1 Introduction

Solar PhotoVoltaic (PV) systems have been one of the most attractive investments for homeowners in Germany during the last 10 years. This is primarily due to the significant support of the government through the Feed-in-Tariff (FiT) program [8] and the simple pre-requirements for installing such systems on the rooftops of homes or garages. Therefore, the widespread adoption of solar PV systems was critical in increasing the renewable fraction in electric grid power mix. Unfortunately, solar energy is limited by its intermittency and a time-bound generation of electricity, specifically midday. As a result, shifting electrical loads seems to be a necessity. However, recent improvements in the energy storage (batteries) technologies, as well as improvements in efficiency and reductions in price, could aid in mitigating this challenge.

Despite the improvement in storage technologies, and the benefits of storage such as backup power and bill management, the level of PV adoption in Germany has slowed down in recent years; there was a high level of adoption between 2010 and 2012 [7]. Thus, we seek to study the reasons for this change in people’s desires and explore the scenarios that are possible in the near future. We note that the Renewable Energy Act (EEG; Erneubare Energie Gesetz) [6] was amended to reduce the FiT, in addition to the typical annual depreciation, since the prices for PV panels had dropped significantly in 2009. A secondary focus of our work is to estimate the grid impact of PV-battery system adoption.

Using system modeling to explore different energy policies can be beneficial in understanding the impact of policies affecting PV and battery (PV-battery) system adoption. While some models correlate historical adoption data with certain factors, such correlations would not explain the reason for PV adoption and how PV adoption could be effectively influenced. Furthermore, such approaches ignore the role played by social networks in information transfer.

In this paper, we use agent-based modeling. Agent-based models (ABMs) can capture the essential aspects of modeling complex adaptive systems such as emergence of trends, incorporation of socio-technical interactions, and social influence. Agent-based modeling is an approach to modeling complex adaptive systems where agents have certain properties and behaviors, and interact with one another and with their environment [24]. Using this approach, we forecast future scenarios in Germany with respect to the adoption and usage of PV-battery systems. In our ABM, agents are homeowners that have a social network and exist in an environment that can affect their decision and desires. These agents interact with the environment by purchasing PV-battery systems and consuming, generating, or storing electricity.

PV adoption has been studied using ABMs (see Sect. 5) but in this paper, we go one step further by modeling PV and battery adoption. This model has been used to study PV-battery system adoption in Ontario, Canada [1], whereby in German case we model electricity self-consumption strategies for agents as this would affect the electric grid. While we use a survey to inform the modeling process, we also collect data from trusted sources such as official reports and system vendors.

The remainder of this paper is structured as follows: in Sect. 2 we introduce a short economic analysis of PV investment by households and investigate the possibility of grid defection of households in Germany. We discuss agent based modeling in Sect. 3. We present the results of different scenario simulations in Sect. 4 and discuss related work in Sect. 5. We highlight limitations in Sect. 6. We discuss the implications of different policies and identify advisable policies for PV and battery adoption in Sect. 7. We conclude the paper in Sect. 8.

2 Motivations and economic analysis

In this section, we investigate the current trend in PV adoption by German households considering the constraints set by EEG. This analysis clarifies which strategy for consuming on-site generated renewable energy can be followed by the households to get the maximum benefits from their PV-battery systems. That is, an household has the option to completely disconnect from the grid and obtain electricity from a PV-battery system or stay connected to the grid while using the PV-battery system to reduce dependence on the grid; The former is termed full grid defection while the latter is termed partial grid defection. Furthermore, this analysis informs our survey design process.

In Germany the typical structure of electricity tariffs for private clients (including households) is based on fixed and electricity consumption fees [28]; consumers pays a fixed monthly fee between €5 and €10 and an electricity consumption fee at a rate of 0.25 €/kWh. There are also tariffs without fixed fees, but with a slightly higher €/kWh rate. In comparison with other countries such as Canada, there is currently no Time-of-Use (ToU) electricity tariff for households in Germany. This reveals that the German households have no flexibility in deciding the best energy consumption times with respect to economic benefits. In addition to the relatively high electricity price and the reducing FiT in Germany [8], we model a household that has a PV-battery system to use the battery to save the surplus power from solar panels during the midday when solar PV electricity generation is higher than the household electricity load.

