1. Introduction and Research Background
As fossil energy sources gradually deplete and environmental pollution becomes increasingly prominent, the global demand for renewable energy has become more urgent than ever. Solar energy, as a renewable resource with immense potential, is almost universally accessible across the globe. With technological advancements, the conversion efficiency of photovoltaic (PV) systems continues to rise while costs steadily decrease, making solar inverters increasingly competitive in the energy market. In recent years, the continuous progress in power electronics technology has significantly enhanced the efficiency and reliability of grid-connected solar inverters, providing robust support for the widespread application of PV power generation.
Among various inverter topologies, the Cascaded H-Bridge (CHB) inverter stands out for its simple layout, high reliability, ease of modularization, and minimal device count required to synthesize the same number of voltage levels. When CHB inverters are used in PV power generation systems, the DC side is independently powered by PV modules, which enables maximum power point tracking (MPPT) for each module. This configuration not only satisfies the CHB topology’s requirement for multiple independent DC sources but also eliminates the need for DC/DC converters, making CHB inverters an ideal choice for grid-connected PV applications. However, in single-phase CHB inverters, partial shading or damage to PV panels can cause output power imbalance among H-bridge units, leading to overmodulation of modulation wave signals and distortion of grid-connected currents. For three-phase CHB inverters, inter-phase and intra-phase imbalance issues coexist simultaneously, making the system control strategy considerably more complex.
The research on power balance control for CHB solar inverters has drawn considerable attention. For single-phase CHB photovoltaic grid-connected inverters, various strategies have been proposed to maintain stable operation under unbalanced power output conditions. Some studies calculate modulation wave signals of each H-bridge unit based on actual output power of DC-side PV strings, achieving reasonable distribution of active power among units, though the modulation range remains limited with modulation wave amplitudes constrained below unity. Other approaches inject a third harmonic component fixed at -1/6 of the modulation index into overmodulated units, extending the modulation range to 1.155 while reducing direct current voltage utilization. Optimal third harmonic compensation strategies have been developed to precisely calculate compensation quantities, ensuring peak values of overmodulated units remain exactly at unity. For three-phase CHB PV inverters, fundamental frequency zero-sequence voltage injection (FFZSVI) has been proposed to redistribute power among phases for symmetrical grid current output. Double third harmonic zero-sequence voltage injection (DTHZSVI) and double maximum-minimum zero-sequence voltage injection (DMMZSVI) have been developed to address the overmodulation issue caused by severe inter-phase power imbalance.
This work systematically investigates the power balance control optimization of three-phase CHB solar inverters. The main contributions include: comparative analysis of high-frequency carrier modulation techniques; development of an improved overmodulation control strategy for single-phase CHB inverters capable of stable operation when modulation indices exceed 1.155; and integration of zero-sequence voltage injection with optimal third harmonic compensation for three-phase systems, addressing both inter-phase and intra-phase power imbalance simultaneously.
2. Modulation Techniques for CHB Inverters
2.1 CHB Inverter Topology and Operating Principle
A three-phase CHB inverter consists of several H-bridge units connected in series per phase. Taking a three-unit seven-level topology as an example, each phase comprises three H-bridge units, with each unit supplied by an independent DC source. The phase voltage \(u_{AN}\) is the sum of individual H-bridge output voltages:
\[u_{AN} = u_{H1} + u_{H2} + u_{H3}\]
Each H-bridge unit can output three voltage levels: +E, 0, -E, depending on the switching states. With three units per phase, the total output voltage can generate seven distinct levels: 3E, 2E, E, 0, -E, -2E, -3E. Table 1 summarizes the switching states and corresponding output voltages for the CHB inverter.
