# Thermal and Performance Analysis of a Photovoltaic Module with an Integrated Energy Storage System

^{1}

^{2}

^{*}

## Abstract

**:**

_{4}) flat batteries, which constitutes a generation-storage PV unit. The batteries were surface-mounted on the back side of the PV module, distant from the PV backsheet, without exceeding the PV frame size. An additional low-emissivity sheet was introduced to shield the batteries from the backsheet thermal irradiance. The challenge addressed in this paper is to evaluate the PV cell temperature increase, due to the reduced thermal exchanges on the back of the module, and to estimate the temperature of the batteries, verifying their thermal constraints. Two one-dimensional (1D) thermal models, numerically implemented by using the thermal library of Simulink-Matlab accounting for all the heat exchanges, are here proposed: one related to the original PV module, the other related to the portion of the area of the PV module in correspondence of the proposed energy-storage system. Convective and radiative coefficients were then calculated in relation to different configurations and ambient conditions. The model validation has been carried out considering the PV module to be at the nominal operating cell temperature (NOCT), and by specific experimental measurements with a thermographic camera. Finally, appropriate models were used to evaluate the increasing cell batteries temperature in different environmental conditions.

## 1. Introduction

_{4}) flat batteries for energy storage (typical thickness less than 1 cm), connected in series. The batteries were surface-mounted on the back side of the PV module by an aluminum-bar structure which keeps the batteries distant from the PV backsheet without exceeding the PV frame size (typical air-gap was about 2 cm). Thus, the battery disposition didn’t exceed the original PV size, but allowed natural air cooling of the backsheet. An additional low-emissivity, aluminum sheet was introduced to shield the batteries from the backsheet irradiance, in consideration of the usual maximum temperature limit of the batteries (50–55 °C). This paper is aimed at evaluating the PV cell temperature increase due to the reduced thermal exchanges on the back PV side, and to estimate battery temperature in order to verify their thermal limits. A PV model based on material, environmental parameters, and electro-thermal characteristics, was developed, taking into account the energy balance. The entire solar radiation incident on PV module was converted into electrical and heat energy. Consequently, excessive heat and thermal stress can result in cell fault and/or energy losses [8]. Two one-dimensional (1D) thermal models accounting for all the heat exchanges are proposed. The first one concerns the original (commercial) PV module, the second one is related to the PV module with the proposed energy-storage system mounted on the back side. Convective and radiative coefficients were calculated in relation to different configurations and environmental conditions. The considered models were numerically implemented using the thermal library of Simulink-Matlab. The model validation were carried out by the PV module normal operating cell temperature(NOCT) given by the manufacturer, and by specific experimental measurements on the real PV module, including thermographic camera images, with and without the proposed BESS.

## 2. Thermal Model of a Single PV Module

#### 2.1. Models

_{n}is the specific radiation incident on the module’s surface (W/m

^{2}); G

_{n}must be multiplied by the area of the PV module A (m

^{2}) in order to get the total incident power. P

_{pv}(W) is the electrical power generation, proportional to the total incident power, and η is the photovoltaic conversion efficiency. G

_{rif}is the total radiative power reflected from the surface of the PV module that is proportional to the reflection index ρ.

_{conv}and radiative Q

_{rad}exchanges of the front (f) and back (b) sides of the PV module with the surrounding environment.

^{4}). The aluminum plate acted as a thermal shield, reducing overheating of the batteries. However, the IR rays reflected from the backsheet increased the temperature of the PV module. In addition, the presence of batteries led to a restriction in the convective heat exchange, even though air circulation was still possible through the airgap (i.e., almost 2 cm).

- One-dimensional (1D) thermal models.
- Isothermal surface was approximated as a flux node, so edge effects were neglected.
- Negligible thermal capacitances [10].
- Material properties of PV module layers were constant, as shown in Table 1.
- PV cell temperature was considered uniform due to the higher value of its thermal conductivity (k) compared to any of the other layers.
- Apparent sky temperature T
_{s}was calculated according to [11]:$${T}_{s}={T}_{a}-\delta T$$_{a}is the air temperature and δT is the variation depending on atmospheric conditions. - Ground temperature (on the back side of the PV module) was equal to air temperature (T
_{g}= T_{a}). - Convective heat exchange coefficients were evaluated with empirical formulations and it was assumed that wind flowed around the module, both front and back sides [12].
- Reflection (ρ), transmission (τ), and absorption (α) coefficients were independent from temperature.
- Internal reflection phenomena between the layers of PV module were neglected.
- Emissivity of surfaces were independent from temperature and wavelength, values are given in Table 2.
- According to the radiative heat transfer, the view factor was assumed to be unity. With this approximation, the front surface of PV module saw only the sky, whereas the back surface saw only the ground. Radiative heat exchange coefficients were simplified by this assumption.
- All surfaces had the same area A of the PV module: A = 1.31 m
^{2}in the case study. - Batteries did not produce any heat flow while charging or discharging (battery losses were neglected).

