pixels (grid cells) of 200x200m. Independent model runs were performed for each pixel taking into account the shares of different building archetypes per pixel. Table 1 summarises the input data required per archetype for each pixel. Note that building archetypes with existing low carbon heat sources (principally heat pumps) are not included in the model as there is no need to decarbonise their heat supply. The building stock data and archetypes are described further in Section 3. The other model input parameters are summarised in Table 4.
GSA was performed using Sobol sensitivity indexes which measure the model output variance explained by different model inputs [33], combined with efficient sampling of the model input parameter space using the Saltelli method [34]. Evaluating these uncertainties can be computationally challenging as the number of model iterations required for Sobol analysis grows linearly with the number of model parameters.
Table 1
Model input data collected per pixel for each archetype.
Parameter Description Units
ERA Energy Reference Area (ERA) of the given archetype
contained within the pixel. m2
q Current useful heat demand per unit area kWh.m−2. y-1
qSAVINGS Retrofit model heat savings per unit area kWh.m−2.
y-1 CSAVINGS Retrofit model total investment cost for given savings CHF
E Current final energy demand for heat kWh.y-1
Q Current useful heat demand kWh.y-1
P99 99th percentile of hourly heating power demand kW CO2eq Current CO2eq emissions from heating kg.y-1
Therefore, the model developed focuses on a) limiting the number of model parameters to synthesise general trends and b) computational efficiency to allow very large numbers of iterations across both grid pixels and GSA iterations (see Table 2).
To limit the number of parameters, a single synthetic heat generation type was modelled based on the efficiency and cost curves of air source heat pumps (ASHP), omitting constraints on size, noise, and electricity supply capacity. ASHP was selected as the base model as it is the most mature HP technology (by comparison, other low carbon heat sources are less well established and consequently significantly more expensive [29]). This was coupled with a pixel-level model of retrofit costs and low temperature district heat (LTDH) and high temperature district heat (HTDH), to calculate per pixel the shares of building archetypes that are retrofitted, supplied by decentralised heat pumps, or supplied by heat networks fed by centralised heat pumps.
To improve computational efficiency, the model was formulated as independent cost minimisation problems for each pixel as a function of continuous variables, which allowed to use massively parallel in- memory array processing techniques. Furthermore, a subset of param- eters were chosen for GSA using both preliminary calculations and using the results of previous works which highlighted the main drivers of energy costs [29,30]. The GSA method and parameter selection is pre- sented in Section 2.5 and summarised in Table 3.
The model was implemented in Python and Cython and used the following citable packages: Numpy [35], SciPy [36], Pandas [37], Xar- ray [38], matplotlib [39], and Cartopy [40]. The Saltelli sampling and Sobol sensitivity analysis was performed using the existing peer- reviewed package ‘SALib’ [41].
2.2. Levelized cost of heat service
The levelized cost of energy (LCOE) is widely used to compare different technology options. LCOE is commonly calculated as the sum of the annualised system investment, fuel costs, operation and mainte- nance costs, divided by the heat supplied. In this work we consider the provision of heat services, which are also delivered through improved efficiency. Retrofits in particular do not supply energy, therefore calculating the system LCOE using only the heat delivered by the final technology mix would not account for the benefits of demand reduction.
We account for this instead by comparing the levelized cost of heat (LCOH) service. Since there is not a straightforward way to estimate heat service delivery, we use the assumption that the current heat energy demand meets the current heat service needs. We can therefore calculate the cost of the equivalent heat service of today LCOHe as:
LCOHe=CTOTAL/QCURRENT (1)where CTOTAL is the total annualised cost for a given technology mix and QCURRENT is the current useful heat demand. We therefore regard the resulting LCOH value as being the levelized cost for a heat service equivalent to the current situation.
The total annualised costs are for a technology mix for a given pixel are given by:
CTOTAL=∑
T(aT.IT+OMT+CET)(2)where for each technology T; aT
is the annuity factor, IT is the total investment cost, OMT is the operation and maintenance cost, CET is the fuel cost. The annuity factor aT is Table 2
Summary of model outputs collected per simulation pixel.