We assume that the battery is discharged to serve the load during the evening or early morning when the PV output is zero or not enough to meet owner power demands. To analyze the benefits of operating a PV-battery system this way, we consider different solar PV capacities ranging from 2 to 10 kWp, with and without corresponding battery sizes between 2 and 7 kWh. We limit the PV component to 10 kWp since according to the EEG 2014, the full self-consumption privileges apply only for facilities less than 10 kWp. In other words, owner of PV systems with capacities more than 10 kWp have to pay the EEG-apportionment.Footnote 1 However, the homeowner only gets FiT payment for feeding into the grid. For installations between 01.04.2012 and 01.08.2014 homeowners did not receive any additional own-consumption support, but also did not have to pay for solar PV self-consumption [6].

Next, we analyze the cases for partial and full grid defection. For this analysis, we use hourly load data available from over 100 residences in Bavaria, Germany.

2.1 Partial defection

In the partial defection scenario, we analyze the payback period,Footnote 2 Return on Investment (RoI), and system costs associated with purchasing different capacities of PV-battery systems. Here, we take into consideration the cost savings from the battery operation scheme and the profit from selling electricity to the grid through the German FiT program. In our work, we use a discounted payback calculation given by [15]:

$$\begin{aligned} Discounted~payback = \frac{\ln \left( \frac{AI}{AI {\text {-}} Capex\times d}\right) }{\ln (1 + d)} \end{aligned}$$
(1)

where d is the discount rate and AI is the annual cash inflow, which is assumed to be the same every year. In addition, the RoI is given by [22]:

$$\begin{aligned} ROI = \frac{Total~inflow - system~cost}{System~cost} - 100\,\% \end{aligned}$$
(2)

If a system has a \(RoI \le 0\), it is considered to be a bad investment.

We analyze different partial defection scenarios with PV system capacities ranging from 2 to 10 kWp, and battery sizes between 2 and 7 kWh. The results of our analysis are shown in Fig. 1; the payback period, cost, and RoI associated with each system are shown. These results also provide sample systems for our survey questions (see Sect. 3.4), with responses used to identify statistically significant purchase variables and create a parameter space for interpolating the purchase decision.

Fig. 1
figure 1

Sample survey question: which system(s) would you buy?

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2.2 Full defection

The case of full grid defection is analyzed differently from partial grid defection; we estimated PV-battery system capacities that would be sufficient for off-grid operation assuming there is no change in electricity consumption behaviour when consumers fully defect from the grid. We found that off-grid operation would require a PV system of 10 kWp and a battery of about 60 kWh. Given the high price of such a PV-battery system, off-grid operation is not sustainable.

Furthermore, we compare different electricity price and system price scenarios, and compare the cost of off-grid operation and full dependence on the grid for electricity. Figure 2a shows the average losses (i.e., difference in monthly expenditure) obtained with off-grid operations and a variation of battery prices, ceteris paribus; full defection is currently not an economically sound strategy. However, this would change as batteries are projected to cost about 200 €/kWh in 10 years [2].

Fig. 2
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Average annual household losses with off-grid operation

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Table 1 Agent parameters
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Table 2 Environmental parameters
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Similarly to the battery price, we vary the electricity price (Fig. 2b); with the range of possible electricity prices considered—up to four times the current price—the battery price proves to be a more significant variable in the case for full defection. Furthermore, with decreasing PV installation costs, households could become more enthusiastic about more powerful PV-battery systems that meet their electricity demands. Also, the currently decreasing FiT is unlikely to deter full defection given that cause the benefit of selling electricity to the grid is reducing.

3 Methodology

In this section we describe and discuss our ABM approach and elaborate the ABM parameters used in our work.

