A Research on Cascaded H-Bridge Module Level Photovoltaic Inverter Based on a Switching Modulation Strategy

: The stable operating region of a photovoltaic (PV) cascaded H-bridge (CHB) grid-tied module level inverter is extended by adopting the hybrid modulation strategy. However, the traditional single hybrid modulation method is unable to regulate the DC-side voltage of each module precisely, which may aggravate the ﬂuctuation of modules’ DC-side voltages or even cause the deviation of modules’ DC-side voltages under some fault conditions and, thus, degrade the energy harvesting of PV panels. To tackle this problem, a switching modulation strategy for PV CHB inverter is proposed in this paper. When the CHB inverter is operating in normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage ﬂuctuation, thereby, improving the output power of PV modules. When the CHB inverter is operating in fault mode owing to failing solar panels, the hybrid modulation strategy without the zero state is utilized to make the DC-side voltages reach the references and, thus, maintain a higher energy yield under fault conditions. Experimental results achieved by a laboratory prototype of a single-phase eleven-level CHB inverter demonstrate both the feasibility and e ﬀ ectiveness of the proposed method. W. Compared with the HMSWZS, the e ﬃ ciency of the CHB inverter can be improved about 0.56% by adopting the SHMS. Therefore, under the normal mode, the SHMS has a superior capacity of suppressing the DC-side voltage ﬂuctuation compared with the HMSWZS, thereby improving the energy collection of the PV module.


Introduction
With the increasing demand for conversion efficiency during recent years, multilevel converter topologies have become more and more applied to the grid-connected PV generation system [1][2][3][4]. Among all kinds of multilevel inverters, the cascaded H-bridge (CHB) has many advantages, such as modularization, simplicity, and high reliability, which makes it become the most attractive topology [5][6][7][8][9]. In addition, the CHB topology makes it possible to, respectively, regulate each DC-side voltage and, thus, realizing the maximum power point tracking (MPPT) of each PV module. Therefore, the CHB inverter is considered to be one of the most suitable candidates for next generation PV inverters [10,11].
The energy loss caused by non-uniform solar radiation, degradation of PV modules and different types of partial shading is greatly decreased by module level MPPT. However, due to the unequal temperature and irradiance of PV modules, the output power of H-bridge unit varies greatly in the case of severe mismatching. This may lead to over-modulation of H-bridge units with high output power, thus, resulting in system instability and injection current distortion [12].
For the sake of expanding the stable operation range of the CHB inverter, some methods have been proposed. The power balance control strategy based on active component modification of duty cycles, and its effective power balance area are proposed in [13][14][15]. Although the system can operate stably by utilizing this method under slight mismatch conditions, there are still instability problems under severe mismatch conditions. In [16,17], a control strategy of reactive power compensation is proposed, which utilizes the power factor as the degree of freedom to stabilize the operation of the system. However, an increase in reactive power injection will lead to a decrease of the system power factor, which may be undesirable from the perspective of electric dispatchers. A new, improved MPPT method is presented in [18], which changes the working point of the over-modulated H-bridge unit to ensure that all H-bridge units work in the stable operation region to improve the stability margins of the system. However, this will result in lower output power and make the system less-efficient. This is contrary to the original intention that all PV modules operate at a maximum power point to realize higher efficiency in energy harvesting.
Hopefully, In [19][20][21], the hybrid modulation strategy (HMS) is proposed, which utilizes a mixture of low-frequency PWM and high-frequency PWM methods to regulate the DC-side voltage and control the AC current separately. The HMS has been proved to maintain the stabilization of power rectifiers effectively even under critical operating conditions, because it provides higher DC-side utilization (the maximum modulation index of square wave can reach 4/π) compared with conventional sinusoidal pulse width modulation (SPWM). In [22,23], a control method of a grid-connected PV CHB inverter is proposed, which is based on the hybrid modulation strategy containing the zero state (HMSCZS). With HMSCZS, the system can operate stably under heavy mismatching conditions. Once the CHB inverter is operating in the fault mode, owing to failing solar panels, the HMSCZS fails to regulate the DC-side voltages to the references and may lead to low output power of the inverter. In [24], the hybrid modulation strategy without the zero state (HMSWZS) is proposed to maximize the range of stable operation of system. However, the HMSWZS cannot control the DC-side voltage of each module accurately. This may aggravate the fluctuation of modules' DC-side voltages, thus resulting in the decrease of the generated energy of PV modules.
Therefore, a switching hybrid modulation strategy (SHMS) is proposed in this paper. The HMSCZS is selected to suppress DC-side voltages fluctuation when the CHB inverter is operating in normal mode. Once the CHB inverter is operating in fault mode, owing to failing solar panels, the HMSWZS is utilized to control the DC-side voltages to track the references, thus maintaining a higher energy yield under fault condition. With this method, the average output power of the PV modules will be improved both in the normal and fault modes.
The paper is arranged as follows: In Section 2, the system configuration and control method are introduced. In Section 3, the existing problem of the HMSCZS and the HMSWZS is shown. In Section 4, the switching hybrid modulation strategy is put forward. In Sections 5 and 6, the performance of the proposed strategy is verified by simulation and experimental results. Finally, in Section 7, a conclusion is drawn to summarize the paper.

