In the rapidly evolving landscape of renewable energy systems, the integration of photovoltaic (PV) power generation into the electrical grid has become a cornerstone of sustainable development. Among the various topologies for grid-connected PV systems, the single-phase cascaded H-bridge (CHB) inverter stands out as one of the most promising types of solar inverters due to its modular structure, independent maximum power point tracking (MPPT) capabilities, and high efficiency without the need for a bulky line-frequency transformer. However, a critical challenge that limits the performance of these types of solar inverters is the power imbalance among individual H-bridge modules. This imbalance, caused by partial shading, dust accumulation, or temperature variations across different PV panels, leads to a scenario where modules with higher power generation face the risk of over-modulation. When the modulation index (MI) of an H-bridge exceeds unity, the conventional sinusoidal pulse width modulation (SPWM) introduces low-order harmonics, causing grid current distortion, reduced solar energy utilization, and potential system instability.
My research addresses this fundamental limitation by proposing a novel control strategy for a hybrid PV-battery cascaded H-bridge inverter. This architecture represents a significant evolution among types of solar inverters, as it integrates a small-scale battery unit on the DC side to provide an additional degree of freedom for power management. The core objective of my work is to overcome the traditional constraint that limits the linear modulation range of H-bridge modules to a maximum MI of \(4/\pi\). By intelligently scheduling the charge and discharge of the battery based on the system’s operating conditions, my strategy allows the inverter to maintain MPPT operation even under extreme power mismatch conditions, thereby extending the operating range and improving overall system robustness.
To provide a comprehensive understanding, I will detail the architecture, the mathematical modeling of the problem, the proposed five-mode control strategy, the modified harmonic compensation technique, and the experimental validation of my approach.
System Topology and Operating Principles
The topology I employ is a single-phase cascaded H-bridge inverter consisting of \(n\) PV-fed H-bridge modules and one additional H-bridge module connected to a battery storage unit. The AC outputs of all H-bridges are connected in series, and the total output voltage is fed to the grid through a filter inductor \(L\). Each PV module is equipped with its own DC-link capacitor \(C_i\), and the battery unit has a dedicated capacitor \(C_B\). The key parameters defining the system are summarized in Table 1. This hybrid configuration is one of the most versatile types of solar inverters, as it seamlessly combines the benefits of PV generation with the dispatchability of energy storage.
| Parameter | Symbol | Value |
|---|---|---|
| Grid Voltage (amplitude) | \(V_g\) | 60 V |
| Filter Inductance | \(L\) | 4 mH |
| PV Module DC Capacitor | \(C_i\) | 460 μF |
| PV Module 1 Peak Power | \(P_{max1}\) | 350 W |
| PV Module 1 MPP Voltage | \(V_{mp1}\) | 35.2 V |
| PV Module 2 Peak Power | \(P_{max2}\) | 250 W |
| PV Module 2 MPP Voltage | \(V_{mp2}\) | 35.2 V |
| Battery Rated Voltage | \(V_{dcB}\) | 36 V |
| Switching Frequency | \(f_s\) | 10 kHz |
The fundamental principle for extending the operating range is derived from the relationship between the grid current amplitude \(I_g\) and the DC current of the \(i\)-th PV module \(I_{dcPVi}\). For a CHB inverter operating under unity power factor, the modulation index of a module is directly proportional to its output power. Over-modulation (MI > 1) occurs when the condition in Eq. (1) is met.
$$ I_g = 2 I_{dcPVi} \tag{1} $$
When the MI exceeds \(4/\pi\), which is the theoretical limit for conventional linear modulation techniques like SPWM and many harmonic compensation strategies, the condition in Eq. (2) is reached.
$$ I_g = \frac{4\sqrt{2}}{\pi} I_{dcPVi} \tag{2} $$
In a conventional PV-only system, the grid current amplitude \(I_g\) is constrained by the total PV power. However, in my proposed hybrid system, the battery unit provides an additional energy source. By discharging the battery, the total active power injected into the grid increases, thereby increasing \(I_g\). This increase reduces the modulation index of the highest-power modules, pulling them back into the linear operating range. The fundamental phasor relationship is illustrated by the vector diagram where the battery’s output voltage vector \(V_{HB}\) can be decomposed into an active component \(V_{HBd}\) (in phase with \(I_g\)) and a reactive component \(V_{HBq}\) (in quadrature with \(I_g\)). This capability sets this topology apart from many other types of solar inverters that lack integrated storage.
