- Open Access
Comparing solar photovoltaic and battery adoption in Ontario and Germany: an agent-based approach
- Adedamola Adepetu†1,
- Ammar Alyousef†2,
- Srinivasan Keshav1Email authorView ORCID ID profile and
- Hermann de Meer2
© The Author(s) 2018
- Received: 23 January 2018
- Accepted: 23 March 2018
- Published: 26 July 2018
We use Agent Based Models (ABMs) to study and contrast the projected adoption of integrated photovoltaic and battery systems in both Ontario, Canada and Bavaria, Germany.
We carry out surveys in both jurisdictions to elicit Agent Based Model (ABM) model parameters and to learn the decision function that determines whether an agent purchases a system or not. We use our fitted ABMs to assess the impact of different policy variants on Solar Photovoltaic (PV) system adoption in both jurisdictions.
We find that different adoption behaviours exist in both jurisdictions, and that, in jurisdiction, of the polices that we considered, different policy incentives bring about the most significant increase in adoption. For example, reducing PV prices best increases adoption in Ontario but increasing the price of electricity would have the most significant impact in Germany.
ABMs allow policy makers and PV/battery manufacturers to estimate the jurisdiction-specific impact of a range of policy prescriptions.
- Agent-based modeling
- Photovoltaic systems
- Distributed generation
- Energy storage
Due to the threats posed by climate change, many jurisdictions around the world are striving to reduce their carbon footprint, for example, agreeing to the Paris Agreement sponsored by the United Nations1. Solar Photovoltaic (PV) systems, which have zero carbon emissions during operation, provide a viable alternative for energy generation. However, they produce no energy at night and highly variable energy during cloudy periods. PV systems can be combined with storage batteries to provide reliable power despite these limitations. As a result, integrated solar PV and battery (‘PV-battery’) systems represent an attractive alternative for low-carbon and sustainable energy generation.
Recognizing this fact, to encourage the use of solar and storage technologies, different incentives such as subsidies and Feed-in Tariff (FiT) contracts have been implemented in different parts of the world. Unfortunately, the same incentives have been met with varying degrees of success in different jurisdictions (Kazhamiaka et al. 2017). The goal of our work, therefore, is to compare outcomes from a set of plausible policies to determine the best policy incentive from this set that would promote the adoption of PV-battery systems in each jurisdiction. Specifically, we use jurisdiction-specific ABMs to study the different policy incentives that could bring about the greatest increase in adoption in each jurisdiction2.
We find that in Ontario, reducing PV prices significantly impacts adoption but in Germany, increasing the price of electricity would have the most significant impact.
The rest of this paper is structured as follows: In “Background” section, we present a background and literature review. We detail our methodology in “Methods” section. In “Ontario case study” and “Germany case study” sections, we use this methodology to study PV-storage adoption in Ontario and Germany, respectively. In “Comparison between Ontario and Germany case studies” section, we compare the findings of both case studies. Finally, in “Conclusions” section, we conclude and present policy implications.
To encourage the use of solar and storage technologies, different incentives such as subsidies and FiT contracts have been implemented in different parts of the world. For example, the Renewable Energy Act (Ernewbare Energie Gesetz (EEG)) was passed in Germany in 20003. Under this act, homeowners can purchase solar PV systems and sell the generated electricity back to the grid at a price that is guaranteed for 20 years (BNetzA 2015b). When it was introduced, the FiT price was much greater than the price of grid electricity, so all the generated renewable energy was fed into the grid to maximize the profit that it homeowners made on their investment.
Based on this significant government support, the renewable industry in Germany, particularly PV, grew rapidly between 2004 and 2012. The share of energy derived from renewable sources in Germany between 2004 and 2014 increased from 11.5 to 31% – 6.8% of this increase resulted from solar PV (Wirth and Schneider 2015). On sunny weekdays, electricity from PV systems sometimes meets up to 35% of the instantaneous electricity demand, rising to nearly 50% on weekends and holidays (Wirth and Schneider 2015). Note that, although there was a high level of PV adoption in Germany between 2010 and 2012, the adoption rate has slowed down subsequently (BNetzA 2015a). This is probably a result of amendments to the EEG to reduce the FiT to the price that is below the price of grid electricity, making solar investments less profitable. Instead, the higher price of grid electricity incentivizes homeowners to install local storage and meet as much of their needs from local generation as possible. We investigate this trend further in this paper.
