How user behaviour affects emissions and costs in residential energy systems—The impacts of clothing and thermal comfort

The representation of a typical unrefurbished building in Germany is based on an existing model [61], which is implemented in the energy system optimisation framework Backbone [62]. Energy system models in Backbone are composed of grids grouping nodes as well as units converting energy between nodes and across grids. Backbone is highly flexible in terms of systems it can represent, for example sector-coupled individual buildings, municipal systems or multi-national networks [37, 63, 64], and openly available at https://gitlab.vtt.fi/backbone/backbone.

In the building model, which is shown in figure 1, a fuel grid allows for procurement of gas and electricity at retail price levels from 2019 [65, 66] being 62 €/MWh for gas and 305 €/MWh for electricity. Furthermore, the CO₂ emission intensities of electricity and gas are 408 kg/MWh_el [67] and 182 kg/MWh_th, respectively. The only source of carbon-free energy is rooftop PV, whose installation potential is limited according to 80% of the building footprint.

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The building itself is defined by a set of connected nodes in the heat grid as depicted in figure 1. The building's structure, basement and interior are each represented as a node and parameterised according to table 1. Since the effective heat transmission is implemented in W/K, U-values are multiplied with the respective area. For the structure node, a weighted average of the roofs' (1.0 W/(m²K)), walls' (1.4 W/(m²K)) and windows' (2.7 W/(m²K)) U-values has been calculated. To do so, a roof-to-wall ratio of 73% and a window-to-wall ratio of 20% was used. By considering thermal inertia, nodal energy content is endogenously translated into the components' temperature. For the temperature of the ambient ground and air, fixed time-series from a German weather station [68, 69] are used. Unintended energy diffusion occurs between the interior, basement and ambient ground as well as the interior, structure, and ambient air nodes based on U-values and temperature differences. The temperature of the building's nodes can be controlled intentionally by the heating and cooling units' operation via the buffer storage and radiators within certain bounds that are explained in section 2.2. Therefore, heat demand is determined implicitly depending on the desired indoor temperature, temperature differences between the building's and the ambient nodes, U-values and respective areas of structural components.

To meet this heat demand, the model can invest in a heat pump or a gas boiler or utilise waste heat from a fuel cell according to the costs presented in table A1. Via a buffer storage and radiators, this heat is ultimately transmitted to the interior. Furthermore, an electrolyser allows for generating hydrogen, which can be stored in a hydrogen tank and a battery allows for electricity storage. The techno-economic parameters of these units are taken from [72]. An air conditioning (AC) unit is available for cooling. Additionally, an electricity demand must be met that accumulates to 5.5 MWh annually [73].

To summarise the decision space, this model optimises the invested capacities of all appliances (rooftop PV, gas boiler, heat pump, air conditioning, fuel cell, electrolyser, H₂ tank and battery) and for each time step their operation and the use of gas and electricity from the utility grid. Additionally, the energy content of the storage nodes (H₂ tank, battery, buffer storage), the building nodes (basement, interior, structure) and the radiator node are decision variables that can be controlled by the operation of units.

To keep the computation of hundreds of solutions tractable, time-series of ambient air and ground temperature, solar radiation, electricity demand and coefficient of performance (COP) of the heat pump [74] are aggregated from one year in hourly resolution to three typical periods, each one week long with the same resolution. This is achieved by using the Time Series Aggregation Module (TSAM) [75] on all time series of our model. It is used with the settings of a period length of 168 hours, period number of three and cluster method 'hierarchical', which yielded the lowest information loss. Although the resulting typical periods do not exactly depict a specific period of the original data, they can be thought of as representing a winter, transition and summer season. In more detail, the aggregated time-series represent weeks of low (winter, 11 weeks), medium (spring and fall, 16 weeks) and high (summer, 25 weeks) temperatures.

Endogenising indoor air temperature as the energy content of the 'Interior' node allows for assessing the occupants' thermal comfort by using the Predicted Percentage Dissatisfied (PPD). The PPD [31] is an empirically-founded metric prevalent in the scientific literature [50, 55, 76] and national standards [77, 78]. It represents the share of people dissatisfied with the climatic indoor conditions based on the temperature, relative humidity and air speed as well as a person's metabolic rate and clothing insulation.