Operational Modes of PV and Battery Modules
The performance of the PV modules and the battery unit is governed by distinct operating conditions. The PV module’s operating region is defined by its modulation index. To avoid the nonlinearities of over-modulation, I define three regions:
- Region 1 (MI < 1): Standard SPWM is used, and the module operates at its MPP.
- Region 2 (1 < MI < 4/π): The Multiple Harmonic Compensation Strategy (MHCS) is employed to extend the linear range. The module can still operate at MPP.
- Region 3 (MI > 4/π): Traditional linear modulation strategies fail. The module must either be supported by an external energy source (the battery) or be forced to exit MPPT operation.
The battery unit’s behavior is primarily dictated by its state of charge (SOC), denoted as \(SOC_B\). I define three distinct states:
- State 1 (\(SOC_B \ge SOC_{max}\)): The battery is fully charged. It can only supply reactive power (discharging is disabled to prevent overcharging), making the system behave like a standard PV-only inverter.
- State 2 (\(SOC_{min} < SOC_B < SOC_{max}\)): The battery is in its normal operating range. It can be charged or discharged actively, providing both active and reactive power support.
- State 3 (\(SOC_B \le SOC_{min}\)): The battery is undercharged. To prevent deep discharge damage, the battery is prohibited from supplying active power. It can still provide reactive power, but any modules with MI > 4/π must exit MPPT operation to reduce their power output.
These operational states are the foundation for my five-mode control strategy, which intelligently coordinates the PV modules and the battery to maximize energy harvesting from the PV array while ensuring stable grid connection. This dynamic reconfiguration is what enhances the utility of this specific class of types of solar inverters.
The Five-Mode Power Balancing Control Strategy
My proposed control strategy divides the operation of the hybrid CHB inverter into five distinct modes. The transition between modes is governed by the maximum modulation index among the PV-fed modules, \(MI_{max}\), and the battery’s SOC. The logic is detailed in the following decision table.
| Mode | Condition 1 (MI) | Condition 2 (SOC) | Battery Action | PV Module State | Grid Current Impact |
|---|---|---|---|---|---|
| 1 | \(MI_{max} < 1\) | \(SOC_B \ge SOC_{max}\) | Only reactive power (Q) | All at MPP, SPWM | Stable, nominal |
| 2 | \(MI_{max} < 4/\pi\) | \(SOC_B < SOC_{max}\) | Charging (Active + Q) | Highest power unit set to MI=4/π | Slightly reduced amplitude |
| 3 | \(1 < MI_{max} < 4/\pi\) | Any | Only reactive power (Q) | Use MHCS for over-modulated units | Low THD, stable |
| 4 | \(MI_{max} > 4/\pi\) | \(SOC_B > SOC_{min}\) | Discharging (Active + Q) | MI reduced to 4/π, MPPT maintained | Increased amplitude, stabilized |
| 5 | \(MI_{max} > 4/\pi\) | \(SOC_B \le SOC_{min}\) | Only reactive power (Q) | Over-modulated units exit MPPT | Stable, but PV power is curtailed |
In Mode 1, all PV modules receive uniform insolation. The battery is fully charged and only supplies the reactive power required by the filter inductor. The modulation waves for the \(i\)-th PV module and the battery are given by Eqs. (3) and (4), respectively.
$$ m_{PVi} = S_{PVi} \sin(\omega t) \tag{3} $$
$$ m_B = S_{Bq} \cos(\omega t) \tag{4} $$
where \(S_{PVi}\) is the modulation index of the \(i\)-th PV module and \(S_{Bq}\) is the reactive modulation index of the battery.
Mode 2 is a proactive charging mode. To ensure the battery has sufficient energy for future compensation, the system artificially increases the modulation index of the highest-power PV module to \(4/\pi\). The required charging power \(P_B\) is calculated in Eq. (5), where \(P_{PV\Sigma}\) is the total PV power.
$$ P_{B} = \frac{S_{PVmax}}{4/\pi} P_{PV\Sigma} – P_{PV\Sigma} \tag{5} $$
The active component of the battery’s modulation index is then derived from this power.
In Mode 3, partial shading causes one or more modules to enter the range \(1 < MI < 4/\pi\). I employ the MHCS, which injects a calculated set of harmonics into the over-modulated units while injecting opposing harmonics into the units still in the linear range. This prevents the total series voltage from distorting. A key modification I made to the original MHCS is that, because the battery handles the reactive power of the inductor, the PV output voltage is now in phase with the grid voltage, simplifying the reference calculation. The modulation wave for a compensated unit is given by the limiting function in Eq. (6).
$$ m_i = LA[M_i \sin(\omega t)] \tag{6} $$
where \(M_i\) is the target modulation index derived from the power distribution, and \(LA[.]\) is the limiting operation that clamps the signal to \(\pm 1\).