Like Germany, Ontario also has a ‘microFiT’ program targeted to homeowners and small businesses, with a maximum generating capacity of 10 KiloWatt (kW) (IESO 2015a; 2015b; 2016). Ontario also supports a ‘net metering’ program (not available in Germany), where a homeowner pays only for energy consumed net of local generation, and receives credits if the generation exceeds consumption (a relatively rare event). Despite these two programs, there has been a lower level of PV adoption in Ontario than in Germany. Specifically, at the start of 2016, only 23,061 solar PV microFiT contracts had been signed, in a population of approximately 4.9 million households (IESO 2016; Statistics Canada 2011). In this work, we seek to explain this difference in adoption using Agent-Based Models (described in “Methods” section), then use our insights to determine the best policies to encourage the adoption of PV-battery systems in both Ontario and Germany.
We restrict our review of prior work to studies that have used ABMs or similar approaches to study the adoption of solar PV systems.
Using an ABM, Zhang et al. (2015; 2014) study PV adoption in San Diego, California, with a focus on two policies: PV price reduction and seeding PV purchase by giving systems to low-income households. The net present value of a system influences agents’ decisions to purchase PV systems.
Zhao et al. (2011) combine ABMs and system dynamics to study PV adoption. The purchase decision is based on income, payback period, residence location, and advertisements. Also, a willingness-to-pay is used as a threshold for PV adoption. Simulating different scenarios, this study shows that PV adoption is better incentivized in smaller cities.
Robinson et al. (2013) conduct a household PV adoption case study on Austin, Texas. This is based on an ABM with Geographic Information Systems (GIS) features, where agent purchase decisions are defined using the Theory of Planned Behaviour (TPB) and social influence. Similarly, Palmer et al. conduct a case study on PV adoption by households in Italy. The agent purchase decision variables include the agent’s income, care for the physical environment, payback period, and social influence; income has the most significant impact. This study has been extended by Rai et al. (2015), with a focus on rebate programs.
Iachini et al. (2015) study the social and economic factors that affect PV adoption. Similar to Palmer et al. (2015), the purchase decision is influenced by income, care for the physical environment, payback period, and social influence.
Murakami (2014) focuses on the social component of PV adoption. This study incorporates the capacity limits for PV-grid integration, based on grid stability. This study also considers the impact of using batteries in the grid but does not study battery adoption.
We improve on these studies by studying systems that incorporate both batteries and PV systems, rather than PV systems alone. In addition, we conduct case studies in both Ontario and Germany, rather than in a single jurisdiction.
We use ABMs for our study: the approach is summarized here and details can be found in (Adepetu 2016a). An ABM system comprises of agents that have certain properties and behaviours. Agents interact with one another and with their environment (Macal and North 2010); emergent system behaviour arises from the aggregation of their actions and interactions. It has been found that many energy policies can be studied using ABMs, regardless of the complexity of the policy (Van Dam et al. 2012; Nikolic and Ghorbani 2011).
To set up our ABM, we model homeowners as agents who are influenced by their social network when purchasing PV-battery systems (Kulviwat et al. 2009). We use Bass’s (Bass 2004) categorization of adopters as innovators, early adopters, early majority, late majority, and laggards. Innovators tend to adopt new products without any social influence while laggards adopt commonplace products. We model this order of adoption in each agent using a social threshold T where 0≤T≤1 (Granovetter 1978) and the value is drawn from a truncated normal distribution. We use our model to compare emergent behaviour from agent decisions in response to a set of energy policies. Agent parameters are chosen based on data sources, as detailed in each case study.
We aim to model both rational and irrational factors that affect agent behaviour (i.e. purchasing PV-battery systems and consuming electricity). Purchasing PV-battery systems, in particular, can depend on rational factors such as a budget, payback period, system cost, and annual Return on Investment (RoI). Irrational factors include perceived impact of PV systems on the physical environment, concern for the physical environment, prior knowledge of PV systems, and susceptibility to social influence.
We validate our models by simulating historical adoption using the same system prices and market conditions that existed in the past. For each level of adoption in the population, we compare the predicted adoption to the actual adoption during the period being simulated. This is discussed in more detail in “Validation” section.
In this section, we discuss the use of an ABM to study the adoption and usage of PV-battery systems in Ontario.
Environment Parameters (At the Time of the Study)
FiT price ($/kWh)
Price for each unit of electricity generated.
ToU Electricity Price
Price of electricity depending on the time of day, day of week, and season.
Installed Solar PV price ($/kW)
Purchase and installation cost of PV systems.
Installed Battery Price ($/kWh)
Purchase and installation cost of a battery storage system.
Battery Operation Parameters
Battery Depth of Discharge (DoD)
Battery capacity proportion that can be utilized.
Battery Life (years)
Length of time between a battery’s first use and its decommissioning.
Based on typical values for current Li-ion batteries, we choose a battery life of 10 years (Wang et al. 2012)
Battery Charge Efficiency (years)
Percentage of charging energy that is actually stored.
Li-ion batteries have 85% charge efficiency (Wang et al. 2012).
Battery Discharge Efficiency (years)
Percentage of discharged energy that is not lost as heat.