Parameter Description Units
LCOHe Levelized cost of equivalent heat service CHF.y-
1
a.I Annualised total investment cost CHF.y-
1
fERA,Retrofit Fraction of ERA retrofit –
fQ,Retrofit Fraction of heat service provided by retrofit –
fQ,HP Fraction of heat service provided by decentralised heat pumps. Includes heat service in pixels which are partially served by thermal networks
–
fQ,DH Fraction of heat service provided by thermal networks –
Pmax Peak final power demand kW
CO2eq Total GHG emissions kg.y-1
ΔCO2eq GHG emissions savings kg.y-1
Table 3
Summary of subset of model parameters selected for GSA.
Parameter Description Units
δC,Retrofit Cost uncertainty factor for retrofit –
δC,HP Cost uncertainty factor for heat pumps (decentralised
and centralised) –
δC,DH Cost uncertainty factor for thermal network construction –
Pelec Electricity price CHF.
kWh−1 SPFHP Seasonal performance factor for decentralised heat
pumps –
SPFHTDH Seasonal performance factor for heat pump supplying
high temperature network –
SPFLTDH Seasonal performance factor for heat pump supplying
low temperature network –
OMHP Operation and Maintenance cost for heat pumps as a
function of number of units CHF.y-1
OMDH Operation and Maintenance cost for thermal networks as
a function of network capacity CHF.
kWh.y-1 qmin,HTDH Minimum heat demand intensity for viable
implementation of HTDH in a building kWh.m−2. y-1 qmax,LTDH Maximum heat demand intensity for viable
implementation of LTDH in a building kWh.m−2. y-1 HDmin,HTDH Minimum linear heat demand density for viable
construction of high temperature network kWh.m−1. y-1 HDmin,LTDH Minimum linear heat demand density for viable
construction of low temperature network kWh.m−1. y-1
Table 4
Summary of model parameters, indicating the subset used for SA. Initial values and the minimum and maximum bounds for SA analysis are given.
Parameter Units Initial
value Bound
min Bound
max Use for
SA
δC,Retrofit – 1 0.7 1.1 TRUE
δC,HP – 1 0.7 1.1 TRUE
δC,DH – 1 0.7 1.1 TRUE
Pelec CHF.
kWh−1 0.201 0.171 0.231 TRUE
SPFHP – 2.8 2.5 4 TRUE
SPFHTDH – 3 2 4 TRUE
SPFLTDH – 4.5 3 6 TRUE
OMHP CHF.y-1 246 111 407 TRUE
OMDH CHF.kWh.
y-1 0.002295 0.001795 0.002795 TRUE
qmin,HTDH kWh.m−2.
y-1 40 30 70 TRUE
qmax,LTDH kWh.m−2.
y-1 60 40 80 TRUE
HDmin,HTDH kWh.m−1.
y-1 1 0.8 1.2 TRUE
HDmin,LTDH kWh.m−1.
y-1 4.5 3 6 TRUE
LDH years 40 FALSE
LHP years 20 FALSE
α – 14,677 FALSE
β – −0.683 FALSE
C1 CHF.m−1 315 FALSE
C2 CHF.m−2 2225 FALSE
qmax,HTDH kWh.m−2.
y-1 inf FALSE
ql,HTDH – 0.1 FALSE
qmin,LTDH kWh.m−2.
y-1 0 FALSE
ql,LTDH – 0.05 FALSE
calculated using discount rate r (assumed to be 3%), and the lifespan LT
of technology T, which varies for heat pumps and thermal networks.
aT=(1+r)(1+r)LTLT×r
−1 (3)
We define heat service fractions from each technology in the mix.
Similar to the cost of heat service, these are defined with respect to the current heat demand:
fq,T=QT/QCURRENT (4)where fT is the heat service provided by technology T (in the case of retrofit this is equal to the useful heat savings).
