Introduction: the mathematics of energy systems

Abstract

The urgent need to decarbonize energy systems gives rise to many challenging areas of interdisciplinary research, bringing together mathematicians, physicists, engineers and economists. Renewable generation, especially wind and solar, is inherently highly variable and difficult to predict. The need to keep power and energy systems balanced on a second-by-second basis gives rise to problems of control and optimization, together with those of the management of liberalized energy markets. On the longer time scales of planning and investment, there are problems of physical and economic design. The papers in the present issue are written by some of the participants in a programme on the mathematics of energy systems which took place at the Isaac Newton Institute for Mathematical Sciences in Cambridge from January to May 2019—see http://www.newton.ac.uk/event/mes . This article is part of the theme issue ‘The mathematics of energy systems’.

From nucleation and coarsening to coalescence in metastable liquids

“…dynamics of the system, the evolving patterns in it, the evolution of polydisperse particulate assemblages as well as the final state and microstructure of the material. Such processes take place in different areas of applied science ranging from condensed matter physics, materials science and geophysics to chemical industry, biophysics and life science [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Secondary frequency control stabilising voltage dynamics

“…The need for good and stable electricity is a current and urgent quest in our society [11, 12]. Electricity is generated by the conversion of a primary source of energy such are mechanical, chemical, nuclear or thermal to electrical energy.…”

Resource pooling in electricity grids: wind, storage and transmission

“…The decarbonisation of electricity networks gives rise to many interesting problems for mathematical scientists, reviewed in [1,2]. Some of the most challenging involve simultaneously game theory, randomness and network constraints.…”

“…1 The analysis of the auctions producing the merit order is in itself an important problem (reviewed in [5]), and a not surprising feature is that a reduction in competition between generators can lead to perverse incentives that substantially reduce overall benefit. 2 Note that the constraints in Figure 1 dynamically fragment the market for generation: when an area cannot get more energy from outside, there are fewer competitors to moderate the bidding strategies of generators located within the area.…”