When fixing the values of all inputs except the temperature T, the PPD can be approximated as a linear function of the deviation from a set temperature, i.e. using only three parameters m^set, T^set and PPD^offset:

$$\begin{eqnarray}&&\mathrm{PPD}(T)={m}^{\mathrm{set}}\cdot | T-{T}^{\mathrm{set}}| +{\mathrm{PPD}}^{{\rm{offset}}}.\end{eqnarray} \tag{ 1 }$$

In this study, we choose an air speed of 0.1 m/s, which is in line with no ventilation, and a relative humidity of 50%, which is in the range proposed in the standard [77] and also mentioned to have a rather small impact on thermal comfort in moderate climates and even found to be negligible by [76]. By definition of the PPD [31], we fix the offset PPD^offset = 5%. Furthermore, we use time series for the occupants' metabolic rate and clothing level. We assume a metabolic rate of 1.0 met (=58 W/m²) (seated, awake, writing or reading) for daytime from 7 h to 23 h and 0.7 met (lying, sleeping) for nighttime from 23 h until 7 h to reflect typical temporal variations in activity level [76]. To depict a range of possible clothing behaviour, we study three different clothing level scenarios. The daytime clothing ranges from typical summer indoor clothing with 0.5 clo over typical winter indoor clothing with 1.0 clo (=0.155 m²K/W) up to warm clothing with 1.5 clo. Nighttime clothing [76] ranges from short pyjamas and partial coverage with a bed sheet (1.43 clo) up to long pyjamas and full coverage with a quilt (4.56 clo). For more details on clothing and metabolic units the reader is referred to [77–79].

We distinguish the clothing between three seasons (winter, transition, summer) based on the weather data sampling and construct a light, medium and warm clothing scenario. The clothing levels and set temperatures per scenario, season and daytime are shown in table 2.

Table 2. Clothing insulation as well as fitted values for T^set, m^set, ${T}^{\min }$ and ${T}^{\max }$ per scenario, season and time of day.

Scenario	Season	Clothing (clo)		Tset(°C)		mset(%/°C)		${T}^{\min }$ (°C)		${T}^{\max }$ (°C)
		Day	Night	Day	Night	Day	Night	Day	Night	Day	Night
	Winter	0.50	2.40	26.00	23.00	6.27	4.08	23.00	18.50	29.00	27.50
Light	Transition	0.50	1.80	26.00	24.75	6.27	4.98	23.00	21.00	29.00	28.50
	Summer	0.50	1.43	26.00	26.00	6.27	5.73	23.00	22.75	29.00	29.25
	Winter	1.00	4.34	23.25	17.00	4.52	2.65	19.25	10.00	27.25	24.00
Medium	Transition	0.75	2.62	24.75	22.25	4.87	3.82	21.50	17.50	28.00	27.00
	Summer	0.50	1.65	26.00	25.25	6.27	5.18	23.00	21.75	29.00	28.75
	Winter	1.50	4.56	20.50	16.50	3.57	2.54	15.50	9.25	25.50	23.75
Warm	Transition	1.00	2.88	23.25	21.50	4.52	3.51	19.25	16.50	27.25	26.50
	Summer	0.50	2.15	26.00	23.75	6.27	4.50	23.00	19.50	29.00	29.00

For each clothing level and metabolic rate, we fit the parameters m^set and T^set to PPD data obtained with the CBE Thermal Comfort Tool [79]. In figure 2, the fitted functions for PPD(T) are displayed together with the exact PPD values for selected clothing levels and metabolic rates. This results in a time series for each parameter and scenario, which we use as input data for the model. Additionally, upper and lower bounds ${T}^{\min }\leqslant T\leqslant {T}^{\max }$ for the indoor temperature are enforced so that the PPD cannot exceed 30%, i.e. $\mathrm{PPD}({T}^{\min })=\mathrm{PPD}({T}^{\max })=30 \%$. This corresponds to allowed deviations between 3 °C and 7.25 °C from the set temperature. The resulting parameter values are also shown in table 2.

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The simultaneous optimisation of multiple real-valued objective functions is called multi-objective optimisation. A solution to such a problem is called Pareto-optimal if one objective can only be improved when deteriorating another. The set of all Pareto-optimal solutions is called Pareto front. For an overview and introduction to the theory of multi-objective optimisation, see e.g. [80]. As the building representation and comfort metric are implemented and parameterised in an optimising energy system model, objective functions can be included directly in the model without necessity for any coupling to heuristic algorithms or other models.