| S₁₁ S₁₂ S₁₃ | u_H1 | u_H2 | u_H3 | u_AN |
|---|---|---|---|---|
| 1 1 1 | E | E | E | 3E |
| 0 1 1 | 0 | E | E | 2E |
| 1 0 1 | E | 0 | E | 2E |
| 1 1 0 | E | E | 0 | 2E |
| 0 0 1 | 0 | 0 | E | E |
| 0 1 0 | 0 | E | 0 | E |
| 1 0 0 | E | 0 | 0 | E |
| 0 0 0 | 0 | 0 | 0 | 0 |
2.2 Carrier-Based PWM Strategies
Three high-frequency carrier modulation strategies are commonly employed in CHB inverters: Carrier Phase Shift Sinusoidal PWM (CPS-PWM), Level-Shifted PWM (LS-PWM), and Output Voltage Cyclic Adjustment Modulation. Each strategy exhibits distinct characteristics regarding harmonic performance, equivalent switching frequency, and power balance capability.
Carrier Phase Shift PWM (CPS-PWM): In CPS-PWM, carriers for different H-bridge units have identical amplitude and frequency but are phase-shifted by specific angles. For a three-unit CHB inverter, the unipolar CPS-PWM employs six triangular carriers with phase shifts of 2π/3. Each H-bridge unit generates a three-level voltage waveform, and the cascaded output forms a seven-level waveform. The equivalent switching frequency is 2nf (where n is the number of units and f is the carrier frequency), which is six times the actual switching frequency for three units.
Level-Shifted PWM (LS-PWM): In LS-PWM, multiple triangular carriers are stacked vertically and compared with the modulation wave. Three main variants exist: In-Phase Disposition (IPD-PWM), Alternative Phase Opposition Disposition (APOD-PWM), and Phase Opposition Disposition (POD-PWM). For IPD-PWM, all carriers above and below the zero reference are in phase, producing the lowest output voltage THD for line-to-line voltages among LS-PWM variants. However, this method cannot achieve power self-balance among H-bridge units.
Output Voltage Cyclic Adjustment Modulation: This technique combines the advantages of both previous methods. It cyclically adjusts carrier arrangements at quarter-modulation-cycle intervals to ensure each H-bridge unit outputs six essential voltage waveforms over 3/2 modulation cycles, achieving power self-balance among units. Through two optimization steps, redundant carriers are removed and the modulation wave is vertically shifted, simplifying control complexity.
Table 2 presents a comprehensive comparison of these modulation strategies based on simulation results at different modulation indices.
| Modulation Strategy | Modulation Index M | Phase Voltage THD | Line Voltage THD | Power Self-Balance |
|---|---|---|---|---|
| Unipolar CPS-PWM | 0.9 | 22.38% | 18.54% | Yes |
| Unipolar CPS-PWM | 0.5 | 40.22% | 29.19% | Yes |
| IPD-PWM | 0.9 | 22.35% | 11.77% | No |
| IPD-PWM | 0.5 | 39.83% | 24.56% | No |
| Output Voltage Cyclic Adjustment | 0.9 | 22.35% | 11.77% | Yes |
| Output Voltage Cyclic Adjustment | 0.5 | 39.83% | 24.56% | Yes |
3. Power Balance Control for Single-Phase CHB Grid-Connected Systems
3.1 Mathematical Modeling and System Control
The single-phase CHB photovoltaic grid-connected inverter structure consists of n H-bridge units, each connected to a PV string with a parallel capacitor for voltage smoothing. The AC side is connected to the grid through a filter inductor. Based on the controlled-source equivalent circuit model, the dynamic power balance equation of the system can be derived:
\[v_{dci} i_{pvi} = C v_{dci} \frac{dv_{dci}}{dt} + v_{bi} i_g\]
where \(v_{dci}\) is the DC-side capacitor voltage, \(i_{pvi}\) is the PV string output current, \(C\) is the capacitance, \(v_{bi}\) is the fundamental component of the H-bridge AC-side output voltage, and \(i_g\) is the grid current. The relationship between the modulation wave \(m_i\) and system parameters is given by:
\[v_{bi} = m_i v_{dci}\]
\[i_{dci} = m_i i_g\]
The overall system control employs a voltage-current dual closed-loop structure. In the voltage outer loop, each H-bridge unit tracks its maximum power point voltage reference \(v_{dci}^*\) through a PI controller with a 100 Hz notch filter to eliminate the second-harmonic ripple. The current inner loop adopts proportional-resonant control to achieve zero steady-state error tracking of the grid current while maintaining unity power factor operation.