2.3. Technology parametrization
This section defines the models for the cost and energy use for the technologies considered: retrofits, decentralised heat pumps, as well as low- and high- temperature thermal networks fed in both cases by large (centralised) heat pumps. For each technology T we define the terms for IT,OMT, and CET.
2.3.1. Retrofits
Retrofit investment costs and associated energy savings are derived from work by Streicher et al [23,37], who define a cost for the deep retrofit (up to the Passivhaus standard) for building archetypes, which represent typical building types in Switzerland. Costs were selected for the ‘depreciation’ variant (see Section 3). These are determined for each building from a combination of location, age, current heating system.
For each pixel the total retrofit investment IRET is:
IRET=∑
AfRET,AiRET,AERAA (5)where for each archetypeA, fRET,A is the fraction of ERA retrofit, iRET,A is the retrofit investment per unit area for archetype A, and ERAA is the total energy reference area of archetype a in that pixel. We set OMT=0 and CET =0.
For the subsequent heat source calculations, we calculate the new heat demand Quseful as
Quseful=∑
aQ’useful,A− (fRET,AQSuseful,A)(6)where Q’useful,A is the orig- inal heat demand of archetype A and QSuseful,A is the heat savings po- tential from retrofitting that archetype. Similarly, we calculate a new peak power assuming that this scales linearly with the yearly demand:
Pmax,A=∑
aP’max,A*Q’useful,A/Quseful (7)
Note that the heat savings potentials take into account the fact that heat for domestic hot water is not reduced by building envelope retrofit.
2.3.2. Heat pumps
The cost per kW for a heat pump is a function derived empirically as a function of the archetype peak power per building Pmax,A of the form α*Pβmax,A. This function approaches infinity for small P and zero for large P, therefore the input values of Pmax are clipped to the range of input data from which the α and β parameters are derived (see also Section 3).
The heat pump investment for buildings of archetypeA, iHP,A is:
iHP,a=NA*Pmax,A*( α*Pβmax,A
)(8)where NA is the number of buildings of archetype A. The total is the sum across archetypes:
IHP=∑
aiHP,a (9)
Energy costs CEHP are calculated as:
CEHP=pelec*Quseful/SPFHP (10)where Euseful,HP is the useful energy production per year from the HP (kWh/year) and SPFASHPis the HP seasonal performance factor. O&M costs are given as:
OMHP=NHP*omHP (11)where omHP is the unit operation and main- tenance cost per heat pump.
2.3.3. Thermal networks
Calculation of the thermal network application and cost is based on algorithms developed in [7]. The different DHN technologies have different constraints with respect to the building heat demand intensity (kWh.m−2) where they can be applied. This is particularly relevant for low temperature networks where the buildings are directly fed at the network temperature of approximately 50 ◦C (i.e. without additional
temperature boosters within the building).
Therefore, the subset of archetypes where the DHN is applicable is determined by applying constraints on the specific heat demand per building archetype, keeping archetype data where qmin,T<qA<qmax,T. Total building numbers and heat demands for this subset are used in subsequent calculations. The investment costs of DHN IDHN is:
IDHN=Iprod+Ipipe (12)Iprod is the investment cost of the heat pro- duction unit (CHF/year) which is assumed to be a heat pump whose costs are calculated as above. Ipipe is the investment cost of the heat distribution pipe network (CHF/year), given by:
Ipipe= (C1+C2.d)lpipe (13)C1 (CHF/m) and C2 (CHF/m2) are empiri- cally derived based on the work of [42]. The length of the pipe network needed to connect a set of buildings lpipe (m) is estimated from building density (number of buildings per hectare) following the method of [7,43]. The mean pipe diameter d (m) is a function of the linear heat demand density HD (kWh/m) which is estimated based on empirical studies of 134 Swedish thermal networks [42].
d=0.0486ln(HD) +0.0007 (14)
The linear heat density is calculated as the sum of the useful heat demand of the connected buildings divided by Lpipe. Two constraints are applied: the heat network is considered viable for a given pixel if the heat density HD>HDmin and there are at least four buildings in the pixel. The thresholds are different for the different thermal network technologies (high and low temperature) (see Section 3).