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. V PVi and I PVi (I = 1, 2, . . . , m) stand for the output voltage and current of PV module of ith H-bridge. I Ci represents the current flowing through the capacitor on the DC-side of ith H-bridge. V G stands for grid voltage. I S stands for grid current. V Hi (I = 1, 2, . . . , m) is the ith H-bridge output voltage and V HT 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 V PV1 + V PV2 ••• + V PVm . The external voltage loop is in charge of controlling the  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  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].  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 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 ith unit, S i , and their corresponding output voltages are given in Table 1. Table 1. Switch states of the ith unit.

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 ∆V PVi (I = 1, 2, . . . , m) at the DC-side of each H-bridge unit: (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 lth 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 V i and I S > 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 V r is positive. Similarly, it can only be "−1", "0", or "−PWM" when V r 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.

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 2  and S I0  , 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.

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 2 < <   and S I 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.

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 V i and I S > 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 V r . 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), ∆U ci (i = 1, 2, . . . , m), the fluctuation of the DC-side voltage of the ith H-bridge unit during a sorting cycle is composed of two parts: ∆U ci1 and ∆U ci2 . 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: where: If the HMSWZS is utilized, ∆U ci has two possible values: ∆U 1min and ∆U 1max (if the polarity of S i and I s is the same, ∆U ci = ∆U 1min , otherwise, ∆U ci = ∆U 1max ), where: If the HMSCZS is employed, ∆U ci also has two possible values: ∆U 2min and ∆U 2max (if the value of S i is not equal to zero, ∆U ci = ∆U 2min , otherwise, ∆U ci = ∆U 2max ), where: It is obvious that ∆U 1min is equal to ∆U 2min and ∆U 1max is greater than ∆U 2max . 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.  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), ∆Uci (i = 1, 2, …, m), the fluctuation of the DC-side voltage of the ith H-bridge unit during a sorting cycle is composed of two parts: ∆Uci1 and ∆Uci2. 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:   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), ∆Uci (i = 1, 2, …, m), the fluctuation of the DC-side voltage of the ith H-bridge unit during a sorting cycle is composed of two parts: ∆Uci1 and ∆Uci2. 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: stands for "+1"mode stands for "−1"mode stands for "0"mode stands for "PWM"mode modulation wave -V r grid current -I s Mode "+1" or "+PWM" Mode "−1" or "−PWM" Charging + Discharging Charging

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.
It is obvious that ∆U1min is equal to ∆U2min and ∆U1max is greater than ∆U2max. 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.