#### 2.2. Thermal Balance Equations

_{1}, G

_{2}, G

_{3}, and G

_{4}) on the basis of absorption and transmission coefficients. The summary of these thermal balances can be expressed as:

_{cond,al+batt}is the conductive heat transfer between the battery layer and aluminum sheet.

#### 2.3. Convective and Radiative Coefficients

_{conv}[W/(m

^{2}K)] the convective coefficient, A the exchange area (m

^{2}), ΔT the difference between two surfaces at different temperatures, L the characteristic length of the geometry of the PV module (area/perimeter), k the thermal conductivity of the fluid for a reference temperature [W/(m K)], and Nu the dimensionless Nusselt number. In addition to the Nusselt number, the following numbers are helpful in order to determine the heat transfer:

^{2}/s); thermal diffusivity α (m

^{2}/s); gravity acceleration g (m/s

^{2}); isobaric compression ratio β (1/K); temperature difference ΔT, and wind speed u (m/s). All these thermal properties are evaluated at the reference temperature T

_{ref}= (T

_{a}+ T

_{w})/2, where T

_{a}is the air temperature (i.e., the fluid that is surrounding the PV module) and T

_{w}is temperature of the surface under consideration (K).

_{cr}= 10

^{9}, Re

_{cr}= 10

^{5}, Gr

_{cr}= 10

^{9}. Measurements were taken when the wind speed was not too high, so Reynolds number was usually Re < Re

_{cr}. In this way Nusselt number for forced convection is empirically calculated as [14]:

^{2}) is calculated and, according to Gr/Re

^{2}, evaluates the nature of convection: natural, forced or mixed [14]: Gr/Re

^{2}~ 1 means mixed convection; Gr/Re

^{2}>> 1 natural convection; Gr/Re

^{2}<< 1 forced convection. In the case that convection is mixed and the flows of natural and forced convection are in opposition, the largest Nu is considered to be the proper value. In the case that the flows in mixed convection are not in opposition, Nu is considered as:

_{b}is the temperature of the backsheet, and T

_{batt-b}is the temperature of the battery, L

_{1}and L

_{2}are the dimensions of the first and the second plane, respectively.

_{w}* (K) is the average temperature of the plates. The Nu number can be evaluated considering the case of two opened planes surrounded by air, as follows [14]:

_{a}, backsheet temperature T

_{b}, and battery temperature T

_{batt-b}are taken into account. It should be considered that the critical value of the Ra number has never reached (Ra < Ra

_{cr}= 10

^{5}), which justifies the validity of this approach.

_{rad}) is simplified by considering parallel planar bodies with the same area (A), and the radiative heat coefficient (h

_{rad}) is calculated with reference to the unity view factor (i.e., F

_{12}= 1), leading to:

_{1}and T

_{2}are the surface temperatures (K), ε

_{1}and ε

_{2}are the corresponding emissivity coefficients, and σ is the Stephan-Boltzmann constant [5.67 × 10

^{−8}W/(m

^{2}K

^{4})]. Equation (13) is used to evaluate all the radiative exchanges, i.e., sky-PV front side, backsheet-ground, backsheet-aluminum plate, battery-ground, considering the corresponding areas.

## 3. Models Results and Measurements

#### 3.1. Simulink Thermal Models

_{a}, T

_{s}and T

_{g}were set by thermal blocks as ideal temperature sources. Thermal fluxes through the different layers (G

_{1}, G

_{2}, G

_{3}and G

_{4}) were modeled by ideal heat flux sources. All the heat exchanges were modeled according to the previous sections, properly setting the parameters. Temperatures of the different thermal nodes were detected and displayed by ideal temperature sensors.

#### 3.2. Thermal Model Validation

^{2}; tilt angle of PV module 45°. In the case study, NOCT = 46 °C (the temperature-power coefficientis−0.52%/°C). The corresponding PV cell temperature obtained by the Simulink thermal model (without storage batteries) was ≈45 °C, with an acceptable matching.

_{f}, T

_{b}, T

_{batt-b}, T

_{batt-g}) were properly averaged, and compared to the corresponding temperatures obtained by the thermal model. In general, the matching was satisfactory in the areas without the batteries, the difference in temperature being in the order of 1 °C. In the areas occupied by the batteries the difference was in the order of 3 °C. The difference was greater in the model with the batteries, but it was still somewhat acceptable, considering that all the edge effects were neglected in the 1D thermal model.

_{a}and G

_{n}were typical for the given month. In this case, again, the matching was satisfactory with the difference of temperature being within 1 °C.

