Modeling and Experimental Validation of a Hybrid Thermal–Photovoltaic Multi-Stage Solar Desalination System

This study extends previous experimental investigations of a hybrid multi-stage solar desalination (MSD) system by developing and experimentally validating a detailed thermo-energetic model of the same installation. The system combines flat-plate thermal solar collectors with a photovoltaic (PV)-powered immersed electrical heater to supplement thermal energy during operation. A transient thermo-energetic model of the basin and eight distillation stages was developed, accounting for conduction, convection, radiation, and evaporation–condensation heat and mass transfer, and solved using the fourth-order Runge–Kutta (RK4) method in Python (version 3.12.11). The model was validated against experimental measurements collected over multiple campaigns and seasons using real brackish well water (TDS > 3 g/L) at Douar El Hamri, eastern Morocco. Quantitative validation yielded mean absolute temperature errors of 2.41 °C in thermal-only operation and 2.42 °C in hybrid operation, with corresponding mean relative errors of 7.10% and 5.00%, respectively. Daily freshwater production reached 45 kg in thermal-only operation and 93 kg in hybrid operation, while the corresponding simulated values were 44.47 and 92.84 kg. The hybrid configuration also reduced the Specific Energy Consumption from 689.15 to 387.20 kWh·m−3 and increased the overall energy efficiency from 61.83% to 63.12% and the exergy efficiency from 8.69% to 10.86%. These results demonstrate that the developed model accurately reproduces the thermal behavior and freshwater production of the experimental system and provides a useful basis for performance assessment, system sizing, and future optimization of hybrid solar desalination systems for water-stressed regions.