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. 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:

Normal Mode
(1) When (Vr > 0 and IS > 0), (l − 1) units with higher voltage errors are discharging in the "+1" state, (m − l) units with lower voltage errors operate in the "0" state, and the lth unit works in PWM In consideration of the direction of I S and V r , and assuming that the modulation wave V r is in area l, the SHMS method allocates suitable switching modes to each H-bridge unit based on the following rules:

Normal Mode
(1) When (V r > 0 and I S > 0), (l − 1) units with higher voltage errors are discharging in the "+1" state, (m − l) units with lower voltage errors operate in the "0" state, and the lth unit works in PWM state. (2) When (V r > 0 and I S ≤ 0), (l − 1) units with lower voltage errors are charging in the "+1" state, (m − l) units with higher voltage errors operate in the "0" state, and the lth unit works in the PWM state. (3) When (V r ≤ 0 and I S > 0), (l − 1) units with lower voltage errors are charging in the "−1" state, (m − l) units with higher voltage errors operate in the "0" state, and the lth unit works in the PWM state. (4) When (V r ≤ 0 and I S ≤ 0), (l − 1) units with higher voltage errors are discharging in the "−1" state, (m − l) units with lower voltage errors operate in the "0" state, and the lth unit works in the PWM state.

Fault Mode
(1) When (V r > 0 and I S > 0), and the value of (m − l) is even, (m − l)/2 units with lower voltage errors are charging in the "−1" state, the ((m − l + 2)/2)th unit works in the PWM state, and the remaining units operate in the "+1" state. (2) When (V r > 0 and I S > 0), and the value of (m − l) is uneven, (m − l − 1)/2 units with lower voltage errors are charging in the "−1" state, the ((m − l + 1)/2)th unit works in the PWM state, and the remaining units operate in the "+1" state. (3) When (V r > 0 and I S ≤ 0), and the value of (m − l) is even, (m + l − 2)/2 units with lower voltage errors are charging in the "+1" state, the ((m + l)/2)th unit works in the PWM state, and the remaining units operate in the "−1" state. (4) When (V r > 0 and I S ≤ 0), and the value of (m − l) is uneven, (m + l − 1)/2 units with lower voltage errors are charging in the "+1" state, the ((m + l + 1)/2)th unit works in the PWM state, and the remaining units operate in the "−1" state. (5) When (V r ≤ 0 and I S > 0), and the value of (m − l) is even, (m + l − 2)/2 units with lower voltage errors are charging in the "−1" state, the ((m + l)/2)th unit works in the PWM state, and the remaining units operate in the "+1" state. (6) When (V r ≤ 0 and I S > 0), and the value of (m − l) is uneven, (m + l − 1)/2 units with lower voltage errors are charging in the "−1" state, the ((m + l + 1)/2)th unit works in the PWM state, and the remaining units operate in the "+1" state. (7) When (V r ≤ 0 and I S ≤ 0), and the value of (m − l) is even, (m − l)/2 units with lower voltage errors are charging in the "+1" state, the ((m − l + 2)/2)th unit works in the PWM state, and the remaining units operate in the the "−1" state. (8) When (V r ≤ 0 and I S ≤ 0), and the value of (m − l) is uneven, (m − l − 1)/2 units with lower voltage errors are charging in the "+1" state, the ((m − l + 1)/2)th unit works in the PWM state, and the remaining units operate in the "−1" state.

Simulation Verification
To verify the performance of the proposed method, an CHB inverter which consists of five modules is simulated in MATLAB/Simulink. The PV panel is a JAP6-60-255/4BB and the specifications and equivalent circuit parameters are given in Table 2. Table 3 shows the inverter and grid parameters.