3.1 Agent-based model design

An agent-based model (ABM) is an approach for simulating the actions and interactions of autonomous agents that have certain properties and behaviors with a view to assessing their effects on the system as a whole [24]. Agent-based modeling is suitable for studying complex polices such as energy policies given that these policies can be modeled in terms of system (environment) variables that affect how agents behave [26, 32, 33]. An ABM should also be based on data, particularly a survey that adds to the model by binding survey responses to agents.

In our ABM, agents are homeowners that have friends and exist within an environment that can affect their decision and desires. These agents also take actions such as purchasing PV-battery systems, generating electricity, storing energy, and consuming electricity. Different attributes have been assigned to each homeowner in the ABM; these are variables that are vital in modeling the agents’ actions. We explain the agent variables in Table 1. We also create a model environment using environment variables such as the electricity pricing scheme, FiT, PV prices, and battery prices. In particular, the listed variables are used to create different simulation scenarios. Other environment variables include discount rates, battery life, hourly PV generation per kW, and simulation date and time (Table 2). Also, the actions executed by agents are the purchase of PV-battery systems and the consumption of electricity, and these are determined by the agent and environment variables.

3.2 Data description and sources

In this study, we use hourly load profiles of over 100 residences in Bavaria, Germany. These load profiles are generated using a simulator with different household sizes, and matched with actual load profiles. The hourly load data are used in our PV and storage sizing analysis, as well as our economic analysis. In addition to the load data, we use solar PV generation data available from simulations in HOMER [20] with solar radiation data from solar stations in Germany. Other data such as electricity prices, FiT, and PV-battery system prices are obtained from official utility reports and vendors.

3.3 Electricity generation and consumption

We simulate electricity generation, consumption, and storage on an hourly basis. An agent will sell surplus electricity to the grid after meeting its hourly demand and fully charging its battery. Energy stored in the battery is used when the electricity generated by the solar panels is insufficient for the hourly load. Since the current FiT for small-scale systems (\(\le \)10 kWp) is lower than the price of electricity, it is economically beneficial for households to consume electricity from solar panels rather than sell electricity to the grid.

3.4 Survey

A survey can be a source of useful data when obtained from a representative population. We conducted a survey to understand which systems are attractive to respondents and how much the respondents care about factors such as system cost, payback period, and RoI. Figure 1 shows an example of a survey question, where respondents are asked to accept or decline purchasing each system based on the price, RoI, and payback period; payback period and RoI are calculated using Eqs. (1) and (2) respectively.

Furthermore, the survey is used to extract the impact of the respondents greenness (i.e., concern for the sustainability of the environment) and social network on purchase decisions. In addition, some survey questions are used to estimate the respondents’ affective impressions (i.e., emotional sentiment) of concepts such as PV panels, batteries, buying, homeowner, and business or owner. This sentiment is based on Affect Control Theory (ACT) [19] and determined with three dimensions—evaluation, potency, and activity (EPA). Evaluation ranges from good to bad, potency from strong to weak, and activity ranges from active to passive.

The survey was distributed using CrowdFlower [11], with a restriction for only respondents in Germany. We also added test questions to check if respondents were paying attention to the questions. We had 520 survey responses from Germany using CrowdFlower, out of which 150 were valid since they answered our attention test question correctly.

3.5 Feature selection and logistic regression

Making a decision about purchasing a PV-battery system is a complicated process as any other commercial decision, since an agent needs to consider many factors such as capital cost, annual savings, payback period, knowledge of solar PV systems, and spending budget; in addition to these variables considered to be rational, we also include irrationality via variables such as deflection,Footnote 3 attitude towards the environment, and social network. Using Lasso Least Angle Regression (Lasso LARS) [12], we identified the features that had the most impact on purchase decisions. All the valid survey responses were divided into ten randomized folds, and the variable coefficients were recorded. In addition, we set the regularization parameter at \(1.5 \times 10^{-7}\) in order to get a clear distinction of significant variables. Figure 4 shows the average Lasso LARS coefficients for each variable.

