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:

$I = I_{ph} - I_{sat} (e^{n V t V + I R s} - 1) - R ^{sh} V + I R ^{s}$

Where:

$I_{ph}$ : Photocurrent (depends on irradiance $G$ and temperature $T$ )
$I_{sat}$ : Diode saturation current
$R_{s}, R_{sh}$ : Series and shunt resistances
$n$ : Diode ideality factor
$V_{t} = q k T$ : 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 ( $R_{s}, R_{sh}, n, I_{ph}, I_{sat}$ ) based on datasheet values.
Validate I-V and P-V curves under standard test conditions (STC: $G = 1000 W/m^{2}, T = 2 5^{\circ} C$ ).

3. DC-DC Converter (Boost Converter)

Model in Simulink:

Use MOSFET, Diode, Inductor, Capacitor, and PWM Generator blocks.
Parameters: Switching frequency ( $f_{sw} = 20 kHz$ ), 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 $800 W/m^{2}$ to $1000 W/m^{2}$ ).

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	$V_{oc} = 40 V, I_{sc} = 8 A$
Boost Converter	$L = 1 mH, C = 470 μ F, f_{sw} = 20 kHz$
MPPT (P&O)	$Δ D = 0.01$ , 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.