Normal Mode
In order to investigate the performance of both HMSWZS and SHMS in terms of DC-side voltage fluctuation and average output power of the PV module under identical conditions, the DC-side voltage (V PV1 ) and output power (P 1 ) of the PV module in the first H-bridge are shown in Figure 8. The simulation starts with the operation of the system under symmetrical condition (E = 1000 W/m 2 and T = 25 • C). In the simulation, since the focus of this paper is to study the influence of DC-side voltage fluctuation on the energy acquisition of PV module, the reference of the DC-side voltage is set directly at the maximum power point of PV module instead of adopting the MPPT algorithm. As shown in Figure 8, the maximum fluctuation of V PV1 is 4.95 V when HMSWZS is utilized, while that of SHMS is only 3.40 V, which is reduced by up to 31.30%. With the HMSWZS, the output power of the first PV module ranges from 220-255.1 W, and the average is about 251.9 W. Since the SHMS is utilized to reduce the DC-side voltage fluctuation, the output power ranges from 245-255.1 W and the average is about 253.4 W. Figure 9 shows the total output power (P T ) of the CHB inverter with both methods. As shown in Figure 9, with HMSWZS, the total output power of the CHB inverter ranges from 1243-1275 W and the average is about 1262 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1256-1277 W and the average is about 1269.2 W. Compared with the HMSWZS, the efficiency of the CHB inverter can be improved about 0.56% by adopting the SHMS. Therefore, under the normal mode, the SHMS has a superior capacity of suppressing the DC-side voltage fluctuation compared with the HMSWZS, thereby improving the energy collection of the PV module.

Normal Mode
In order to investigate the performance of both HMSWZS and SHMS in terms of DC-side voltage fluctuation and average output power of the PV module under identical conditions, the DC-side voltage (VPV1) and output power (P1) of the PV module in the first H-bridge are shown in Figure 8. The simulation starts with the operation of the system under symmetrical condition (E = 1000 W/m 2 and T = 25 °C). In the simulation, since the focus of this paper is to study the influence of DC-side voltage fluctuation on the energy acquisition of PV module, the reference of the DC-side voltage is set directly at the maximum power point of PV module instead of adopting the MPPT algorithm. As shown in Figure 8, the maximum fluctuation of VPV1 is 4.95 V when HMSWZS is utilized, while that of SHMS is only 3.40 V, which is reduced by up to 31.30%. With the HMSWZS, the output power of the first PV module ranges from 220-255.1 W, and the average is about 251.9 W. Since the SHMS is utilized to reduce the DC-side voltage fluctuation, the output power ranges from 245-255.1 W and the average is about 253.4 W. Figure 9 shows the total output power (PT) of the CHB inverter with both methods. As shown in Figure 9, with HMSWZS, the total output power of the CHB inverter ranges from 1243-1275 W and the average is about 1262 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1256-1277 W and the average is about 1269.2 W. Compared with the HMSWZS, the efficiency of the CHB inverter can be improved about 0.56% by adopting the SHMS. Therefore, under the normal mode, the SHMS has a superior capacity of suppressing the DCside voltage fluctuation compared with the HMSWZS, thereby improving the energy collection of the PV module.

Fault Mode
The following simulation evaluates the performance of HMSCZS and SHMS under the fault mode where the second PV module fails. The simulation starts with the operation of the system under symmetrical condition (E = 1000 W/m 2 and T = 25 • C). At t = 1.5 s, the second PV module is removed owing to the fault and, thus, the CHB inverter is operating in the fault condition. Figure 10 depicts the total modulation voltage (V r ) and DC-side capacitor current of the second H-bridge (I C2 ) with both methods. As shown in Figure 10a I C2 is always negative regardless of the polarity of V r and, thus, V PV2 gradually diverges from the reference value. As a result, all the DC-side voltages diverge from the references in steady state, which is visible in Figure 11a. For comparison, the SHMS is also subjected to the same test under the identical condition. As presented in Figure 10b, I C2 can be positive and negative whether V r is positive or negative and, thus, the DC-side capacitor of the second H-bridge could realize the equalization of the charge-discharge. Therefore, the CHB inverter is able to operate properly under fault condition, which is obvious in Figure 11b. Figure 12 shows the output power of the PV module in all H-bridges with both methods. As shown in Figure 12, due to the removal of the second PV module, the output power of the second H-bridge is, therefore, zero. The output power of the PV module in other H-bridges ranges from 243.2-255.1 W by using SHMS and the average is about 253.2 W. However, due to the deviation of the DC-side voltage, the output power of the PV module in other H-bridges ranges from 221.4-255.1 W by utilizing HMSCZS and the average is only about 245.3 W. The total output power (P T ) of the CHB inverter with both methods are shown in Figure 13. As could be seen from Figure 13, with HMSCZS, the total output power of the CHB inverter ranges from 935.9-1016 W and the average is about 982.2 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1000-1020 W and the average is about 1014 W. Compared with the HMSCZS, the efficiency of the CHB inverter can be improved about 3.12% by adopting the SHMS. Therefore, under the fault mode, the SHMS is still able to make the DC-side voltages reach the references, thus maintaining a higher energy yield.

