In recent years, the integration of distributed photovoltaic (PV) systems into the power grid has gained significant attention due to the growing demand for renewable energy. Among various power conversion topologies, the quasi-Z-source cascaded multilevel inverter (QZS-CMI) has emerged as a promising solution for solar inverters, as it combines the benefits of both quasi-Z-source networks and cascaded multilevel structures. This solar inverter topology enables single-stage boost and inversion functions without the need for dead-time settings, reducing output waveform distortion and simplifying control. Moreover, each power unit in a QZS-CMI can be independently controlled, eliminating capacitor voltage balancing issues common in clamped multilevel inverters, making it highly suitable for modular solar inverter applications. However, traditional modulation techniques, such as simple boost control, often lead to increased switching frequencies and losses, while power imbalances between modules can cause over-modulation, degrading system performance. To address these challenges, this paper proposes a comprehensive approach involving a multi-carrier phase-shifted pulse-width modulation (MPSPWM) method, a master-division control strategy, and a third-harmonic injection technique. These innovations enhance the efficiency, dynamic response, and stability of solar inverters in PV systems, as validated through simulations and experiments on a three-module cascaded seven-level QZS-CMI.
The quasi-Z-source inverter (QZSI) utilizes a unique impedance network to couple the inverter main circuit with the power source, allowing the use of shoot-through states that are typically forbidden in conventional inverters. This enables voltage boost functionality in a single stage, eliminating the need for additional DC-DC converters in solar inverters. The QZS-CMI extends this concept by cascading multiple QZSI modules, each powered by an independent PV panel. This modular approach facilitates scalable solar inverter designs for distributed generation. The operating states of a QZSI include shoot-through and non-shoot-through modes. In the shoot-through state, the diodes are reverse-biased, allowing inductors to store energy and capacitors to discharge, resulting in zero inverter output voltage. In the non-shoot-through state, the diodes conduct, and the inverter functions as a current source, with inductors releasing energy to charge the capacitors. The boost factor \( B \) of the QZSI is derived from the volt-second balance principle, given by:
$$ B = \frac{1}{1 – 2D_0} $$
where \( D_0 \) is the shoot-through duty cycle. The DC-link voltage \( V_{dc} \) relates to the input voltage \( V_{in} \) as \( V_{dc} = B \cdot V_{in} \). For a cascaded multilevel inverter (CMI) with \( N \) modules, the output voltage \( v_o \) is the sum of individual module voltages \( v_{oi} \), expressed as:
$$ v_o = \sum_{i=1}^{N} v_{oi} $$
where each module’s output voltage is \( v_{oi} = V_{dci} \cdot m_i \), with \( V_{dci} \) being the DC-link voltage and \( m_i \) the modulation index of the \( i \)-th module. The system model for grid-connected operation includes a filter inductor \( L \), grid voltage \( v_g \), and grid current \( i_g \), governed by the equation:
$$ v_o = L \frac{di_g}{dt} + v_g $$
This foundation underscores the importance of advanced modulation and control strategies in solar inverters to optimize performance in PV applications.
Traditional modulation methods for QZS-CMI, such as simple boost modulation, insert shoot-through states during zero vectors of the inverter output, which doubles the switching frequency and increases losses. To mitigate this, we propose an MPSPWM technique that reduces switching frequency by half. In MPSPWM, triangular carriers are vertically shifted by \( D_0/2 \) for upper and lower switches in each bridge arm. This ensures that shoot-through states are inserted at switching instants, rather than during zero vectors, thereby minimizing switching losses. The modulation principle involves comparing a sinusoidal reference wave with phase-shifted carriers to generate gate signals. For a three-module solar inverter, carriers are shifted by \( \pi/N \) horizontally, and by \( D_0/2 \) vertically, ensuring shoot-through time \( T_{sh} \) per switching period \( T_s \) is \( T_{sh} = D_0 T_s \). This approach maintains the boost capability while enhancing the efficiency of solar inverters, as demonstrated in subsequent sections.
Control strategies for QZS-CMI are critical for maintaining stability and power quality in solar inverters. We introduce a master-division control framework that combines centralized current control with distributed voltage regulation. The division controller for DC-link voltage uses proportional-integral (PI) control to stabilize the capacitor voltage \( V_{C1} \) in each module, indirectly regulating the DC-link voltage. The transfer function for the voltage loop is designed to ensure robustness against disturbances. The master controller for grid current employs an improved deadbeat control (DBC) method, which predicts the next sampling period’s current based on system dynamics. The discrete-time equation for the inverter output voltage reference \( v_{oref}(k) \) is:
$$ v_{oref}(k) = \frac{L}{T_s} \left( i_{ref}(k) – i_g(k) \right) + v_g(k) $$
where \( T_s \) is the sampling period, \( i_{ref} \) is the reference current, and \( k \) denotes the sampling instant. To address digital delay issues, the improved DBC uses a weighted average of current errors over two samples, enhancing tracking accuracy and reducing total harmonic distortion (THD). The stability analysis shows that the system remains stable for \( 0 < K < 2 \), where \( K \) is the ratio of actual to nominal inductance, compared to \( 0 < K < 1 \) for traditional DBC. This control strategy ensures fast dynamic response and low harmonic distortion in solar inverters, crucial for grid compliance.
