In the field of marine power systems, the conversion of DC grid power to single-phase AC for household appliances is a critical application. The single-phase inverter plays a pivotal role in this process, but it inherently introduces challenges such as input second harmonic currents due to the pulsating nature of the output power. This article explores the mechanisms behind these harmonic currents in a three-stage single-phase inverter topology and proposes a suppression method using a Proportional-Resonant (PR) controller. The single-phase inverter is widely used in various applications, including marine environments, where efficiency and reliability are paramount. By focusing on the single-phase inverter design, we aim to address the issue of harmonic distortion that can affect the entire power system.
The three-stage single-phase inverter topology discussed here consists of a front-end DC/DC converter with a Boost stage followed by an LLC resonant circuit, and a rear-end H-bridge inverter. This configuration is chosen for its ability to handle wide input voltage ranges (e.g., DC 350 V to DC 640 V) and provide electrical isolation, which is essential for marine equipment. The single-phase inverter output is AC 230 V at 50 Hz, commonly used for powering生活电器. The control strategy involves independent optimization of the DC/DC and DC/AC stages, with the Boost converter regulating voltage and the LLC operating in open-loop mode for isolation. However, the instantaneous power pulsation at twice the output frequency in the single-phase inverter leads to second harmonic currents in the input, which can degrade system performance and efficiency.
The generation of second harmonic currents in a single-phase inverter stems from the energy conservation principle. The output power of the single-phase inverter varies sinusoidally, causing the input current to exhibit a 100 Hz ripple component when the DC input voltage is relatively constant. This ripple increases current stress on switching devices, reduces soft-switching ranges, and lowers overall efficiency. In marine systems, where power quality is crucial, suppressing these harmonics is vital. Traditional methods, such as increasing bus capacitance or adding passive filters, often lead to larger size and weight, compromising power density. Alternatively, active techniques like power decoupling or feedforward control add complexity. This article introduces a PR control-based approach integrated into the Boost converter’s current loop, offering a simple yet effective solution for harmonic suppression in the single-phase inverter.
To understand the topology selection, consider the requirements: wide input voltage range, isolation, and high efficiency. The Boost converter handles voltage regulation, while the LLC resonant circuit provides fixed-frequency operation near resonance for zero-voltage switching (ZVS) and zero-current switching (ZCS). The H-bridge inverter uses unipolar SPWM modulation for the single-phase output. The control block diagrams for the Boost and inverter stages are summarized below, highlighting the dual-loop control with voltage and current feedback. For the single-phase inverter, the output voltage and filter inductor current are sampled to form outer and inner loops, respectively.
| Parameter | Value | Unit |
|---|---|---|
| Input Voltage (v_in) | 440 | V DC |
| Input Current (i_in) | 20 | A DC |
| Output Voltage (v_ac) | 230 | V AC |
| Output Current (i_ac) | 44 | A AC |
| Load Resistance (R_ac) | 4.2 | Ω |
| Load Inductance (L_ac) | 10 | mH |
| Power Factor | 0.8 | – |
The second harmonic current in a single-phase inverter arises because the output power p_out(t) is given by:
$$p_{\text{out}}(t) = v_{\text{ac}}(t) \cdot i_{\text{ac}}(t) = V_{\text{ac}} I_{\text{ac}} \cos(\phi) \left[1 – \cos(2\omega t)\right] / 2 + \text{higher harmonics}$$
where ω is the angular frequency (2πf), and φ is the phase difference. Assuming ideal conditions, the input power must equal the output power, leading to an input current i_in with a DC component and a second harmonic component. For a single-phase inverter with constant input voltage, the input current i_in can be expressed as:
$$i_{\text{in}} = I_{\text{dc}} + I_{\text{shc}} \cos(2\omega t + \theta)$$
where I_dc is the average current, and I_shc is the second harmonic current amplitude. This harmonic flows through the DC/DC converter and bus capacitor, increasing losses and stress.
The PR controller is designed to suppress this second harmonic by providing high gain at the specific frequency. The continuous-time transfer function of the PR controller is:
$$G_{\text{PR}}(s) = K_p + \frac{2 K_r \omega_c s}{s^2 + 2\omega_c s + \omega_o^2}$$
where K_p is the proportional gain, K_r is the resonant gain, ω_o is the resonant frequency (2π·100 rad/s for 50 Hz systems), and ω_c controls the bandwidth. For digital implementation, this is discretized using the Tustin method, resulting in:
$$G_{\text{PR}}(z) = \frac{A_1 z^2 + B_1 z + C_1}{A_2 z^2 + B_2 z + C_2}$$
The coefficients are derived based on sampling time and controller parameters. In software, this is implemented as a difference equation, with factors such as b0 = A1/A2, b1 = B1/A2, etc., enabling real-time harmonic compensation in the single-phase inverter control loop.
Simulation studies were conducted using PSIM to model the three-stage single-phase inverter. The Boost converter with PR control showed a significant reduction in input second harmonic current compared to the original controller. Under rated conditions, the harmonic content decreased from 0.8 A to 0.18 A, demonstrating the effectiveness of the PR approach for the single-phase inverter. The dynamic performance was also evaluated; although the PR controller slightly slowed the response during load transients, the trade-off is acceptable given the harmonic suppression benefits. For instance, when switching from full load to no-load, the bus voltage stabilization time increased from 2 s to 3 s, but the efficiency improved due to reduced ripple losses.
| Component | Parameter | Value | Notes |
|---|---|---|---|
| Boost Circuit | Inductor L_B | 2 mH | KDDCI36 core |
| Diode D_B | 1200 V, 40 A | Parallel configuration | |
| MOSFET P1 | 1200 V, 40 A | Two in parallel | |
| Capacitor C_LLC | 560 μF | Series-parallel arrangement | |
| LLC Circuit | MOSFET Q1-Q4 | 1200 V, 80 A | At 25°C |
| Resonant Inductor L_r1 | 4 μH | Transformer leakage | |
| Capacitor C_r1 | 0.176 μF | 1200 V rating | |
| Magnetizing Inductance L_m1 | 400 μH | – | |
| Diodes D_R1-D_R4 | 1200 V, 40 A | Parallel sets | |
| Inverter Circuit | IGBT T1-T4 | 1200 V, 300 A | At 25°C |
| Filter Inductor L_f | 450 μH | Rated for 60 A | |
| Filter Capacitor C_f | 20 μF | 400 V rating |
Experimental validation was performed on a 10 kVA prototype of the three-stage single-phase inverter. The input current waveforms were measured with and without the PR controller. Without PR control, the input current exhibited a 4.2 A peak-to-peak ripple at 100 Hz. With PR control, the ripple reduced to 2 A, representing an 11% decrease relative to the rated current. This confirms the PR controller’s efficacy in suppressing second harmonic currents in the single-phase inverter. The setup involved careful tuning of controller gains, and the digital implementation ensured stable operation across varying loads. The single-phase inverter maintained output voltage quality while minimizing input disturbances, highlighting the practicality of this method for marine applications.
In conclusion, the integration of a PR controller into the Boost converter’s current loop effectively suppresses input second harmonic currents in a three-stage single-phase inverter. This approach avoids additional hardware, simplifies control, and enhances efficiency. The single-phase inverter benefits from reduced harmonic distortion, improved power quality, and better compatibility with marine power systems. Future work could focus on optimizing the PR parameters for wider operating ranges and exploring adaptive control techniques to further enhance the performance of single-phase inverters in dynamic environments.