Fault Mode
The following simulation evaluates the performance of HMSCZS and SHMS under the fault mode where the second PV module fails. The simulation starts with the operation of the system under symmetrical condition (E = 1000 W/m 2 and T = 25 °C). At t = 1.5 s, the second PV module is removed owing to the fault and, thus, the CHB inverter is operating in the fault condition. Figure 10 depicts the total modulation voltage (Vr) and DC-side capacitor current of the second H-bridge (IC2) with both methods. As shown in Figure 10a IC2 is always negative regardless of the polarity of Vr and, thus, VPV2 gradually diverges from the reference value. As a result, all the DC-side voltages diverge from the references in steady state, which is visible in Figure 11a. For comparison, the SHMS is also subjected to the same test under the identical condition. As presented in Figure 10b, IC2 can be positive and negative whether Vr is positive or negative and, thus, the DC-side capacitor of the second H-bridge could realize the equalization of the charge-discharge. Therefore, the CHB inverter is able to operate properly under fault condition, which is obvious in Figure 11b. Figure 12 shows the output power of the PV module in all H-bridges with both methods. As shown in Figure 12, due to the removal of the second PV module, the output power of the second H-bridge is, therefore, zero. The output power of the PV module in other H-bridges ranges from 243.2-255.1 W by using SHMS and the average is about 253.2 W. However, due to the deviation of the DC-side voltage, the output power of the PV module in other H-bridges ranges from 221.4-255.1 W by utilizing HMSCZS and the average is only about 245.3 W. The total output power (PT) of the CHB inverter with both methods are shown in Figure 13. As could be seen from Figure 13, with HMSCZS, the total output power of the CHB inverter ranges from 935.9-1016 W and the average is about 982.2 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1000-1020 W and the average is about 1014 W. Compared with the HMSCZS, the efficiency of the CHB inverter can be improved about 3.12% by adopting the SHMS. Therefore, under the fault mode, the SHMS is still able to make the DC-side voltages reach the references, thus maintaining a higher energy yield.

Experimental Results
As shown in Figure 14, an experimental prototype with five H-bridge units has been established to validate the effectiveness of the proposed strategy. The prototype includes a central controller and five local controllers. The BECKHOFF industrial PC (CX2040) is utilized as the central controller and TMS320F28335 processors are used as local controllers which communicate with each other through an EtherCAT real-time communication network. The EtherCAT protocol features not only enhance the effective synchronization between master and slave clocks, but also improves the synchronization between the H-bridge units. Since the testing equipment of the university laboratory is limited, only the first H-bridge unit is connected to a Chroma62020H-150S PV simulator, and the DC side of the four other H-bridge units are connected to a 36 V switching power supply through a 0.5 Ω resistance, respectively, to simulate PV modules. Given that there are only five H-bridge units in the experiment, the output of the inverter is connected to the 130 V AC grid regulated by a voltage regulator. The other parameters of the experimental system are the same as the simulation parameters.

