Quantifying benefits of renewable investments for German residential Prosumers in times of volatile energy markets

The COVID-19 pandemic and the Russian invasion of Ukraine have led to unseen disruptions in the global energy markets since the end of 2021. Residential renewable investments like photovoltaic systems, battery home storage systems, and heat pumps are therefore gaining traction. However, the benefits of those technologies during the energy crisis and beyond have not been fully quantified yet. Therefore, in this study, we benchmark renewable investments for a broad variety of single-family homes by evaluating potential cost savings and emission reductions. In addition, the study considers the influence of recent political incentives and subsidies. The results show that photovoltaic systems are a no-regret investment decision, both economically and environmentally. At the climax of the energy crisis, a typical German household with a heat pump could save 1850 € and reduce equivalent CO2 emissions by 250 g/kWh annually. Politically introduced price breaks on electricity and natural gas do not reverse this advantage. Furthermore, when owning an electric vehicle renewable investments are often more beneficial.


Component modelling
The investment costs for photovoltaic (PV), home storage system (HSS), heat pump (HP), and hot water storage (HWS) are modelled in dependence of the scenario year.For PV systems and HSS investment costs have increased during the energy crisis [1].Moreover, for these components we make the assumption that investment costs in 2023 are identical to those in 2022.For 2030, for solar PV installations an average cost reduction of 2% per year from 2022 on is considered, according to [2].For HSS investment costs are projected to decline by at least 54% from 2016 towards 2030 [3].Considering an average system price (exclusive inverter) of 1,364 e/kWh for an HSS in 2016 [4,5], the price for 2030 is calculated to 627 e/kWh accordingly.For battery and PV inverters, we assume a constant price of 100 e/kW for all scenarios, derived from [6].For 2020 air-source HP investment costs we assume a value of 1,856 e/kW th , which is the average value for 2019 reported in [7] (with a conversion factor of 0.88 from USDollar to euros).In addition, it is assumed that there is a general price decrease for HP and a technology advance towards 2030, according to [8].Furthermore, for HP investments we do not consider additional costs for exchange of radiators, window replacement, or additional insulation of the building.Recent studies show that for a substantial share of German buildings a HP can be installed without these additional measures [9,10].For all components, fixed annual costs for operation and maintenance are stated as percentages of the total initial investment costs.
The PV potential of German households depends on the regional topology and is higher on the countryside than in urban settlements [11].Therefore, a smaller (8.7 kWp) and a larger (13.7 kWp) solar PV-systems are modelled to account for a typical range of households.For the HSS system, we do only consider one size (9.4 kWh).This is chosen as Figgener et al. [1] find that on average home owners purchase this size of HSS which is close to the size of the average PV system power.Furthermore, the purchase of an HSS is mainly driven by ideological reasons with regard to the energy transition and the striving for self-sufficiency rather than by economics [4].For heating, most single-family homes (SFH) in Germany have a combined central system that supplies space heating (SH) as well as hot water (HW) for direct use through a boiler [12].The typical size for a combined thermal storage in combination with a gas-fired boiler is assumed to be 25 kWh [13].Therefore, for thermal storage we model a combined tank with a size of 25 kWh for SH and HW supply, both for a SFH with gas boiler (GB) and air-source HP.For modelling of air-source HP, a variable coefficient of performance (COP) is considered (average 3.99).It is calculated according to the formula in (1) with T source as the variable ambient air temperature [14].For simplification reasons, we assume that an average supply temperature T sink of 50 • C is sufficient for all household configurations [7].The quality grade η HP of the air-source HP is chosen to be 0.4, according to [14].In addition, for HP installations the sizes are separately optimized for each household configuration.The electric top-up coil (TC) is only optimized for scenarios including a HP to cover high peaks in heat demand.For storage components, self-discharge losses of 0.17% per day for HSS [15] and 4.1% per day for thermal storage [16] are accounted for in the modelling.Another parameter to be set for storage is the energy-to-power (E2P) ratio.For HSS we choose a typical value of two hours [5] whereas for HWS it is set to 0.25 hours with the assumption that power availability is not critical for a thermal buffer storage.
In contrast to the operation of renewable components the manufacturing accounts for substantial greenhouse gas (GHG)-emissions as it requires substantial amounts of materials and use of energy.For solar PV an emission factor of 810 kg CO2eq./kWp is taken from [17] which accounts for modules manufactured in China with high shares of fossil electricity.Only for the future 2030 scenario we assume that a substantial solar PV manufacturing can be established in Europe and the emission factor decreases to 480 kg CO2eq./kWp[17].For battery manufacturing, in a worst case assumption 106 kg CO2eq./kW are taken from [18].For the heating components, Naumann et al. [19] perform a life cycle assessment (LCA) analysis between air source heat pumps and condensing GBs.For an air source heat pump the study estimates life cycle emissions of 24.4 gCO2eq./MJ of heat of which 3% can be assigned to manufacturing.With the total energy supplied over 20 years of operation and an output size of 5 kW th of the heat pump, also taken from [19], the emission factor is calculated to 163 kg CO2eq./kWp.For the GB no relevant emissions during manufacturing are taken into account [19].The emission factor for inverters is calculated from the solar PV only case in Krebs et al. [20].By dividing the manufacturing related emission factor of a component by its service life a yearly factor can be calculated.

Figure 1 :
Figure 1: Visualization of the information flow within the Prosumer model of the FOCUS Framework [21] for energy system optimization developed at RWTH Aachen University.

Figure 2 :
Figure2: Visualization of the rolling horizon method with predictions that is used to find a lower threshold for the optimal solution.
hour last week typically the electricity consumption is similar on the same weekdays thermal demand same hour last day corresponds to air temperature which might change within a few days electric vehicle (EV) demand same hour last week typically the driving schedule is similar on the same weekdays solar irradiation same hour last day usually the weather can change within a few days air temperature same hour last day usually the weather can change within a few days 4. Modelling data

5 .
Evaluation of additional key performance indicator (KPI)s (a) Variation of number of residents, for a building constructed between 1979 and 1990.(b) Variation of years of construction of a building, for a three-person household.

Figure 3 :
Figure 3: self-consumption index (SCI) that is reached for different renewable SFH topologies.For selected years * , variable instead of fixed electricity tariffs are applied.

Figure 4 :
Figure 4: self-sufficiency index (SSI) that is reached for different renewable SFH topologies.For selected years * , variable instead of fixed electricity tariffs are applied.

Figure 5 :
Figure 5: capital expenditure (CAPEX) for different renewable SFH topologies.For selected years * , variable instead of fixed electricity tariffs are applied.

Figure 6 :
Figure 6: operational expenditure (OPEX) for different renewable SFH topologies.For selected years * , variable instead of fixed electricity tariffs are applied.

Figure 7 :
Figure7: Savings that can be achieved for different SFH topologies, compared to a standard fossil household utilizing natural gas (NG) for heating purposes.For selected years * , variable instead of fixed electricity tariffs are applied.

Figure 8 :
Figure 8: Equivalent CO 2 reductions per kWh of consumed energy that can be achieved for different SFH topologies, compared to a standard fossil household utilizing NG for heating purposes.For selected years * , variable instead of fixed electricity tariffs are applied.

Table 1 :
Prediction methods used for the rolling horizon approach.

Table 2 :
Used input profile data.The data is resampled to meet the required resolution of 15 min for the optimization.

Table 3 :
Overview of modeled components that are relevant for the household topologies that are illustrated in Figure??.All prices indicated are exclusive of value added tax (VAT) and subsidies.