Mode 4 is the critical mode where the battery’s storage capability is fully leveraged. When \(MI_{max} > 4/\pi\) and the battery has sufficient charge (\(SOC_B > SOC_{min}\)), the battery is discharged. The primary goal is to inject enough active power to reduce the highest MI down to \(4/\pi\). The required active power \(P_B\) is given by Eq. (7), where \(K\) is the over-modulation factor (\(MI_{max} = 4K/\pi\)).
$$ P_B = \frac{P_{PVmax}}{4/\pi} \frac{V_g}{V_{max}} – \frac{P_{PVmax}}{4K/\pi} \frac{V_g}{V_{PVmax}} \tag{7} $$
This action ensures that all PV modules can continue to operate at their individual MPPs, maximizing solar energy harvesting even under severe imbalance. This is a key differentiator for my proposed architecture when compared to other simpler types of solar inverters.
Finally, Mode 5 represents the failure mode. If the battery is depleted (\(SOC_B \le SOC_{min}\)) and over-modulation persists, the affected PV modules are forced to exit MPPT. Their operating voltage is increased, moving them down the P-V curve to a lower power point, thus reducing their MI to an acceptable level (e.g., \(4/\pi\)). This is a protective measure to ensure grid stability, albeit at the cost of curtailed PV power.
Modified Multiple Harmonic Compensation Strategy
The MHCS is central to the operation in Modes 3 and 4. The original MHCS, as presented in literature for PV-only inverters, requires a complex calculation of the inverter output voltage vector via dq transformation to find the phase angle \(\theta_r\) between the inverter voltage and the grid voltage. In my hybrid system, the battery unit absorbs all the reactive power demand of the filter inductor. Consequently, the total output voltage of all *PV* modules is naturally in phase with the grid voltage. This simplifies the control significantly.
For a module operating in the over-modulated region, the fundamental component of the output voltage can be maintained proportional to the reference even when the modulating signal is clipped. The relationship between the desired fundamental voltage amplitude \(V_{ref}\) and the actual reference amplitude \(V_{dc}\) (the DC bus voltage) for a square-wave modulated system is shown in Eq. (8).
$$ \frac{V_{ref}}{V_{dc}} = \frac{4}{\pi} \tag{8} $$
The MHCS works by intentionally clipping the modulating signal and then injecting specific low-order harmonics (primarily the third harmonic) into the non-saturated units to counterbalance the distortion created by the saturated ones. This ensures that the total series voltage of the CHB inverter remains a pure sinusoid. The modulation signal for a saturated module after applying the limiting operator, \(LA\), is a quasi-square wave. The specific harmonic content is predictable and is compensated for within the control loop.
This advanced modulation technique is one of the reasons why the CHB topology remains one of the most sophisticated types of solar inverters for research and practical applications, as it requires precise control to handle non-linearities while maintaining high power quality.
Control Framework
The overall control system for my hybrid inverter is a hierarchical structure with three main layers: a master control layer, a battery control layer, and a harmonic compensation layer. The master control layer is responsible for grid synchronization and current regulation. I use a voltage-current dual-loop control scheme. The outer voltage loop, using a PI controller, regulates the average DC voltage of the PV modules. The output of this loop sets the amplitude of the reference grid current. The inner current loop uses a Quasi-Proportional Resonant (QPR) controller to track this reference current, generating the total required inverter voltage \(v_H\). A Phase-Locked Loop (PLL) provides the grid phase angle to ensure unity power factor operation at the overall system level.
The battery control layer receives the modulation indices \(S_{PVi}\) from the master layer. It then applies the logic from Table 2 to determine the operating mode. In Mode 2, it calculates the charging power \(P_B\) and the corresponding active modulation component \(S_{Bd}\). In Mode 4, it calculates the discharging power and the new modulation index for the saturated PV units, setting it to \(4/\pi\). The final modulation wave for the battery H-bridge, \(m_B\), is the sum of its active and reactive components.