Normal Mode
The first experiment has been carried out under the initial conditions of PV simulator with irradiance of 1000 W/m 2 and a temperature of 25 °C. In this case, the input power of the first H-bridge unit is approximately 255 W. The reference of the other four H-bridge units' DC-side voltages is 32.02 V, and therefore the output power of the other four H-bridges is about 255 W in theory. As depicted in the Figure 15, both SHMS and HMSWZS enable the CHB inverter to operate at unity power factor  Figure 13. Simulation results of the total output power of the CHB inverter under the fault mode with: (a) HMSCZS and (b) SHMS.

Experimental Results
As shown in Figure 14, an experimental prototype with five H-bridge units has been established to validate the effectiveness of the proposed strategy. The prototype includes a central controller and five local controllers. The BECKHOFF industrial PC (CX2040) is utilized as the central controller and TMS320F28335 processors are used as local controllers which communicate with each other through an EtherCAT real-time communication network. The EtherCAT protocol features not only enhance the effective synchronization between master and slave clocks, but also improves the synchronization between the H-bridge units. Since the testing equipment of the university laboratory is limited, only the first H-bridge unit is connected to a Chroma62020H-150S PV simulator, and the DC side of the four other H-bridge units are connected to a 36 V switching power supply through a 0.5 Ω resistance, respectively, to simulate PV modules. Given that there are only five H-bridge units in the experiment, the output of the inverter is connected to the 130 V AC grid regulated by a voltage regulator. The other parameters of the experimental system are the same as the simulation parameters.

perimental Results
As shown in Figure 14, an experimental prototype with five H-bridge units has been establ lidate the effectiveness of the proposed strategy. The prototype includes a central controlle ocal controllers. The BECKHOFF industrial PC (CX2040) is utilized as the central controlle 320F28335 processors are used as local controllers which communicate with each other thr herCAT real-time communication network. The EtherCAT protocol features not only enh fective synchronization between master and slave clocks, but also improves the synchroniz een the H-bridge units. Since the testing equipment of the university laboratory is limited, rst H-bridge unit is connected to a Chroma62020H-150S PV simulator, and the DC side o other H-bridge units are connected to a 36 V switching power supply through a 0.5 Ω resist ctively, to simulate PV modules. Given that there are only five H-bridge units in the experim utput of the inverter is connected to the 130 V AC grid regulated by a voltage regulator parameters of the experimental system are the same as the simulation parameters.

ormal Mode
The first experiment has been carried out under the initial conditions of PV simulator iance of 1000 W/m 2 and a temperature of 25 °C. In this case, the input power of the first H-b

