Optimal installation of renewable electricity sources: the case of Italy

Abstract

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.

A Principal-Agent Framework for Optimal Incentives in Renewable Investments

“…The recent literature already considers optimal installation of renewable power plants (see, e.g. Koch and Vargiolu (2021), Awerkin and Vargiolu (2021)) as a stochastic control problem of a pricemaker company. Besides, Kharroubi et al (2019) focus on the regulation of renewable resource exploitation assuming a geometric state under drift control only.…”

Optimal Installation of Solar Panels with Price Impact: A Solvable Singular Stochastic Control Problem

“…turns out to be the graph of a function F , which is thus to be found with the help of functional equations which originate from C 2,1 regularity. While in some cases these functional equations are easy and give directly the free boundary F , possibly in terms of integrals to be computed numerically (see, e.g., [1,2,4,13,21] for examples), our functional equation turns out to be an ODE, whose solution cannot be computed analytically but that we prove to admit a unique global solution. (See [5] for an analogous result and also Remark 2.4 for highlights on the differences of methods used there versus ours.)…”

“…This makes the company indifferent to daily or weekly spikes and/or seasonality. 2 On the other hand, time homogeneous Ornstein-Uhlenbeck processes give tractable analytical tools (like known solutions of related ODEs). With the same arguments, we are also neglecting the stochastic and seasonal effects of solar production: in fact, since here we are interested in a long-term optimal behavior, we interpret the average electricity produced in a generic unit of time as proportional to the installed power.…”

“…This can be justified if we interpret our fundamental price to be, for example, a weekly average price as in[2], where a calibration of this model to the Italian power market data is also carried out.Downloaded 09/30/21 to 147.162.22.227 Redistribution subject to SIAM license or copyright; see https://epubs.siam.org/page/terms…”

“…Here, we exploit the result from Step 1 in the proof of Theorem 3.1 in [20] in order to obtain (4). Moreover, (5) follows from (2), and in particular from equation (A-3) with k = 0.…”