In recent years, the global focus on energy security and environmental issues has intensified, driving the urgent need to advance renewable energy development. With the orderly promotion of carbon reduction initiatives, solar power generation has once again encountered opportunities for rapid growth. Among these, solar inverters are critical components in advancing solar power generation. Single-phase cascaded H-bridge (CHB) solar inverters offer modular structures and multi-level output characteristics, enabling component-level maximum power point tracking (MPPT), single-inductor filtering, and direct grid connection without bulky line-frequency transformers. These features make solar inverters highly promising in the photovoltaic power generation sector.
However, factors such as varying component aging, surface dust, and partial shading lead to inherent power mismatch issues in single-phase CHB solar inverters. In severe cases, this can cause over-modulation in H-bridge units transmitting higher power, resulting in significantly distorted grid currents and even oscillatory overcurrents, failing to meet grid requirements. Existing research has addressed this problem but with limitations. To tackle this, a power matching control strategy based on specific harmonic compensation for single-phase CHB solar inverters is proposed. By injecting optimal 3rd, 5th, 7th, and 9th harmonics into over-modulated H-bridge units, the linear modulation range expands from 1 to 1.2438. Simultaneously, a closed-loop control method compensates for reverse harmonics in non-over-modulated H-bridges, ensuring stable inverter operation under significant input power disparities while maintaining low total harmonic distortion (THD) in grid currents. Experimental results validate the feasibility and effectiveness of the proposed control strategy.
The power mismatch in single-phase CHB solar inverters arises from series-connected H-bridge units, where each H-bridge is independently connected to a photovoltaic module on the DC side and coupled to the grid via filter inductors on the AC side. Let $U_g$ and $I_g$ represent the grid voltage and current, respectively, while $U_{dc,i}$ and $I_{dc,i}$ denote the DC-side voltage and current of the $i$-th H-bridge, with $i = 1, 2, \ldots, n$. The output voltage of the $i$-th H-bridge is $u_i$, and $P_i$ is the active power transmitted by the $i$-th H-bridge. The total power $P_T$ delivered to the grid by the single-phase CHB solar inverter is given by:
$$ P_T = \sum_{i=1}^{n} P_i = \frac{U_g I_g}{2} $$
Here, $U_g$ and $I_g$ are the amplitudes of the grid voltage and current, respectively. The modulation index $M_i$ for the $i$-th H-bridge module is defined as the ratio of its output voltage amplitude to the DC-link voltage. When partial shading or other factors reduce the output power of certain photovoltaic modules (e.g., $P_{t+1}$ to $P_n$ for $1 < t < n$), $P_T$ decreases. Since $U_g$ remains constant, $I_g$ must decrease. As all H-bridges are series-connected, the grid current flows through each unit. For H-bridges with higher power transmission (e.g., the first $t$ units), the amplitude of $u_i$ increases, raising $M_i$ and risking over-modulation. Thus, the fundamental cause of over-modulation in solar inverters is the significant disparity in power transmission among H-bridges, where the actual power transmitted by some units exceeds their capacity.
To address this, a harmonic compensation principle is applied. For a fundamental sinusoidal wave with amplitude $F$ and angular frequency $\omega$, specific odd-order harmonics are injected to reduce the peak amplitude of the modulated signal. The compensated signal $u_x$ is expressed as:
$$ u_x = F \sin(\omega t) + \sum_{r} Q_r F \sin(r \omega t) $$
where $Q_r$ represents the compensation coefficient for the $r$-th harmonic, and $r = 3, 5, 7, 9$ for optimal results. To avoid over-modulation, the amplitude of $u_x$ must not exceed 1. Calculations show that compensating only the 3rd harmonic with $Q_3 = 0.1667$ achieves a maximum linear modulation range of 1.155. However, by compensating 3rd, 5th, 7th, and 9th harmonics with $Q_3 = 0.285$, $Q_5 = 0.13$, $Q_7 = 0.06$, and $Q_9 = 0.02$, the linear modulation range expands to 1.2438. This harmonic injection reduces the peak amplitude of the modulation wave, allowing H-bridges to operate linearly even under high power disparities. The effectiveness of harmonic compensation is summarized in Table 1, which compares modulation ranges for different harmonic combinations.
| Harmonic Orders Compensated | Optimal Coefficients | Maximum Linear Modulation Range |
|---|---|---|
| 3rd | $Q_3 = 0.1667$ | 1.155 |
| 3rd, 5th, 7th, 9th | $Q_3 = 0.285$, $Q_5 = 0.13$, $Q_7 = 0.06$, $Q_9 = 0.02$ | 1.2438 |
The system control strategy for single-phase CHB solar inverters comprises a main controller and $n$ H-bridge controllers. Each H-bridge controller performs MPPT for its corresponding photovoltaic module and generates switching signals based on a carrier phase-shift modulation strategy, using the modulation wave $u_i$ provided by the main controller. The MPPT algorithm yields the reference DC-side voltage $U_{dc,ref,i}$ for the $i$-th H-bridge. The average DC-side voltage $\overline{U_{dc,i}}$ is obtained by filtering $U_{dc,i}$ with a 100 Hz notch filter, and a PI regulator controls $\overline{U_{dc,i}}$ to match $U_{dc,ref,i}$. The regulator output is the DC-side reference current $I_{dc,ref,i}$, which is multiplied by $U_{dc,i}$ to obtain $P_i$. In the main controller, a phase-locked loop (PLL) analyzes $U_g$ to extract its amplitude $U_g$ and phase angle $\theta$. A second-order generalized integrator transforms $U_g$ into in-phase and quadrature components $U_d$ and $U_q$, where $U_d$ aligns with $U_g$ in phase and amplitude, and $U_q$ lags by 90°. Park transformation relative to $U_d$ yields feedback active current $I_d$ and reactive current $I_q$. The sum of all $P_i$ values gives $P_T$, and dividing $P_T$ by $U_g/2$ provides the active current reference $I_{d,ref}$, while the reactive current reference $I_{q,ref}$ is set to zero for unity power factor operation. H-infinity control and current feedforward decoupling yield the reference active voltage amplitude $U_d$ and reactive voltage amplitude $U_q$.