Normal Mode
The first experiment has been carried out under the initial conditions of PV simulator with irradiance of 1000 W/m 2 and a temperature of 25 • C. In this case, the input power of the first H-bridge unit is approximately 255 W. The reference of the other four H-bridge units' DC-side voltages is 32.02 V, and therefore the output power of the other four H-bridges is about 255 W in theory. As depicted in the Figure 15, both SHMS and HMSWZS enable the CHB inverter to operate at unity power factor with good grid current quality. It can also be seen that SHMS contains four output modes: "+1", "−1", PWM, and "0" mode, which is never adopted in HMSWZS. with good grid current quality. It can also be seen that SHMS contains four output modes: "+1", "−1", PWM, and "0" mode, which is never adopted in HMSWZS. For the sake of evaluating the characteristic of both two modulation methods in terms of DCside voltage fluctuation and average output power of the PV module, the following experiments have been performed under the same conditions as the first experiment. As shown in Figure 16, the maximum fluctuation of VPV1 by adopting HMSWZS is 5.3 V, but the value is only 4.1V for SHMS, which is reduced by about 22.64%. In order to compare the output power of the two methods under normal mode, the total output power of the CHB inverter is recorded by the upper computer, respectively. As can be seen from Figure 17, with HMSWZS, the total output power of the CHB inverter ranges from 1218-1244.2 W and the average is about 1233.7 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1230-1249.3 W and the average is about 1239.8 W. Compared with the HMSWZS, the efficiency of the CHB inverter can be improved about 0.48% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 18. As can be seen from Figure 18, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSWZS. Therefore, under normal mode, the SHMS is able to effectively suppress the DC-side voltage fluctuation compared with the HMSWZS, thereby improving the energy acquisition of the PV module.  For the sake of evaluating the characteristic of both two modulation methods in terms of DC-side voltage fluctuation and average output power of the PV module, the following experiments have been performed under the same conditions as the first experiment. As shown in Figure 16, the maximum fluctuation of V PV1 by adopting HMSWZS is 5.3 V, but the value is only 4.1V for SHMS, which is reduced by about 22.64%. In order to compare the output power of the two methods under normal mode, the total output power of the CHB inverter is recorded by the upper computer, respectively. As can be seen from Figure 17, with HMSWZS, the total output power of the CHB inverter ranges from 1218-1244.2 W and the average is about 1233.7 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1230-1249.3 W and the average is about 1239.8 W. Compared with the HMSWZS, the efficiency of the CHB inverter can be improved about 0.48% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 18. As can be seen from Figure 18, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSWZS. Therefore, under normal mode, the SHMS is able to effectively suppress the DC-side voltage fluctuation compared with the HMSWZS, thereby improving the energy acquisition of the PV module. with good grid current quality. It can also be seen that SHMS contains four output modes: "+1", "−1", PWM, and "0" mode, which is never adopted in HMSWZS. For the sake of evaluating the characteristic of both two modulation methods in terms of DCside voltage fluctuation and average output power of the PV module, the following experiments have been performed under the same conditions as the first experiment. As shown in Figure 16, the maximum fluctuation of VPV1 by adopting HMSWZS is 5.3 V, but the value is only 4.1V for SHMS, which is reduced by about 22.64%. In order to compare the output power of the two methods under normal mode, the total output power of the CHB inverter is recorded by the upper computer, respectively. As can be seen from Figure 17, with HMSWZS, the total output power of the CHB inverter ranges from 1218-1244.2 W and the average is about 1233.7 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 1230-1249.3 W and the average is about 1239.8 W. Compared with the HMSWZS, the efficiency of the CHB inverter can be improved about 0.48% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 18. As can be seen from Figure 18, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSWZS. Therefore, under normal mode, the SHMS is able to effectively suppress the DC-side voltage fluctuation compared with the HMSWZS, thereby improving the energy acquisition of the PV module.

Fault Mode
The last experiment is conducted to evaluate the performance of SHMS and HMSCZS in the fault mode where the PV module fails. Initially, the CHB inverter and PV modules are operating in normal mode as indicated in the first experiment. Then the second PV module is removed. As can be seen from Figure 19a,b, both the HMSCZS and SHMS can keep the CHB inverter stable and operating at a unity power factor without interruption. As is presented in the Figure 19a, by using the HMSCZS, the fault H-bridge unit can operate only in "0" or "+PWM" mode when VG is positive and "0" or "−PWM" mode when VG is negative. In such condition, the fault H-bridge unit is always in discharge status and unable to realize the equalization of the charge-discharge. Consequently, as presented in Figure 19c, the DC-side voltages of all H-bridge units diverge from the references in the steady state, which may result in low generated power of the CHB inverter. However, as presented in the Figure  19b, by utilizing the SHMS, the fault H-bridge unit can operate in "+1", "+PWM", "−1" or "−PWM" mode whether the grid voltage (VG) is positive or negative. Therefore, as depicted in the Figure 19d, the SHMS is capable of realizing the equalization of the charge-discharge of the fault H-bridge unit and maintaining the DC-side voltage balance of the other H-bridge units. In order to compare the output power of the two methods under fault mode, the total output power of the CHB inverter is recorded by the upper computer respectively. As can be seen from Figure 20, with HMSCZS, the total output power of the CHB inverter ranges from 919.2-986.4 W and the average is about 948.8 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 972.3-988.6 W and the average is about 978.2 W. Compared with the HMSCZS, the efficiency of the CHB inverter can be improved about 2.89% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 21. As can be seen from Figure 21, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSCZS. Therefore, under the fault mode, the SHMS is able to make the DC-side voltages reach the references, thus maintaining a higher energy yield.

