(489b) Optimal Control of Concentrating Solar Power Plants By Utilizing Stochastic Differential Equation Model of Solar Radiance

With the threat of climate change ever-increasing, there is a growing demand for carbon-neutral energy production system that does not rely on fossil fuels. One such approach is the Concentrating Solar Power (CSP) plant, which utilizes mirrors or lenses to directly concentrate solar radiation. The collected heat energy is used to heat a fluid which can be transported to further application. In particular, the CSP often cooperates with the thermal energy storage (TES) system to re-used the energy at a later time.

As the source of energy for the CSP plant is solar power, its productivity is heavily dependent on the stochastic dynamics of available solar radiance. Therefore, accurately predicting and reflecting the solar radiance dynamics is a major challenge in evaluating the economic benefits and optimizing plant operation. To date, different levels of stochastic models have been used to reflect these effects, such as using linear stochastic processes, scenario-based, machine learning-based approaches, and functional principal component analysis methods. Furthermore, the optimization and scheduling methods also vary depending on the specific stochastic model, like various approximate dynamic programming, real-time optimization, and economic model predictive control.

This study employs a stochastic differential equation (SDE) model to predict the stochastic dynamic of solar radiance to conduct the dynamic optimization and economic analysis of a CSP plant. The use of the SDE model can increase the accuracy in a probability distribution metric and also enables reflection of the variance effect of solar radiance on the expectation of economic benefits, which is not possible with expectation-based models. Both theoretical and quantitative analyses are performed to demonstrate this variance effect. Additionally, dynamic optimization is conducted with full information about the future probability distribution, which can be achieved by transforming the SDE equation into the Fokker-Planck Equation and performing the optimization over the partial differential equations. Then, the control is implemented in a stochastic model predictive control fashion. The advantages of employing the full future probability distribution are highlighted in both expected value and risk evaluations.