Finally, the harmonic compensation layer monitors the \(S_{PVi}\) values. If any value exceeds 1, the MHCS is activated. This layer calculates the specific harmonic components to inject into the non-saturated modules based on the degree of saturation of the over-modulated modules, ensuring that the sum of the clipped and compensating signals is a pure sinusoid. Table 3 summarizes the role of the battery in each mode, highlighting its crucial function as a power buffer.
| Mode | Battery’s Primary Function | Battery Active Power Flow | Impact on System |
|---|---|---|---|
| 1 | Reactive Power Compensation | \(P_B = 0\) | Maintains unity power factor for PV. |
| 2 | Proactive Charging | \(P_B < 0\) (Absorbing) | Pre-charges battery for future support. |
| 3 | Reactive Power Compensation | \(P_B = 0\) | Supports zero-voltage-switching for PV. |
| 4 | Active Power Support | \(P_B > 0\) (Injecting) | Reduces MI, maintains MPPT of all PV units. |
| 5 | Reactive Power Compensation | \(P_B = 0\) | Protects battery, curtails PV power as last resort. |
Experimental Verification
To validate the effectiveness of my proposed strategy, I constructed a low-voltage laboratory prototype of the hybrid CHB inverter. The prototype consisted of three H-bridge modules: two connected to PV simulators (DC power supplies with series resistors to emulate different power levels) and one connected to a small battery pack. The controller was a TMS320F28335 DSP from Texas Instruments. The experiments were designed to validate the smooth transition between all five modes under various operating conditions.
The experimental results for each mode confirmed the theoretical analysis. In Mode 1, the battery voltage \(v_{HB}\) was observed to lead the grid current \(i_g\) by 90°, confirming it was only supplying reactive power. In Mode 2, the phase angle between \(v_{HB}\) and \(i_g\) shifted to between 90° and 180°, indicating active power absorption (charging). In Mode 3, the grid current maintained a low total harmonic distortion (THD) even though one PV module was over-modulated, thanks to the MHCS. The most compelling validation came from Mode 4. When a severe power imbalance caused the over-modulated module’s MI to exceed \(4/\pi\), the grid current became visibly distorted. Upon the activation of Mode 4 and the discharge of the battery, the grid current waveform immediately improved, and its amplitude increased as the battery injected active power to the grid. The MI of the saturated module was effectively reduced to \(4/\pi\). Finally, Mode 5 was validated by discharging the battery to its \(SOC_{min}\) limit and observing the controller seamlessly transition the affected PV module to a lower power operating point.
The key performance indicators from the experiments are summarized in Table 4. The traditional MPPT efficiency of a similar PV-only inverter under the same severe imbalance would have dropped dramatically due to the necessity of exiting MPPT. My hybrid strategy maintained near 100% MPPT efficiency for all PV modules until the battery was depleted.
| Operating Condition | Mode | Grid Current THD | PV MPPT Efficiency | Battery SOC Change |
|---|---|---|---|---|
| Balanced (1000 W/m²) | 1 | < 3% | ~100% | Stable (Full) |
| Unbalanced (1000/600 W/m²) | 3 | < 4% | ~100% | Stable |
| Severely Unbalanced (1000/400 W/m²) | 4 | < 4% | ~100% | Decreasing |
| Severely Unbalanced + Low Battery | 5 | < 3% | ~70% (one module) | Stable (Low) |
Conclusion
My research presents a robust and effective control strategy for a hybrid PV-battery cascaded H-bridge inverter. The key conclusions from this work are:
- Extended Operating Range: By integrating a small battery unit and intelligently managing its charge/discharge cycles, the strategy successfully overcomes the traditional modulation limit of \(4/\pi\) for H-bridge modules. This allows the inverter to maintain MPPT operation under previously untenable power mismatch conditions, significantly boosting energy yield in partially shaded environments.
- Enhanced Grid Stability: The smooth transitions between the five operating modes ensure minimal disturbance to the grid current. The dynamic support provided by the battery, both in terms of reactive power (for standard operation) and active power (for over-modulation mitigation), ensures low THD and a stable power injection, outperforming many other types of solar inverters that lack such integrated support.
- Optimal Utilization of Storage: Unlike strategies that only use the battery as a last resort, my approach actively manages the battery’s SOC. It proactively charges the battery in Mode 2 to ensure it is ready for a discharge event, and it utilizes the battery to compensate for filter inductance reactive power even when no over-modulation is present. This maximizes the utility of the relatively small storage unit.
In conclusion, my proposed power balance control strategy provides a practical and efficient solution to one of the most significant challenges facing cascaded H-bridge inverters, further establishing the CHB topology as one of the most advanced and adaptable types of solar inverters for future high-penetration renewable energy grids.