Optimal Common-Mode Voltage Selection for NPC Converters

Introduction

The proposed static converter is a three-phase NPC inverter designed to act as a grid former. Its operation includes islanded mode, where it mimics the behavior of a synchronous generator, and grid-connected mode, where it controls exported or imported power according to external grid voltage and frequency references.

Figure 1: Proposed Inverter Topology.

System Specifications

Critical parameters such as DC bus voltage, filter inductance, and capacitor values were selected to optimize converter efficiency and stability in both islanded and grid-connected modes. The system specifications are detailed in Table 1.

Description	Symbol	Value
Nominal Power	$S_{nom}$	225 kVA
DC Bus Voltage	$V_{DC}$	1000 V
Capacitance of Capacitor	$C_{1,2}$	1500 uF
Filter Inductance	$L_f$	0.5 mH
Series Resistance of Inductor	$L_f$	0.05 $\Omega$
Filter Capacitance	$C_f$	150 uF
Damping Resistance	$R_d$	0.1 $\Omega$
Grid Nominal Voltage	$V_{grid}$	440 V
Grid Nominal Frequency	$f_{grid}$	60 Hz
Switching Frequency	$f_{sw}$	20 kHz
Deadtime	$t_{dead}$	50 ns

Table 1: System Specifications.

Modulation Method

The paper proposes an optimal common-mode voltage selection method for NPC and T-Type topology inverters. The method involves selecting a common-mode voltage $v_0$ to control the current $i_0$ through the midpoint of DC bus capacitors. This control facilitates tracking a voltage reference $V_{c_2}$ at the midpoint, which is precisely half of $V_{DC}$, ensuring balanced voltage division across capacitors $C_1$ and $C_2$.

Control Law

The focus of the study is on the converter modulation. The control law involves an inner current loop based on state feedback with gains determined by DLQR. The outer voltage loop imposes a reference current for the inner loop and uses a state feedback proportional-resonant controller, also employing DLQR. For detailed information on this law, refer to references.

Simulation

The electrical plant, modulation, and control laws were simulated using Virtual Hardware-In-The-Loop (VHIL) with a simulation step of 0.25 µs. The implementation was made modular and suitable for microcontrollers, developed in C language format as a dynamic-linked library (DLL) using the Typhoon HIL Control Center software.

Results

Simulation results for islanded mode operation and the impact of midpoint voltage control on various load conditions are presented.

Steady State for Different Loads

Results for different loads show the comparison between reference and measured voltages, reference and measured currents, unfiltered voltage waveforms, and modulating signals for phases A, B, and C.

• Case 1: No Load.
• Case 2: Resistive Load.
• Case 3: Inductive Load.
• Case 4: Capacitive Load.

Midpoint Voltage Control Impact

The dynamic behavior of the midpoint voltage $V_{mid}$ under varying conditions, with and without active control, is illustrated. This demonstrates the effectiveness of the proposed control method in stabilizing $V_{mid}$.

Usage

For further details, please refer to the complete PDF document provided in this repository.

References

• André Pacheco Meurer. CONTROLE HIERÁRQUICO PARA INVERSORES FORMADORES DE REDE EM MICRORREDES AC. PhD thesis, UFSM, 2023.
• Typhoon HIL. C function. 2023. Available at: Typhoon HIL Documentation.
• Gleisson Balen et al. Optimum Geometric Carrier-Based Modulation for NPC and T-Type Inverters. In: IECON 2019 - 45th Annual Conference of the IEEE Industrial Electronics Society, 2019. DOI: 10.1109/IECON.2019.8927073.
• Alexandre T. Pereira and Humberto Pinheiro. Inner Loop Controllers for Grid-Forming Converters. In: 2022 14th Seminar on Power Electronics and Control (SEPOC), 2022. DOI: 10.1109/SEPOC54972.2022.9976425.