Building upon an implementation [37] of the augmented epsilon-constraint method (AUGMECON) in Backbone, we optimise the model for three objectives simultaneously. The objectives to be minimised are system costs, carbon emissions and thermal discomfort. System costs

$$\begin{eqnarray}&&{f}^{\mathrm{cost}}=\displaystyle \sum _{t}{w}_{t}\cdot \left({c}_{t}^{\mathrm{VOM}}+{c}_{t}^{\mathrm{fuel}}\right)+{c}^{\mathrm{FOM}}+{c}^{\mathrm{invest}},\end{eqnarray} \tag{ 2 }$$

include costs for variable and fixed operation and maintenance (${c}_{t}^{\mathrm{VOM}}$ and c^FOM), fuel ${c}_{t}^{\mathrm{fuel}}$ and annualised investments c^invest. Carbon emissions

$$\begin{eqnarray}&&{f}^{\mathrm{emission}}=\displaystyle \sum _{t}{w}_{t}\cdot \left(\displaystyle \frac{408\,\mathrm{kg}}{\mathrm{MWh}}\cdot {e}_{t}^{\mathrm{use}}+\displaystyle \frac{182\,\mathrm{kg}}{\mathrm{MWh}}\cdot {g}_{t}^{\mathrm{use}}\right),\end{eqnarray} \tag{ 3 }$$

arise from the use of grid electricity ${e}_{t}^{\mathrm{use}}$ and natural gas ${g}_{t}^{\mathrm{use}}$. Occupants' average thermal discomfort

$$\begin{eqnarray}&&{f}^{\mathrm{discomfort}}=\frac{{\sum }_{t}{w}_{t}\cdot {m}_{t}^{\mathrm{set}}\cdot | {T}_{t}-{T}_{t}^{\mathrm{set}}| }{{\sum }_{t}{w}_{t}}+{\mathrm{PPD}}^{\mathrm{offset}}\end{eqnarray} \tag{ 4 }$$

is based on the PPD metric. Each time step t is weighted with w_t ≥ 1 to account for the longer period it represents.

Applying AUGMECON [60], the multi-objective optimisation problem

$$\begin{eqnarray}&&\min \{{f}^{\mathrm{cost}},{f}^{\mathrm{emission}},{f}^{\mathrm{discomfort}}\}\end{eqnarray} \tag{ 5 }$$

is reformulated to

$$\begin{eqnarray}&&\min \{{f}^{\mathrm{cost}}-c\cdot \left({s}_{1}/{k}_{1}+{s}_{2}/{k}_{2}\right)\}\qquad {\rm{s}}.{\rm{t}}.\end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray}&&{f}^{\mathrm{emission}}+{s}_{1}={\varepsilon }^{\mathrm{emission}}\qquad \mathrm{and}\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{f}^{\mathrm{discomfort}}+{s}_{2}={\varepsilon }^{\mathrm{discomfort}}\end{eqnarray} \tag{ 8 }$$

by introducing a small scalar c ≈ 10⁻⁶...10⁻³, two non-negative slack variables s_1,2 and two constants k_1,2 reflecting the typical order of magnitude of the objectives f^emission and f^discomfort, respectively. The implementation of the PPD as well as the comfort and other objective functions in Backbone is openly available from https://gitlab.vtt.fi/backbone/backbone.

For each choice of upper bounds ε^emission and ε^discomfort, the solution to this reformulated problem is a Pareto-optimal solution to the original multi-objective optimisation problem (5). Solving the reformulated problem multiple times for varying upper bounds yields a representative subset of the whole Pareto front. Single-objective optimisations of (2), (3) and (4) give estimates of the Pareto front boundaries and hence the region $\left[{\varepsilon }_{\min }^{\mathrm{emission}},{\varepsilon }_{\max }^{\mathrm{emission}}\right]\times \left[{\varepsilon }_{\min }^{\mathrm{discomfort}},{\varepsilon }_{\max }^{\mathrm{discomfort}}\right]\subset {{\mathbb{R}}}^{2}$ that should be covered by the two upper bounds.