Fig. 3
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Solar PV Prices

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Fig. 4
figure 4

Feature selection using Lasso LARS

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From the feature selection process, we find that the payback period, maximum budget stated by the respondent, greenness, and social effect on purchase decision are the significant variables. Interestingly, the deflection did not appear to have any influence on the purchase decision. This could indicate that when the capital outlay is high, homeowners are driven to be rational rather than sentimental in their actions.

We use logistic regression to estimate the probability of the purchase decision based on the significant variables from the feature selection process; we exclude variables that do not fall within the preferred 95 % confidence interval. The p value indicates the statistical significance of each variable, where a p value of 0.05 indicates a 95 % confidence interval; variables with \(p>0.05\) are excluded from the model. Here, we set a decision to purchase the system as 0 and a decision to not purchase the system is 1. Table 3 shows the logistic regression results; a higher budget results in a higher likelihood of a system purchase while a longer payback period reduces the likelihood of a system purchase.

Table 3 Logistic regression result
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3.6 PV-battery purchase

The simulated period is divided into epochs (set at 6 months), during which each agent who has not owned a PV-system would make a decision to purchase a PV-battery system or not. This decision is based on the logistic regression model shown in Table 3. Using the survey questions, we created a sample space of possible PV-battery systems from which the agent can choose. Three different sizes of PV are considered—3, 6, and 10 kWp—each without and with batteries of 4 and 8 kWh capacity. A maximum PV capacity of 10 kWp is based on the maximum PV capacity for households under the FiT regulations.

The purchase decision is influenced by the adoption of the entire population because of the observability of the system. According to Bass [3], adopters of products or services can be categorized as follows: innovators, early adopters, early majority, late majority, and laggards. Innovators are those who adopt new products regardless of social influence while laggards adopt a product after it is commonplace. In our work, we represent this level of adoption with the social threshold T where \(0 \le T \le 1\) . An agent will not adopt a product if the fraction of its social network that has adopted that product is less than the agent’s \(T_i\). We should point out that \(T_i\) is unique to each agent i. To summarize, the algorithm for the PV-battery system purchase decision process is shown in Algorithm 1 [1]. After an agent selects a list of systems that it can purchase, it has to select randomly from this group of systems. We take this approach since it is difficult to specify which system a person would choose in reality given the system alternatives.

3.7 Validation

German FiT program started at August 2004, and the number of FiT contracts signed each month up to the end of 2014 has been published by Bundesverband Solarwirtschaft e.V (BSW-Solar) [10]; at the end of 2014, the number of installed PV systems in Germany was about 1.5 million [10]. We assume that all PV FiT contracts were by households, and we scale down this number of systems to the agent population in the ABM (i.e., 13,250 agents replicated from the survey). To validate our model, we set the environment variables such as PV and battery prices, electricity pricing, and FiT to vary in our simulation as they did in reality during this period of time. We obtain required data as follows:

figure d
  1. 1.

    The FiT change over time is obtained from an official report of “Fraunhofer Institute” [16].

  2. 2.

    The change in electricity prices over time is obtained from Bundesverband der Energie-und Wasserwirtschaft (BDEW) [4]. The BDEW is an association of about 1800 German companies, representing approximately 90 % of electricity sales.

  3. 3.

    The PV installation cost change over time is also obtained from a BDEW report [5]. We compare this with information provided by some active PV system vendors.

We tried to fit parameters for the five categories of adopters discussed previously. We represent these categories using a normal distribution of T from which we assign \(\mathbf T _i\) to each agent. We ran simulations with different means \(\mu \) and standard deviations \(\sigma \) for T in order to find the best match for historical adoption. For each \(\mu \) and \(\sigma \) of T, we executed 20 runs and report the average adoption results. Figure 5 shows the errors associated with each T distribution; the combination (\(\mu \), \(\sigma \)) with lowest error and closet fit is \(\mu =0.26\) and \(\sigma =0.18\). Figure 6 shows the scaled historical adoption compared to the simulated adoption. As a result, these values are used to run the ABM simulation of future scenarios as explained in Sect. 4.