## 4. Temperature Extrapolation

_{a}and G

_{n}) corresponding to the average temperature for each month of the year, at the solar midday. Specifically, the reference conditions are in accordance with an installation of Bologna, Italy (latitude 44°30′, tilt angle of PV modules 30°). Concurrently, the temperature of the batteries was determined in order to verify the restrictions given by the manufacturer. Thermal powers G

_{1}, G

_{2}, G

_{3}and G

_{4}were calculated according to Equation (3). Wind speed was set to 1 m/s for both the front to back sides of PV module (i.e., mixed convection).

_{pv}= 0). In particular, for the commercial PV model (without batteries) T

_{f}, T

_{c,pv}, and T

_{b}represent the front, PV cell, and back temperatures, according to Figure 3. The same temperatures are shown for the two relevant regions of the modified PV module with integrated energy storage: the area covered by the batteries, and the remaining area (not covered by batteries). In this case, the average PV cell temperature T

_{c,pv+batt}was calculated as the weighted average of T

_{c,pv}in the two regions, with respect to the size of the corresponding areas. The temperatures of the batteries were considered as well, both of the backsheet and the ground side (T

_{batt-b}and T

_{batt-g}), according to Figure 3. In the end, the over-temperature ΔT was calculated to illuminate the difference in PV cell temperatures between the original commercial PV module and the modified one with the integrated energy storage.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Heat exchanges of PV module: (

**a**) without battery storage system; (

**b**) with storage battery system. G

_{n}is the specific radiation incident on the module’s surface (W/m

^{2}); P

_{pv}(W) is the electrical power generation, proportional to the total incident power; η is the photovoltaic conversion efficiency; G

_{rif}is the total radiative power reflected from the surface of the PV module that is proportional to the reflection index ρ.

**Figure 3.**Battery and PV module layers. T is temperature; b is backsheet; e is ethylene vinyl acetate (EVA); f is front side; g is ground and batt is battery.

**Figure 4.**Natural convection between plane plates (i.e., backsheet and battery). d is the distance between the PV unit and the battery; T

_{b}is the temperature of backsheet; and T

_{batt-b}is the temperature of the battery; Ta is the temperature of the air; L

_{1}and L

_{2}are the dimensions of the first and the second plane, respectively.

**Figure 6.**Thermal (

**left**) and visual (

**right**) images of the PV modules with and without the battery storage system for ambient conditions T

_{a}≅ 8 °C and G

_{n}≅ 600 W/m

^{2}.

**Figure 7.**Thermal images of front and back sides of the PV modules, with and without the battery storage system for ambient conditions T

_{a}≅ 15 °C and G

_{n}≅ 900 W/m

^{2}.

**Figure 8.**Visual and thermal images of the PV modules: without (

**left**) and with (

**center**) the battery storage system, and with covered backsheet (

**right**), for ambient conditions T

_{a}≅ 24 °C and G

_{n}≅ 800 W/m

^{2}.

**Figure 9.**Back side view details of PV modules: (

**a**) thermal image with and without battery storage system; (

**b**) visual picture of the installed battery and layout.

**Figure 10.**Estimation of the power from the PV module with integrated storage batteries in % compared to the original PV module without batteries, corresponding to Table 4.

**Figure 11.**Average PV cells temperature profile over the day (April 15) with and without integrated storage batteries, and corresponding air temperature (T

_{a}) and sun irradiance (G

_{n}).

**Table 1.**Thickness (s), thermal conductivity (k), and optical coefficients (ρ, τ, α) of the PV module layers.

Layer’s Material | s [mm] | k [W/(m·K)] | ρ | τ | α |
---|---|---|---|---|---|

Glass | 4.0 | 1.8 | 0.1 | 0.88 | 0.02 |

Ethylene Vinyl Acetate (EVA) | 0.4 | 0.35 | - | 0.97 | 0.03 |

Silicon PV cell | 0.4 | 150 | - | - | 1 |

Backsheet | 0.3 | 0.3 | - | - | 1 |

ε | |
---|---|

PV module front surface (glass) (f) | 0.91 |

PV module back surface (backsheet) (b) | 0.85 |

Sky | 0.91 |

Ground | 0.94 |

Polished aluminum plates | 0.04 |

Commercial PV Module | Modified PV Module with Integrated Energy Sotrage | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

°C | W/m^{2} | Without Batteries (°C) | Area Covered by Batteries (°C) | Area Not Covered by Batt. (°C) | avg (°C) | (°C) | |||||||||

T_{a} | G_{n} | T_{f} | T_{c,pv} | T_{b} | T_{f} | T_{c} | T_{b} | T_{batt-b} | T_{batt-g} | T_{f} | T_{c} | T_{b} | T_{c,pv+batt} | ΔT | |

