The increasing demand for renewable energy integration has driven the development of advanced solar inverters, particularly in grid-connected photovoltaic (PV) systems. Traditional cascaded H-bridge (CHB) solar inverters face significant challenges, such as double-line frequency voltage ripple and power mismatch issues, which can degrade system performance and reliability. Power mismatch can be categorized into inter-phase and intra-phase imbalances, often caused by partial shading, dust accumulation, or module degradation. Inter-phase imbalance arises from unequal power distribution among the three phases, while intra-phase imbalance occurs between modules within the same phase. Existing solutions, like zero-sequence voltage injection or reactive power compensation, rely on complex control algorithms and centralized controllers, which become impractical as the number of modules increases due to communication bottlenecks and single points of failure. To address these limitations, this paper proposes a modular three-phase solar inverter topology based on a four-port LLC resonant converter. This structure inherently resolves inter-phase power imbalance and suppresses double-line frequency ripple through magnetic flux cancellation. Additionally, a distributed adaptive boost control strategy is introduced to enhance intra-phase power mismatch tolerance, expanding the stable operating range of solar inverters. The distributed architecture minimizes inter-module communication, reducing control complexity and improving scalability for large-scale PV systems.
The proposed modular solar inverter topology, as illustrated in the following figure, integrates a four-port LLC resonant converter with a three-phase H-bridge inverter in each module. The four-port LLC converter includes a multi-winding transformer that provides power channels between phases, enabling automatic balancing of inter-phase power. Each module’s output H-bridges can be cascaded to achieve higher voltage levels and improved harmonic performance, eliminating the need for centralized filters. The key innovation lies in the multi-winding transformer, which allows power from the PV input to be equally distributed to the three phases via magnetic coupling. This design not only isolates the PV modules from the grid but also facilitates maximum power point tracking (MPPT) under varying irradiance conditions. By leveraging the transformer’s flux cancellation properties, the double-line frequency ripple in the output power is suppressed, reducing the reliance on large DC-link capacitors for power decoupling. Consequently, the solar inverter achieves higher power density and cost-effectiveness, making it suitable for modular and scalable PV systems.
The operation of the solar inverter relies on the principle of magnetic flux cancellation to decouple power. For a three-phase system, the instantaneous output power of each phase consists of a DC component and a double-line frequency component. For phase A, the output voltage and current are given by:
$$ u_a = \sqrt{2}U \sin(\omega t) $$
$$ i_a = \sqrt{2}I \sin(\omega t – \beta) $$
where $U$ and $I$ are the RMS values of voltage and current, $\omega$ is the grid angular frequency, and $\beta$ is the power factor angle. The instantaneous power $P_a$ is derived as:
$$ P_a = u_a \times i_a = 2UI \sin(\omega t) \sin(\omega t – \beta) = UI[\cos \beta – \cos(2\omega t – \beta)] = P_a – P_{a2\omega} $$
Similarly, for phases B and C:
$$ P_b = UI \left[ \cos \beta – \cos\left(2\omega t + \frac{2\pi}{3} – \beta\right) \right] = P_b – P_{b2\omega} $$
$$ P_c = UI \left[ \cos \beta – \cos\left(2\omega t – \frac{2\pi}{3} – \beta\right) \right] = P_c – P_{c2\omega} $$
The total power from the PV module is:
$$ P_{pv} = P_a + P_b + P_c = 3UI \cos \beta $$
$$ P_{a2\omega} + P_{b2\omega} + P_{c2\omega} = 0 $$
This shows that the double-line frequency components cancel out in the transformer core, leaving only the DC component. The DC-link capacitors in each H-bridge only handle high-frequency ripple, allowing for smaller capacitor sizes. The current on the secondary side of the transformer, after full-bridge rectification, is expressed as:
$$ i_{2a} = \frac{4}{\pi} \cdot \frac{UI}{V_{dc}} [\cos \beta – \cos(2\omega t – \beta)] \sin(\omega_1 t) $$
$$ i_{2b} = \frac{4}{\pi} \cdot \frac{UI}{V_{dc}} \left[ \cos \beta – \cos\left(2\omega t + \frac{2\pi}{3} – \beta\right) \right] \sin(\omega_1 t) $$
$$ i_{2c} = \frac{4}{\pi} \cdot \frac{UI}{V_{dc}} \left[ \cos \beta – \cos\left(2\omega t – \frac{2\pi}{3} – \beta\right) \right] \sin(\omega_1 t) $$
where $\omega_1 = 2\pi f_1$ and $f_1$ is the switching frequency of the LLC converter. The magnetomotive force (MMF) in the transformer is given by Ampère’s law:
$$ F = N i = \Phi R_m $$
where $N$ is the number of turns, $i$ is the current, $\Phi$ is the magnetic flux, and $R_m$ is the reluctance. The total flux $\Phi$ is:
$$ \Phi = \frac{F_1 + F_{2a} + F_{2b} + F_{2c}}{R_m} = \frac{1}{R_m} \left[ N_1 I_1 + 3N_2 \frac{4}{\pi} \cdot \frac{UI}{V_{dc}} \cos \beta \right] \sin(\omega_1 t) $$
This confirms the absence of double-line frequency components, validating the power decoupling capability of the solar inverter.
