**2. System Configuration**

The structure of the single-phase PV CHB module level grid-tied inverter is shown in Figure 1. The CHB module level inverter consists of *m* H-bridge units. Each H-bridge unit is connected to a PV module. VPV*i* and IPV*i* (*I* = 1, 2, ... , *m*) stand for the output voltage and current of PV module of *i*th H-bridge. IC*i* represents the current flowing through the capacitor on the DC-side of *i*th H-bridge. VG stands for grid voltage. IS stands for grid current. V H*i* (*I* = 1, 2, ... , *m*) is the *i*th H-bridge output voltage and VHT is the total output voltage of H-bridges. Figure 2 shows the configuration of the control diagram of CHB module level inverter. The voltage and current double closed-loop control are utilized to obtain the goal of the controlling. In order to decrease third harmonic component in the grid current, a digital 100 Hz notch filter is utilized to eliminate the second order harmonic in the total DC-side voltage VPV1 + VPV2••• + VPV*<sup>m</sup>*. The external voltage loop is in charge of controlling the filtered total DC-side voltages to the sum of the references VPV1\* + VPV2\*••• + VPV*m*\* by a conventional PI controller. The internal current loop is responsible for controlling the grid current to a sinusoidal

shape in phase with the grid voltage. In the paper, a direct-quadrature rotating frame control method for the single-phase inverter is used to achieve this goal because it can achieve zero steady-state error by utilizing a traditional PI regulator [25]. The output of the current loop regulator, Vr, serves as the modulation wave. In order to compensate for the harmonic component of the CHB inverter caused by the distorted grid voltage, the third, fifth, and seventh harmonic compensation algorithm is utilized [26,27].

**Figure 1.** Structure of single-phase PV CHB module level inverter.

**Figure 2.** The control diagram of single-phase PV CHB module level grid-tied inverter.

The balancing algorithm allocates suitable switching modes to each unit during every switching period based on the instantaneous value of modulation wave. For HMSCZS, only one unit operates in PWM state, the K − 1(K = 1, 2, ... , *m*) units operate in the "+1" or "−1" state and other units work in the "0" state. However, for HMSWZS, only one unit operates in the PWM state, while the other units work in the "+1" or "−1" mode. Probable switching states of the *i*th unit, S*i*, and their corresponding output voltages are given in Table 1.


**Table 1.** Switch states of the *i*th unit.

#### **3. Review of The Existing Hybrid Modulation Strategy**

#### *3.1. The Hybrid Modulation Strategy Containing the Zero State (HMSCZS)*

The HMSCZS proposed in [19,23] maximizes the steady operation range of the system, because it provides higher DC-side utilization by adopting a square wave modulation. The major procedures of HMSCZS can be summarized as follows:

(1) Calculating the voltage error ΔVPV*i* (*I* = 1, 2, ... , *m*) at the DC-side of each H-bridge unit:

$$
\Delta \mathbf{V}\_{\rm PVi} = \mathbf{V}\_{\rm PVi} - \mathbf{V}\_{\rm PVi}^\* \tag{1}
$$


$$\sum\_{i=1}^{l-1} \mathbf{V}\_i < |\mathbf{V}\_r| < \sum\_{i=1}^{l} \mathbf{V}\_i \tag{2}$$

(5) Updating the H-bridge units' operating state. The *l* − 1 (*l* = 1, 2, ... , *m*) units with the higher DC-side voltage are selected to be discharged in state "+1" or "−1" (according to the direction of grid-connected current), the *l*th unit works in the PWM state, and the rest operate in state "0".

As shown in Figure 3, the switching modes for an eleven-level CHB inverter with the HMSCZS method is presented. For instance, when 3 *i*=1 V*i* < Vr < 4 *i*=1 V*i* and IS > 0, the switching modes of the five H-bridge modules are, respectively, "0", "+PWM", "+1", "+1", and "+1". According to the rules of HMSCZS, the switching mode of each H-bridge unit can only be "+1", "0", or "+PWM" when Vr is positive. Similarly, it can only be "−1", "0", or "−PWM" when Vr is negative. As shown in Figure 4, once the CHB inverter is operating in fault mode owing to failing PV modules, the fault H-bridge unit is always in the discharge state, whether the switching mode is "+1", "+PWM", "−1" or "−PWM". The result is that the DC-side voltages of all H-bridge units diverge from the reference value and the generation of CHB inverter is low.

**Figure 3.** The switching modes for an eleven-level CHB inverter with the HMSCZS method.

**Figure 4.** The switching modes of the fault H-bridge unit with the HMSCZS method.

#### *3.2. The Hybrid Modulation Strategy without the Zero State (HMSWZS)*

To overcome the shortcoming of the HMSCZS, the HMSWZS is presented in [21,24]. Different from the HMSCZS, in the HMSWZS the units with the lower voltage errors are selected to be charged in state "+1" or "−1" (according to the direction of grid-connected current) and no unit operates in the "0" mode. Figure 5 shows the switching modes for an eleven-level CHB inverter with the HMSWZS method. As depicted in the Figure 5, when 1 *i*=1 V*i* < Vr < 2 *i*=1 V*i* and IS > 0, the switching modes of the five H-bridge modules are, respectively, "−1", "−PWM", "+1", "+1", and "+1". According to the rules of HMSWZS, as shown in Figure 6, the switching mode of the fault H-bridge unit can be "+1", "+PWM", "−1", or "−PWM" regardless of the polarity of Vr. Therefore, compared with the HMSCZS, the HMSWZS is able to maintain the DC-side voltages balance and a higher energy yield under fault condition.