3.2 Power Imbalance Analysis
When PV panels experience partial shading or temperature variations, the maximum power point differs among H-bridge units, causing uneven DC-side input power distribution. Taking a three-unit CHB inverter as an example, if the PV strings operate at their maximum power points \(P_{MPPT1}\), \(P_{MPPT2}\), and \(P_{MPPT3}\), the average power can be expressed as:
\[P_{vag} = \frac{P_{MPPT1} + P_{MPPT2} + P_{MPPT3}}{3}\]
When \(P_{MPPT1} > P_{vag}\), the excess power charges the DC-side capacitor, raising the capacitor voltage and causing the PV panel to deviate from its MPPT point. Conversely, when \(P_{MPPTi} < P_{vag}\), the capacitor discharges to compensate for the power deficit, decreasing the capacitor voltage until the unit fails to operate. Therefore, power balance control strategies are essential to maintain stable operation under unbalanced conditions.
3.3 Power Balance Strategies Based on Input Power Distribution
Strategy 1: Equal Distribution of Reactive Power
The ACMDC-based power equilibrium control adjusts the active duty cycle component of each H-bridge unit according to the actual power distribution while evenly distributing the reactive power. The vector diagram analysis under this strategy yields the modulation constraint:
\[\frac{P_i}{P_T} \leq \frac{V_g}{U_{dci}} \sqrt{1 – \left(\frac{\omega L_s I_s}{\sum_{k=1}^{3} v_{dck}}\right)^2}\]
Strategy 2: Proportional Distribution of Reactive Power
In this strategy, the reactive power is distributed proportionally to the input active power of each H-bridge unit. The corresponding constraint condition is:
\[\frac{P_i v_{dci}}{P_T} \leq \frac{U_g}{U_s} \sqrt{1 – \left(\frac{\omega L_s I_s P_i}{U_s v_{dci}}\right)^2}\]
Both strategies can maintain system stability within a limited modulation range, but their stability boundaries differ under various power imbalance conditions.
3.4 Overmodulation Analysis
As the power imbalance among H-bridge units intensifies, the modulation wave amplitude of high-power-output units may exceed unity, causing overmodulation. The mechanism can be understood by considering three PV strings with powers P₁, P₂, P₃ and total AC output power \(P_{ac}\):
\[P_{ac} = P_1 + P_2 + P_3\]
When P₂ and P₃ decrease due to shading while P₁ remains constant, the total AC power and grid current decrease. To maintain the original output power, the first H-bridge unit increases its duty cycle, causing its AC-side fundamental voltage \(V_{B1}\) to rise. As P₂ and P₃ continue to decrease, the modulation wave \(m_1\) eventually exceeds unity, triggering overmodulation.
3.5 Third Harmonic Injection Strategies
Traditional Third Harmonic Compensation (THCS): The core principle of THCS is to inject a third harmonic component with amplitude -1/6 of the fundamental modulation index into overmodulated units, reducing their peak values. The relationship between the peak value of the modulated wave and the compensation coefficient k can be derived from:
\[m_x = m + m_t = M \cos(\omega t + \theta) + kM \cos(3\omega t + 3\theta)\]
The maximum reduction occurs when k = -1/6, yielding a peak value of 0.866M. Therefore, the modulation range can be extended to M = 1/0.866 = 1.155 before overmodulation occurs. However, THCS has two major drawbacks: (1) under slight power imbalance, excessive third harmonic injection reduces DC voltage utilization; (2) when multiple units are overmodulated, non-overmodulated units may receive excessive reverse third harmonics, causing reverse overmodulation.
