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:

matlab
Copy
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 MOSFETDiodeInductorCapacitor, and PWM Generator blocks.
  • Parameters: Switching frequency (fsw=20 kHz), inductance (L), capacitance (C).

4. MPPT Algorithm (Perturb & Observe)

MATLAB Function Block:

matlab
Copy
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

  1. Components:
    • PV Array Model → Boost Converter → Load (Resistor/Battery)
    • Voltage and Current Sensors → MPPT Algorithm → PWM Generator
  2. 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:

matlab
Copy
% 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.