To save modellers' and computational time, the steps of (i) single-objective optimisations, (ii) determination of upper bounds and (iii) multi-objective optimisations with AUGMECON are automated and parallelised using a python script that is openly available from https://gitlab.ruhr-uni-bochum.de/ee/backbone-tools. While the three steps have to be carried out subsequently, parallelisation is possible within each step. In the third and most computationally heavy step, where thousands of optimisation problems are solved, this parallelisation is particularly beneficial for reducing computational time.

Since the discomfort objective contains an absolute value, a reformulation is necessary for the implementation in a linear ESM. Generally, to linearise the absolute value ∣x∣ of a variable with upper bound ${x}^{\max }$, introduce two non-negative variables x⁺, x⁻ ≥ 0 and a binary variable b ∈ {0, 1} such that

$$\begin{eqnarray}&&x={x}^{+}-{x}^{-},\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{x}^{+}\leqslant b\cdot {x}^{\max }\ \mathrm{and}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&{x}^{-}\leqslant \left(1-b\right)\cdot {x}^{\max }.\end{eqnarray} \tag{ 11 }$$

Then, the linear expression x⁺ + x⁻ takes the absolute value of x. This can be shown by considering the two cases b = 0 and b = 1 and noting that x⁺ = x and x⁻ = 0 if x > 0 and x⁺ = 0 and x⁻ = x if x < 0. To implement the comfort objective function in Backbone, we used the above approach with $x=| {m}_{t}^{\mathrm{set}}\cdot \left({T}_{t}-{T}_{t}^{\mathrm{set}}\right)|$ for each time step t and a high enough value for ${x}^{\max }$ to not impose any additional constraints on the model.

For the building energy system model, about 500 Pareto-optimal solutions are determined per clothing level, each of which is an hourly investment and operational optimisation. To generate insights from the resulting amount of data, we choose to fix some of the objectives (cost, emission, discomfort) at a certain level and analyse changes along the remaining degrees of freedom. Some of the quantitative results presented in section 3, e.g. saving potentials for costs, emissions, energy or gas, depend on this choice of objective values and are therefore somewhat illustrative. However, we aim at indicating and visualising how the results change under varying choices. The complete results are available and can be explored interactively at https://apps.ee.ruhr-uni-bochum.de/Comfort.

To study the impact of human behaviour related to thermal comfort, we analyse two ways of influence separately. First, we investigate the medium clothing scenario and compare different comfort levels, and second, we keep a constant comfort level and compare different clothing scenarios. For both analyses, we show results in three ways: the whole Pareto front(s) in 3D solution space, subsets of the Pareto front(s) in 2D for which either discomfort or clothing scenario is kept constant (referred to as slices) as well as the heat and power generation per technology along those slices. The quantitative results of costs, emissions and energy consumption always refer to the modelled period of one year. Investment costs are annualised and the PPD results are time-averaged. Additionally, we show the invested generation and storage capacities as well as full load hours for three such slices and analyse what deviations from the optimal temperature lead to certain levels of discomfort.

The shape of the whole Pareto front for medium clothing as shown in figure 3 indicates that a strong trade-off exists between costs and emissions, whereas the trade-offs between costs and comfort as well as comfort and emissions are weaker. To inspect the results in more detail, we analyse slices at fixed discomfort levels of 5.3%, 8.9% and 12.8% average PPD, which are highlighted in figure 3 in darkening shades of grey. As a general pattern, the slices are shifted to lower emissions and lower costs for higher discomfort. In particular, the boundaries of the slices depend on the comfort level. The lowest possible costs and emissions exhibit differences of 600 € and 0.7 t, respectively, between the outermost slices. Lowest possible emissions are driven by the limited available carbon-free energy from rooftop PV investments and the emission factor of grid electricity, which is an exogenous model parameter that is constant in time. By using temporally resolved emission factors, further decarbonisation could be achieved by the model. The highest Pareto-optimal costs and emissions exhibit differences of 2900 € and 1.3 t, respectively. The trade-off between costs and emissions is rather independent of the comfort level, as indicated by the slope of the slices. For the slice with 5.3% PPD, the steeper region from 2.9 t to 4.8 t has an almost constant slope with average CO₂ abatement cost of 570 €/t. The flatter region above 4.8 t has a slope of 90 €/t, while the very low emissions below 2.9 t come at marginal CO₂ abatement costs of 7130 €/t. The slices with higher discomfort exhibit regions with similar steepness, but the regions themselves are shifted towards lower emissions and costs. The marginal CO₂ abatement costs indicate, what (additional) carbon prices would be necessary as a financial incentive for purely cost-minimising actors to achieve the respective emission reduction.

