A coupled model of global energy production and ERoEI applied to photovoltaic and wind, an estimation of net production

Abstract

Photovoltaic (PV) and wind energy production modelling essentially follows bottom-up approaches, based on physical considerations. These models focus mostly on the calculation of Energy Return on Energy Invested (ERoEI), while some also present calculation of energy payback time or energy cannibalism, to evaluate the ability of these technologies to handle energy transition. Besides, sigmoïd or S-curve function are often used to fit the production of these industries over time, based on economical considerations, rather than physical ones. This paper aims at coupling net production and ERoEI, using energy conservation and ERoEI definition, to develop a model that could reproduce a S-curve function and allow to investigate the net energy delivered by PV and wind industries. This approach allows to explain the inconsistency which sometimes exists between bottom-up and top-down studies on PV ERoEI calculation. It also explains why the classic relationship between net and gross energy, that is a ratio equal to (ERoEI−1)/ERoEI, does not apply to low carbon energy industries before they reach a steady-state or a quasi-static evolution. As an example, net PV production is still close to zero whereas wind production began to produce a net substantial energy around 2007–2010. It finally allows to investigate how fast the energy transition can physically be to see if a risk of energy disruption exists during that transition, due to fossil fuel depletion.