In recent years, the global energy crisis and environmental pollution have become critical issues, driving the rapid development of renewable energy sources. Solar energy, due to its accessibility and convertibility, has emerged as one of the most widely adopted renewable resources. Solar inverters play a pivotal role in converting direct current (DC) from photovoltaic (PV) modules into alternating current (AC) for grid integration. Among various inverter topologies, the cascaded H-bridge (CHB) solar inverter stands out for its low switching stress, reduced filter inductance, and high system efficiency. However, solar inverters face challenges such as partial shading, module aging, and uneven irradiation, leading to power imbalances among H-bridge units. This imbalance can cause over-modulation in certain units, resulting in distorted grid currents and system instability. This paper proposes a segmented control strategy to expand the operating range of solar inverters under severe power imbalance conditions. The strategy involves harmonic compensation techniques, including third and multiple harmonics, and power reduction for critically over-modulated units, ensuring stable operation and high-quality grid currents.
The CHB solar inverter consists of multiple H-bridge units connected in series, each powered by an independent PV module. This configuration allows for individual maximum power point tracking (MPPT), optimizing energy harvest. However, when power imbalance occurs, the modulation index of certain units may exceed unity, leading to over-modulation. Traditional control strategies, such as sinusoidal pulse width modulation (SPWM), fail to address this issue effectively. Existing methods like hybrid modulation strategies (HMS) and reactive power compensation have limitations, including increased DC voltage fluctuations and reduced power factor. Harmonic compensation strategies, such as third harmonic compensation, can extend the linear modulation range to 1.155, but they are inadequate for severe imbalances. This paper introduces an improved approach that combines power limitation and multiple harmonic compensation to handle modulation indices beyond 1.27, thereby enhancing the robustness of solar inverters.
The system configuration of a single-phase CHB solar inverter is illustrated in the figure above. It comprises n H-bridge units, each with four switches. The DC side is fed by PV modules, and the AC side is connected to the grid via inductors. Each unit can output three voltage levels: -1, 0, and 1, enabling the inverter to generate 2n+1 output levels. The key parameters include PV output current \(I_{pvn}\), DC capacitor voltage \(V_{dcn}\), and AC output voltage \(V_{Hn}\) for the n-th unit. The grid voltage \(V_{grid}\) and current \(I_{grid}\) are regulated through control loops. The dynamic behavior of the solar inverter can be modeled using the following equations:
The modulation index for the x-th unit is defined as:
$$m_x = \frac{V_{Hx}}{V_{dcx}}$$
where \(V_{Hx}\) is the output voltage of the x-th H-bridge unit, and \(V_{dcx}\) is its DC voltage. The current through each unit is identical due to series connection:
$$I_{Hx} = m_x I_{grid}$$
The DC side dynamics are given by:
$$\frac{dV_{dcx}}{dt} = \frac{1}{C} (I_{pvx} – I_{Hx})$$
where \(C\) is the DC capacitance. The grid current dynamics are expressed as:
$$L \frac{dI_{grid}}{dt} = \sum_{x=1}^{n} m_x V_{dcx} – R I_{grid} – V_{grid}$$
The power output of each PV module is:
$$P_x = I_{pvx} V_{dcx} = m_x V_{dcx} I_{grid}$$
and the total power is:
$$P_T = \sum_{x=1}^{n} P_x$$
Under balanced conditions, all units operate with modulation indices below unity. However, power imbalance causes some units to exceed this limit, leading to over-modulation. The condition to avoid over-modulation is:
$$S_x \leq 1$$
where \(S_x\) is the peak modulation wave amplitude. For severe imbalances, this condition is violated, necessitating advanced control strategies.
The proposed segmented control strategy categorizes units based on their modulation indices. For units with modulation indices between 1 and 1.155, third harmonic compensation is applied. The compensation wave is derived as:
$$m_{comp,3} = -\frac{1}{6} \sin(3\theta)$$
where \(\theta\) is the phase angle. This reduces the peak amplitude of the modulation wave, preventing over-modulation. For units with indices between 1.155 and 1.27, multiple harmonic compensation is employed. The compensation wave includes third, fifth, and seventh harmonics:
$$m_{comp,multi} = -\sum_{h=3,5,7} k_h \sin(h\theta)$$
where \(k_h\) are compensation coefficients optimized to minimize total harmonic distortion (THD). For units exceeding 1.27, the output power is reduced to fix the modulation index at 1.27, followed by multiple harmonic compensation. The adjusted power for such units is:
$$P_{X_i} = 1.27 \cdot \frac{V_{dcx}}{V_r} \cdot P_T$$
where \(V_r\) is the reference voltage amplitude. The total power is recalculated as:
$$P_T’ = \sum_{i=1}^{h} P_i + \sum_{i=h+1}^{n} P_{X_i}$$
and the modulation indices are updated accordingly:
$$M_i = \begin{cases}
\frac{P_i V_r}{P_T’ V_{dcx}} & \text{for } i = 1, \ldots, h \\
1.27 & \text{for } i = h+1, \ldots, n
\end{cases}$$
This approach ensures that all units operate within the linear range, and the grid current THD remains within acceptable limits.
To validate the strategy, simulations were conducted for a three-unit CHB solar inverter. The PV module parameters are listed in Table 1, and the inverter and grid parameters in Table 2.
| Parameter | Value |
|---|---|
| Maximum Power \(P_{max}\) (W) | 213.15 |
| Open-Circuit Voltage \(V_{oc}\) (V) | 36.3 |
| Short-Circuit Current \(I_{sc}\) (A) | 7.29 |
| Voltage at MPP \(V_{MPP}\) (V) | 29 |
| Current at MPP \(I_{MPP}\) (A) | 7.35 |
| Parameter | Value |
|---|---|
| DC Capacitance \(C_i\) (mF) | 2.0 |
| Filter Inductance \(L\) (mH) | 5.0 |
| Grid Voltage Peak \(V_M\) (V) | 311 |
| Grid Frequency \(f_{grid}\) (Hz) | 50 |
| Switching Frequency \(f_{car}\) (kHz) | 10 |
Initially, all units received uniform irradiation of 1000 W/m². At t=1s, the irradiation for unit 2 was reduced to 300 W/m² and for unit 3 to 200 W/m², causing unit 1 to become severely over-modulated. Under traditional control, the grid current THD increased to 26.6%, indicating severe distortion. With the proposed strategy, the modulation indices were controlled, and harmonic compensation was applied. The grid current THD was reduced to 3.26%, meeting grid standards. The DC voltages stabilized near the MPP voltages, demonstrating effective power management.
The modulation waves for all units were maintained within bounds, as shown in simulation results. Unit 1, with a modulated index above 1.27, underwent power reduction and multiple harmonic compensation. Units 2 and 3 received reverse harmonic injections to cancel out distortions. The segmented approach ensured computational efficiency by applying simpler third harmonic compensation where sufficient, and multiple harmonics only when necessary.
In conclusion, the proposed segmented control strategy significantly enhances the operating range of solar inverters under power imbalance conditions. By combining power limitation and harmonic compensation, it prevents over-modulation and maintains low THD in grid currents. This method is particularly beneficial for large-scale solar inverters where reliability and power quality are critical. Future work will focus on optimizing harmonic coefficients and extending the strategy to three-phase systems.