Fig. 5
figure 5

PV adoption validation RMSE

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Fig. 6
figure 6

PV adoption validation and scaled historical adoption

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Fig. 7
figure 7

Coefficients for PV price, battery price, and FiT in base case and alternative scenarios

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4 Result

Investigating the future of PV adoption requires determining the sensitivity of PV purchase to changes in different environment variables, particularly electricity price, system price, and FiT. Since the previous mentioned variables affect the decision of installing a PV-battery system, we vary the listed environment variables over the course of the simulation using the coefficients shown in Figs. 7 and 8. Since our goal is to estimate the impact of different policies, we simulate different policy scenarios. This includes the base case where prices change at their current rate and there is no intervention. The justification for the base case values are as follows:

  1. 1.

    The current FiT in Germany is low, given that the FiT is less than the price of electricity. We assume that the FiT will decrease linearly to zero over a period of 10 years (2015–2025).

  2. 2.

    According to a study [23] revised by Karlsruher Instituts für Technologie (KIT), electricity prices in Germany could increase by 70 % by 2025. The authors highlight the cost of the energy transition—Energiewende [13]—and the planned phasing out of nuclear power. We use this rate of increase in electricity price in the base case simulation.

  3. 3.

    Fraunhofer Institute for Solar Energy Systems (ISE) has published a forecast of trends in costs of the PV modules in May, 2015 [17]. A price decline of 20 % is expected from a double fold of total installed PV capacity. The so-called experience curve effect is also expected to continue, with solar PV system costs falling to as low as 40 % in 2025. In our simulation, a similar price decay is applied.

  4. 4.

    According to a recent study by AECOM [2], all battery technologies are likely to drop in price over the next 5 years; Li-ion battery technologies may experience the largest dip of all—60 % by 2020. We extrapolate a decay in price to 2025, assuming a price reduction of 50 % by 2020.

Fig. 8
figure 8

Coefficients for electricity price in base case and increased kWh-price scenario

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The following changes in alternate scenarios are made (Figs. 7, 8): slowed FiT reduction, increased electricity price, reduced PV price, and reduced battery price. We also combine some of these scenario changes to estimate the combined effect of different policies.

Two common approaches for selling electricity to the grid are the FiT and net metering. However, only FiT is implemented in Germany. Unlike net metering, where the homeowners receive bill credits because of renewable energy fed into the grid, homeowners are paid only for the electricity energy produced on-site and sold to the grid. In this simulation, we consider two cases:

  1. 1.

    Self-consumption scenario which seems to be the future scenario in Germany because of a low FiT level that is far below the retail electricity rate.

  2. 2.

    A homeowner who installs renewable energy will feed into the grid all energy gotten from PV by FiT compensation, then the grid will serve home’s on-site electricity demand any time but with the current price of electricity [16].

Fig. 9
figure 9

Total PV adoption in different scenarios with single variables changed from base case

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Fig. 10
figure 10

Total PV adoption in different scenarios with multiple variables changed from base case

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4.1 PV adoption

The main goal of this study is to evaluate the impact of different policies on PV-battery adoption and usage. To clarify the effect of the different environment variables, we categorize the scenarios into scenarios with only one environment variable changed from the base case and scenarios with multiple variables changed from the base case—Figs. 9 and 10, respectively. In the base case, we can see that solar PV adoption grows very slow except during 2015 where the FiT rate was relative high compared to the next years where selling the all PV output of PV to the grid is still relative attractive to the homeowners, as well as battery cost is high. But after 6 years the PV adoption increases at faster rate. This trend is due to the simultaneous reduction in PV and battery prices and increase in electricity prices, which results in improving the attractiveness of having batteries and PV systems with bigger capacities to avoid buying the expensive energy from the grid since the cost of electricity from PV systems is cheaper than the effective price from the grid.

Another insight from Figs. 9 and 10 is that increasing electricity prices (kWh) has a larger effect rather than PV and battery prices. Therefore, in all scenarios where the electricity price is increased, the PV adoption rate is higher than those in other scenarios. The highest rate of adoption (\(\approx \)28 %) can be achieved by combining an extreme increase of electricity prices with reduced PV and battery prices. In conclusion, the adoption rate in Germany will keep increasing over the next 10 years. The low FiT encourages a self-consumption strategy while consumers can take advantage of the reductions in PV and battery prices.

