**ABSTRACT:**

Three-Level A passivity-based control (PBC) strategy with improved robustness for single-phase three-level rectifiers feeding resistive and constant power loads (CPLs) is proposed. It is shown that the control of the rectifier can be achieved if the damping injection is applied to the grid current only. In this case, the knowledge of load resistance is required in the computation of reference grid current amplitude.

**INDUCTANCE**

Since the output voltage and load current are dc quantities, the load resistance can b e estimated easily. Then, the amplitude of the reference grid current is calculated from the power balance equation of the rectifier. The transfer function from reference grid current to actual grid current is derived. The derived transfer function is analyzed under variations in the filter inductance.

**PBC**

The results reveal that the proposed PBC offers strong robustness to variations in the filter inductance when a suitable damping gain is selected. The performances of the proposed PBC strategy under undistorted and distorted grid voltage as well as, variations in inductor are investigated via experimental studies during steady-state and transients caused by the resistive load and CPL changes. In all cases, the output voltage is regulated at the desired value, and grid current tracks its reference.

**KEYWORDS:**

- Passivity-based control
- Damping injection
- Three-level T-type rectifier
- Constant power load

**SOFTWARE:** MATLAB/SIMULINK

**SCHEMATIC DIAGRAM:**

Figure 1. Single-Phase Three-Level T-Type Rectifier Feeding Resistive Load And Cpl.

**EXPECTED SIMULATION RESULTS:**

Figure 2. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Five-Level Voltage (Vxy ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), And Capacitor Voltages (Vc1 And Vc2) Under Undistorted Grid Voltage.

Figure 3. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), And Capacitor Voltages (Vc1 And Vc2) Under Distorted Grid Voltage.

Figure 4. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), And Capacitor Voltages (Vc1 And Vc2) Under Rl D 25: (A) Le < L (Le D 1:6 Mh) And &1 D 1, (B) Le < L (Le D 1:6 Mh) And &1 D 20, (C) Le > L (Le D 2:4 Mh) And &1 D 20.

Figure 5. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), Grid Current Error (X1), Output Voltage Error (X2), And Capacitor Voltages (Vc1 And Vc2) For A Step Change In &1 From 1 To 20 When Le D L.

Figure 6. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), Resistive Load Current (Ir ), And Capacitor Voltages (Vc1 And Vc2) For A Step Change In V _ Dc From 250v To 300v Under Resistive Load R D 25.

Figure 7. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ), Resistive Load Current (Ir ), Cpl Current (Icpl), Total Load Current (Il), And Capacitor Voltages (Vc1 And Vc2) For A Step Change In: (A) R From 100 To 50, (B) Cpl From 0.625kw To 1.25kw.

Figure 8. Waveforms Of Grid-Voltage (Eg), Grid Current (Ig) And Its Reference (I_ G ), Output Voltage (Vdc ) And Its Reference (V _ Dc ), Cpl Current (Icpl), And Capacitor Voltages (Vc1 And Vc2) For A Step Change In V _ Dc From 250v To 300v Under Cpl.

**CONCLUSION:**

This paper presented a robust PBC strategy for single-phase three-level T-type rectifiers feeding resistive and constant power loads. It is pointed out that both dc output voltage and grid current of the rectifier can be controlled if the damping injection is applied to the grid current only. It is shown that the proposed PBC strategy possesses strong robustness to variations in the inductance when the damping gain is selected in accordance with the grid current transfer function magnitude.

**DC **

The performance of the proposed PBC strategy is investigated by experimental studies during steady-state and transients caused by the load and reference voltage changes under undistorted and distorted grid voltage conditions and variations in inductance. It is shown that the dc output voltage is regulated at its reference value, and grid current tracks its reference in all conditions, particularly under constant power load, which may endanger the stability of the system due to the negative resistance characteristic.

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