Optimal Third Harmonic Compensation (OTHCS): To address THCS limitations, OTHCS precisely calculates the compensation quantity to ensure overmodulated units have peak values exactly at unity. For non-overmodulated units, the reverse third harmonics are rationally distributed according to each unit’s allowable compensation margin. The compensation coefficient k for an overmodulated unit with amplitude M is determined by curve fitting the relationship:
\[k = A_5 M^5 + A_4 M^4 + A_3 M^3 + A_2 M^2 + A_1 M + A_0\]
Table 3 lists the polynomial fitting coefficients:
| Coefficient | A₅ | A₄ | A₃ | A₂ | A₁ | A₀ |
|---|---|---|---|---|---|---|
| Value | -0.1676 | 0.8959 | -1.9137 | 2.0432 | -1.0902 | 0.2326 |
For a system with n H-bridge units where p units are overmodulated and q units are non-overmodulated, the total third harmonic compensation injected into overmodulated units is:
\[m_T = \sum_{i=1}^{p} k_i M_i \cos(3\omega t + 3\theta_i)\]
The reverse third harmonic distributed to the ith non-overmodulated unit is:
\[m_{oi} = -\frac{M_{oi}}{\sum_{j=1}^{q} M_{oj}} m_T\]
where \(M_{oi} = 1 – M_i\) represents the allowable amplitude margin of the ith non-overmodulated unit. The final modulation wave for this unit after compensation is:
\[m_{ofi} = M_i \cos(\omega t + \theta_i) – \frac{1 – M_i}{\sum_{j=1}^{q} (1 – M_j)} \sum_{j=1}^{p} k_j M_j \cos(3\omega t + 3\theta_j)\]
3.6 Improved Overmodulation Control Strategy
When the power imbalance among H-bridge units becomes severe, the modulation index of overmodulated units may exceed 1.155, beyond the capability of conventional THCS and OTHCS. To address this challenge, I propose an improved overmodulation control strategy that combines amplitude adjustment, precise third harmonic compensation, and current harmonic suppression.
Overmodulation Compensation Principle: For an overmodulated unit with modulation index M > 1.155, the modulation wave undergoes amplitude adjustment followed by third harmonic injection:
\[m_x = M_b \cos(\omega t + \theta) + k_x M_b \cos(3\omega t + 3\theta)\]
where \(M_b\) is the adjusted amplitude and \(k_x\) is the compensation coefficient. The amplitude is adjusted as:
\[m_{bi} = (M_i – 1.155) \cos(\omega t + \theta)\]
and the fixed third harmonic injected is:
\[m_{hi} = -0.1925 \cos(3\omega t + 3\theta)\]
System Control Architecture: The proposed control strategy block diagram comprises power outer loop, current inner loop, overmodulation compensation, and current harmonic suppression. The Second-Order Generalized Integrator (SOGI) generates orthogonal signals for Park transformation. The transfer functions of SOGI are:
\[G_d(s) = \frac{k\omega s}{s^2 + k\omega s + \omega^2}\]
\[G_q(s) = \frac{k\omega^2}{s^2 + k\omega s + \omega^2}\]
The harmonic suppression loop employs a 50 Hz notch filter to extract harmonic currents, a quasi-PR controller to amplify harmonic current errors, and a distribution mechanism based on allowable compensation margins of non-overmodulated units. The notch filter transfer function is:
\[G_{notch}(s) = \frac{s^2 + \omega^2}{s^2 + \frac{\omega}{Q} s + \omega^2}\]
The quasi-PR controller transfer function is:
\[G_{QPR}(s) = k_{hP} + \frac{2k_{hI} \omega_c s}{s^2 + 2\omega_c s + \omega_h^2}\]
Table 4 summarizes the key parameters of the proposed control system.