January | 2.9 | 741 | 26.6 | 27.7 | 27.2 | 42.6 | 44.6 | 44.5 | 9.3 | 9.3 | 33.9 | 35.4 | 35.1 | 38.9 | 11.2 |

February | 5.8 | 869 | 33.4 | 34.8 | 34.1 | 52.0 | 54.3 | 54.2 | 13.3 | 13.3 | 41.7 | 43.4 | 43.0 | 47.5 | 12.8 |

March | 12.1 | 994 | 42.7 | 44.3 | 43.6 | 63.6 | 66.2 | 66.1 | 20.3 | 20.3 | 51.5 | 53.5 | 53.0 | 58.3 | 14.0 |

April | 17.0 | 1079 | 49.6 | 51.3 | 50.5 | 71.6 | 74.4 | 74.3 | 26.0 | 26.0 | 58.6 | 60.7 | 60.2 | 65.9 | 14.6 |

May | 21.5 | 1106 | 54.2 | 55.9 | 55.6 | 76.4 | 79.3 | 79.2 | 30.3 | 30.2 | 63.0 | 65.2 | 64.6 | 70.5 | 14.6 |

June | 26.3 | 1107 | 58.5 | 60.2 | 59.4 | 80.0 | 82.9 | 82.8 | 34.8 | 34.8 | 66.9 | 69.1 | 68.5 | 74.3 | 14.1 |

July | 28.9 | 1107 | 60.7 | 62.4 | 61.6 | 82.0 | 84.9 | 84.8 | 37.3 | 37.3 | 68.9 | 71.1 | 70.5 | 76.3 | 13.9 |

August | 28.3 | 1095 | 59.8 | 61.6 | 60.7 | 81.0 | 83.8 | 83.8 | 36.6 | 36.6 | 68.0 | 70.2 | 69.7 | 75.4 | 13.8 |

September | 24.1 | 1034 | 54.4 | 56.1 | 55.3 | 74.8 | 77.5 | 77.4 | 32.2 | 32.1 | 62.5 | 64.6 | 64.1 | 69.5 | 13.4 |

October | 17.0 | 914 | 44.5 | 45.9 | 45.6 | 63.2 | 65.6 | 65.5 | 24.6 | 24.6 | 52.3 | 54.1 | 53.7 | 58.5 | 12.5 |

November | 10.0 | 777 | 33.9 | 35.2 | 34.7 | 50.4 | 52.4 | 52.3 | 16.5 | 16.4 | 41.2 | 42.8 | 42.4 | 46.4 | 11.2 |

December | 4.8 | 701 | 26.9 | 28.0 | 27.5 | 41.8 | 43.6 | 43.6 | 10.5 | 10.4 | 33.8 | 35.2 | 34.9 | 38.4 | 10.4 |

**Table 4.**PV cell temperatures obtained by thermal models in the case of PV conversion (P

_{pv}≠ 0, η = 12%) and corresponding percentage decrease of electric power.

Temperatures (°C) | Power | |||
---|---|---|---|---|

T_{c,pv} | T_{c,pv+batt} | ΔT | ΔP% | |

January | 24.3 | 34.1 | 9.8 | −5.1 |

February | 30.9 | 42.1 | 11.2 | −5.8 |

March | 40.0 | 52.3 | 12.3 | −6.4 |

April | 46.7 | 59.6 | 12.9 | −6.7 |

May | 51.4 | 64.3 | 12.9 | −6.7 |

June | 55.7 | 68.2 | 12.4 | −6.5 |

July | 58.0 | 70.2 | 12.3 | −6.4 |

August | 57.1 | 69.3 | 12.2 | −6.3 |

September | 51.8 | 63.6 | 11.8 | −6.1 |

October | 42.0 | 53.0 | 11.0 | −5.7 |

November | 31.8 | 41.5 | 9.8 | −5.1 |

December | 24.8 | 33.8 | 9.1 | −4.7 |

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**MDPI and ACS Style**

Hammami, M.; Torretti, S.; Grimaccia, F.; Grandi, G.
Thermal and Performance Analysis of a Photovoltaic Module with an Integrated Energy Storage System. *Appl. Sci.* **2017**, *7*, 1107.
https://doi.org/10.3390/app7111107

**AMA Style**

Hammami M, Torretti S, Grimaccia F, Grandi G.
Thermal and Performance Analysis of a Photovoltaic Module with an Integrated Energy Storage System. *Applied Sciences*. 2017; 7(11):1107.
https://doi.org/10.3390/app7111107

**Chicago/Turabian Style**

Hammami, Manel, Simone Torretti, Francesco Grimaccia, and Gabriele Grandi.
2017. "Thermal and Performance Analysis of a Photovoltaic Module with an Integrated Energy Storage System" *Applied Sciences* 7, no. 11: 1107.
https://doi.org/10.3390/app7111107