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

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  • Gholaminejad, Tahereh
  • Khaki-Sedigh, Ali

Abstract

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 Almería, 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.

Suggested Citation

  • Gholaminejad, Tahereh & Khaki-Sedigh, Ali, 2022. "Stable deep Koopman model predictive control for solar parabolic-trough collector field," Renewable Energy, Elsevier, vol. 198(C), pages 492-504.
    • Handle: RePEc:eee:renene:v:198:y:2022:i:c:p:492-504
    DOI: 10.1016/j.renene.2022.08.012
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    References listed on IDEAS

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    1. Masero, Eva & Maestre, José M. & Camacho, Eduardo F., 2022. "Market-based clustering of model predictive controllers for maximizing collected energy by parabolic-trough solar collector fields," Applied Energy, Elsevier, vol. 306(PA).
    2. Eduardo F. Camacho & Antonio J. Gallego & Adolfo J. Sanchez & Manuel Berenguel, 2018. "Incremental State-Space Model Predictive Control of a Fresnel Solar Collector Field," Energies, MDPI, vol. 12(1), pages 1-23, December.
    3. Bethany Lusch & J. Nathan Kutz & Steven L. Brunton, 2018. "Deep learning for universal linear embeddings of nonlinear dynamics," Nature Communications, Nature, vol. 9(1), pages 1-10, December.
    4. Lourdes A. Barcia & Rogelio Peon & Juan Díaz & A.M. Pernía & Juan Ángel Martínez, 2017. "Heat Transfer Fluid Temperature Control in a Thermoelectric Solar Power Plant," Energies, MDPI, vol. 10(8), pages 1-11, July.
    5. Ruiz-Moreno, Sara & Frejo, José Ramón D. & Camacho, Eduardo F., 2021. "Model predictive control based on deep learning for solar parabolic-trough plants," Renewable Energy, Elsevier, vol. 180(C), pages 193-202.
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