I present an improved control strategy for cascaded H‑bridge (CHB) solar inverter to extend its operation range under severe power imbalance among photovoltaic modules. The proposed method combines power limiting on over‑modulated cells with a third harmonic compensation scheme, ensuring unity power factor operation and low grid current distortion even when the modulation index exceeds 1.155. Detailed mathematical analysis, simulation results, and experimental verification are provided.
CHB solar inverters have attracted significant attention due to their modularity, low harmonic content, high efficiency, and the ability to perform independent maximum power point tracking (MPPT) for each PV string. However, when partial shading or dust accumulation causes a large disparity in output power among the H‑bridge cells, the cells delivering higher power may enter over‑modulation. Over‑modulation leads to severe distortion of the grid current and can cause system instability. Several mitigation techniques have been proposed, such as hybrid modulation, reactive power compensation, and third harmonic injection. Among these, third harmonic injection can extend the linear modulation range to 1.155 while maintaining unity power factor and low DC‑link voltage ripple. Nevertheless, when the modulation index exceeds 1.155, even the third harmonic injection fails to prevent over‑modulation. In this work, I propose a strategy that first limits the modulation index of severely over‑modulated cells to 1.155 by reducing their PV power, then applies the third harmonic injection to all cells. This approach preserves all advantages of third harmonic compensation and guarantees normal operation under extreme power imbalance.
The topology of a single‑phase CHB solar inverter with n H‑bridge modules is shown in the figure below. Each module is fed by a separate PV panel, and the AC sides are connected in series through filter inductors L1 and L2 to the grid. The grid voltage is vg and the grid current is ig.
Under steady‑state conditions, for the i‑th H‑bridge module, the modulation index mi is defined as:
$$ m_i = \frac{V_{Hi}}{V_{PVi}} $$
where VHi is the amplitude of the fundamental component of the AC‑side output voltage of the i‑th module, and VPVi is the DC‑link voltage of that module. The power balance of the solar inverter yields:
$$ P_T = \sum_{i=1}^{n} P_i $$
where Pi is the power delivered by the i‑th PV module and PT is the total AC‑side power. Ignoring losses, the output voltage amplitudes of the H‑bridge modules are proportional to their input powers:
$$ \frac{V_1}{P_1} = \frac{V_2}{P_2} = \cdots = \frac{V_i}{P_i} = \frac{V_r}{P_T} $$
Here Vr is the amplitude of the total reference voltage of the inverter. Combining these relationships, the modulation index of the i‑th module becomes:
$$ S_i = \frac{V_i}{V_{PVi}} = \frac{P_i}{P_T} \cdot \frac{V_r}{V_{PVi}} $$
When Pi is much larger than the average, Si can exceed 1, leading to over‑modulation. The well‑known condition for avoiding over‑modulation without any compensation is:
$$ i_g \ge \sqrt{2} \, I_i $$
where ig is the RMS grid current and Ii is the RMS output current of the i‑th module. If this condition is violated, the solar inverter cannot operate normally.
The third harmonic compensation strategy proposed in prior work is an effective method when 1 < Si ≤ 1.155. In this approach, a third harmonic component is added to the modulation signals of the over‑modulated cells to reduce their peak amplitude to unity, while an equal but opposite phase third harmonic is injected into the cells with Si ≤ 1, so that the total output voltage of the CHB inverter remains free of third harmonic. The control block diagram consists of an H‑bridge local controller for MPPT and DC‑link voltage regulation, and a central controller for grid current control and harmonic distribution. The central controller uses a second‑order generalized integrator (SOGI) and Park transformation to obtain the active and reactive current feedback. The total modulation voltage amplitude Vr and angle θr are computed from the current loop outputs.
