PV single stage

The simulation results confirm the correct operation of: MPPT dq-regulation PLL synchronization LCL harmonic filtering

1 Introduction

Grid-connected photovoltaic systems can be implemented using either a single-stage or two-stage topology. A single-stage system directly connects the photovoltaic array to the grid via a DC-to-AC inverter and LCL filter. The inverter performs both maximum power point tracking (MPPT) and grid control, ensuring proper synchronization and power delivery.

Development and modeling of a single-stage grid-connected photovoltaic system in Simulink, including:

1. 1. PV array model
2. 2. MPPT controller
3. 3. Two-level inverter
4. 4. Output LCL filter
5. 5. Phase-locked loop (PLL)
6. 6. Grid-side voltage, current, and injected power measurement
7. 2 Simulink Model System Components
8. 2.1 Single-Stage PV System Architecture

Figure 1 Model

2.2 Solar Array and MPPT

The solar array generates voltage and current based on irradiance and temperature.

Your MPPT implementation uses the Perturb & Observe algorithm, generating a DC reference voltage 𝑉𝑑𝑐_𝑟𝑒𝑓

Figure 2 MPPT Implementation

2.3 Perturb & Observe algorithm MPPT

MAT Function:

function Vref = RefGen (V,I)

Vrefmax = 909;

Vrefmini =0;

Vrefinit = 750;

deltaVref = 1;

persistent Vold Pold Vrefold;

dataType = 'double';

if isempty(Vold)

Vold=0;

Pold=0;

Vrefold = Vrefinit;

end

P= V*I;

dV= V - Vold;

dP= P - Pold;

if dP ~= 0

if dP < 0

if dV < 0

Vref = Vrefold + deltaVref;

else

Vref = Vrefold - deltaVref;

end

else

if dV < 0

Vref = Vrefold - deltaVref;

else

Vref = Vrefold + deltaVref;

end

end

else Vref = Vrefold;

end

if Vref >= Vrefmax | Vref <= Vrefmini

Vref = Vrefold;

end

Vrefold = Vref;

Vold = V;

Pold = P;

2.4 Inverter Control (dq-reference frame)

The inverter control follows the dq-frame structure:

1. PLL block extracts grid phase angle 𝜔𝑡
2. abc → dq0 transforms convert grid and inverter measurements into synchronous frame
3. PI controllers regulate:
4. 𝑖𝑑 for active power (linked to MPPT)
5. 𝑖𝑞=0 for unity power factor
6. The voltage control loop produces reference modulation signals

Your screenshot clearly shows the implementation of:

1. DC voltage control loop
2. Current control loops
3. dq→abc inverse transform
4. PWM generator
5. 2.5 LCL Filter

An LCL filter is installed between the inverter and the grid to suppress switching harmonics. The simulation corresponds to a standard LCL filter.

3 Simulation Results and Analysis

3.1 The solar array generates power

The PV array produces power according to the MPPT, as the maximum product of voltage and current

Figure 3 Scope Power

3.2 Voltage and Current at Inverter Side (Before LCL Filter)

A screenshot of the before LCL filter in Scope shows:

Three-phase voltages with high-frequency switching harmonics

Three-phase currents steadying out after a short transient

Currents decrease as luminosity decreases by approximately 0.24 s

Figure 4 Before LCL Filter

This behavior is consistent with expectations, since as irradiance decreases, the PV system power decreases → the MPPT decreases. 𝑉𝑑𝑐_𝑟𝑒𝑓→ the inverter supplies less current.

3.3 Voltage and Current at Grid Side (After LCL Filter)

Screenshot of the LCL filter at the oscilloscope output:

• Smooth sinusoidal voltage and current waveforms
• Very low harmonic levels
• The current amplitude drops within 0.24 seconds, confirming proper interaction between the MPPT and the grid control.

Figure 5 After LCL Filter

This matches the expected LCL characteristics.

4 Discussion

The results confirm that:

1. The PLL system successfully synchronizes the inverter with the grid
2. The MPPT correctly regulates power depending on illumination
3. The dq control loops regulate the injected current and ensure a unity power factor
4. The LCL filter effectively eliminates switching harmonics
5. Power injection precisely matches illumination conditions

Overall, the designed single-stage PV system operates correctly.

5 Conclusion

This exercise demonstrated the modeling and operation of a single-stage grid-connected PV system in Simulink, including PV system modeling, MPPT, inverter control, and grid power delivery. The simulation results confirm the correct operation of:

1. MPPT
2. dq-regulation
3. PLL synchronization
4. LCL harmonic filtering
5. illumination-dependent power regulation

The system is stable and delivers a clean sinusoidal current to the grid.