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The three slices allow for analysing the potential cost and emission savings achievable by reducing comfort, as indicated by the black boxes in figure 3. For fixed emissions of about 2.9 t (dash-dotted boxes), costs decrease from 5400 € to 4600 € and 4000 € when increasing discomfort from 5.3% PPD to 8.9% PPD and 12.8% PPD, respectively. At this emission level, the relative cost saving potential through decreasing comfort by 7.5% points amounts to 26%. At higher emissions of 4.5 t (dotted boxes), the absolute cost-saving potential is only half as high. Allowing for the first discomfort reduction of 3.6% points reduces system cost by roughly 400 €. The cost saving reduces to 300 € for the next 3.9% point difference in PPD. Generally, we observe a typical trend of diminishing marginal utility, i.e. increases in discomfort have the largest impact close to the lowest possible PPD and lowest possible emissions and diminish with further increases in discomfort or emissions.

In terms of energy, increased discomfort reduces the overall power and heat generation. At emissions of 4.5 t, for instance, the generated heat reduces from over 42 MWh to 34 MWh, i.e. by 19% for a 7.5% points higher PPD. Furthermore, the use of heat pumps and grid electricity decreases, being replaced by increased utilisation of the gas boiler. Since increased discomfort allows for larger or longer deviations from the set temperature, the required heat generation decreases for increased discomfort. If allowed emissions are fixed, the model saves costs by using a higher share of gas for heating thus decreasing the more costly use of heat pumps that would also require more grid electricity.

Viewed from the other objective direction, when maintaining a fixed level of system cost at around 4400 € (solid boxes), emissions drop from 4.8 t to 3.2 t when allowing 8.9% PPD instead of 5.3% PPD. For the subsequent increase in discomfort to 12.8% PPD, emissions decrease further to 2.4 t. This roughly translates to an emission reduction potential of 6.9% of per % point increase in discomfort. Here, the relative emission saving potential amounts to 50% through accepting an increase of 7.5% points in discomfort without increasing costs.

In terms of energy, decarbonisation is achieved by increased utilisation of heat pumps that replace gas boilers for heating. This leads to increased power demand which is met by increased solar PV generation as well as imports from the utility grid. This also implies a shift in imported energy from gas to power resulting from the price and efficiency assumptions that make gas heating cheaper but more carbon-intensive as compared to a heat pump combined with grid electricity. This trend additionally reveals a gas saving potential of 16 MWh heat energy between the outermost slices without any cost increase. This is partially compensated by increased use of grid electricity, which increases by 2 MWh difference. Since the current share of gas in the German power mix is around 15%, the increase in utilised grid electricity hardly reduces the effective gas saving potential.

Furthermore, the use of air conditioning increases with decreasing emissions. Hence, increased cooling in summer is a more emission-efficient way of achieving the same average discomfort level. The fact that this trend coincides with higher PV generation and battery investments (see figure 6) can possibly be explained by an increased self-consumption of the emission-free PV power in summer replacing grid electricity in winter. This is due to the higher natural correlation between electricity demand for cooling and PV generation. The finding can also be explained by the variations in clothing level and its effect on the temporal distribution of discomfort over the seasons.

Generally, it is challenging to compare our quantitative findings with other studies. First, the studied objects are often not comparable. Second, different studies employ different objective functions in terms of both cost and comfort. Third, many studies do not explicitly model design choices between different energy generation technologies. While this again emphasises the novelty of our work as described in the introduction, it means that a direct comparison of absolute saving potentials or the explicit design and operation of the energy system is impossible. However, by comparing the slope of Pareto front slices, comparisons can be made regarding the trade-offs between comfort and costs as well as comfort and overall energy consumption.