The total heat demand for the network QDHis calculated as QDH=Quseful,DH*(1+ql)(15)where Quseful,DH is the total heat demand of the archetypes within the network and ql is the network distribution thermal loss. We assume that a single large, centralized heat pump supplies this demand with an SPF specific to the network type (see Section 3), giving the final energy demand as:
Efinal,DH=QDH/SPFDH (16)
Note that given limited data on large heat pumps, a lower bound is placed on the heat pump investment cost per unit power (see Section 3).
2.4. Technology optimal mix model
The cost-optimal mix of heat service provision technologies is calculated for each pixel by minimising the LCOHe. For this work we assume full replacement of all fossil fuel heating systems by a mix of the technologies described.
The optimizer outputs the fraction of the heat service provided by retrofit, heat pumps, and district heating (combining high and low temperature systems): fQ,Retrofit, fQ,HP, fQ,DH. Since we apply a full system transformation, these fractions account for the full heat service supply i.
e. fQ,Retrofit +fQ,HP+fQ,DH =1. Applying a full replacement also simplifies the problem of selecting the heat supply: the retrofit fraction for each archetype per pixel is set and the lowest cost supply technology (HP, HTDH, LTDH) is chosen (eq 17). This has the additional benefit of avoiding the need for a mixed integer linear programming (MILP) solver, allowing significantly shorter model runtimes thereby facili- tating the large number of model runs needed to perform GSA.
CTOTAL =min(CHP,CHTDH,CLTDH) +CRETROFIT(17)
Note that for HTDH and LTDH, the costs include the installation of a decentralized HP for buildings which are not suitable for connection to the respective DH system. Table 1 summarises the outputs stored per pixel for one model run.
2.5. Sensitivity analysis
GSA was performed using Sobol sensitivity analysis with Saltelli sampling. These were selected as being well established methods with readily available software implementations (SALib package [41]). Sobol sensitivity analysis decomposes the variance of the output of the model into fractions which can be attributed to inputs or sets of inputs. We focus on first order sensitivity indexes; it should be noted that these
fractions can sum to more than 1 since there may be second or higher order effects due to the covariance of model parameters. Parameter sample sets were generated using Saltelli sampling, which is an efficient method of sampling the parameter space for Sobol analysis [34].
The optimisation model was run on each pixel dataset for each sample set and the model technology mix characterisation parameters recorded for each pixel. Sobol sensitivity indexes were calculated for each pixel and for spatial aggregates across model runs. The sampling and Sobol index calculations were performed using the SALib package [41].
The sensitivity analysis aims to explore the sensitivity of model outputs to a) physical and b) cost parameters. The physical parameter chosen for the SA is the heat supply efficiency. Although all heat supply is assumed to be provided by heat pumps, separate SPF values are used for the decentralised, high temperature network, and low temperature network. Notably, the SPF for low temperature networks can be signif- icantly higher thanks to the low temperature lift provided by the HP [44]. The cost parameters are the O&M for the heat pumps and net- works, and the cost reduction uncertainty. The latter parameter sum- marises cost changes for the different technologies and is introduced as a fractional cost modifier parameter δCT for a technology T, which alters the technology investment costs described in the previous sections as:
C’T=δCT.CT (18)
Sobol sensitivity analysis was performed for a selection of model parameters. Table 3 summarises the parameters selected for the SA. We did not attempt to apply SA on exogenous model inputs, notably the estimates of the building archetype characteristics (such as floor areas), as these are not directly relevant to the understanding of the decar- bonisation pathway.
