An important issue in various domains of renewable energy is the use of technological improvement trends to project future capabilities of energy technologies. This paper analyzes two pairs of renewable energy technologies and finds that the annual improvement rate of cost/investment is quite different for the four technological domains: namely, solar photovoltaics (PV) (9.0% per year), wind turbines (2.9%), batteries (3.1%) and capacitors (21.1%). While these trends have been reasonably consistent over long time frames, projecting these trends into the future without a better understanding of the underlying causes of the improvements is not at all reliable. This paper establishes theoretical fundamentals for explaining the differences in such rates and a framework for empirically probing such explanations using patent data. Employing this framework, this study collects and analyzes a set of highly representative patents for each of the four domains, allowing measurement of: patenting rates, reliance on scientific literature and other characteristics of the different fields. Our study of the inventions, while not establishing an indisputable causal relationship for the differing rates, establishes a broader theoretical basis for why such rates differ so greatly and why they might be stable over time. Among many possible effects, this study indicates that the age of knowledge utilized in the patents and the percentage of very important inventions in the field are the most likely significant contributors to higher rates of advance.