Li-ion batteries have ≈ 100% discharge efficiency (Wang et al. 2012).
We distributed the survey online using Crowdflower (Crowdflower Inc. 2017) to target Ontario residents. In an attempt to exclude poor-quality responses, we included questions to test the attentiveness of respondents and removed all responses from respondents who answered these questions incorrectly. We had 648 survey respondents from Ontario; 381 responses were valid.
Feature selection and logistic regression
Logistic Regression Result (Ontario)
Agents in our model can consume electricity, purchase PV and/or storage systems, and having done so, can generate electricity. We discuss these behaviours next.
We use an hourly model for electricity consumption, as described in “Data” section.
An agent considers buying a PV-battery system if it does not own a PV-battery system and its social threshold parameter exceeds the fraction of its social network that owns PV-battery systems. Algorithm 1 shows the purchase decision process.
The system options available are solar PV system capacities of 3, 6, and 9 kW, each without and with batteries of 4 and 8 KiloWatt hour (kWh) capacity. From a list of possible system options that an agent is willing to purchase, one option is chosen randomly. This is because the survey shows that all the systems meet the purchase criterion, and there is no obvious way for us to rank one system over another.
Electricity generation and storage operation
If an agents purchases a PV system, they can operate it either using a FiT or a net metering contract. FiT contracts are attractive when the FiT rate is higher than the price of electricity, otherwise the agent uses a net metering contract. Agents use energy from the battery store, if possible, during the peak electricity price period while the battery is charged during other periods.
The social threshold parameter for the ith agent, Ti, is assumed to be drawn from a truncated normal distribution. However, the mean and standard deviation of this distribution are free parameters. To discover the best values for these parameters, we simulate PV adoption for 26,160 agents between 2010 and 2014, each modeled using survey responses, for different values of these parameters and compare it with the actual FiT contract adoption for this period (IESO 2015b). The best FiT values of these parameters are then used in our simulations.
Base case: The system prices change based on current trends (Ontario Energy Board 2015b; Parkinson 2015). To model the historical decline in FiT prices in Ontario, we assume that the FiT price will continue to decrease linearly towards 0 $/kWh
Less slow reduction in FiT, to continue to encourage solar adoption (compared to the base case)
Increase in grid (ToU) electricity price by a ratio of 6:1 (compared to 2:1 in the base case)
Reduced price of PV systems (compared to the base case)
Reduced price for battery storage (compared to the base case)
Recall that there are approximately 26,000 agents, so there is about 15% penetration at the end of the simulation period in all cases. This growth is driven primarily by the expected drop in PV prices, with no additional policy stimulus. Nevertheless, there is a significant improvement possible due to the use of appropriate policies. In particular, a reduction in PV prices, over and above market price, due to purchase tax credits for example, can significantly improve PV adoption. It is also clear that increased grid prices tend to suppress FiT contracts and incentivize net metering contracts.
In this section, we use ABMs to study PV-battery system adoption in Germany. In the interests of space, we only highlight the differences between this study and the Ontario study. Note that, unlike Ontario, homeowners in Germany can only sign FiT contracts, but not net metering contracts. Therefore, if the FiT price is lower than the price of grid electricity, an agent sells its excess electricity to the grid. This is similar in principle to net metering. However, if the FiT price is higher than the price of grid electricity, and agent sells all of its PV generation to the grid at that price and uses electricity from the grid instead.
Feature selection and logistic regression
Logistic Regression Result (Germany)
Similar to the Ontario study, we used simulations to compare predicted adoption with historical adoption between 2004 and 2014 (BSW-Solar 2015), because the German FiT program started in August 2004. With the assumption that only households purchased FiT contracts, the historical adoption was scaled to the agent population size, i.e., 13,250 agents. Environment variables such as FiT, PV prices, battery prices, and price of electricity were replicated based on historical data during the simulated years (BDEW 2015b; Wirth and Schneider 2015; BDEW 2015a).
Base Case: This is the scenario where current market trends continue. We vary the environment variables based on best-fit extrapolations (Pescia et al. 2015; Energiewende 2015; AECOM 2015). As with Ontario, we reduce the FiT at a linear rate towards a price of 0.0/kWh in 2025
Reduced price of PV systems (compared to the base case)
Increased electricity (kWh) price by a ratio of 2.4:1 (compared 1.6:1 to the base case)
Reduced battery price (compared to the base case)
The highest rate of adoption – 28% – is when electricity price is increased and PV prices are simultaneously reduced. In addition, we find that increasing the price of electricity has the most significant impact of PV adoption. Based on our findings, we expect the ownership of PV-battery systems to continue to increase in the long term, particularly with self-consumption of PV electricity becoming a more attractive option for households.