3. Datasets
3.1. Building stock data
General building characteristics and geospatial data on the Swiss building stock was drawn from the Swiss building registry [45]. As the main repository of building data in Switzerland for various purposes including sales and leases, construction permitting, etc, this is a highly reliable source. The building and building element specific data was drawn from the Swiss building registry, energy certificates, and further modelled data. Buildings already equipped with heat pumps were filtered from the data, since there is no need to apply the decarbon- isation model to these.
Building archetypes were defined by Streicher et al. [46] on the basis of building age, type, heating system, and location all drawn from the Swiss building registry. Building heat demand and heat energy saving potentials were drawn from the archetype model, which used a combi- nation of building characteristics from the Swiss building registry and building energy certificate dataset to develop a steady-state thermal model of the building envelope [22,46]. The useful and final energy demands per ERA for each archetype building were derived and have been validated in previous works [47]. The application of retrofit packages was modelled as a function of the building archetype and the costs and energy savings were estimated. Costs were used from the
‘depreciation’ approach proposed in the referenced work. This approach takes into account the fact that on the one hand part of the energy retrofit costs should considered as required maintenance and not count towards the energy-related costs of retrofit, while on the other hand replaced building elements could may not have reached the end of their useful lifespan. The approach therefore increases the costs based on the residual value of building elements at the time of replacement, as a function of the expected remaining lifetime of the building element.
Power demands were derived from load distribution curves, drawn from a model based on measured heat demands for single buildings and existing district heat networks [48].
Streicher et al. considered only buildings used fully or mainly for
residential purposes. This was extended to provide energy demand es- timates for service sector buildings, including offices, shops, and hotels, which were added by re-calibrating the residential results from the aforementioned model with the results of Schneider et al. [49] for non- residential buildings. The latter modelled Swiss buildings based on measured load curves from selected buildings and existing thermal networks. It was assumed that non-residential buildings had thermal characteristics similar to multi-family buildings of the same age within the same region (canton), but with different utilisation. For these buildings, a scaling factor was calculated as the ratio between the yearly useful heat demand calculated by Schneider and by Streicher. This allowed heat demands and costs to be estimated for a wider range of buildings. Data was aggregated to 200x200meter pixels, resulting in a set of values for each parameter by archetype and pixel and made available from an open data archive (https://doi.org/10.26037/yareta:
sluzlbggmjfxjj7qmyptxs7zoa).
3.2. Energy model parameter data
Model parameter values are presented in Table 4. Heat pump effi- ciencies and costs are drawn from data on air source heat pumps (ASHP), as these represent the most mature technology available today. Effi- ciencies for the heat pumps are given by analyses performed by the Swiss construction administration (KBOB) [50]. The heat pump cost curves and O&M are derived from a review of ASHP cost data from a range of sources, which are used to fit the parameters α and β in eq.7. This fit highlights significant economies of scale, as the price drops from 4900CHF/kW for a 5 kW installation to 850CHF/kW for a 65 kW installation. As the input data covered only a range of heat pump rated power from 5 to 65 kW, we clip the values such that the maximum price per kW is that of the 5 kW system and the minimum is that of the 65 kW system. Where the power demand is much greater than 65 kW, this can be thought of as using several systems of up to 65 kW each.
Default values for the heat demand intensities requirements for the heat networks are derived from [7]. HTDH networks are considered suitable for buildings with ≥40 kWh.m−2 while LTDH networks are suitable where demand is ≤60 kWh.m−2.
For parameters selected as GSA targets, a bounding box was defined surrounding the default value that was drawn from past research. Values for OMHP , this was determined based on the work of [29]. Values for OMDH are from the range of values reported by the Danish energy ministry for energy transport in thermal networks [51]. For the remaining values the box is set at ±20% of the base value, except for the cost adjustment factors δCT which are set to +10% − 30% in order to sample more of the parameter space for cost reductions rather than cost increases.
GHG emission estimates were calculated in CO2 equivalent (CO2eq) kg, using the GHG intensity of the Swiss consumer electricity mix of 0.102 kg.kWh−1 (which is significantly higher than the GHG intensity of domestically produced electricity of 0.027 kg.kWh−1) [50].
