# Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector

^{*}

## Abstract

**:**

## 1. Introduction

^{2}and from the PV 194.79 kWh/m

^{2}. The PV cell operating temperatures were lower in the PVT over a year. In their study, the PV panel had a higher rated power than the PVT collector. However, a numerical comparison between the PVT and PV is required to find out the impact of different PVT variables, such as the mass flow rate, packing factor and inlet temperature, on the comparison.

## 2. Methodology

#### 2.1. Description of Photovoltaic-Thermal (PVT) Collector

_{STC}) of 17.3% at the reference operating temperature (T

_{ref}) of 25 °C. The packing factor (r

_{c}) and the temperature coefficient (β

_{T}) are 0.804 and 0.405%/K, respectively. The diameter of the tubes is 9 mm, and the number is 10. The tilt angle of the PVT collector is 30°, which is only used to estimate transmittance of the cover glass in this study. Regarding to [14] the influence of the tilt angle on the transmittance is irrelevant. The inlet temperature of the water-glycol coolant fluid is 20 °C. Table 1 summarizes the main geometrical, thermo-physical, optical properties and the parameters of the PVT collector used in the simulation and analyses.

- 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}than in Strasbourg.

#### 2.3. Mathematical Model

#### 2.3.1. Numerical Model of PVT for Energy Analysis

_{g-e,CV}) and radiative losses (Q

_{g-e,RD}). On the other hand, there is the convective and radiative heat transfer from the glass to the PV layer in the air gap (Q

_{g-pv,CV}and Q

_{g-pv,RD}) and heat absorbed by the glass Q

_{g}[13].

_{g-e,CV}) is expressed through the correlation proposed by [28] and is widely used for numerical PVT models. The correlation covers the wind speed from 0 to 10 m/s.

_{g-e,RD}) is calculated based on the emissivity of glass (ε

_{g}), the Stefan–Boltzmann constant (σ = 5.67 × 10

^{−8}W/m

^{2}/K

^{4}) and the equivalent radiative temperature of the sky (T

_{sky}). The temperature of the sky can be calculated as a linear function of the ambient temperature and the sky cloud coverage in octaves (N) [25]. If clear sky conditions are assumed or there is no data available on the cloud coverage, Equation (5) can be further simplified to Equation (6), with less than 1% effect on the thermal and electrical output of the system [29,30].

_{g-pv,CV}) takes into account the convective heat transfer in the air gap.

_{gap}and k

_{air}are the thickness of the air gap between glazing and PV layer and thermal conductivity of air, respectively. The radiative coefficient between the glass and the PV panel (h

_{g-pv,RD}) is expressed below:

_{pv−g,CV}and Q

_{pv−g,RD}) from the glass layer, the conductive heat transfer to the absorber layer (Q

_{pv−a,CD}) through the adhesive layer and the conductive heat transfer through the adhesive layer to the tube at the tube bonding position, the heat absorbed by the PV layer (Q

_{pv}), and electricity production (E).

_{pv}is the effective absorbance. In Equation (9):

_{pv}, which causes a reduction of the electrical efficiency of the PV cell. Due to this, the electrical efficiency of the PV depends linearly on the temperature T

_{pv}, the temperature coefficient β

_{PV}and on the efficiency at standard conditions T

_{ref}. The efficiency is calculated according to the following relation:

_{a−pv,CD}), the heat transfer to the fluid (Q

_{a−f}) and the heat loss to the exterior through the insulation (Q

_{a−e,CD}).

_{a−pv,CD}) is the same as in Equation (10).

_{t-a,CD}), PV layer (Q

_{t-pv,CD}), insulation (Q

_{t-i,CD}) and the coolant fluid (Q

_{t-f}).

_{f−t}) and the heat accumulated by the fluid (Q

_{f}) as follows:

_{t-f}) is calculated in Equation (24). T

_{f}is the mean temperature of the fluid. The mass flow rate of the fluid in the channels is $\text{}\dot{\mathrm{m}}$ (kg/s) and T

_{f,in}and T

_{f,out}are the inlet and outlet temperatures of the fluid, respectively.

#### 2.3.2. Numerical Model for Exergy Analysis

_{in}) comes from solar irradiation. However, solar irradiation is not seen as pure exergy and due to this a conversation coefficient is included in the calculation of the PVT incoming exergy [10]:

_{sol}is the solar temperature and T

_{0}is the reference temperature which according to the literature should be a constant, for example, T

_{0}= 20 °C, T

_{0}= 25 °C or the average temperature of the month. In this study, the monthly average outdoor temperatures, presented in Section 2.2, were used in the exergy analysis as reference temperatures. N

_{c}is the number of the collectors.

