Optimal installation of renewable electricity sources: the case of Italy

Starting from the model in Koch and Vargiolu (SIAM J Control Optim 59(4): 3068–3095, 2021), we test the real impact of current renewable installed power in the electricity price in Italy, and assess how much the renewable installation strategy which was put in place in Italy deviated from the optimal one obtained from the model in the period 2012–2018. To do so, we consider the Ornstein–Uhlenbeck (O–U) process, including an exogenous increasing process influencing the mean-reverting term, which is interpreted as the current renewable installed power. We estimate the parameters of this model by using real data of electricity prices and energy production from photovoltaic and wind power plants from the six main Italian price zones. We obtain that the model fits well the North, Central North and Sardinia zones: among these zones, the North is impacted by photovoltaic production, Sardinia by wind and the Central North does not present significant price impact. Then, we implement the solution of the singular optimal control problem of installing renewable power plants, in order to maximize the profit of selling the produced energy in the market net of installation costs. We extend the results of Koch and Vargiolu (SIAM J Control Optim 59(4): 3068–3095, 2021) to the case when no impact on power price is presented and to the case when N players can produce electricity by installing renewable power plants. To this extent, we analyze both the concepts of Pareto optima and of Nash equilibria. For this latter, we present a verification theorem in the 2-player case and an explicit characterization of a Nash equilibrium in the no-impact case. We are thus able to describe the optimal strategy and compare it with the real installation strategy that was put in place in Italy.