4. Results
The model was run for each Saltelli parameter sample set, resulting in 2500 iterations across 103′712 pixels (259′280′000 optimiser evalu- ations). Total run time was 17hrs on 14CPUs (Intel E5-2680v4), 96 GB of data was generated and stored in compressed Zarray format. Note that since buildings that were already equipped with heat pumps are not included in the model, the resulting energy demands, LCOHe, etc.
concern only buildings where the heat decarbonisation was applied.
4.1. Aggregate results
In this section we present aggregates (means, standard deviations) of the model characterisation parameters across model runs on the SA (Saltelli) parameter samples. Since the SA sampling aims for uniform
coverage of the multidimensional parameter space, these results should not be interpreted as realistic ‘mean’ scenarios (to achieve this would require the real distributions of input parameter values). Nevertheless, this can highlight broad trends. Notably, the standard deviation across model runs on the parameter samples gives a global summary of the spatial sensitivity of the result per pixel. Subsequent sections present the Sobol sensitivity indicators for each input variable.
Fig. 1 summarises the building density in the study area, showing the mix of urban zones (red) and rural areas (blue). A smaller subsample (corresponding to Geneva canton) is shown that will be used for illus- trative mapping, allowing a clearer view of the spatial variation of the results.
In our simplified decarbonisation model, the spatial mean of LCOH for a given model run ranged between 0.14CHF/kWh to 0.22CHF/kWh (Fig. 2), which roughly coincides with the base electricity price of 0.18CH/kWh but is higher than typical prices of fossil heating fuels in
Switzerland (e.g. 0.07–0.12CHF/kWh for natural gas). These values are for a simplified model and aggregated across GSA runs, so the output distribution does not reflect a realistic input parameter distribution but rather a systematic exploration of the parameter space. Nevertheless, the results suggest that decarbonisation could result in levelized costs for the equivalent heating service of today of an order of magnitude similar current electricity prices.
The LCOHe has a strong spatial dependence, as illustrated in Fig. 3 for a portion of the study region. Inspecting this map and cross refer- encing with the building density (Fig. 1 b) shows that LCOHe is lower in areas of high building density – i.e. that it is cheaper per unit energy to decarbonise denser urban areas. Interestingly, the variability in LCOHe (measured through the standard deviation per pixel across model runs) does not show the same spatial dependence. The lower unit cost in areas of high building density is partly a consequence of the assumed ubiq- uitous applicability of air source heat pumps (which are currently con- strained by space and power needs, as well as visual and sound disturbance), as well as the effective efficiency of scale (large buildings and heat demands concentrated in small areas).
The median CO2 savings across pixels and model runs was 93%, ranging between a minimum and maximum of 92% and 95%. This high value is expected due to the full electrification of the heating supply side and the use of the CO2 intensity of the Swiss consumer electricity mix, which is relatively low.
Fig. 4 highlights the very high potential for reduction in final energy demand. The useful energy savings are due to retrofits while the final energy savings are the combination of retrofits and heat pump effi- ciencies. Energy efficiency has therefore a very high importance in providing heat services. Despite the significant final energy savings, the electrification of heat supply could significantly increase the peak power demand. The current peak power demand in the region studied (Geneva and Vaud cantons) is about 1.4 GW [52], while the sum of additional Fig. 1. a) Building area density per hectare over study area, b) subsample (Geneva canton) used for illustrative maps.
Fig. 2. Distribution of spatial mean of LCOHe across model runs.
Fig. 3.Illustrative maps of a) mean and b) standard deviation of LCOH across model runs.
peak electricity demands (where the peak demand is the value used for sizing heat pump capacities) in model runs was 1.1GW, 80% of current electricity demand. Note that since peak demand times are not neces- sarily aligned for all buildings/archetypes, this is does not necessarily imply that an additional 1.1 GW of maximum power supply capacity would be required (this is further addressed in the Discussion).