_{th}) and electric (Ex

_{el}) energy are respectively calculated as follows [5]:

_{pv}presents the PV cell efficiency and r is a packing factor which is a ratio of PV cell area to the collector area. By Equations (32)–(34) both thermal (ξ

_{th}) and electrical exergy (ξ

_{el}) efficiencies and the overall exergy efficiency (ξ) of the PVT collector can be calculated as follows:

#### 2.3.3. Model Validation

^{2}, ambient temperature 30 °C and wind speed 1 m/s, and is presented in Figure 5. The model is in good agreement with the experimental data of the reference.

## 3. Multi-Objective Optimization of PVT Collector

#### Multi-Objective Optimization Using Gamultiobj Function

_{m}(x), m = 1, 2, …, M;

Subject to g

_{j}(x) ≥ 0, j = 1, 2, …, J;

h

_{k}(x) = 0, k = 1, 2, …, K;

x

_{i}

^{(L)}≤ x ≤ x

_{i}

^{(U)}, i = 1, 2, …, n;

_{el}and ξ

_{th}are the electrical and thermal exergy efficiencies, respectively.

## 4. Results and Discussion

#### 4.1. Simulation Results

#### 4.2. Comparison between PVT Collector and Photovoltaic (PV) Panel

^{2}and the same reference cell efficiency of 17.3%.

_{c}) of the collector. However, this is not a case in the PV panels that are fully covered with the PV cells. Because of the packing factor, the better cell efficiency in the PVT collector does not always lead to higher electricity production compared to the PV panel.

^{2}in May and in Strasbourg 29.5 kWh/m

^{2}in July. The annual electrical output of the PV panel and base case PVT collector was 142.7 kWh/m

^{2}and 144.4 kWh/m

^{2}, respectively, in Tampere. This result indicates that although the packing factor of the PVT was 80%, 1.2% higher electrical output was reached because of the cooling effect underneath the PV cells. In Strasbourg, the annual electrical output of the base case PVT collector was 1.5% higher than from the PV panel resulting in 152.8 kWh/m

^{2}and 150.5 kWh/m

^{2}electrical energy yield, respectively. In Strasbourg, the annual electrical output of the fully packed PVT collector was 190.2 kWh/m

^{2}, which is 26.4% more electrical output than from the PV panel. In Tampere, the fully packed PVT produced annually 180.1 kWh/m

^{2}, which is 26.2% more electrical output than from the PV panel.

#### 4.3. Multi-Objective Optimization

^{2}, ambient temperature of 16 °C and wind speed of 2 m/s. These conditions present average weather conditions in Tampere and Strasbourg during the best PVT operation months. The selected decision variables of the optimization are discussed in Section 4. The other parameters are presented in Section 2. The relation of the variables to the electrical and thermal exergy efficiencies are shown in Figure 15.

- 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.

^{2}, and the electric-driven PVT design produced 155.1 kWh/m

^{2}, which is 3% more, although the packing factor was 0.8. The annual electrical output of the trade-off design was 149.1 kWh/m

^{2}, which is only 1% less than from the PV panel.

^{2}, which is 4.2% less than from the PV panel. However, the production was not significantly lower than from the PV output if taking into account the beneficial thermal output of the PVT collector as well. Based on the simulation results in Section 4.2, it could be assumed that the fully packed thermal exergy-driven PVT design could produce higher electrical output than the PV panel.

## 5. Conclusions

- 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.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Nomenclature

A | area, m^{2} |

c | specific heat, J/(kg K) |

D | diameter, m |

E | DC power, energy, W |

Ex | exergy, W |

G | solar irradiation density, W/m^{2} |

H | thickness, m |

h | heat transfer coefficient, W/(m^{2} K) |

k | thermal conductivity, W/(mK) |

L | length, m |

M | number of objectives |

m | mass, kg |

$\dot{m}$ | mass flow rate, kg/s |

N | number of collectors |

Nu | Nusselt number |

P | power, W |

Pr | Prandlt number |

Q | heat flux, W |

Re | Reynolds number |

r | packing factor |

T | temperature, °C, K |

T* | reduced temperature, K m^{2}/W |

U | internal energy, J |

v | wind speed, m/s |

W | tube spacing, m |

Greek symbols | |

η | efficiency |

α | absorbance |

(ατ) | effective absorbance |

β | temperature coefficient, %/K |

ε | emissivity |

ξ | exergy efficiency |

τ | transmittance |

ρ | density, kg/m^{3} |

σ | Stefan–Boltzmann constant, W/m^{2}/K^{4} |

Subscripts | |

a | absorber |

adh | adhesive layer |

c | collector |

CD | conduction |

CV | convection |

d | destruction |

e | environment |

el | electrical |

f | fluid |

f_{in} | fluid inlet |

f_{out} | fluid outlet |

g | glass cover |

gap | air gap |

irr | irradiation |

o | outer |

pv | photovoltaic |

PV_{g} | photovoltaic glass |

RD | radiation |

sol | solar |

ted | tedlar layer |

th | thermal |

tot | total |

0 | reference |

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**Figure 1.**The PVT collector: (

