Optimal reinstallation of photovoltaic panels

Vargiolu Tiziano, University of Padova
Ferrari Giorgio, Center for Mathematical Economics (IMW), Bielefeld University

A large number of power producers own a photovoltaic field, each of maximal nominal capacity S, where panels are subjected to degradation, modeled as a geometric Brownian motion, over time. These producers can reinstall a quantity of panels in order to bring the capacity back to S. Their final aim is maximizing the total revenues of the photovoltaic field net of reinstallation costs, which are assumed to be affine in the additional installation. We first study the related optimal impulse control problem of one single producer when we assume that the electricity price is given, and show that it is optimal to reinstall all the capacity back to S every time that the residual installation goes below a threshold s, which turns out to be the solution of an algebraic equation. This allows to prove asymptotics for the threshold when the installation costs tend to zero, and that the problem with unbounded total capacity (i.e. the case S = +∞) is ill-posed. Then we present the case of a related mean-field game where the electricity price is impacted by the installation of many symmetric producers, each one reinstalling optimally with the strategy seen before.

Area: CS49 - Analytical and numerical methods for energy transition (Tiziano Vargiolu and Athena Picarelli)

Keywords: impulsive stochastic control; photovoltaic production; mean field games; stationary distribution.

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