| Parameter | Symbol | Value |
|---|---|---|
| Proportional gain of SOGI | k | 0.707 |
| Quality factor of notch filter | Q | 1 |
| Proportional coefficient of QPR | k_hP | 2 |
| Resonant coefficient of QPR | k_hI | 100 |
| Bandwidth coefficient of QPR | ω_c | 3.14 rad/s |
| Resonant angular frequency | ω_h | 300π rad/s |
The operating states of H-bridge units are determined by their modulation indices: (1) State 1: 1 < M ≤ 1.155, OTHCS compensation; (2) State 2: M > 1.155, amplitude adjustment with fixed third harmonic; (3) State 3: M ≤ 1, receiving distributed reverse harmonics from the harmonic suppression loop.
3.7 Simulation Results for Single-Phase Systems
Simulations were conducted using a three-unit CHB photovoltaic grid-connected inverter model in Matlab/Simulink. Table 5 lists the system parameters.
| PV String | Value | Inverter | Value |
|---|---|---|---|
| Maximum output power P_max | 189 W | H-bridge DC capacitance C | 8 mF |
| Open-circuit voltage V_oc | 44.8 V | Grid voltage amplitude V_g | 90 V |
| Short-circuit current I_sc | 5.5 A | Grid frequency f_g | 50 Hz |
| MPP current I_mpp | 5.14 A | Filter inductance L_s | 3 mH |
| MPP voltage V_mpp | 36.7 V | Switching frequency f | 3000 Hz |
Experimental Group 1: Initially, three PV strings operate at irradiances of 1000 W/m², 800 W/m², and 1000 W/m², producing powers P₁=189W, P₂=150W, and P₃=189W. At t=0.5s, irradiance changes cause output powers to become P₁=131W, P₂=65W, and P₃=189W. Table 6 summarizes the performance of different control strategies.
| Control Strategy | THD before 0.5s | THD after 0.5s | Modulation Range M |
|---|---|---|---|
| Input Power Distribution | 1.53% | 13.81% | M < 1 |
| THCS | 1.53% | 4.40% | M < 1.155 |
| OTHCS | 1.53% | 2.48% | M < 1.155 |
Experimental Group 2: The irradiance of the first H-bridge unit decreases further to 650 W/m², producing P₁=122W, P₂=65W, and P₃=189W. The third unit’s modulation index approaches 1.5, exceeding the OTHCS limit. Table 7 compares the results.
| Control Strategy | THD before 0.5s | THD after 0.5s | Modulation Range M |
|---|---|---|---|
| OTHCS | 1.53% | 8.22% | M < 1.155 |
| Proposed Overmodulation Strategy | 0.82% | 2.16% | M > 1.155 |
The simulation results demonstrate that the proposed overmodulation control strategy successfully maintains stable operation even when the modulation index exceeds 1.155, achieving the lowest THD of 2.16% under severe power imbalance conditions. The DC-side capacitor voltages remain near their MPPT reference values, confirming effective power balance maintenance.
4. Power Balance Control for Three-Phase CHB Grid-Connected Systems
4.1 System Configuration and Problem Statement
The three-phase CHB photovoltaic grid-connected inverter topology consists of n H-bridge units per phase, with PV strings independently powering each unit. The units are connected in series and then star-connected to form the three-phase system. In practical applications, both inter-phase and intra-phase power imbalance occur simultaneously due to uneven irradiance distribution and temperature variations across PV panels.