**a**) direct flow collector geometry; (

**b**) cross section of the PVT collector [16].

**Figure 2.**Climate conditions during the summer week in Tampere and Strasbourg: (

**a**) solar irradiation; (

**b**) ambient temperature; (

**c**) wind speed.

**Figure 3.**Climate conditions during the winter week in Tampere and Strasbourg: (

**a**) solar irradiation; (

**b**) ambient temperature; (

**c**) wind speed.

**Figure 7.**The electrical exergy efficiency, PVT surface, fluid outlet and ambient temperature during a summer day.

**Figure 9.**Thermal, electrical and overall monthly exergy efficiencies in (

**a**) Tampere and (

**b**) Strasbourg.

**Figure 10.**The PV cell operating temperatures and electrical efficiency (

**a**) in Tampere and (

**b**) in Strasbourg during the three summer days.

**Figure 11.**Monthly maximum PV cell operating temperatures of the PV panel and PVT collector with different packing factors in (

**a**) Tampere and (

**b**) Strasbourg.

**Figure 12.**Monthly electrical output of the PV panel and PVT collector with different packing factors in Tampere, Finland.

**Figure 13.**Monthly electrical output of the PV panel and PVT collector with different packing factors in Strasbourg, France.

**Figure 15.**The sensitivity of the decision variables to electrical and thermal exergy efficiencies: (

**a**) mass flow rate, (

**b**) inlet temperature, (

**c**) air gap thickness and (

**d**) insulation thickness.

**Figure 16.**The Pareto optimal front in the objective space of the electrical and thermal exergy efficiencies.

**Table 1.**The geometrical, thermo-physical and optical properties of the photovoltaic-thermal (PVT) collector.

Property | Glass | Air Gap | PV | Thermal Absorber | Fluid | Insulation | Unit |
---|---|---|---|---|---|---|---|

Emissivity (ε) | 0.88 | - | 0.96 | - | - | - | - |

Absorbance (α) | 0.1 | - | 0.9 | - | - | - | - |

Transmittance (τ) | 0.93 | - | - | - | - | - | - |

Thickness (H) | 0.004 | 0.02 | 0.0002 | 0.0002 | - | 0.015 | m |

Area (A) | 2 | 2 | 1.6 | 2 | - | 2 | m^{2} |

Mass flow | - | - | - | - | 0.044 | - | kg/s |

Density (ρ) | 2200 | - | 2330 | 2702 | 1050 | 20 | kg/m^{3} |

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] |
---|---|---|

January | −6.4 | 2.3 |

February | −6.9 | 3.3 |

March | −2.8 | 7.0 |

April | 3.3 | 11.5 |

May | 9.7 | 15.7 |

June | 14.1 | 19.4 |

July | 16.9 | 20.6 |

August | 15 | 19.8 |

September | 9.8 | 15.8 |

October | 4.6 | 11.3 |

November | −0.6 | 6.5 |

December | −4.5 | 3.3 |

Symbol | Decision Variable | Bounds | Unit |
---|---|---|---|

$\dot{m}$ | Fluid mass flow rate | 0.0083 ≤ x(1) ≤ 0.044 | kg/s |

T_{in} | Inlet temperature | 15 ≤ x(2) ≤ 45 | °C |

H_{gap} | Air gap thickness | 0.02 ≤ x(3) ≤ 0.25 | m |

H_{i} | Insulation thickness | 0.015 ≤ x(4) ≤ 0.09 | m |

Production | Strasbourg [kWh/year] | Tampere [kWh/year] |
---|---|---|

E_{th} | 992.1 | 915.5 |

E_{el} | 305.5 | 288.8 |

E_{in} | 2191.8 | 2064.8 |

Ex_{th} | 17.4 | 30.1 |

Ex_{el} | 305.5 | 288.8 |

Ex_{in} | 2046.2 | 1930 |

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**MDPI and ACS Style**

Kallio, S.; Siroux, M. Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector. *Energies* **2020**, *13*, 5106.
https://doi.org/10.3390/en13195106

**AMA Style**

Kallio S, Siroux M. Energy Analysis and Exergy Optimization of Photovoltaic-Thermal Collector. *Energies*. 2020; 13(19):5106.
https://doi.org/10.3390/en13195106

**Chicago/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