International model for diffusion of residential solar power

Eric Williams, Rochester Institute of Technology, 585-475-7211,

Rexon Carvalho, Rochester Institute of Technology,

Matthew Ronnenberg, Rochester Institute of Technology,

Overview

Through subsidies and other mechanisms, governments around the world are active in promoting the adoption of residential photovoltaic (PV) power. Modeling that links policy and economic conditions to PV adoption by households would support decision-making on how to promote PV. This work explores the hypothesis that a unified quantitative model could describe residential PV adoption across multiple countries/regions. We start with a simple model, using net present value as the explanatory variable for the rate of residential PV adoption (MW/million households-year). NPV is calculated from the resident’s perspective, accounting for region specific government subsidies and prices. Analyzing adoption in five regions, California, Hawaii, Germany, Japan and China, there is a surprisingly tight correlation between adoption rate and NPVWhen NPV is negative, the annual adoption rate is small, 5-15 MW/year-household, presumably attributable to a green consumer market. For recent years in California, Germany, Japan, NPV is positive, $1,000-$2,000/kW, with corresponding annual adoption of 15-50 MW/million households. NPV in Hawaii is recently in the $4,800-$5,500/kW range, with much higher annual adoption of 400-590 MW/million households. This pattern, if it is indeed robust, informs subsidy levels needed to reach targeted levels of adoption. As caveats, note that this explanation neglects other variables that contribute to PV adoption and the analysis should be expanded to additional regions and years. This said, we hope that this analysis brings attention to the potential of a sparse adoption model that leverages data over multiple regions and years.

Methods

There is a substantial history of modeling to understand relationships between PV adoption, policy choices and consumer behavior. Modeling frameworks includeBass diffusion models, multivariable regression and agent-based models. Bass and related diffusion models describe penetration rates in terms of regression-determined parameters, e.g.(1) . Regression models have been used to analyze the impacts ofof local environmental, social, economic and political variables on the adoption of residential solar PV (2,3)to identify demographic characteristic that enable the adoption of residential solar PV through third party ownership (4), and spatial adoption patterns (5).Agent-based models of household residential PVadoption often aim to simulate spatially-resolved PV diffusion with explanatory variables such as socio-economic demographics, behavioral motivations, and/or technical advancements, e.g. (6-9). Distinct in this work is construction of a top-down model that directly maps per capita adoption rate to a sparse number of transformed variables, directly tunable with policy.

The idea is to build a sparse model that relates residential PV adoption with variables describing the economic and policy context of a purchase. PV adoption is measured by the capacity (MW) installed divided by the number of detached homes. The latter assumes that most residential PV is installed in single-family residences.

There are many economic, policy and social variables that could play a role in the rate of PV diffusion. In this initial model we consider one only explanatory variable: the Net Present Value as experienced by a resident in a given region in a given year. This variable combines a number of economic and policy variables such as system cost, electricity price and subsidies into one value. The basic equation for the NPV of a residential PV system can be written as

(1)

where y is the year, j is a region. is the investment cost of the PV system, Sj is the direct subsidy. is the electricity production based on solar resources in region j, is the displaced electricity costor the price premium from a Feed-in-Tariff (FIT) program. If the country uses a FIT the equation needs to be adjusted for self-consumption versus export at FIT price and for the economics after the term of the FIT expires.

Drawing on international, national and state level sources, data was collected on residential PV adoption, PV installed system costs, electricity prices, number of detached houses, and subsidy types and levels. Currencies were converted using power purchase parities and inflation rates to constant US$2014. Constrained by availability of data, years treated are 2007-2014 for California, Germany and Japan, 2008-2014 for Hawaii and 2011-2014 for China.

Results

Figure 1 shows 35 data points for annual residential PV adoption and NPV in five regions for different years. Notably, the two variables are tightly correlated. Expressing this correlation as a regression relationship for an exponential, the resulting r-squared is 0.76. Given the many possible variables that influence adoption rates, we were surprised by the explanatory power of NPV over multiple regions, using only two free parameters

While the proposed approach does not explicitly study non-economic factors relating to solar adoption, those factors are implicitly included in the use of empirical adoption rates. To contrast, a purely economic model would suggest that projects with negative NPV would not be chosen, while those with positive NPV would be overwhelmingly adopted. However, Figure 1 illustrates that neither of these is the case – because of other factors, some adoption of rooftop solar occurs at any level of project NPV, with accelerating adoption at higher NPV levels. By using these data in our adoption model, we are accounting for those non-economic factors in consumer decision making.

Conclusions

While the empirical results are promising, additional regions and years ought to be studied to strengthen the empirical base. Additional explanatory variable could be added to improve explanatory power, these could include the measures of knowledge/experience of the PV industry (e.g. scale of PV installation industry), measures of the risk of the investment (e.g. electricity price volatility, FIT term). An appropriately validated model could feed into a policy planning tool that will supporting design of a portfolio of government incentives to promote solar power

References

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