Power imbalances among PV modules due to varying irradiance levels can lead to over-modulation in solar inverters, where the modulation index \( M_i \) exceeds \( 1 – D_{0i} \). This causes current distortion and system instability. To prevent this, we propose a third-harmonic injection technique. By adding a third-harmonic component to the modulation wave of over-modulated modules and an opposing third-harmonic to non-over-modulated modules, the effective modulation index is reduced, expanding the stable operating range. The modified modulation wave \( m \) is given by:
$$ m = M \sin(\omega t) + k M \sin(3\omega t) $$
where \( k \) is the injection factor. The maximum value of \( m \) is minimized at \( k = 1/6 \), allowing the modulation index to reach 1.15 times the original limit. For non-over-modulated modules, the injection is scaled based on the power discrepancy, ensuring the total output voltage remains unchanged. This method significantly improves the power handling capability of solar inverters under unbalanced conditions.
Simulation and experimental results validate the proposed methods for solar inverters. A three-module QZS-CMI was simulated with parameters including PV open-circuit voltage of 43.1 V, short-circuit current of 10.3 A, quasi-Z-source inductors of 1.0 mH, capacitors of 0.3 mF, grid voltage amplitude of 150 V, filter inductor of 2.0 mH, and switching frequency of 10 kHz. The DC-link voltage was maintained at 70 V, and the output voltage exhibited seven levels with a peak of 210 V. The MPSPWM method reduced switching losses by 50% compared to simple boost modulation. The improved DBC achieved a THD of 0.86% for grid current, outperforming traditional PR control (THD of 2.84%). Under power imbalances, the third-harmonic injection prevented over-modulation, maintaining THD below 1%. Experimental tests on a prototype solar inverter confirmed these findings, with stable operation under varying irradiance conditions and effective power sharing among modules.
In conclusion, the proposed QZS-CMI with master-division control and MPSPWM offers a robust solution for solar inverters in PV systems. The key contributions include a reduced-switching-frequency modulation technique, a fast-response current control strategy, and an over-modulation prevention method. These advancements enhance the efficiency, reliability, and scalability of solar inverters, supporting the widespread adoption of renewable energy. Future work could focus on extending these techniques to higher-level cascaded structures and integrating energy storage for hybrid systems.
| Technique | Switching Frequency | Implementation Complexity | Efficiency |
|---|---|---|---|
| Simple Boost Modulation | High (2× carrier) | Low | Moderate |
| Space Vector PWM | Low | High (for N>3) | High |
| MPSPWM (Proposed) | Low (1× carrier) | Moderate | High |
| Control Method | Stability Range (K) | THD (%) | Response Time (ms) |
|---|---|---|---|
| Traditional DBC | 0 < K < 1 | 1.2 | 20 |
| Improved DBC (Proposed) | 0 < K < 2 | 0.86 | 5 |
| PI/PR Control | N/A | 2.84 | 10 |
The mathematical modeling of solar inverters involves analyzing the steady-state and dynamic behaviors. For instance, the power balance in a QZS-CMI module is expressed as:
$$ P_{pvi} = \frac{V_{dc} i_{dc}}{2} = \frac{V_{oi} I_g}{2} $$
where \( P_{pvi} \) is the input power from the PV panel, \( V_{oi} \) is the output voltage amplitude, and \( I_g \) is the grid current amplitude. The power distribution factor \( \alpha_i \) for each module is defined as:
$$ \alpha_i = \frac{P_{pvi}}{P_T} $$
with total power \( P_T = \sum_{i=1}^{N} P_{pvi} \). This ensures proportional power sharing among modules in the solar inverter. The modulation index for each module is then calculated as:
$$ m_i = \alpha_i \frac{v_{oref}}{V_{dci}} $$
These equations form the basis for the master-division control, enabling precise regulation of solar inverters in diverse operating conditions.
In summary, the integration of advanced modulation and control strategies in solar inverters, such as the QZS-CMI, addresses key challenges in PV systems. The MPSPWM method reduces switching losses, the master-division control enhances dynamic performance, and the third-harmonic injection ensures stability under power imbalances. These innovations contribute to the development of efficient and reliable solar inverters for future energy grids. Further research could explore real-time optimization algorithms and fault-tolerant designs to expand the capabilities of solar inverters in large-scale applications.