The total modulation voltage amplitude $U_T$ and phase angle $\theta$ for the single-phase CHB solar inverter are calculated as:
$$ U_T = \sqrt{U_d^2 + U_q^2} $$
$$ \theta = \arctan\left(\frac{U_q}{U_d}\right) $$
where $U_T$ represents the amplitude of the fundamental component. Since the current through each H-bridge is identical, $M_i$ is proportional to $P_i$, and the modulation index for the $i$-th H-bridge is:
$$ M_i = \frac{U_{mi}}{U_{dc,i}} = \frac{P_i}{P_T} U_T $$
Based on Equation (4), H-bridges with $M_i > 1$ are identified as over-modulated, while those with $M_i \leq 1$ are normal. Suppose the first $t$ H-bridges are over-modulated ($1 < M_i \leq 1.2438$), and the remaining $n-t$ H-bridges are normal ($0 < M_i \leq 1$). To prevent over-modulation, the over-modulated H-bridges are injected with 3rd, 5th, 7th, and 9th harmonics, so the modulation wave $u_i$ becomes:
$$ u_i = M_i \sin(\omega t + \theta) + Q_3 M_i \sin(3\omega t + 3\theta) + Q_5 M_i \sin(5\omega t + 5\theta) + Q_7 M_i \sin(7\omega t + 7\theta) + Q_9 M_i \sin(9\omega t + 9\theta) $$
for $i = 1, 2, \ldots, t$. To eliminate these harmonics from the grid current, normal H-bridges compensate with reverse harmonics of equal amplitude but opposite phase. A closed-loop approach is employed, where a harmonic compensator controls the 3rd, 5th, 7th, and 9th harmonic components of the grid current to zero. The output of this compensator is the total reverse harmonic voltage $u_{NHT}$ for normal H-bridges. This voltage is distributed among normal H-bridges based on their capacity to avoid over-modulation. The maximum compensatable voltage amplitude for the $j$-th normal H-bridge ($j = t+1, \ldots, n$) is:
$$ U_{NH,max,j} = (1 – M_j) U_{dc,j} $$
If distributed proportionally, the reverse harmonic voltage $u_{NH,j}$ for the $j$-th normal H-bridge is:
$$ u_{NH,j} = \frac{U_{NH,max,j}}{\sum_{k=t+1}^{n} U_{NH,max,k}} u_{NHT} $$
Thus, the modulation wave for the $j$-th normal H-bridge is:
$$ u_j = M_j \sin(\omega t + \theta) + u_{NH,j} $$
This strategy ensures that all H-bridges operate within their linear modulation ranges while minimizing grid current THD.
Experimental validation was conducted on a single-phase CHB solar inverter prototype with five H-bridge units, filter circuits, and a main controller. TMS320F28335 microcontrollers served as H-bridge controllers, and an industrial PLC (CX2040) acted as the main controller, with data exchange via EtherCAT. Five Chroma 62020-150S photovoltaic simulators powered the H-bridges, each with a maximum output power of 200 W and MPP voltage of 30.6 V. The DC-link capacitance was 27.2 mF, grid-side filter inductance was 1.5 mH, H-bridge switching frequency was 2.5 kHz, and grid voltage was 130 V at 50 Hz. Initial conditions set all simulators to 20°C, with irradiance levels: $E_1 = E_2 = 1000$ W/m², $E_3 = 550$ W/m², $E_4 = 500$ W/m², $E_5 = 450$ W/m². Theoretical power transmission for each H-bridge was $P_1 = P_2 = 200$ W, $P_3 = 110$ W, $P_4 = 100$ W, $P_5 = 90$ W, indicating severe power imbalance. With only 3rd harmonic compensation, the linear modulation range is 1.155, insufficient for this scenario, leading to over-modulation and high grid current THD of 9.89%. Using the proposed control method with 3rd, 5th, 7th, and 9th harmonic compensation, all H-bridges operate linearly, and grid current THD reduces to 2.18%. Table 2 summarizes the experimental results under different compensation strategies.
| Compensation Strategy | Grid Current THD | Modulation Range | Stability |
|---|---|---|---|
| 3rd Harmonic Only | 9.89% | 1.155 | Unstable |
| Proposed Method (3rd, 5th, 7th, 9th) | 2.18% | 1.2438 | Stable |
The proposed power matching control strategy for single-phase CHB solar inverters leverages specific harmonic compensation to expand the linear modulation range of H-bridges from 1 to 1.2438, enabling stable operation under significant power disparities. By injecting optimal 3rd, 5th, 7th, and 9th harmonics into over-modulated units and employing closed-loop reverse harmonic compensation in normal units, the grid current THD is minimized, meeting grid standards. This approach enhances the reliability and efficiency of solar inverters in practical applications, addressing inherent challenges in photovoltaic systems. Future work could explore adaptive harmonic compensation for dynamic environmental conditions and integration with advanced MPPT techniques for further optimization of solar inverters.
In summary, the development of solar inverters is crucial for advancing renewable energy, and the proposed control strategy significantly improves their performance in unbalanced power scenarios. The use of harmonic compensation not only resolves over-modulation issues but also ensures high-quality power injection into the grid, reinforcing the role of solar inverters in modern energy systems. Continued innovation in control methodologies will further solidify the position of solar inverters as key components in sustainable power generation.