Valuation of power plants

In this paper we develop continuous-time stochastic control models for valuation and operation of three stylised types of power plants in an electricity market: a renewable plant, a conventional plant and a storage plant. Examples of these types of power plants are respectively wind turbines, gas-fired generation units and hydroelectric facilities. We demonstrate how to derive analytical or quasi-analytical solutions in spite of many details in modeling. In particular, we model uncertainty in electricity prices and in production input/output when it is relevant for the technology considered. Input/output is assumed to follow a diffusion process, whereas the price process may include jumps. Our models account for special characteristics of the technologies, including a non-Normal distribution of wind speeds as well as start-up and shut-down costs of thermal units. We use our models to assess the impact of conjectured future market conditions such as increasing average price level, price volatility and correlation between renewable production and electricity prices.