Fig. 5 shows the distributions of the fractions of equivalent heat service provided by each technology across model runs. These fractions are calculated as the useful energy provided by each technology divided
by the original heat demand for a given model run, the values are recorded for each model run. As previously explained, this allows us to compare retrofits on an equal basis to the heat supplies, as the heat savings from retrofits are treated as ‘equivalent’ energy supplies. As noted for LCOHe, these distributions represent explorations of the parameter space rather than reflecting input uncertainties.
Retrofits provide 10–20% of heat service share in the majority of model iterations (90th percentile is 22%), highlighting the challenge presented by high cost of retrofits in Switzerland even when further cost reductions are allowed in the model. According to the heat service fractions, district heating is more attractive than retrofit but decentral- ized is by far the most chosen option. The heat service fraction distri- butions for heat pumps and district heating appear to consist of several overlayed distributions (or clusters). This could indicate that the system optimum has multiple regions of stability depending on the ranges of model parameters, the implications of which are discussed further in Section 5.3.
The heat service fractions also show significant spatial variation.
Fig. 6 illustrates this by mapping the standard deviations of the fraction of the equivalent heat service provided by each technology modelled across model runs (maps for the full study region can be found in the Appendix). The share of retrofits does not show a strong spatial trend, unlike that of air source heat pumps and heat networks, where the heat networks tend to provide a higher share in urban zones. These results are in line with previous findings as well as general intuition about the suitability of heat networks for urban heat supply. Nevertheless, these results are significant because unlike previous work that has mapped heat network potential based on ‘rules of thumb’ for required building and heat densities derived from previous projects [7], these results stem from bottom-up modelling of heat network costs. Inspection of the Fig. 4. Distribution of useful and final energy savings and CO2-equivalent
savings across runs.
Fig. 5. Distribution of heat service fractions for retrofit (fQ,Retrofit), decentralised heat pumps (fQ,HP), and district heating (fQ,DH). Values presented are the mean service fraction across the geographic area, for each of 2500 model runs.
Fig. 6.Standard deviation per pixel of the fraction of heat service provided by retrofit (a), decentralised ASHP (b), heat networks (c); across SA model runs.
standard deviation maps highlights that spatial patterns of variance in the heat service fractions are different for each heat service type. A common pattern is that variance is higher in semi-dense urban zones, reflecting the wider variety of technology combinations that could be suitable there. In the dense urban regions, there is much higher uncer- tainty with respect to the heat supply as the variance in both decen- tralised heat pumps and heat networks is very high. This suggests that the trade-off between centralised and decentralised technologies is sensitive to the model parameters, this will be treated in detail in the following sections. In less dense areas the variance is much smaller as heat pumps generally win out in all conditions.
4.2. Sobol sensitivity indicators
This section presents the Sobol sensitivity index ST to quantify the GSA of selected model outputs to the chosen model parameters. Sobol indexes were calculated per-pixel for each model output with respect to the selected model parameters presented previously.
Fig. 7 illustrates the spatial mean of ST for the selected model inputs and outputs. The sum of ST is >1 for all variables, indicating the pres- ence of second order interactions between model parameters. Higher order effects were however not investigated due to the increased computational intensity (addressing 2nd order effects would at least double the computation time).
The results for all parameters are not particularly sensitive to the electricity price Pelec, this is likely because all heat sources in this model are electric and therefore the price does not have a strong influence in terms of favouring one solution or another. This does suggest that adjusting levies/taxes on the electricity price may not be particularly effective for promoting a given technology in the context of massive electrification of heating.
The breakdown highlights the influence of the decentralised heat pump characteristics (efficiency SPFASHP and cost δCASHP) for all model outputs. This is particularly true for the fraction of building area to be retrofitted, where the relative advantage of retrofitting before using a heat-pump compared to installing an (oversized) heat pump alone clearly depends heavily on their relative costs and the efficiency po- tential of the heat pump.
The potential for cost reductions of retrofits δCRetrofit significantly impacts the shares of heat service provided by retrofits and heat pumps, and to a lesser extent heat networks. This is in line with previous work that found that retrofit upfront costs are the most significant barrier to increase retrofit adoption.
