Special Issue of EJAM: The Mathematics in Renewable Energy

Abstract

The conversion, storage and distribution of energy from renewable sources drive some of the most inno-vative technologies with the goal to meet global energy demands and to mitigate climate change. For instance, research in photovoltaics, which combines materials science, device modelling and optics, has seen intensive growth in all areas and on all relevant scales during the past decades. The role of mathematics has been key to understand and develop novel optimised photovoltaic devices. However, while the global cumulative solar capacity is growing fast, the temporal variability of photovoltaic or wind-generated electricity from intra-day to seasonal scales constitutes a major obstacle for matching demand. Energy storage plays a major role in addressing this problem, for example via large-scale stationary battery systems, or photochemical hydrogen production. Most importantly, the growing complexity of power distribution across coupled distribution grids constitutes perhaps the hardest current challenge. Apart from setting up the infrastructure, monitoring and planning, these increasingly complex networks pose difficult mathematical problems, relating to fluctuations in coupled energy networks, that are also impacted by market regulations. The focus of research articles in this special issue of the European Journal of Applied Mathematics presents some of the mathematical challenges encountered in the prediction of power grid responses on different temporal and spatial scales and to various types of disturbances. In particular, contributions to the special issue report findings on coupled energy networks composed of gas and electric power networks of realistic size, that are coupled to stochastic fluctuations due to fluctuating demands and supplies. Others address the stability of electrical power grids, develop guiding principles for power grid operation, control and design, and perform case studies on optimisation of energy generation, taking into account sustainability goals for 2050 in Europe, under uncertain future market conditions. In addition, a modelling framework that enables researchers to quantify degradation effects of lithium-ion battery cells and a new approach to model parabolic trough power plants are presented. Such complex problems require a broad spectrum of