Incoming radiation and ambient temperature are used to calculate the PV cell temperature based on a five-layer thermal model. The cell temperature in the electrical model is updated according to the thermal model to accurately adjust the electrical characteristics of the PV cell output. To test and validate the electrical and thermal properties of the PV cell, a custom setup was built that allows temperature measurements on the PV cell and glass surfaces.
Performance of the electrical-thermal model in both forward and reverse-bias region is verified using experimental data in realistic scenarios.
Introduction
- The Sun Radiation
- Structure of a PV Cell
- Effect of Irradiance and Temperature on PV Cell
- Common Thermal-Related Applications of PV
It is used to check the accuracy of the PV model against measurements from the PV cell. The power measurements are fed back into the simulation in real time to update the model values. The average solar flux on the sunlit half of the earth's surface is around 680 W/m2.
30% of incoming solar radiation is reflected back to space, while 70% is absorbed by Earth and re-emitted as infrared.
Electric-Thermal PV Model
Electric Model
Photocurrent Iphis the flow of electrons excited by incoming radiation from the sun G, air mass modifier M, and the difference between the PV temperature T and nominal temperature Tn, which is defined as follows. As can be seen in equation (1), the photocurrent is a dynamic variable which is affected by the inputs to the system, which are temperature, irradiance and air mass conditions. The thermal voltage V is an important factor in both forward and reverse diodes, defined as.
The forward diode Df conducts a current Idf when the PV is biased, and the governing equation for its current is. The reverse diode Dr conducts when PV is reverse biased and the governing equation for its current Idris. The shunt resistance Rshi is inversely proportional to the input light since the effective shunt resistance increases as the illumination decreases and is defined as.
The effective shunt resistance increases as the incoming irradiance decreases and is therefore inversely proportional to G. In equation (10), the output of the PV cells cannot be solved explicitly using ordinary elementary functions, but requires non-linear solution techniques. In this work, the Newton-Raphson method is used, which is a widely used nonlinear solver to obtain roots of implicit transcendental equations.
Then, using this initial value of Vd, parameters that depend on Vd will be calculated such as forward and reverse diode current, shunt resistance current and parallel capacitance current. After that, the right side of equation (10) will be calculated and the results will go through a loop to keep it within an acceptable tolerance value (0.0001 in this work).
Thermal Model
This method is popular in the field of iterative computer applications due to its simplicity and rapid convergence. The temperature of the model is determined by calculating the thermal energy exchange of each layer with the environment and surrounding layers through the main heat transfer paths of conduction, convection, and radiation, as shown in the figure. Each layer is defined based on (12), according to the heat transfer path experienced by the layer.
In the top layer of glass, the convective heat transfer between the glass surface and the surrounding air in the environment and the conduction heat flow from layer 2 affect the overall thermal exchange in the layer. For the crystalline PV cell, short-wave and long-wave heat transfer, heat flow from adjacent layers, and electricity-generated heat contribute to the heat transfer equation, according to. Where is the heat flow from layer 2, is the heat flow from layer 4, and is the heat generated by electrical loss.
The lower air gap is also a medium for heat exchange between the two adjacent layers. In the lower glass layer, the convection heat transfer between the glass surface and ambient air in the environment and the heat flow from layer 4 affect the total thermal exchange in the layer. After obtaining total heat capacity and relevant heat flow for each layer, the rate of temperature change over the simulation time step interval h is calculated.
Then it is added to the layer temperature of the previous time step Tk to determine the current temperature Tk+1, as follows.
Electric and Thermal Model Interaction
The PV cell temperature is fed back to the electrical model to accurately adjust the PV electrical model. All outputs of the system (PV voltage and power, the temperature of each layer and the processing time of the electrical and thermal block) can be observed in real-time simulation through the console block. The model with electrical and thermal blocks works simultaneously using parallel calculations, with two cores for fast processing time: one core for the electrical model and one core for the thermal model [7], [8].
Experimental Setup
PV cell experimental Setup
PHILS Setup
Electrical-Thermal PV Model Validation
Parameter values
Static Condition Verification
- Multiple I-V Curve with Different Irradiance
- Reverse-bias Characteristic Validation
- Fixed PV Voltage Operation
- Fixed PV Current Operation
In order to confirm the operation of the PV model in the reverse bias region and the effect of the temperature of the PV cell on its electrical characteristics, another test was carried out. First, a current sweep is performed from the open circuit voltage of the cell to -17.8 V under dark conditions (0 W/m2) with an ambient temperature of about 293 K, and then the last operating point is held for 60 seconds to observe the change in the electrical properties of the cell . When the cell's operating point moves into the reverse bias region, the cell acts as a load instead of a power source.
As the temperature increases, the operating voltage of the cell decreases in the reverse-bias region, as shown in Fig. The thermal model in Simulink is investigated under an insulation of 1060 W/m2 and the operating point is fixed at a constant voltage level of 0.4 V with an ambient temperature of 304 K. The simulation is run under the same conditions for 480 sec and the cell temperature results are compared in Fig.
As shown, the average temperature of the simulation cell is 325.9 K, which is close to the results from. The settling time of the simulation is about 70 s, which is relatively fast compared to the actual temperature settling rate. The thermal model in Simulink is examined at an irradiance of 960 W/m2, and the operating point is fixed at a constant current of 1.9 A at an ambient temperature of 303 K.
The simulation is run under the same conditions for 480 sec, and the cell temperature results are compared in Fig. As shown, the average temperature of the simulation cell is 324.6 K, which is close to the experimental results of 325.7 K.
Dynamic Condition Verification Using PHILS
- Load Step Test
- MPPT test
In the PHILS system, there are delays from the simulation time step, the dynamics of the programmable DC power supply, and the feedback current measurement. To determine the level of impact these delays have on the accuracy of the PHILS system, a load step test was performed on the experimental PV cell and on the PV model emulated with the PHILS system. 17(a) shows the step and ramp changes of the output load current, which consists of a full step up, full step down, two half steps up and a ramp-down sequence for the PV operating range of 0.1 A to 2.0 A over 70 sec.
There is an inherent response delay after the large load steps based on the simulation step time, but the PHILS results closely match the experimental results with no observable overshoot. The measured voltage of the PV panel is slightly lower than that of the PHILS system, with an error of 1.86%. This error arises from a model error combined with communication delay and inherent drift from the limited resolution of the equipment and sensors used in the PHILS setup, but is still within an acceptable range for most applications.
Then the PHILS system is used for an MPPT test to emulate a PV cell and connect it to a power inverter that integrates the MPPT function. The current starts at 1.20 A and increases to 2.28 A during the first 18 seconds; Next, a triangular waveform ranging from 2.22 to 2.28 A was shown to emulate the MPPT current waveform of a DC-DC converter. Although there is a small deviation due to the aforementioned model and equipment error, the dynamic performance of the PHILS system is in good agreement with the measured experimental results.
18(b) compares the cell temperature measured in the experiment and calculated in the PHILS model, showing that the temperature results fit well. These results show that the electrical-thermal model implemented in PHILS accurately calculates and emulates the operation of the PV cell.
Discussion
As shown, the angle of the cell can go up to 150 degrees Celsius, but in the model, this kind of phenomenon has not yet been taken into account and will be an improvement for the next update. As previously mentioned, the second breakdown is a defect in PV operation that causes the I-V curve of the affected PV to alternate.
Conclusion
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