Leírás
In this talk, we quantitatively study various reserve contracts in an energy balancing context.
Under these contracts, the owner of a storage device, such as a battery, helps smooth fluctuations in electricity demand and supply by using the device to increase either electricity consumption or generated electricity in the network.
We assume that the imbalance process evolves as a stochastic process and the electricity price in the network can be derived from the instantaneous imbalance level. We consider optimal timing of transactions, thus optimal stopping and optimal switching problems from the storage operator's point of view. We obtain analytical solutions in case the imbalance process is a Wiener process, and obtain numerical solutions in case the imbalance process is an Ornstein\textendash Uhlenbeck process.
For the analytical treatment we use the results by Dayanik and Karatzas to characterize the value function as the smallest nonnegative concave majorant of the reward function. For the numerical treatment we use the results by Øksendal and Sulem to characterize the value function as the viscosity solution of the corresponding Hamilton-Jacobi-Bellman Quasi Variational Inequality.
We propose various model extensions such as Jump Added Ornstein\textendash Uhlenbeck processes, exercise decisions contingent on Poisson processes, and also Markovian regime switching underlying processes. Practical interpretations of the results are discussed.
References:
- Dayanik, Savas, and Ioannis Karatzas. "On the optimal stopping problem for one-dimensional diffusions." Stochastic processes and their applications 107.2 (2003): 173-212.
- Øksendal, Bernt, and Agnes Sulem. Stochastic Control of jump diffusions. Springer Berlin Heidelberg, 2005.
- Szabó, Dávid Zoltán, Peter Duck, and Paul Johnson. "Optimal trading of imbalance options for power systems using an energy storage device." European Journal of Operational Research 285.1 (2020): 3-22.
- Szabó, Dávid Zoltán, and Randall Martyr. "Real option valuation of a decremental regulation service provided by electricity storage." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375.2100 (2017): 20160300.