The trade-off between cost and comfort in this work can be approximated to a 3.5% decrease in annual cost per % point increase in discomfort, which is in line with other studies. [52] found a trade-off between cost and the total percentage of discomfort hours as approximately 3.3% cost reduction per % point increase in discomfort. Similarly, [57], where the comfort objective is to minimise the highest value of PPD, the trade-off with operation costs can be approximated by a 2.6% cost reduction per % point increase in comfort.

Regarding the trade-off between energy use and comfort, we find a value of 2.5% decrease in energy use per % point increase in discomfort in this work. Although [52] quantify specific energy intensity per square metre, they found a trade-off of similar magnitude with 1.75% decrease in energy use per % point increase in their discomfort metric. The same energy use metric is utilised by [49], who employed a comfort objective of 'discomfort time ratio' and found a trade-off of 3.2% decrease in energy use per % point increase in the discomfort metric.

Increased discomfort corresponds to a greater deviation of the realised interior temperature T from the set temperature T^set. For example, during daytime (1.0 met) in the transition season and the medium clothing level of 0.75 clo, the slope of the linear fit is m^set = 4.87 %/°C. Therefore, PPD differences of 3.6% points and 7.5% points correspond to an additional average deviation ∣T_set − T∣ of 0.7 °C and 1.5 °C, respectively. Hence, the respective changes in average PPD as discussed in section 3.1 could result from exactly this additional but small and constant deviation in each time step and from temperatures above or below the set temperature. The results as shown in figure 4, however, reveal most deviations to be in the eleven winter weeks, i.e. rare and heterogeneous, below the set temperature, i.e. asymmetric, and larger than a constant deviation would necessitate, e.g. from 3 °C to 7 °C for a PPD of 8.9%. More specifically, hours accumulate around the highest possible deviations of −7 °C during night and −4 °C during daytime in winter.

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This trend towards negative deviations of high magnitude in winter is caused by two factors. The first is the geographical region, i.e. the fact that ambient temperatures are mostly lower than the set temperatures with the largest differences in winter causing higher heat transmission losses towards the ambient air and ground. The second factor is the PPD's characteristic that its slope m^set decreases with higher clothing levels, i.e. the fact that in winter, when warmer clothing is used, the same temperature deviation translates into a smaller PPD difference than it would in summer with lighter clothing (compare figure 2 and table 2). Hence, few strong temperature deviations in winter require less heating energy than many small deviations in other seasons and can therefore reduce emissions.

However, reducing emissions in this way reduces overall comfort. To reduce emissions while keeping overall discomfort constant, figure 4 reveals that temperature deviations shift from summer to transition and finally to winter. This is achieved by making increased use of the solar energy source for cooling and heating when it is most abundant. While positive temperature deviations might appear cost-inducing at first, this is not the case in warmer seasons, where outdoor temperatures above the set temperatures would require cooling.

While figure 4 only shows results for one level of discomfort, we can say that deviations are reduced for decreasing PPD levels, which leads to accumulations shifting towards 0 °C.

Instead of altering comfort levels, occupants may change their clothing to affect the perceived thermal comfort. To illustrate the effects of clothing, Pareto-optimal solutions of three scenarios with light, medium and warm overall clothing (see table 2) are presented in figure 5 as a blue, grey and red surface, respectively. Each scenario consists of a time series of clothing levels, which can differ by season (summer, transition, winter) and time of day (day, night). The light clothing scenario is almost unadapted to the seasons. In the medium and warm clothing scenarios, the clothing gets increasingly warmer in transition and winter while remaining almost unchanged in summer. In that sense, the medium and warm clothing scenarios can be considered more 'appropriate'.

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The relative positions of the three Pareto fronts indicate that lighter, unadapted clothing (blue surface) correlates with higher costs and emissions while warmer clothing (red surface) in winter and transition season correlates with lower costs and emissions. By considering slices at a PPD of 5.3%, which are highlighted as dots, we analyse the cost, emission, energy and gas savings achievable through more appropriate clothing without comfort losses. The slices show a general shift towards lower emissions and costs for increasing clothing level. The Pareto front boundaries vary significantly between the clothing levels. The lowest possible costs differ by 700 € or a factor of 6/7 between the light and warm clothing. The lowest possible emissions change by 1 t or a factor of 2/3, indicating that certain decarbonisation or cost targets can only be achieved with adapted clothing. In particular, the previously compared levels of 2.9 t and 4400 € (see section 3.1) cannot be achieved with light clothing. The level of the CO₂ abatement costs is almost independent of the clothing scenario, but a shift of the more or less steep regions can be observed.

