Accuracy of progress ratios determined from experience curves: the case of photovoltaic technology development

Abstract

Learning curves are extensively used in policy and scenario studies. Progress ratios (PRs) are derived from historical data and are used for forecasting cost development of many technologies, including photovoltaics (PV). Forecasts are highly sensitive to uncertainties in the PR. A PR usually is determined together with the coefficient of determination R2, which should approach unity for a good fit of the available data. Although the R2 is instructive, we recommend using the error in the PR determined from the fit because it is a direct measure of the range in PR values that is recommended to be used in sensitivity analyses within scenario studies. We present a simple equation to calculate the error in PR from the fit parameters. In the case of crystalline PV module technology development we find a PR = 0·794 ± 0·003 by fitting price data of the period 1976-2006. A moving average approach with a 10-year time window shows that PR varies from 0·818 ± 0·017 up to a starting year of 1987, and is reduced considerably to a minimum value of 0·704 ± 0·014 for the starting year 1991. For the most recent starting year 1997, the average PR is considerably higher at 0·884 ± 0·022, highlighting the recent silicon feedstock supply problem. When available, error in individual data points can be used to perform weighted fits in order to decrease fitting errors. To illustrate this approach, an analysis of Dutch PV system price development over the period 1992-2002 shows that PR is 0·876 ± 0·010, where the error is decreased with respect to unweighted fitting. The PR = 0·794 has been used to analyze the cost targets stated in the Strategic Research Agenda as formulated by the European PV Technology Platform for the years 2013, 2020 and 2030. Assuming that such a PR is maintained, it is concluded that these targets may be attained at sustained annual growth rates of 21-42%, which seems feasible.