4.2 Zero-Sequence Voltage Injection for Inter-Phase Power Balance
Fundamental Frequency Zero-Sequence Voltage Injection (FFZSVI): A fundamental frequency zero-sequence voltage is injected into each phase’s output voltage to redistribute power among phases. The injected zero-sequence voltage amplitude is:
\[V_o = \frac{\sqrt{( \lambda_a – \lambda_b)^2 + (\lambda_b – \lambda_c)^2 + (\lambda_c – \lambda_a)^2}}{(\lambda_a + \lambda_b + \lambda_c)} \cdot \frac{V_g}{2}\]
The phase angle α of the zero-sequence voltage is determined by the power imbalance coefficients and the sector table. As inter-phase power imbalance increases, the zero-sequence voltage amplitude grows, potentially causing overmodulation in phases with higher output power.
Double Third Harmonic Zero-Sequence Voltage Injection (DTHZSVI): To overcome FFZSVI limitations, DTHZSVI injects an additional -1/6 of positive-sequence and zero-sequence third harmonic voltages:
\[v_{DTH} = v_a^+ – \frac{1}{6} V_a^+ \cos(3\omega t + 3\theta) + \frac{1}{6} V_o \cos(3\omega t + 3\alpha)\]
This approach reduces the peak value of the output voltage, preventing overmodulation at higher power imbalance levels.
Double Maximum-Minimum Zero-Sequence Voltage Injection (DMMZSVI): DMMZSVI adds max-min sequences of both positive-sequence and zero-sequence voltages to reduce the output voltage amplitude:
\[v_{DMM} = V_o \cos(\omega t + \alpha) + \text{max-min}(v_{ao}, v_{bo}, v_{co}) + \text{max-min}(v_a^+, v_b^+, v_c^+)\]
The max-min sequence of three-phase voltages is defined as:
\[\text{max-min}(x_a, x_b, x_c) = -\frac{1}{2}[\max(x_a, x_b, x_c) + \min(x_a, x_b, x_c)]\]
4.3 Integrated Control Strategy with ZSVI and OTHCS
Traditional approaches combining zero-sequence voltage injection with active component modification of duty cycles (ZSVI+ACMDC) cannot handle scenarios where intra-phase overmodulation occurs. I propose a novel ZSVI+OTHCS strategy that integrates zero-sequence voltage injection for inter-phase balance with optimal third harmonic compensation for intra-phase balance.
The control architecture comprises power outer loops, a current inner loop with dq decoupling, inter-phase voltage balancing loops, and phase power balancing mechanisms. The current inner loop is designed based on grid voltage orientation, with the mathematical model:
\[L \frac{di_d}{dt} + Ri_d = \omega L i_q + v_d – e_d\]
\[L \frac{di_q}{dt} + Ri_q = -\omega L i_d + v_q – e_q\]
Decoupling control is achieved through:
\[v_d = e_d – \omega L i_q + (k_p + \frac{k_i}{s})(i_d^* – i_d)\]
\[v_q = e_q + \omega L i_d + (k_p + \frac{k_i}{s})(i_q^* – i_q)\]
The inter-phase voltage loop for phase A adjusts the phase voltage reference based on the deviation of total DC-side capacitor voltage from its reference:
\[v_{ar} = (1 + \Delta v_{dcaT}) v_{ao}\]
For the ith H-bridge unit in phase j, the modulation wave and modulation index are determined by:
\[m_{ij} = \frac{P_{ij} v_{ir}}{P_i v_{dcij}}\]
\[M_{ij} = \frac{P_{ij} V_{ir}}{P_i v_{dcij}}\]
where \(P_{ij}\) is the output power of the jth unit in phase i, \(P_i\) is the total phase power, and \(v_{ir}\) is the phase modulation voltage after zero-sequence injection.