4.2 Battery adoption

As we did in Sect. 4.1 when we studied PV adoption, we will distinguish two cases according to the number of changed variables from the base case: one variable in Fig. 11 and multiple variables in Fig. 12.

Figure 11 shows that battery adoption in base case will be very low during the first 5 years and will not start increasing significantly before 2020. It can stand to a reason that at that time the cost of electricity from PV systems would be significantly cheaper than the effective price from the grid and saving energy instead of feeding it to the grid will be more beneficial. An argument could support our assumption is: reducing only battery prices or increasing only electricity prices have the same effect on PV adoption as seen in Fig. 11. Also combining these two variables will cause a high adoption rate as seen in Fig. 12. Similar to PV adoption, the highest battery adoption level can be achieved by combining an extreme increase of electricity prices with reduced PV and battery prices.

Fig. 11
figure 11

Battery adoption in different scenarios with single variables changed from base case

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Fig. 12
figure 12

Battery adoption in different scenarios with multiple variables changed from base case

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Fig. 13
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Weekly peak loads

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4.3 Impact on electric grid

Figure 13 shows the total weekly loads which are approximately same in all scenarios during the first 5 years, due to the low and expected level of PV adoption during this time period—only 9 % in scenario with the highest level of adoption—and the low levels of Battery adoption, but after 5 years the situation will change. Specifically from 2021 the adoption level start increasing rapidly till reach 28 % in scenario with the highest level of adoption. Which enforced lower peaks in the net domestic load and the homeowners will be more motivated to disconnect completely from the grid because of high electricity prices and low installation cost. In Fig. 14 we fix the daily peak load in the base case as a reference point and calculate the reduction in daily peak load in two scenarios with the highest level of adoption. We represent it as percentages of the peak load in base case. Figure 14 shows a reduction of about 25 % in the scenario with the highest level of adoption which could reflect on the grid stability.

Fig. 14
figure 14

Reduction in daily peak load in different scenarios in relation to the base case

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5 Related work

We discuss studies with similar approaches with a focus on the adoption of solar PV.

Zhang et al. [35, 36] develop an ABM to study policies that affect residential solar PV adoption. Here, an agent’s decision to purchase a PV system is affected by the net present value (NPV) of the PV system and the number of PV systems near the agent’s house location. This work includes a case study on San Diego, where two policies are considered: reducing PV system price and giving PV systems to low-income households.

Zhao et al. [37] create a model that integrates agent-based modeling and system dynamics. Factors affecting PV adoption include income, payback period, residential location, and advertising. In addition, the purchase decision function comprises a willingness-to-pay variable that acts as a threshold for an agent to decide to purchase. This study simulates the impact of different policies and their results show that adoption is more likely to be incentivized in smaller cities than in larger cities.

In a study [30] that focuses on residential solar PV adoption, Robinson et al. design a GIS-integrated ABM and conduct a case study on Austin, Texas. Here, the agent purchase decision model is based on the theory of planned behaviour (TPB), with a consideration for social influence. This work incorporates household data to create an agent population in the case study.

Similarly, Palmer et al. [27] simulate residential solar PV adoption in Italy using an ABM. An agent’s decision to purchase a PV system is an utility function based on the agent’s income, care for the physical environment, payback period, and social influence. Based on the results, income influences solar PV adoption more than other utility variables. Rai et al. [29] extend the study by Robinson et al. with a study of rebate program design.

Iachini et al. [21] develop an ABM where policies focus on social and economic factors influencing solar PV adoption. Similar to Palmer et al. [27], the agents decide to purchase systems based on income, care for the physical environment, payback period, and social influence. They also conduct a case study using the Emilia–Romagna region in Italy.

Murakami [25] studies solar PV adoption with a focus on the social aspect of the adoption process. Unlike most other studies, this work models the technical limit of integrating PV systems at the distribution level of the electric grid. In addition, the use of batteries is modeled for scenarios where batteries are used to buffer the intermittent PV electricity generation. This study, however, does not model battery adoption and does not appraise different policies.

