MATLAB Simulation of Modeling of a Solar PV Cell
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Introduction
Mathematical modeling of a solar PV cell using MATLAB. Instead of using built-in PV blocks, this approach explains how a solar PV cell is modeled using analytical equations, which helps in clearly understanding the effect of irradiance and temperature on PV voltage, current, and power.
This method is widely used in academics, research work, and MPPT algorithm development.
🌞 Why Mathematical Modeling of a PV Cell?
A solar PV cell behaves as a nonlinear source, and its output varies with environmental conditions. Mathematical modeling helps to:
✔ Analyze I–V and P–V characteristics✔ Understand maximum power point behavior✔ Study temperature and irradiance effects✔ Implement custom PV models in MATLAB/Simulink
⚙️ Step 1: Define Standard Test Conditions (STC)
The reference parameters of a PV cell are defined at standard test conditions:
Gs = 1000 W/m²Ts = 25 °C
These values are used as the base reference for all PV calculations.
🌍 Step 2: Actual Operating Conditions
In real-time operation, the PV cell works under varying conditions:
G = Actual irradiance (W/m²)Tc = Actual cell temperature (°C)
Any change in these parameters directly affects PV performance.
🔋 Step 3: PV Cell Parameters from Datasheet
At STC, the following electrical parameters are taken from the PV datasheet:
Iscs – Short-circuit currentImps – Maximum power point currentVocs – Open-circuit voltageVmps – Maximum power point voltage
These parameters define the basic electrical behavior of the PV cell.
🌡️ Step 4: Temperature Coefficients
To include temperature effects, two coefficients are used:
α – Temperature coefficient of current (A/°C)β – Temperature coefficient of voltage (V/°C)
📌 Current slightly increases with temperature📌 Voltage significantly decreases with temperature
🔌 Step 5: Voltage Correction Equations
🔹 Maximum Power Point Voltage
The actual maximum power point voltage is calculated as:
Vmp = Vmps + β (Tc − Ts)
This equation shows that Vmp decreases as temperature increases.
🔹 Open-Circuit Voltage
The actual open-circuit voltage is given by:
Voc = Vocs + β (Tc − Ts)
⚠️ Higher temperature → Lower PV voltage
⚡ Step 6: Current Correction Equations
🔹 Maximum Power Point Current
The actual maximum power point current is:
Imp = Imps (G / Gs) [1 + α (Tc − Ts)]
This equation indicates that PV current is directly proportional to irradiance.
🔹 Short-Circuit Current
The actual short-circuit current is:
Isc = Iscs (G / Gs) [1 + α (Tc − Ts)]
As irradiance increases, the short-circuit current increases almost linearly.
🧮 Step 7: Calculation of Model Constants
To accurately represent the nonlinear I–V characteristics, two constants are calculated.
🔹 Constant k₂
k2 = (Vmp / Voc − 1) / ln(1 − Imp / Isc)
🔹 Constant k₁
k1 = (1 − Imp / Isc) exp(−Vmp / (k2 Voc))
These constants define the curvature of the PV I–V characteristic.
🔁 Step 8: PV Output Current Equation
The PV output current at any operating voltage is expressed as:
Ipv = Isc [1 − k1 (exp(Vpv / (k2 Voc)) − 1)]
Here,Vpv is the PV terminal voltage,Ipv is the PV output current.
This equation represents the complete nonlinear behavior of the PV cell.
🔋 Step 9: PV Output Power
The PV output power is calculated using:
Ppv = Vpv × Ipv
The peak of this power curve corresponds to the maximum power point (MPP).
📈 Step 10: Generating I–V and P–V Characteristics
To obtain PV characteristics in MATLAB:
🔹 Fix irradiance and temperature🔹 Vary PV voltage from zero to open-circuit voltage
Vpv = 0 → Voc
At each voltage value:
Ipv = Isc [1 − k1 (exp(Vpv / (k2 Voc)) − 1)]Ppv = Vpv × Ipv
⭐ Step 11: Maximum Power Point
The maximum power point is defined as:
Pmax = Vmp × Imp
MPPT algorithms aim to operate the PV system at this point.
🌦️ Step 12: Effect of Irradiance Change
When irradiance decreases:
✔ PV current decreases✔ PV power decreases✔ MPP shifts downward
This explains why MPPT is required in PV systems.
🌡️ Step 13: Effect of Temperature Change
When temperature increases:
✔ Open-circuit voltage decreases✔ Maximum power point voltage decreases✔ Overall PV efficiency reduces
✅ Advantages of This PV Model
✔ Simple mathematical structure✔ Easy MATLAB implementation✔ No complex diode parameters✔ Suitable for MPPT and control studies✔ Ideal for academic and research applications
🏁 Conclusion
This blog explained the mathematical modeling of a solar PV cell using MATLAB with simple and clear equations. By varying irradiance and temperature, the I–V and P–V characteristics of the PV cell can be accurately obtained. This model forms a strong foundation for MPPT algorithms, grid-connected PV systems, and advanced PV simulations.
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