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

2026-08-10

AI Summary

This study addresses the challenge of optimally dispatching nuclear power units to track stochastic net load and switch operating modes in power systems with high renewable penetration. It formulates the problem, for the first time, as a finite-horizon optimal switching problem with stochastic demand, explicitly incorporating ramping constraints and mode transition costs. The value function is characterized via a Hamilton–Jacobi–Bellman quasi-variational inequality, and the optimal policy is computed using a monotone semi-Lagrangian scheme. The analysis quantifies how factors such as loss-of-load cost, switching cost, ramping capability, and market access influence nuclear flexibility, revealing its distinct economic value in both regulated and liberalized electricity markets. These findings provide theoretical foundations for designing compensation mechanisms and market structures that support low-carbon flexible resources.

Abstract

The integration of weather-dependent renewable generation increases the volatility of residual demand and raises the value of dispatchable low-carbon flexibility. This paper studies the optimal operation of a load-following nuclear power plant owned by a producer that must balance stochastic residual demand while accounting for ramping limits and costly changes in operating regimes. Nuclear output can be increased, decreased, or kept constant, and the production decision is formulated as a finite-horizon optimal switching problem. We analyze both a closed-economy benchmark, where excess production cannot be sold and shortages require costly back-up generation, and an open-economy setting, where the producer can trade electricity at prices driven by aggregate market residual demand. The value functions are characterized as viscosity solutions of a system of Hamilton-Jacobi-Bellman quasi-variational inequalities, and optimal policies are computed using a monotone semi-Lagrangian scheme. The numerical results show how shortage costs, switching costs, ramping capability, and market access shape optimal nuclear load following. The analysis highlights the economic value of controllable low-carbon capacity in renewable-intensive systems and provides implications for flexibility remuneration, balancing-market design, and interconnection policy.

Problem

• load-following nuclear power
• optimal switching
• residual demand
• ramping limits
• dispatchable low-carbon flexibility

Innovation

• optimal switching
• load-following nuclear power
• Hamilton-Jacobi-Bellman quasi-variational inequalities
• viscosity solutions
• semi-Lagrangian scheme