However, if Si exceeds 1.155, even the third harmonic injection cannot prevent over‑modulation. To address this limitation, I propose an improved strategy. Suppose the first y cells have Si > 1.155, the next (x‑y) cells have 1 < Si ≤ 1.155, and the remaining cells have Si ≤ 1. The key idea is to limit the modulation index of the first y cells to exactly 1.155 by reducing their input power. The power of these cells is forced to:
$$ P_{Xi} = 1.155 \frac{P_T V_{PVi}}{V_r}, \quad i = 1,\dots,y $$
Then the total system power PT is recalculated as:
$$ P_T’ = \sum_{i=1}^{y} P_{Xi} + \sum_{i=y+1}^{n} P_i $$
The modulation indices for all cells are then:
$$ S_i = \begin{cases} 1.155, & i = 1,\dots,y \\ \frac{P_i}{P_T’} \cdot \frac{V_r}{V_{PVi}}, & i = y+1,\dots,n \end{cases} $$
Since PXi automatically adjusts the DC‑link voltage of the limited cells away from the MPPT point, these cells operate at a reduced power level, but their modulation index stays at 1.155, which is within the linear range after third harmonic injection. The remaining cells continue MPPT, and their modulation indices are computed normally. After applying the third harmonic compensation to all cells (with appropriate phase relationships), every H‑bridge operates below the over‑modulation boundary.
To validate the proposed strategy, I conducted simulations using Matlab/Simulink with a 4‑module CHB solar inverter. The parameters of the PV modules (JAP6‑60‑260/3BB) and the grid/interfacing components are summarized in the following table.
| Parameter | Value |
|---|---|
| PV Maximum Power Pmax | 260 W |
| Open Circuit Voltage Voc | 37.98 V |
| Short Circuit Current Isc | 9.04 A |
| MPP Voltage VMPP | 30.63 V |
| MPP Current IMPP | 8.49 A |
| DC‑link Capacitor Ci (each) | 27.2 mF |
| Filter Inductors L1, L2 | 0.75 mH |
| Grid Voltage Peak VM | 100 V |
| Grid Frequency fgrid | 50 Hz |
| Switching Frequency fcar | 2500 Hz |
In the first simulation, I used conventional control without the proposed power limiting. Initially, the irradiance for four modules was E1=1000, E2=1000, E3=850, E4=700 W/m². At t=0.4 s, I changed E3 to 350 and E4 to 400 W/m², creating severe imbalance. The grid current THD increased from 2.28% to 16.6%, and the current waveform became highly distorted. In contrast, when I applied the proposed strategy under identical conditions, the modulation indices of the first two cells (which would otherwise exceed 1.155) were clamped at 1.155, and their output powers decreased accordingly. The grid current THD remained at only 3.16%, demonstrating that the solar inverter operated correctly.
I also observed the DC‑link voltages. Under the proposed strategy, the voltages of the first two modules deviated from their MPPT voltage (30.63 V) to approximately 32–33 V, while the other two modules stayed near their MPPT points. This confirmed that the power limiting worked as intended.
To further confirm the practical feasibility, I built an experimental prototype using a Chroma 62020H‑150S PV simulator for each module. The experimental parameters were identical to those in the simulation. With the conventional method, the grid current THD jumped from 1.23% to 12% after the irradiance change. Using the proposed method, the THD was only 2.87% after the same change, and the current waveform remained sinusoidal. The four DC‑link voltages showed the expected behavior: the first two cells had stable but elevated voltages, while the last two cells exhibited a slight increase due to the change in power distribution.
The following table provides a comparison of key performance indices between the conventional and proposed control strategies for the imbalanced case (E3=350, E4=400 W/m²).
| Metric | Conventional | Proposed |
|---|---|---|
| Grid Current THD (simulation) | 16.6% | 3.16% |
| Grid Current THD (experiment) | 12% | 2.87% |
| Power Factor | ≤0.95 (distorted) | ~1.0 |
| Max Modulation Index | >1.155 (over‑modulated) | ≤1.155 |
| DC‑link Voltage Ripple | Large (due to distortion) | Small (2× line) |
| System Operation | Unstable / distorted current | Stable / sinusoidal current |
In summary, the proposed control strategy effectively extends the operation range of the cascaded H‑bridge solar inverter under severe power imbalance. By limiting the modulation index of critically over‑modulated cells to 1.155 and then applying third harmonic compensation to all cells, the system maintains unity power factor, low THD (<5%), and stable DC‑link voltages. The method is straightforward to implement and does not require additional hardware. Simulation and experimental results consistently confirm its effectiveness. This work provides a practical solution for solar inverter applications where partial shading or module mismatch is unavoidable.