Intra-phase power imbalance in cascaded solar inverters arises from unequal power generation among modules, leading to voltage mismatches. In an input-independent output-series (IIOS) system, the output current is uniform, so modules with higher input power require higher output voltages. The modulation index $M_k$ for the $k$-th module is defined as:
$$ M_k = \frac{V_k}{V_{k,\text{MAX}}}, \quad M_k \in [0, 1] $$
where $V_k$ is the output voltage RMS and $V_{k,\text{MAX}}$ is the maximum allowable voltage. The power ratio $\lambda_k$ is:
$$ \lambda_k = \frac{P_k}{P_{\text{tot}}} $$
and the output voltage satisfies:
$$ V_k = \lambda_k V_G $$
where $V_G$ is the grid voltage RMS. To prevent over-modulation, $V_{k,\text{MAX}} \geq \lambda_k V_G$. The maximum unbalanced power ratio $\lambda_{k,\text{MAX}}$ is:
$$ \lambda_{k,\text{MAX}} = \frac{V_{k,\text{MAX}}}{V_G}, \quad \lambda_{k,\text{MAX}} \in (0, 1] $$
This ratio indicates the solar inverter’s tolerance to intra-phase imbalance. For the proposed topology, the output voltage of module $k$ is related to the DC-link voltage $V_{dc,k}$ and modulation index:
$$ M_k = \frac{\sqrt{2} V_k}{V_{dc,k}} $$
Using power conservation:
$$ P_{pv,k} = V_{pv,k} I_{pv,k} = 3 V_k I_k = \frac{3}{2} M_k V_{dc,k} I_k $$
Thus, the output voltage is:
$$ V_k = \frac{1}{2} M_k V_{dc,k} = \frac{1}{3} \cdot \frac{P_{pv,k}}{I_k} $$
This equation highlights that higher power modules necessitate higher voltages, and intra-phase imbalance can lead to over-modulation if not managed properly.
The distributed adaptive boost control strategy enhances the solar inverter’s resilience to intra-phase power mismatch. The control structure employs a master controller for grid synchronization and sub-controllers for each module, reducing communication overhead. The sub-controller implements MPPT and input voltage control for the LLC stage, and a voltage-current double-loop control for the H-bridge inverter. The average DC-link voltage of the three phases is regulated using a variable reference voltage $V_{\text{dc,ref},k}^*$. The control logic is as follows:
- If $M_k \leq M_{\text{Lim},k}$ (where $M_{\text{Lim},k}$ is the maximum modulation index limit), then $V_{\text{dc,ref},k}^* = V_{\text{dc,ref},k}$, and the output voltage is controlled by $M_k$:
$$ V_k = \frac{1}{2} M_k V_{\text{dc,ref},k} $$
- If $M_k > M_{\text{Lim},k}$, then $M_k$ is clamped at $M_{\text{Lim},k}$, and $V_{\text{dc,ref},k}^* = V_{\text{dc,ref},k} + \Delta V_{dc}$, where $\Delta V_{dc}$ is generated by an additional current control loop. The output voltage becomes:
$$ V_k = \frac{1}{2} M_{\text{Lim},k} (V_{\text{dc,ref},k} + \Delta V_{dc}) $$
The DC-link voltage boost is limited by the LLC converter’s maximum gain $G_{k,\text{MAX}}$. If the gain is exceeded, the PV voltage $V_{pv,k}$ rises, reducing the output power and enabling automatic power balancing. The adaptive boost control process is summarized in the following flowchart:
Start → Check if $M_k \leq M_{\text{Lim},k}$ → If yes, $V_k = M_k V_{\text{dc,ref},k}$, $P_k = P_{\text{MPP},k}$ → If no, check if $G_k \leq G_{k,\text{MAX}}$ → If yes, $V_k = M_{\text{Lim},k} G_k V_{\text{MPP},k}$, $P_k = P_{\text{MPP},k}$ → If no, $V_k = M_{\text{Lim},k} G_{k,\text{MAX}} V_{pv,k}$, $P_k < P_{\text{MPP},k}$ → End.
