  We consider a price-maker company which generates electricity and sells it in
the spot market. The company can increase its level of installed power by
irreversible installations of solar panels. In absence of the company's
economic activities, the spot electricity price evolves as an
Ornstein-Uhlenbeck process, and therefore it has a mean-reverting behavior. The
current level of the company's installed power has a permanent impact on the
electricity price and affects its mean-reversion level. The company aims at
maximizing the total expected profits from selling electricity in the market,
net of the total expected proportional costs of installation. This problem is
modeled as a two-dimensional degenerate singular stochastic control problem in
which the installation strategy is identified as the company's control
variable. We follow a guess-and-verify approach to solve the problem. We find
that the optimal installation strategy is triggered by a curve which separates
the waiting region, where it is not optimal to install additional panels, and
the installation region, where it is. Such a curve depends on the current level
of the company's installed power, and is the unique strictly increasing
function which solves a first-order ordinary differential equation (ODE).
Finally, our study is complemented by a numerical analysis of the dependency of
the optimal installation strategy on the model's parameters.
