Pricing Hydroelectric Power Plants with/without Operational Restrictions: a Stochastic Control Approach

Abstract. In this paper, we value hydroelectric power plant cash flows under a stochastic control framework, taking into consideration the implication of operational constraints such as ramping and minimum flow rate constraints for the purpose of environmental protection. The power plant valuation problem under a ramping constraint is characterized as a bounded stochastic control problem, resulting in a Hamilton-Jacobi-Bellman (HJB) partial integrodifferential equation (PIDE). The valuation problem without the ramping restriction is characterized as an unbounded stochastic control problem; we propose an impulse control formulation, resulting in an HJB variational inequality, for the valuation problem under this scenario. We develop a consistent numerical scheme for solving both the HJB PIDE for the bounded control problem and the HJB variational inequality for the unbounded control problem. We prove the convergence of the numerical scheme to the viscosity solution of each pricing equation, provided a strong comparison result holds. Numerical results indicate that failing to consider operational constraints may considerably overestimate the value of hydroelectric power plant cashflows.