For the proposed solar inverter, $\lambda_{k,\text{MAX}}$ under adaptive boost control is:
$$ \lambda_{k,\text{MAX}} = \frac{M_{\text{Lim},k} G_{k,\text{MAX}} V_{\text{MPP},k}}{N_k \sqrt{2} V_G} $$
where $N_k$ is the transformer turns ratio. In contrast, traditional solar inverters have:
$$ \lambda_{k,\text{MAX}} = \frac{M_{\text{Lim},k} V_{\text{MPP},k}}{N_k \sqrt{2} V_G} $$
The improvement factor is $G_{k,\text{MAX}}$, which significantly enhances the imbalance tolerance. For example, with $G_{k,\text{MAX}} = 2$, the proposed strategy allows more modules to operate at zero power without losing MPPT, as shown in the comparative analysis below.
| Total Modules in Cascade | Max Zero-Power Modules (Traditional) | Max Zero-Power Modules (Proposed) |
|---|---|---|
| 10 | 2 | 4 |
| 20 | 4 | 8 |
| 30 | 6 | 12 |
| 40 | 8 | 16 |
| 50 | 10 | 20 |
Simulation and experimental results validate the solar inverter’s performance. The system parameters are listed in the following table:
| Parameter | Value |
|---|---|
| Rated Power, $P_{\text{tot}}$ | 900 W |
| Number of Modules, $n$ | 3 |
| Module Rated Power, $P_{\text{in}}$ | 300 W |
| Input Voltage, $V_{pv}$ | 40 V |
| DC-Link Voltage, $V_{dc}$ | 40 V |
| LLC Resonant Frequency, $f_r$ | 200 kHz |
| Resonant Inductance, $L_r$ | 336 nH |
| Resonant Capacitance, $C_r$ | 470 nF |
| Magnetizing Inductance, $L_m$ | 1.68 μH |
| Grid Frequency, $f$ | 50 Hz |
| Input Capacitance, $C_{\text{in}}$ | 10 μF |
| DC-Link Capacitance, $C_{dc}$ | 10 μF |
| H-Bridge Switching Frequency, $f_c$ | 50 kHz |
| Filter Inductance, $L_f$ | 20 μH |
| Grid Voltage Amplitude, $V_g$ | 100 V |
| Transformer Turns Ratio, $N$ | 1:1:1:1 |
In simulation, all solar inverter modules initially operate at 300 W. Under mild imbalance (e.g., modules 2 and 3 at 220 W and 260 W), the system maintains MPPT with modulation index adjustment. The DC-link voltage ripple is approximately 1.6 V, demonstrating effective power decoupling. Under severe imbalance (modules 2 and 3 at 100 W and 120 W), module 1’s DC-link voltage boosts adaptively while retaining MPPT. In extreme cases (modules 2 and 3 at 20 W and 40 W), module 1’s PV voltage increases, limiting power output but maintaining sinusoidal grid currents. Experimental results on a prototype solar inverter confirm these findings, showing stable operation with minimal ripple and robust response to power mismatches.
In conclusion, the proposed modular three-phase solar inverter topology with distributed adaptive boost control effectively addresses inter-phase and intra-phase power imbalances in PV systems. The four-port LLC converter enables inherent power balancing and ripple suppression, while the control strategy enhances operational range without complex communication. This approach advances the development of reliable and scalable solar inverters for future energy systems.