To model a photovoltaic (PV) system and implement Maximum Power Point Tracking (MPPT) using MATLAB
To model a photovoltaic (PV) system and implement Maximum Power Point Tracking (MPPT) using MATLAB, follow these structured steps:
1. PV Cell Modeling
Mathematical Model:
The single-diode model represents a PV cell with the equation:
I=Iph−Isat(eV+IRsnVt−1)−V+IRsRsh
Where:
- Iph: Photocurrent (depends on irradiance G and temperature T)
- Isat: Diode saturation current
- Rs,Rsh: Series and shunt resistances
- n: Diode ideality factor
- Vt=kTq: Thermal voltage
MATLAB Implementation:
function I = PV_Model(V, G, T, Rs, Rsh, n, Iph_ref, Isat_ref, Eg) % Constants k = 1.3806e-23; % Boltzmann constant q = 1.602e-19; % Electron charge T_ref = 298.15; % Reference temperature (25°C) % Temperature-adjusted parameters Iph = Iph_ref * (G / 1000) * (1 + 0.001*(T - T_ref)); Isat = Isat_ref * (T / T_ref)^3 * exp(-Eg/(n*k) * (1/T - 1/T_ref)); Vt = n * k * T / q; % Solve I using Newton-Raphson method I = 0; for iter = 1:20 f = Iph - Isat*(exp((V + I*Rs)/Vt) - 1) - (V + I*Rs)/Rsh - I; df = -Isat*(Rs/Vt)*exp((V + I*Rs)/Vt) - Rs/Rsh - 1; I = I - f/df; end end
2. Simulate PV Array in Simulink
- Use Simscape Electrical blocks to build the PV model.
- Configure parameters (Rs,Rsh,n,Iph,Isat) based on datasheet values.
- Validate I-V and P-V curves under standard test conditions (STC: G=1000 W/m2,T=25∘C).
3. DC-DC Converter (Boost Converter)
Model in Simulink:
- Use MOSFET, Diode, Inductor, Capacitor, and PWM Generator blocks.
- Parameters: Switching frequency (fsw=20 kHz), inductance (L), capacitance (C).
4. MPPT Algorithm (Perturb & Observe)
MATLAB Function Block:
function D = P_and_O(V, I, D_prev, delta_D) P_prev = V_prev * I_prev; % Store previous power P = V * I; if (P > P_prev) if (V > V_prev) D = D_prev - delta_D; % Decrease duty cycle else D = D_prev + delta_D; % Increase duty cycle end else if (V > V_prev) D = D_prev + delta_D; else D = D_prev - delta_D; end end D = max(min(D, 0.8), 0.2); % Limit duty cycle between 20% and 80% end
5. System Integration in Simulink
- Components:
- PV Array Model → Boost Converter → Load (Resistor/Battery)
- Voltage and Current Sensors → MPPT Algorithm → PWM Generator
- Simulation Setup:
- Use Variable Step Solver (ode23tb) for stiff systems.
- Simulate under varying G and T (e.g., step changes in irradiance from 800 W/m2 to 1000 W/m2).
6. Results and Validation
- Without MPPT: Fixed duty cycle → Power varies with irradiance.
- With MPPT: Power stabilizes near maximum power point (MPP).
Plot P-V Curve and Operating Points:
% Extract simulation data V_pv = simout.logsout.get('V_pv').Values.Data; I_pv = simout.logsout.get('I_pv').Values.Data; P_pv = V_pv .* I_pv; % Plot P-V curve figure; plot(V_pv, P_pv, 'b', 'LineWidth', 1.5); xlabel('Voltage (V)'); ylabel('Power (W)'); title('PV Array P-V Curve with MPPT'); grid on;
7. Advanced Enhancements
- Incremental Conductance Algorithm: Replace P&O with a more efficient MPPT method.
- Environmental Variability: Use Signal Builder blocks to simulate dynamic G and T.
- Hardware-in-the-Loop (HIL): Connect to real-time hardware for validation.
Key Parameters
Component | Parameters |
---|---|
PV Array | Voc=40 V,Isc=8 A |
Boost Converter | L=1 mH,C=470 μF,fsw=20 kHz |
MPPT (P&O) | ΔD=0.01, Sampling time = 1 ms |
Conclusion
This framework provides a comprehensive approach to model a PV system and implement MPPT in MATLAB/Simulink. Adjust parameters based on specific PV panel and converter specifications for accurate results.