We now compare the results from both jurisdictions. While these results are suggestive, we caution that they are each dependent on numerous modeling assumptions. We therefore have made an attempt to only draw conclusions that appear to be robust to modeling errors. First, in comparing the penetration of solar PV systems in Ontario and Germany, we must keep in mind that they are at already at different stages of PV adoption. Specifically, in January 2015 the household penetration of solar PV systems in Ontario was about 0.4% while that in Germany was over 3.5%, about an order of magnitude greater. This difference in the phase of penetration results in the differneces in the adoption decision functions shown in Tables 3 and 4. Note that in these tables, while the payback and stated budget are common to both PV-battery system adoption functions, greenness and social effect are also significant in the decision of German respondents to purchase PV-battery systems, unlike Ontario respondents. Thus, taking the physical environment into consideration when buying solar PV systems seems to correspond to the emphasis on renewable energy in German policies such as the Energiewende (Pescia et al. 2015).
Second, our simulation results indicate that in the Ontario base case, we can expect a steady increase over the entire time period (Fig. 10). In contrast, in the German base case, we predict a plateau in adoption for the first six years, followed by an increase; the plateau phase ends around 2019 when PV prices are sufficiently low and electricity prices are expected to be high (Fig. 21). We believe that one of the policies suggested in this paper would reduce the duration of the plateau. For example, a greater rate of increase in electricity prices would cause the plateau to end about a year sooner.
Finally, of the set of polices that we studied, reducing the price of PV systems appears to result in the highest increase adoption of PV systems in Ontario, while increasing the price of electricity in Germany results in the highest level of adoption. We attribute this difference to the fact that the price of electricity in Germany is relatively higher, so that further increasing the electricity price may be the best way to further improving adoption there.
We present an ABM-based approach to model and forecast PV-battery adoption and usage, with case studies in both Ontario and Germany. Different populations adopt PV-battery systems differently, based on local economic variables as well as non-economic factors such as self-perceived ‘greenness.’ Thus, it is important to understand the population and evaluating existing adoption dynamics before suggesting new policy prescriptions. We have been diligent in selecting appropriate data sources to model each jurisdiction. Moreover, ABM parameters, such as the purchase decision function, are determined by conducting surveys in the target populations, hence the expectation to accurately reflect biases in the population. With this ABM-based approach, the adoption and usage of PV-battery systems can be estimated before policies are actually implemented.
We used historical adoption patterns to both choose a free model variable (the adoption threshold) as well as to validate the accuracy of our model. With the proper selection of ABM parameters, we find that our models are able to model historical adoption to a reasonable degree of accuracy.
We use our ABMs to simulate the impact of a set of different policy prescriptions in both jurisdictions. While we caution that our models are only approximate, it appears that in Germany, ‘greenness’ (i.e., concern for the environment) plays a role in the decision to purchase a PV system, unlike Ontario. Based on this difference, as well as differences in the number of existing solar installations, grid electricity price, and cost of PV systems in both jurisdictions, we find that different policies bring about the most significant increase in adoption. Specifically, reducing PV prices appear to have the most significant impact on adoption in Ontario while increasing the price of electricity would appear to have the most significant impact in Germany.
We also found that policy prescriptions can indeed play a significant role in the adoption of battery systems in both jurisdictions. Without any intervention, there is insignificant adoption of battery systems in both jurisdictions until 2021 or 2022. However, by providing tax credits or discounts for battery systems, or by increasing the price of grid electricity, these systems could be made more desirable.
To conclude, we believe that ABMs, when properly calibrated, are a useful and pragmatic approach to evaluate the impact of potential policy prescriptions in different jurisdictions. We have used this approach to compare the impact of impact of different policies in both Ontario and Germany, finding specific policies that can be used to significant improve adoption in both jurisdictions.
Due to confidentiality requirements, these sources cannot be named
Prices listed in this study are in Canadian Dollars, unless stated otherwise
Ancillary charges, such as delivery and clean energy charges, constitute a significant part of the electricity bill in Canada. It is unclear how these charges are estimated. Consequently, we excluded these charges from our electricity bill calculations.
Ridge regression allows feature selection even in the presence of correlated features.
Please note that in order to emphasize the difference between various policies, we have chosen to use different Y-axis scales in our results.
This work was supported by Cisco Systems Canada and the Canadian Natural Sciences and Engineering Research Council under a Cooperative Research and Development grant and has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 713864 (ELECTRIFIC).
Availability of data and materials
Please contact the authors to obtain anonymized survey data and source code for the ABM models.
AA and AA were responsible for conducting the survey, carrying out simulations, and reporting on the results. They also wrote the first draft of the paper. SK and HdM provided research direction, supervision, and funding. They also helped to write the final version of the paper. All authors read and approved the final manuscript.
We do not have competing interests in the research presented in this paper.
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