In the rapidly evolving field of renewable energy, solar inverters play a pivotal role in converting direct current (DC) from photovoltaic (PV) panels into alternating current (AC) for grid integration. Among various topologies, the cascaded H-bridge (CHB) solar inverter has garnered significant attention due to its modular structure, high efficiency, and superior power quality. However, a critical challenge arises when power imbalances occur among the H-bridge modules, often due to partial shading, dust accumulation, or module mismatches. These imbalances can lead to over-modulation in certain modules, resulting in distorted grid currents and even system failure. In this paper, we propose an enhanced control strategy based on third harmonic compensation to extend the operational range of CHB solar inverters under severe power imbalance conditions. Our approach ensures unit power factor operation, maintains low total harmonic distortion (THD) in grid currents, and minimizes DC-link voltage fluctuations. Through detailed analysis, simulation, and experimental validation, we demonstrate the effectiveness of this strategy in real-world applications for solar inverters.
The CHB solar inverter topology consists of multiple H-bridge modules connected in series on the AC side, with each module independently supplied by a PV panel on the DC side. This configuration allows for individual maximum power point tracking (MPPT), maximizing energy harvest from each panel. However, when power imbalances exist, the modules transmitting higher power may experience over-modulation, as the modulation index exceeds unity. Traditional control methods, such as reactive power compensation or hybrid modulation, have limitations in terms of power factor degradation or voltage fluctuations. Our improved strategy addresses these issues by intelligently limiting the modulation index and applying third harmonic injection, thereby expanding the linear operating range of the solar inverter. This paper is structured as follows: we first present the system model and analyze the over-modulation mechanism; then, we review existing control strategies and introduce our proposed method; next, we provide simulation and experimental results; and finally, we conclude with key insights.
To understand the power imbalance problem, consider a single-phase CHB solar inverter with n H-bridge modules, as illustrated in the following figure. Each module includes a DC-link capacitor fed by a PV panel, and the AC outputs are summed via filtering inductors to connect to the grid. The switching states of the modules generate a multilevel voltage waveform, reducing harmonic content and improving grid compatibility. In a well-balanced system, all modules operate near their MPPs, but under imbalances, the modulation indices diverge. Define the modulation wave for the i-th module as:
$$m_i = \frac{v_{Hi}}{V_{PVi}}$$
where $v_{Hi}$ is the fundamental component of the AC output voltage $V_{oi}$, and $V_{PVi}$ is the DC-link voltage. The power transmitted by each module $P_i$ relates to the total power $P_T$ as:
$$\sum_{i=1}^{n} P_i = P_T$$
Assuming the grid voltage $v_g$ and current $i_g$ are sinusoidal, the amplitude of the modulation wave $S_i$ for module i is:
$$S_i = \frac{V_i}{V_{PVi}} = \frac{P_i}{P_T} \cdot \frac{V_r}{V_{PVi}}$$
where $V_i$ is the amplitude of $v_{Hi}$, and $V_r$ is the amplitude of the total reference voltage. When $S_i > 1$, the module enters over-modulation, causing harmonic distortion. For stable operation, a condition to avoid over-modulation is:
$$I_g \geq 2 I_i$$
where $I_g$ is the grid current RMS value, and $I_i$ is the DC current from the PV panel. However, under severe imbalances, this condition may not hold, necessitating advanced control for the solar inverter.
Existing control strategies for CHB solar inverters include hybrid modulation, reactive power compensation, and third harmonic compensation. Hybrid modulation combines low-frequency square waves with high-frequency PWM to increase voltage utilization, but it leads to significant DC-link voltage fluctuations. Reactive power compensation injects quadrature currents to balance modulation indices, yet it sacrifices power factor. Third harmonic compensation, initially proposed for three-phase inverters, adds a third harmonic component to the modulation wave, expanding the linear range to a modulation index of 1.155. For a solar inverter, this method maintains unit power factor and reduces voltage ripple, but it fails when modulation indices exceed 1.155. Our improved strategy overcomes this limitation by first adjusting the power output of over-modulated modules.
We propose an enhanced third harmonic compensation strategy for CHB solar inverters. The key idea is to limit the modulation index of any module that would otherwise exceed 1.155 by reducing its power output, then apply third harmonic injection to all modules to keep modulation indices within unity. Specifically, assume that among n modules, the first y modules have modulation indices $S_i > 1.155$, the next x-y modules have $1 < S_i \leq 1.155$, and the remaining modules have $S_i \leq 1$. For modules with $S_i > 1.155$, we compute a revised power reference $P_{Xi}$ to force $S_i = 1.155$:
$$P_{Xi} = 1.155 \cdot \frac{P_T \cdot V_{PVi}}{V_r}$$
The total power is recalculated as:
$$P_T = \sum_{i=1}^{y} P_{Xi} + \sum_{i=y+1}^{n} P_i$$
Then, the modulation indices become:
$$S_i = \begin{cases} 1.155, & i = 1,2,\dots,y \\ \frac{P_i}{P_T} \cdot \frac{V_r}{V_{PVi}}, & i = y+1,\dots,n \end{cases}$$
Since all $S_i \leq 1.155$, third harmonic compensation can be applied to ensure $S_i \leq 1$ in practice. The third harmonic component is added to the modulation waves of modules with $S_i > 1$ and subtracted from those with $S_i < 1$, such that the net third harmonic in the AC output cancels out. This maintains grid current quality and unit power factor. The control architecture for the solar inverter includes a central controller for grid current regulation and individual module controllers for MPPT and DC-link voltage control. The central controller computes the total reference voltage $V_r$ and angle $\theta_r$ based on grid synchronization and power balance, then distributes modulation waves to each module.