Our work improves on these mentioned studies by modeling battery adoption with solar PV adoption, and modeling electric grid impact. We believe that policies should not focus on only solar PV adoption, but also on managing the increased adoption of such a disruptive technology. Therefore, we model the impact on the electric grid. Furthermore, our work includes a case study on solar PV adoption in Germany.

6 Limitation

The limitations of our work are as follows:

  1. 1.

    Our survey contains responses (about 30 %) obtained directly from specialists or researchers and some responses collected on CrowdFlower. The survey data was quite noisy given that respondents were asked to choose systems they would purchase despite no actual purchase taking place. However, we utilize the survey data by identifying statistically significant purchase decision variables. As a result, we still provide viable information for policymakers and industry stakeholders.

  2. 2.

    EEG in Germany has changed during the last 10 years rapidly and recently the self-consumption issues have been taken into account. Hence, it makes validation of ABM model very difficult, if we consider all details of EEG. Therefore, we ignored some details such as where the PV system is installed: rooftop or ground-mounted systems. As a result, we could not find a curve matching the historical data but we still believe it is valid and good enough to determine the correct values of adoption threshold (T).

7 Policy implications

The main two motives for the households to seek alternatives to the grid electricity: an expected reduction in PV-battery system prices, and increase in electricity prices. The latter is the most influential and important with taking into account that Germany has the highest electricity prices for household consumers in Europe [14]. As a result, we expect that customers will be pushed towards having their own PV-battery systems with higher capacities. Furthermore, the low FiT combined with high electricity price will encourage consumers to follow a self-consumption strategy, tending towards disconnection from the electric grid.

There are efforts by EEG to put more constraints on self-consumption, whereby the homeowners have to pay “EEG-Umlage” for their consumed on-site generated electricity, which is about 0.0635 €/kWh, if the producer and the consumer are not the same persons. If they are the same person, this is only 40 % of these 6.35 € cent/kWh. It is also depends on the size of PV system, if the PV installation is \(\le \)10 kWp, homeowners do not have to pay at all.

According to a report from Rocky Mountain Institut et al. [9], utilities could also see PV-battery systems as an opportunity to add value to the grid and their business models, even though they see the impending arrival of PV-battery grid parity as a threat. One area of future consideration is to evaluate how utilities could adjust their existing business models or adopt new business models—either within existing regulatory frameworks or under a new one—to tap into and maximize new sources of value. Other areas of future research include the evaluation of EEG constraints on the self-consumption for PV systems bigger than 10 kWp and designing alternative electricity pricing schemes (in place of the base price scheme).

8 Conclusion

In this work, we investigate the situation of PV-battery adoption in Germany in the next 10 years using an ABM. Indeed, the current low FiT rate and the expected reduction of PV and battery price could probably motivate homeowners to follow self-consumption strategy to consume on-site generated energy despite of the constraints of EEG on this type of consumption.

To achieve this goal, we create an ABM with agents that behave as a part of the energy market by generating or consuming some energy or taking a decision to store some of their own generated energy instead of selling it to the grid. We use a survey to build a data-driven model. The collected responses are only from German people and analyzed to estimate their attitudes towards PV-battery system and what system they might purchase under different market conditions. Using Lasso LARS, the features that had an impact on purchase decision were identified—payback period, maximum budget, concern about the environment, and the social influence. Different scenarios are considered to cover most of the cases and include unpredictable changes of variables such as battery and electricity prices. The focus was on changing PV-battery system adoption level and the impact on the electric grid.

The results show that without any policy intervention, PV adoption would increase from 4 % in 2015 to just 8 % in 2025. We find that increasing electricity prices in Germany can encourage the customers to install PV-battery systems. Also, this has a larger impact on PV-battery system adoption than reduced PV and battery prices. Given that PV-battery system prices are reducing, policies that encourage customers to stay connected to the grid should be encouraged as this improves the grid’s capacity for different services.