Fault Mode
The last experiment is conducted to evaluate the performance of SHMS and HMSCZS in the fault mode where the PV module fails. Initially, the CHB inverter and PV modules are operating in normal mode as indicated in the first experiment. Then the second PV module is removed. As can be seen from Figure 19a,b, both the HMSCZS and SHMS can keep the CHB inverter stable and operating at a unity power factor without interruption. As is presented in the Figure 19a, by using the HMSCZS, the fault H-bridge unit can operate only in "0" or "+PWM" mode when V G is positive and "0" or "−PWM" mode when V G is negative. In such condition, the fault H-bridge unit is always in discharge status and unable to realize the equalization of the charge-discharge. Consequently, as presented in Figure 19c, the DC-side voltages of all H-bridge units diverge from the references in the steady state, which may result in low generated power of the CHB inverter. However, as presented in the Figure 19b, by utilizing the SHMS, the fault H-bridge unit can operate in "+1", "+PWM", "−1" or "−PWM" mode whether the grid voltage (V G ) is positive or negative. Therefore, as depicted in the Figure 19d, the SHMS is capable of realizing the equalization of the charge-discharge of the fault H-bridge unit and maintaining the DC-side voltage balance of the other H-bridge units. In order to compare the output power of the two methods under fault mode, the total output power of the CHB inverter is recorded by the upper computer respectively. As can be seen from Figure 20, with HMSCZS, the total output power of the CHB inverter ranges from 919.2-986.4 W and the average is about 948.8 W. When SHMS is utilized, the total output power of the CHB inverter ranges from 972.3-988.6 W and the average is about 978.2 W. Compared with the HMSCZS, the efficiency of the CHB inverter can be improved about 2.89% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 21. As can be seen from Figure 21, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSCZS. Therefore, under the fault mode, the SHMS is able to make the DC-side voltages reach the references, thus maintaining a higher energy yield. average is about 978.2 W. Compared with the HMSCZS, the efficiency of the CHB inverter can be improved about 2.89% by adopting the SHMS. Furthermore, the efficiency of the CHB inverter with both methods is presented in Figure 21. As can be seen from Figure 21, the SHMS is capable of improving the efficiency of the CHB inverter compared with the HMSCZS. Therefore, under the fault mode, the SHMS is able to make the DC-side voltages reach the references, thus maintaining a higher energy yield.

Conclusions
This paper proposes a switching hybrid modulation strategy, which can effectively reduce the fluctuation of DC-side voltage and maximize the output power of a PV CHB grid-connected inverter. When the CHB inverter is operating in the normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage fluctuation, thereby improving the output

Conclusions
This paper proposes a switching hybrid modulation strategy, which can effectively reduce the fluctuation of DC-side voltage and maximize the output power of a PV CHB grid-connected inverter. When the CHB inverter is operating in the normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage fluctuation, thereby improving the output power of PV modules. Once the CHB inverter is operating in the fault mode, owing to failing solar

Conclusions
This paper proposes a switching hybrid modulation strategy, which can effectively reduce the fluctuation of DC-side voltage and maximize the output power of a PV CHB grid-connected inverter. When the CHB inverter is operating in the normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage fluctuation, thereby improving the output

Conclusions
This paper proposes a switching hybrid modulation strategy, which can effectively reduce the fluctuation of DC-side voltage and maximize the output power of a PV CHB grid-connected inverter. When the CHB inverter is operating in the normal mode, the hybrid modulation strategy containing the zero state is adopted to suppress DC-side voltage fluctuation, thereby improving the output power of PV modules. Once the CHB inverter is operating in the fault mode, owing to failing solar panels, the hybrid modulation strategy without the zero state is utilized to make the DC-side voltages reach the references, thus, maintaining a higher energy yield under the fault condition. A set of experimental results demonstrate that, with this method, the output energy of the PV modules is improved both in the normal mode and fault mode.