A stochastic model for the optimal allocation of hydropower flexibility in renewable energy markets

Abstract

This paper considers the revenue maximization problem for a hydropower company. The company can generate excess electricity by releasing water from a reservoir and then sell it to the energy market. On the other hand, the company has an obligation to keep the reservoir level above a pre-determined level, which may require the company to purchase electricity in order to fulfill the customers’ power demand. The electricity price and reservoir level are both represented by diffusion processes. We refer to a one-factor diffusion model for electricity price, which is known to fit the data well. After applying Bellman dynamic programming principle, we derive the associated state-constrained Hamilton-Jacobi-Bellman (HJB) equation to characterize the value function. Then we prove that the value function is the viscosity solution of the state-constrained HJB equation and it is unique in this constrained optimization problem.

Keywords:

• Stochastic control
• hydropower flexibility
• renewable energy market
• one-factor diffusion
• Hamilton-Jacobi-Bellman equation
• viscosity solution

MATHEMATICS SUBJECT CLASSIFICATION:

• 91B02
• 91B24
• 91B70
• 91B74
• 91B76
• 91G80
• 93E20

Acknowledgments

We would like to thank Bonneville Power Administration (BPA) for the funding support on the research project (TIP342). We additionally thank the anonymous reviewers for their comments which have greatly improved the quality of the exposition.