However, as is illustrated in [23], the HMSWZS may aggravate the DC-side voltages fluctuation of H-bridge units and, thus, lead to losses in energy harvesting of PV modules. As shown in Equation (3), ΔU*ci* (i = 1, 2, ... , *m*), the fluctuation of the DC-side voltage of the *i*th H-bridge unit during a sorting cycle is composed of two parts: ΔU*ci*1 and ΔU*ci*2. Based on the superposition theorem of linear circuits, the fluctuation of the DC-side voltage could be regarded as the sum of fluctuations produced by two separate parts:

$$\begin{split} \Delta \mathbf{U}\_{\rm ci} &= \frac{1}{\mathbf{C}\_{i}} \int\_{0}^{\frac{1}{f\_{\rm surf}}} (\mathbf{I}\_{\rm PVi} - \mathbf{S}\_{i} \mathbf{I}\_{s}) dt \\ &= \frac{\mathbf{I}\_{\rm PVi}}{\mathbf{C}\_{i} f\_{\rm wt}} - \frac{1}{\mathbf{C}\_{i}} \int\_{0}^{\frac{1}{f\_{\rm sat}}} \mathbf{S}\_{i} \mathbf{I}\_{s} dt \\ &= \Delta \mathbf{U}\_{\rm ci1} + \Delta \mathbf{U}\_{\rm ci2} \end{split} \tag{3}$$

*Energies* **2019**, *12*, 1851

where:

$$
\Delta \mathbf{U}\_{\rm cj1} = \frac{\mathbf{I}\_{\rm FVi}}{\mathbf{C}\_{\rm i} f\_{\rm sort}} \tag{4}
$$

$$
\Delta \mathbf{U}\_{\rm c2} = -\frac{1}{\mathbf{C}\_i} \int\_0^{\frac{1}{\zeta\_{\rm str}}} \mathbf{S}\_i \mathbf{I}\_s dt \tag{5}
$$

If the HMSWZS is utilized, ΔUc*i* has two possible values: ΔU1min and ΔU1max (if the polarity of S*i* and Is is the same, ΔUc*i* = ΔU1min, otherwise, ΔUc*i* = ΔU1max), where:

$$\begin{aligned} \Delta \mathbf{U}\_{1\text{min}} &= \Delta \mathbf{U}\_{\text{ci1}} - |\Delta \mathbf{U}\_{\text{ci2}}| \\ \Delta \mathbf{U}\_{1\text{max}} &= \Delta \mathbf{U}\_{\text{ci1}} + |\Delta \mathbf{U}\_{\text{ci2}}| \end{aligned} \tag{6}$$

If the HMSCZS is employed, ΔU*ci* also has two possible values: ΔU2min and ΔU2max (if the value of S*i* is not equal to zero, ΔU*ci* = ΔU2min, otherwise, ΔU*ci* = ΔU2max), where:

$$\begin{aligned} \Delta \mathbf{U}\_{2\text{min}} &= \Delta \mathbf{U}\_{\text{ci1}} - |\Delta \mathbf{U}\_{\text{ci2}}| \\ \Delta \mathbf{U}\_{2\text{max}} &= \Delta \mathbf{U}\_{\text{ci1}} \end{aligned} \tag{7}$$

It is obvious that ΔU1min is equal to ΔU2min and ΔU1max is greater than ΔU2max. Compared with the HMSCZS, the HMSWZS may lead to larger fluctuation of DC-side voltages of H-bridge units and thus more energy will be lost.

**Figure 5.** The switching modes for an eleven-level CHB inverter with the HMSWZS method.

**Figure 6.** The switching modes of the fault H-bridge unit with the HMSWZS method.

#### **4. The Switching Hybrid Modulation Strategy**

A switching hybrid modulation strategy (SHMS) based on the HMSCZS and HMSWZS is proposed to maximize the output power of PV panels. When the CHB inverter is operating in the normal mode, the HMSCZS is adopted to suppress DC-side voltages fluctuation and, thus, realizing higher efficiency in energy harvesting. When the CHB inverter is operating in the fault mode owing to failing solar panels, the HMSWZS is utilized to control the DC-side voltages to reach the references, thus, maintaining a higher energy yield under the fault condition. Figure 7 shows the major procedures of the SHMS, which are basically the same as HMSCZS.

**Figure 7.** Flowchart of the proposed switching hybrid modulation strategy.

In consideration of the direction of IS and Vr, and assuming that the modulation wave Vr is in area *l*, the SHMS method allocates suitable switching modes to each H-bridge unit based on the following rules:
