Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass
2. Horizon 2020 Project SFERA III
- networking activities to improve the cooperation between the research infrastructures, the scientific community, industries and other stakeholders;
- transnational access activities aiming at providing access to all European researchers from both academia and industry to singular scientific and technological solar research infrastructures;
- joint research activities to improve the infrastructure’s integrated services.
3. Modeling of the Solar Reactor
3.1. Description of the Model
- When no oxygen is injected—DNI is higher than 800 Wm—only the endothermic gasification of biomass occurs, with an enthalpy change kJ mol. This reaction is as follows:
- When oxygen is injected—DNI is lower than 800 —combustion occurs in the cavity along with gasification, with an enthalpy change kJ mol. Combustion of the biomass resource—the reaction is exothermic—can be described as follows:
3.2. Simulation of the Model
3.2.1. Without Oxygen Injection
3.2.2. With Oxygen Injection
4. Control of the Solar Reactor
4.1. Reference (PID/RB) Controller
4.1.1. Adaptive PID Controller for the Oxygen Flow Rate
- is the proportional gain, helping the controller reach the setpoint faster, with the risk of overshooting; a small value will result in an important steady-state error;
- is the integral gain, helping to eliminate the steady-state error; a large value can result in a longer settling time and higher oscillations;
- is the derivative gain, generating a fast response and a stabilizing effect in dynamic regime.
- : The reactor’s aperture is closed () to limit radiative losses, which affects the thermal equilibrium of the system. The PID controller manages the system by injecting a minimum of 0.88 th of oxygen.
- : The reactor’s aperture is open, and the amount of DNI received is not sufficient to maintain the reactor’s temperature without oxygen injection. The PID controller determines the oxygen flow rate allowing to minimize the error between the setpoint and the measured temperature.
- : The excess of DNI forces the PID controller to recommend a minimal oxygen flow rate allowing the reactor to cool down and play on defocusing if the reactor’s temperature is higher than the setpoint.
4.1.2. Rule-Based Controller for the Defocusing Factor
- if and K, ;
- if 800 Wm and K, .
4.2. MPC Controller
4.3. DNI Forecasting
4.3.2. Smart Persistence Forecasts
4.3.3. Image-Based Forecasts
- An HDR image is processed to detect clouds using a segmentation model and estimate their motion with the aim of localizing the part of the image that will interact with the Sun at time . This region is called the region of interest (ROI) in the sequel.
- The cloud fraction (CF) in the ROI () is calculated. is defined as the ratio of the number of cloud pixels to the number of clear-sky pixels in the ROI.
- The model decides if a ramp will occur by analyzing the variation of between two consecutive time steps. If this variation is greater than 3% of the maximum value of , then a ramp is expected. This value is chosen to avoid ramp detection due to noise in the signal. This approach also determines the ramp’s direction, since an increase in indicates a possible decrease in DNI and vice versa.
- The DNI forecast at time is obtained by a persistence (if no ramp is expected) or a persistence to which the ramp magnitude RM is added (if a ramp is expected):
4.3.4. Performance Criteria
- The root mean squared error (RMSE) is calculated as follows:
- The skill factor (SF) is employed to evaluate the models’ performance versus the smart persistence model (a positive skill factor means that the proposed model outperforms the smart persistence model). It is defined as follows:
- The mean average error (MAE) is calculated as follows:
- Finally, a criteria called ramp detection index (RDI) is used . It is designed to evaluate the ability of the model to predict ramps, which have an important impact on CSP plants: predicting them can thus be helpful in the control process. First, the ramp magnitude (RM) is calculated as:Usually, high-magnitude DNI ramps are defined by and moderate DNI ramps are defined by . A ramp detection (also called a hit) is achieved if the two following conditions are satisfied:The chosen value represents ramps with high occurrence probability, thus increasing the challenge of scoring a high RDI by increasing the number of considered ramps in the RDI calculation. The ramp is not detected (a miss) if Equation (20) is met while Equation () is not. Finally, the ramp detection index is calculated as follows:
4.3.5. Forecasting Results
5. Control Results
5.1. Performance Criteria
5.2. Comparative Study
- . This initialization is chosen so that the optimal input found is near 1, which means solar energy is used at its best;
- . This initialization is chosen so that the optimizer converges fast to the optimal solution, which is around . Other initialization values resulted in an increase in computation time and some performance degradation.
5.3. Case Study
6. Computationally-Tractable MPC Controller
6.1. Model Simplification
- for a given reactor’s temperature, is mainly a linear function of the oxygen flow rate (0 th th);
- for a given oxygen flow rate, is a linear function of the reactor’s temperature ().
6.2. MPC Controller with Simplified Reactor Model vs. MPC Controller with Original Reactor Model
6.3. MPC Controller with Simplified Reactor Model vs. Reference Controller
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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|DNI [Wm]||Static Gain [-]||[min]||[min]|
|DNI < 150 Wm||150 Wm ⩽ DNI ⩽ 800 Wm||DNI > 800 Wm|
|1.6 × 10||3.4 × 10||1.5 × 10|
|0||9.0 × 10||1.5 × 10|
|1.2 × 10||2.5 × 10||1.0 × 10|
|H [min]||Time Support (Observations)||LSTM Layers (Units)||Fully Connected Layers (Units)|
|Prediction Horizon of the MPC Controller [min]|
|Prediction Horizon of the MPC Controller (min)|
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Karout, Y.; Curcio, A.; Eynard, J.; Thil, S.; Rodat, S.; Abanades, S.; Vuillerme, V.; Grieu, S. Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass. Clean Technol. 2023, 5, 329-351. https://doi.org/10.3390/cleantechnol5010018
Karout Y, Curcio A, Eynard J, Thil S, Rodat S, Abanades S, Vuillerme V, Grieu S. Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass. Clean Technologies. 2023; 5(1):329-351. https://doi.org/10.3390/cleantechnol5010018Chicago/Turabian Style
Karout, Youssef, Axel Curcio, Julien Eynard, Stéphane Thil, Sylvain Rodat, Stéphane Abanades, Valéry Vuillerme, and Stéphane Grieu. 2023. "Model-Based Predictive Control of a Solar Hybrid Thermochemical Reactor for High-Temperature Steam Gasification of Biomass" Clean Technologies 5, no. 1: 329-351. https://doi.org/10.3390/cleantechnol5010018