Intraday renewable electricity trading: advanced modeling and numerical optimal control

• Published in: Journal of mathematics in industry Vol. 10; no. 1; pp. 1 - 17
• Main Authors: Glas, Silke, Kiesel, Rüdiger, Kolkmann, Sven, Kremer, Marcel, Graf von Luckner, Nikolaus, Ostmeier, Lars, Urban, Karsten, Weber, Christoph
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 04.02.2020; Springer Nature B.V; SpringerOpen
• Subjects: Applications of Mathematics; ECMI 2018 - Progress in Industrial Mathematics; Electricity; Hamilton–Jacobi–Bellman equation; Intraday trading; Math. Appl. in Environmental Science; Mathematical analysis; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Numerical optimization; Optimal control; Wind power; 49L99; Hamilton–Jacobi–Bellman equation; 65K10; Numerical optimization; 91G80; Intraday trading
• ISSN: 2190-5983; 2190-5983
• DOI: 10.1186/s13362-020-0071-x

As an extension of (Progress in industrial mathematics at ECMI 2018, pp. 469–475, 2019 ), this paper is concerned with a new mathematical model for intraday electricity trading involving both renewable and conventional generation. The model allows to incorporate market data e.g. for half-spread and immediate price impact. The optimal trading and generation strategy of an agent is derived as the viscosity solution of a second-order Hamilton–Jacobi–Bellman (HJB) equation for which no closed-form solution can be given. We construct a numerical approximation allowing us to use continuous input data. Numerical results for a portfolio consisting of three conventional units and wind power are provided.