At emissions of 4.5 t (dashed black boxes), changing from the light to the medium clothing scenario, i.e. to warmer clothing in winter and transition season, reduces cost by roughly 860 €, whereas changing from medium to warm clothing reduces cost only by 400 €. These absolute differences are almost constant for emissions below 4.5 t (and above 3.5 t) and decrease for higher emissions. With warmer clothing, cooler indoor temperatures result in the same comfort, hence the heat and power generation decrease. At 4.5 t, for instance, heat generation reduces from 45 MWh to 37 MWh, i.e. by 18% between the light and warm clothing. At unchanged emissions, this induces the cost saving potential, as less heat generation has to be shifted from the cheaper but more carbon-intensive gas boiler towards the more costly but less carbon-intensive heat pump.

In the other objective direction, solutions of equal costs reveal emission savings for higher clothing levels. For costs of roughly 4700 € (solid black boxes), emissions are reduced from 5.9 t to 3.9 t for changing from the light to the medium clothing scenario, and finally to 3.1 t for the warm clothing scenario. Thus, changing from lighter, unadapted to warmer, more appropriate clothing in transition and winter can reduce total emissions by almost 48%. In terms of energy generation, this decarbonisation is achieved by reducing the use of gas boilers and increasing the use of heat pumps together with solar PV and grid electricity. This indicates that at this cost level, 21 MWh heat energy in the form of gas can be saved by adapted clothing without increased discomfort or increased cost. This gas saving is to a small extent compensated by increased consumption of grid electricity that partially relies on gas itself, but mostly constitutes a genuine gas saving.

As with the behavioural impacts in terms of different comfort levels, comparing the quantitative findings regarding the impact of clothing levels to other literature is challenging due to differences in modelling approach and scope. In terms of trade-offs between clothing and energy consumption, [34] stated that a clothing level adaptation of 0.1 clo can lead to energy savings of 16% in summer and 13.7% in winter. In our work, the seasonally weighted difference between the light and warm clothing scenario is 0.6 clo, which translates to a significantly lower value of 3% per 0.1 clo. This difference could be explained by many factors. First, our quantitative findings in terms of saving potentials due to behavioural changes in terms of clothing vary significantly between and within the Pareto front slices, i.e. they depend on the choice of comfort, cost and emission levels. Second, in our multi-objective optimisation model, energy savings are not an objective, but one of many possibilities to achieving the more fundamental targets of saving costs or emissions, thus potentially leaving energy saving options undiscovered. Third, we implement clothing changes for different metabolic rates during day and night time, which impacts its effect on the set temperature, but might be a more realistic assumption.

In terms of invested storage and conversion capacities as well as the latter's full load hours (see figure 6), we make four observations. First, the model achieves decarbonisation through substituting the gas boiler investments by investments in a heat pump across all scenarios. Generally, the results are dominated by bivalent systems with significant capacities of both heat pump and gas boiler. Low full load hours indicate that the gas boiler tends to serve peak loads, in particular for lower emissions. Above 4.8 t for light, 4.0 t for medium and 3.7 t for warm clothing, decarbonisation is achieved by increased utilisation of almost constant heat pump capacities, while reducing the utilisation of almost constant gas boiler capacities. This indicates that a certain amount of decarbonisation can be achieved by operational changes. Deeper decarbonisation below aforementioned emission levels requires changes in the system design in the form of over-proportional heat pump investments together with a phase-out of the gas boiler. This is indicated by the strong decrease in heat pump full load hours, in particular for very low emissions and low clothing. Furthermore, the decarbonisation by changed clothing levels at a constant cost level of 4700 € manifests in differently sized appliances as indicated by table 3. Most significantly, the optimal gas boiler capacity reduces by 72% from light to warm clothing. Not each combination of installed gas boiler and heat pump capacities might be widely used or feasible in reality. However, constraining the model to certain discrete capacities limits the solutions obtained and hence does not generate more, but only less insights.

