Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector
2.1. Description of Photovoltaic-Thermal (PVT) Collector
- The temperature distribution is uniform in the layers.
- It is assumed that there are no heat losses through the edges.
- The optical and thermal properties of the materials and fluids are constant.
- No surrounding shading or dust is taken into account.
- The thermal resistance between the layers is negligible.
- The ambient temperature is equal around the PVT collector.
2.2. Meteorological Data
2.3. Mathematical Model
2.3.1. Numerical Model of PVT for Energy Analysis
2.3.2. Numerical Model for Exergy Analysis
2.3.3. Model Validation
3. Multi-Objective Optimization of PVT Collector
Multi-Objective Optimization Using Gamultiobj Function
Subject to gj(x) ≥ 0, j = 1, 2, …, J;
hk(x) = 0, k = 1, 2, …, K;
xi(L) ≤ x ≤ xi(U), i = 1, 2, …, n;
4. Results and Discussion
4.1. Simulation Results
4.2. Comparison between PVT Collector and Photovoltaic (PV) Panel
4.3. Multi-Objective Optimization
- Electric-driven: the priority is to maximize electricity production within the Pareto optimal;
- Thermal exergy-driven: the priority is to maximize thermal exergy production within the Pareto optimal;
- Trade-off solution: the priority is to produce optimally electricity and thermal exergy within the Pareto optimal front.
- Despite the northern location of Tampere, the similar electric power generation conditions were reached during the summer period than in Strasbourg.
- The monthly electrical efficiency reached 0.4–6.8% higher values in the northern location due to the cooler ambient conditions and lower PV cell operating temperature. However, during the summer months, the electrical efficiency was 13.8% in both locations.
- The annual thermal and electrical energy production and solar gain were 8.4%, 5.8% and 6.2%, respectively, higher in Strasbourg than Tampere. The total annual energy production was 7.7% higher in Strasbourg.
- Based on the exergy analysis, the thermal energy produced in the northern location of Tampere was of “higher quality” because the thermal exergy production in Tampere was 72.9% higher than Strasbourg. However, the total exergy production was 1.27% higher in Strasbourg than Tampere because of 5.8% higher electrical exergy production.
- The climate conditions with high solar irradiation but relatively low temperatures are favorable for thermal exergy production.
- In both locations, the monthly maximum PVT operating temperatures were lower than in the PV panel. The maximum operating temperature of the PVT was around 32–35 °C and of the PV 60–61 °C. The lower operating temperatures resulted in around 1%-unit higher cell efficiency in the PVT compared to the PV panel.
- The electrical output was significantly influenced by the PVT packing factor. The fully packed PVT collector resulted in the 26% higher annual electrical output than the PV panel.
- The PVT collector had a higher electrical output during the summer months compared to the PV panel.
- The annual PVT electrical output is competitive with the PV panel.
Conflicts of Interest
|c||specific heat, J/(kg K)|
|E||DC power, energy, W|
|G||solar irradiation density, W/m2|
|h||heat transfer coefficient, W/(m2 K)|
|k||thermal conductivity, W/(mK)|
|M||number of objectives|
|mass flow rate, kg/s|
|N||number of collectors|
|Q||heat flux, W|
|T||temperature, °C, K|
|T*||reduced temperature, K m2/W|
|U||internal energy, J|
|v||wind speed, m/s|
|W||tube spacing, m|
|β||temperature coefficient, %/K|
|σ||Stefan–Boltzmann constant, W/m2/K4|
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|Property||Glass||Air Gap||PV||Thermal Absorber||Fluid||Insulation||Unit|
|Specific heat (c)||670||-||900||800||3605||670||J/(kgK)|
|Thermal conductivity (k)||1.1||-||140||310||0.615||0.034||W/(mK)|
|Month||Tampere, Average Temperature [°C]||Strasbourg, Average Temperature [°C]|
|Fluid mass flow rate||0.0083 ≤ x(1) ≤ 0.044||kg/s|
|Tin||Inlet temperature||15 ≤ x(2) ≤ 45||°C|
|Hgap||Air gap thickness||0.02 ≤ x(3) ≤ 0.25||m|
|Hi||Insulation thickness||0.015 ≤ x(4) ≤ 0.09||m|
|Production||Strasbourg [kWh/year]||Tampere [kWh/year]|
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Kallio, S.; Siroux, M. Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector. Energies 2020, 13, 5106. https://doi.org/10.3390/en13195106
Kallio S, Siroux M. Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector. Energies. 2020; 13(19):5106. https://doi.org/10.3390/en13195106Chicago/Turabian Style
Kallio, Sonja, and Monica Siroux. 2020. "Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector" Energies 13, no. 19: 5106. https://doi.org/10.3390/en13195106