It is interesting to consider the combination of the role of retrofit costs with the relatively significant impact of qmax,LTDH, i.e. how ineffi- cient a building can be and still make sense to connect to a low tem-
perature network. Essentially, this shows that the fraction of heat service from LTDH depends a lot on how many buildings can be connected according to the technical feasibility guidelines; two ways to bring buildings within the technical feasibility range for LTDH are to perform retrofits or to increase the feasibility range (i.e. increase qmax,LTDH). The threshold ranges used are drawn from literature on current practices – it may be that new technological developments or implementation method improvements could change this value; this could significantly increase the appeal of LTDH systems compared to alternatives.
Fig. 8 illustrates the spatial distribution of ST for the LCOHe, and highlights that the sensitivities vary across space in different ways for different parameters. It confirms our conclusion that the sensitivities for LCOHe tend to increase with increasing building density (see Fig. 1).
Fig. 9 instead illustrates the spatial distribution of ST for each model output parameter with respect to the change in retrofit cost CRetrofit . Note that these variations are representative of those across the whole study region, the subsample is shown for better legibility. For retrofit costs, the sensitivity for LCOHe does increase with building density, but this is not the case for all model outputs. It is intriguing to observe that the sensitivity of the amount of heat service provided by retrofit (fQ,Retrofit) has a higher spatial dependence on δCRetrofit in less dense areas, i.e.
changes in retrofit cost are more likely to influence decarbonisation technology selection in less dense areas. This is likely due to the models’ strong preference for district heating in dense areas. The spatial distri- bution of fQ,Retrofit and Pmax sensitivities are near identical, which is ex- pected as the maximum power is scaled by the building efficiency. The fQ,DH shows no data (blank) for many areas, due to the optimiser never selecting DH as a heat source. Instead, we see heat pump fraction fQ,HP to be much higher outside of the urban centres. These results reflect that different subsets of technologies are competitive in different regions, in urban centres district heating competes with heat pumps while outside these areas it is a question of the trade-off between retrofit amount and heat pump sizing. As a result of these relatively complex interactions, the sensitivity for CO2 savings (ΔCO2) shows a very mixed spatial distribution.
To determine the direction and strength of the correlations, the Spearman rank correlation between the per-pixel values of ST for a given output/input parameter pair and the logarithm of per-pixel building density log(ERA/ha) was calculated. These results are tabulated in Table 5 and plotted in Fig. 10. These results show clearly that while most model outputs show more variance with respect to model inputs as building density increases, for some parameters the opposite is true (although the negative correlations tend to be weaker than the positive ones). A possible explanation is that district heating systems are found to be largely infeasible outside of built-up areas. This reduces the number of technology options to retrofit and heat pumps in these regions, which Fig. 7. Breakdown of total ST for model outputs with respect to each studied parameter.
would therefore increase the model output’s sensitivity to the retrofit and heat pump parameters (since no variance could be attributed to district heating).
5. Discussion
5.1. Decarbonised heating
As previously noted, the aggregated model results for the GSA runs should be not be considered as providing definitive estimates of new energy system characteristics, since the GSA explores uniformly the parameter space irrespective of the true probability of occurrence of
given parameter values or value combinations. Nevertheless, the ranges of results can give a good indication of the general properties of the resulting system, especially when the spread is relatively low. Further- more, the variations and sensitivities are of more interest than absolute values, since they should indicate general properties of the thermal energy system.
The range of LCOHe results suggest that decarbonisation of the heating supply could be achieved at annualised costs comparable to the current electricity price in Switzerland. However, this is still higher than current fossil energy prices. It has been highlighted that part of this is due to counter-productive inconsistencies in levies and environmental taxes on electricity compared to fossil fuels for heating, where various Fig. 8. Illustrative map of subsample area (Geneva canton) of spatial distribution of ST for LCOH with respect to the different model parameters.