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Second, power demand for heating is increasingly powered by investments in PV. At emissions of 4.5 t, for instance, 15.1 kW, 11.8 kW and 10.8 kW PV are installed in the light, medium and warm clothing scenarios, which corresponds to 85%, 67% and 61% of the potential, respectively. Investments increase to above 15 kW for very low emissions. The point where investment in PV reaches its upper limit of 18 kW always coincides with the point of total gas boiler phase-out, which occurs at 3.6 t, 2.9 t and 2.4 t for light, medium and warm clothing, respectively.

Third, we observe investments in thermal buffer storage around 70 kWh (1000 litres to 1333 litres at usable ΔT of 60 °C to 45 °C, respectively) with an increasing trend for decreasing emissions. In contrast, battery investment stays almost constant at around 10 kWh. Battery and buffer storage are mainly used as daily storages with one cycle per day that shifts solar energy to later hours of the day. The buffer storage additionally acts as a very small seasonal storage in some solutions that shifts energy from summer to autumn. There is a dip in buffer storage investments from 3.9 t to 4.5 t for medium clothing and 3.6 t to 4.2 t for warm clothing, where more immediate utilisation of PV energy in summer reduces the surplus that can be stored for later use in early autumn and hence reduces the installed storage capacity. In turn, the heat pump full load hours peak in exactly the same region.

Finally, H₂ storage, electrolyser and fuel cell are only invested in extremely low emission cases as a small seasonal storage accompanied by a significant cost increase. In these cases, it is used purely as a seasonal storage with only one cycle over the whole year. The high use of hydrogen storage for very low emissions might not be realistic, but it can be considered a strength of the multi-objective optimisation method that it represents the whole feasible space, even very extreme cases.

Besides the typical limitations associated with using data-driven models and limited data, several limitations apply specifically to the methodology presented in this paper.

First, by studying a single building, the assumption of an exogenous power grid provides flexibility to the model without considering system effects on a larger scale. On the one hand, high levels of heat pump penetration may lead to higher costs for grid reinforcements especially in cold climates [81], that would ultimately have to be borne by the consumers. Furthermore, through increased grid electricity demand, electricity prices or carbon emissions [82] could rise, which adversely affects the adoption benefits. On the other hand, the invested storages could limit peaks in electricity demand [83] and reduce curtailment [84] when being operated in a system-friendly way. By integrating a building representation into a highly flexible energy system model, the presented methodology allows to study interactions between buildings and electricity networks at regional or national scales within one model. This would not be possible with commonly used building-level simulation models. Future work could therefore include multiple aggregated or connected buildings and sophisticated representations of electricity distribution or transmission networks to analyse their interplay. Alternatively, the model could be coupled with an agent-based model, that better represents social factors and interactions with peers that influence the decision process ² , to iteratively simulate technology adoption decisions and optimise the resulting energy system.

Second, the comfort objective based on the PPD comes with a number of limitations. People's perception of comfort is heterogeneous, which was alluded to in the work of [26], where the comfort experienced in a single dwelling varied greatly between different occupants. Furthermore, minimum discomfort is realised in our model by always following the set temperature exactly. This disregards the impacts of temperature changes on comfort, which can be observed in particular for cooling processes [87]. Following set temperatures exactly overestimates the peak heat load at boundaries of seasons and day-/ nighttime where set temperatures change, because the building interior has to be heated or cooled by a few degrees Celsius within a single time step. However, the model can decide to increase interior temperatures gradually if the resulting discomfort is acceptable, thereby utilising the flexibility available in this model from thermal inertia. Moreover, using the annual average discomfort as the optimisation objective allows shifting the 'discomfort-budget' between summer and winter, which humans are unlikely to do. Finally, fixing the indoor air speed disregards the possibility to improve thermal comfort by an indoor fan in summer without changing the indoor temperature. Although the PPD is empirically-founded and used in norms and standards, it suffers from these limitations, which could be addressed in future research by considering other comfort metrics or further developing the PPD and how it is implemented. For instance, the shiftable 'discomfort-budget' could be addressed by constraining discomfort to be more equally distributed across seasons.

Third, there are more interests driving residential heating decisions than costs, carbon emissions and thermal comfort, which we neglect. This shortcoming could be addressed by additional objectives, other approaches to reducing structural uncertainties such as Modelling to Generate Alternatives [88] or agent-based models.