An Optimal Energy Production Problem with Energy Source Switching and Load Following Nuclear Power Plants

Battle Count: 62

The paper is primarily about energy production optimization and electricity market design rather than financial trading. However, it has indirect relevance: (1) the open-economy price-taker/price-maker framework involves electricity price dynamics driven by residual demand, which is relevant for electricity futures and derivatives trading; (2) the merit-order price model with three price levels (renewable/nuclear/fossil) captures key electricity market microstructure; (3) the stochastic control and dynamic programming techniques are transferable to optimal execution and market-making problems; (4) understanding nuclear load-following behavior informs supply-side modeling for electricity price forecasting. The paper does not address trading strategies, portfolio construction, or risk management in a financial sense.

High complexity due to: (1) multi-dimensional state space (2D for closed economy, 3D for open economy) requiring grid-based PDE solutions; (2) system of coupled HJB quasi-variational inequalities with interconnected obstacles; (3) viscosity solution theory for rigorous characterization; (4) semi-Lagrangian scheme with Euler-Maruyama discretization, 2^d-point stencil, and monotone interpolation; (5) fixed-point iteration for the switching sub-problem at each time step; (6) regularization of discontinuous drift and price functions; (7) backward recursion over time with regime-dependent continuation values. The Matlab code is provided, but understanding and extending the numerical scheme requires expertise in stochastic control, PDE theory, and numerical analysis.

Matlab code is publicly available on GitHub (https://github.com/fabioBaschetti/OSNPP). All model parameters are explicitly stated. Residual demand data is sourced from Terna's publicly available Download Center (Italian market, 15-minute frequency, 2024-2025). The estimation procedure (OLS on AR(1) discretization of OU process) is fully described in Appendix B. However, nuclear operating parameters are stylized/normalized rather than calibrated to specific plant data, and the regularization parameter K for the smooth approximation is not explicitly set in the numerical experiments.