4.4 Simulation Results for Three-Phase Systems
Simulation parameters for the three-phase CHB system are listed in Table 8.
| PV String | Value | Inverter | Value |
|---|---|---|---|
| Maximum output power P_max | 189 W | H-bridge DC capacitance C | 8 mF |
| Open-circuit voltage V_oc | 44.8 V | Grid voltage amplitude V_g | 80 V |
| Short-circuit current I_sc | 5.5 A | Grid frequency f_g | 50 Hz |
| MPP current I_mpp | 5.14 A | Filter inductance L_s | 3 mH |
| MPP voltage V_mpp | 36.7 V | Switching frequency f | 3000 Hz |
In the simulation, phases B and C experience power reduction after 0.5s due to irradiance changes. The power imbalance coefficients are (λ₁=1, λ₂=0.42, λ₃=0.56). Table 9 compares the grid current THD values under different control strategies.
| Control Strategy | THD(iga) | THD(igb) | THD(igc) |
|---|---|---|---|
| FFZSVI+ACMDC | 13.24% | 6.43% | 7.12% |
| DMMZSVI+ACMDC | 3.9% | 4.77% | 4.43% |
| DTHZSVI+ACMDC | 2.24% | 2.76% | 3.01% |
| FFZSVI+OTHCS | 12.8% | 6.41% | 7.02% |
| DMMZSVI+OTHCS | 1.43% | 2.54% | 2.48% |
| DTHZSVI+OTHCS | 1.02% | 1.54% | 1.4% |
The simulation results reveal several important findings. Under FFZSVI+ACMDC, severe inter-phase power imbalance leads to excessive zero-sequence voltage injection, causing overmodulation in phase A with modulation wave amplitude exceeding unity. This results in significantly higher THD values. The DMMZSVI and DTHZSVI methods effectively address inter-phase overmodulation, reducing THD values considerably. However, when applying only ZSVI+ACMDC, intra-phase power imbalance persists, particularly in phases B and C where some H-bridge units still experience overmodulation.
The proposed ZSVI+OTHCS strategies achieve superior performance by simultaneously addressing both inter-phase and intra-phase imbalance. Notably, DTHZSVI+OTHCS achieves the lowest THD values across all three phases (1.02%, 1.54%, and 1.4%), demonstrating excellent power quality even under severe unbalanced operating conditions. The combination of double third harmonic zero-sequence voltage injection for inter-phase balance and optimal third harmonic compensation for intra-phase balance effectively prevents overmodulation throughout the entire system.
5. Conclusions and Future Work
This research systematically investigated power balance control strategies for three-phase cascaded H-bridge solar inverters. The main conclusions are summarized as follows:
First, among the three main modulation strategies—CPS-PWM, LS-PWM, and output voltage cyclic adjustment modulation—the output voltage cyclic adjustment method combines the advantages of both CPS-PWM and IPD-PWM, achieving power self-balance among H-bridge units while maintaining superior line voltage quality with lower THD values.
Second, for single-phase CHB photovoltaic grid-connected systems, the proposed improved overmodulation control strategy significantly extends the modulation range beyond the 1.155 limit of conventional third harmonic compensation methods. Under extreme power imbalance where modulation indices approach 1.5, the proposed strategy maintains system stability with the grid current THD as low as 2.16%, compared to 8.22% for OTHCS. This is achieved through precise amplitude adjustment, fixed third harmonic injection, and a current harmonic suppression loop that distributes reverse compensation to non-overmodulated units based on their allowable margins.
Third, for three-phase CHB photovoltaic grid-connected systems, the proposed DTHZSVI+OTHCS control strategy effectively addresses both inter-phase and intra-phase power imbalance simultaneously. When both types of imbalance cause overmodulation, this strategy achieves the best grid-connected power quality with THD values of 1.02%, 1.54%, and 1.4% for the three phases, substantially outperforming conventional ZSVI+ACMDC methods.
Several aspects warrant further investigation in future research. The overmodulation control strategy, while ensuring stable operation, causes slight DC-side capacitor voltage offset in high-power units and may reduce PV panel power generation efficiency. Future work should focus on optimizing this trade-off. Additionally, the current control strategies assume ideal grid conditions; under unbalanced grid voltage or frequency fluctuations, the effectiveness of power balance control requires further validation. Finally, experimental verification of the proposed control strategies is needed to complement the simulation results.