To validate our strategy, we conducted simulations using MATLAB/Simulink for a CHB solar inverter with four modules. The system parameters are summarized in Table 1, representing typical values for a residential solar inverter setup. The PV panels are modeled with standard characteristics, and the grid conditions are set to nominal values. We compared traditional control (without compensation) and our improved strategy under power imbalance scenarios, such as sudden irradiance drops on some panels.
| Parameter | Value |
|---|---|
| PV Panel Maximum Power ($P_{max}$) | 260 W |
| Open-Circuit Voltage ($V_{oc}$) | 37.98 V |
| Short-Circuit Current ($I_{sc}$) | 9.04 A |
| MPP Voltage ($V_{MPP}$) | 30.63 V |
| MPP Current ($I_{MPP}$) | 8.49 A |
| DC-Link Capacitance ($C_i$) | 27.2 mF |
| Filter Inductance ($L_1$, $L_2$) | 0.75 mH |
| Grid Voltage Peak ($V_M$) | 100 V |
| Grid Frequency ($f_{grid}$) | 50 Hz |
| Switching Frequency ($f_{car}$) | 2500 Hz |
In the simulation, we initially set irradiance levels for the four panels to 1000, 1000, 850, and 700 W/m², representing a mild imbalance. At time $t = 0.4$ s, we abruptly changed the irradiance for the third and fourth panels to 350 and 400 W/m², creating a severe imbalance. With traditional control, the solar inverter exhibited over-modulation in the first two modules, leading to a distorted grid current with THD of 16.6%, as shown by the waveform analysis. In contrast, with our improved strategy, the modulation indices were limited to 1.155 for the over-modulated modules, and third harmonic compensation was applied. The grid current THD remained below 3.2%, demonstrating effective operation. The DC-link voltages for the modules adjusted accordingly: the first two modules deviated from MPP to maintain stability, while the others stayed near MPP, with minimal fluctuations. This highlights the robustness of our approach for solar inverters in dynamic environments.
We further verified the strategy through experimental tests on a prototype CHB solar inverter with four modules, using programmable PV simulators to emulate irradiance changes. The experimental parameters matched those in Table 1. Under similar imbalance conditions, traditional control resulted in a grid current THD of 12%, whereas our strategy maintained THD below 3%. The DC-link voltage waveforms confirmed that the over-modulated modules adjusted their power outputs, ensuring all modulation indices stayed within the linear range. These results align with simulations, proving the practical feasibility of our method for real-world solar inverter applications.
The mathematical formulation of our control strategy involves several key equations. The grid current control loop uses a synchronous reference frame approach. Let $v_g = V_M \sin(\theta)$ and $i_g = I_g \sin(\theta – \phi)$, where $\theta$ is the grid angle from a phase-locked loop (PLL), and $\phi$ is the power factor angle. Using second-order generalized integrators (SOGI), we obtain orthogonal components $i_D$ and $i_Q$ for Park transformation. The current references are set as $I_d^* = 2P_T / V_M$ and $I_q^* = 0$ for unit power factor. PI controllers generate voltage references $U_d$ and $U_q$, leading to:
$$V_r = \sqrt{U_d^2 + U_q^2}, \quad \theta_r = \arctan\left(\frac{U_q}{U_d}\right)$$
The modulation wave for each module is then:
$$m_i = \frac{P_i}{P_T} \cdot \frac{V_r}{V_{PVi}} \cdot \sin(\theta + \theta_r) + h_3 \cdot \sin(3(\theta + \theta_r) + \psi_i)$$
where $h_3$ is the third harmonic amplitude, and $\psi_i$ is the phase adjustment for cancellation. For modules with $S_i > 1.155$, $P_i$ is replaced by $P_{Xi}$ as per earlier equations. This ensures that the solar inverter operates smoothly even under extreme imbalances.
Our strategy offers several advantages for CHB solar inverters. First, it extends the operational range without sacrificing power factor, unlike reactive compensation methods. Second, it minimizes DC-link voltage fluctuations compared to hybrid modulation. Third, it maintains low grid current THD, complying with grid standards. Additionally, the approach is scalable to any number of modules, making it suitable for large-scale solar inverter systems. The computational overhead is moderate, as it involves basic arithmetic and harmonic injection, easily implementable on digital signal processors. In practice, this can enhance the reliability and efficiency of solar inverters in installations with partial shading or aging panels.
In conclusion, we have presented an improved control strategy for cascaded H-bridge solar inverters to address power imbalance-induced over-modulation. By combining power limiting and third harmonic compensation, our method ensures stable operation under severe imbalances, unit power factor, and low harmonic distortion. Simulations and experiments validate its effectiveness, highlighting its potential for widespread adoption in photovoltaic systems. Future work may explore integration with energy storage or advanced MPPT techniques to further optimize solar inverter performance. This contribution underscores the importance of adaptive control in modern solar inverters for sustainable energy integration.