Stable deep Koopman model predictive control for solar parabolic-trough collector field

Concentrated Solar Power plants (CSP) have the energy storage capability to generate electricity when sunlight is scarce. However, due to the highly non-linear dynamics of these systems, a simple linear controller will not be able to overcome the variable dynamics and multiple disturbance sources affecting it. In this paper, a deep Model Predictive Control (MPC) based on the Koopman operator is proposed and applied to control the Heat Transfer Fluid (HTF) temperature of a distributed-parameter model of the ACUREX solar collector field located at Almeria, Spain. The Koopman operator is an infinite-dimensional linear operator that fully captures a system's non-linear dynamics through the linear evolution of functions of the state-space. However, one of the major problems is identifying a Koopman linear model for a non-linear system. Koopman eigenfunctions are involved in converting a non-linear model to a Koopman-based linear model. In this paper, a deep Long Short-Term Memory (LSTM) autoencoder is designed to calculate Koopman eigenfunctions of the solar collector field. The Koopman linear model is then used to design a linear MPC with terminal components to ensure closed-loop stability guarantees. Simulation results are utilized to show the satisfactory tracking performance of the proposed approach.