A New Single-Phase Transformerless Current Source Inverter for Leakage Current Reduction

Abstract: A new single-phase transformerless current source inverter is proposed in this paper. The proposed inverter can achieve leakage current reduction, which is crucial for the conventional current source inverter. The basic concept of the proposed solution is to develop the new inverter by the duality principle from the voltage source inverter. The theoretical analysis is carried out to determine the switching states of the proposed inverter for the leakage current reduction. Also, a new modulation strategy is presented to achieve the optimized switching states. Finally, the experimental results are presented. Comparing with conventional single-phase current source inverter, the leakage current can be significantly reduced by the proposed inverter, which verifies the effectiveness of the proposed solution.


Introduction
Power generation with solar energy is one of the most attractive solutions towards the utilization of renewable energy sources [1].Typically, the inverter is used to interface the solar photovoltaic (PV) panel to the grid via a transformer.This kind of transformer is bulky, low-efficient and not cost-effective.This is the reason why transformerless PV inverters have been developed in recent years [2][3][4].In practice, however, leakage current would arise due to a lack of galvanic isolation.The leakage current leads to the electromagnetic interference and potential safety issues [5,6].Therefore, the VDE standard specifies that the leakage current should be less than 300 mA.Otherwise, the grid-connected inverter should be disconnected from the grid.Typically, the inverter is used to interface the PV panel and grid.
In order to solve the above mentioned problem, many solutions have been proposed in the last decades.To reduce the common-mode voltage (CMV), the novel modulation methods have been proposed [7][8][9][10][11][12][13][14].An improved modulation with modified reference was proposed in [7].Another modified modulation for reducing the CMV with specified vectors was proposed in [8].Lian et al. reduce the CMV by introducing the average-value-reduction space vector modulation method.It applies the specified switching states with less CMV.Bradaschia et al. [15,16] proposed effective methods to reduce leakage current which only need additional fast-recovery diodes.To increase the optional switching states, the extra switch can also be added to the system.The principle of this method is to isolate the PV array and the grid during the zero switching states [17][18][19][20][21][22][23][24].The methods may result in extra cost, losses, and increases control complexity.However, the electromagnetic interference (EMI) filter that is used to improve the output current quality could be removed from system if the leakage current is eliminated effectively.Thus, the cost of the EMI filter will be saved and the size of the inverter will be decreased.Miveh et al. [25][26][27] proposed four-wire inverters which only need extra neutral wire.For this reason, the direct current (DC)-link Energies 2018, 11, 1633 2 of 12 midpoint connects with the neutral point of the grid, and the voltages between the PV array and the ground are limited to a constant value.So, the leakage current can be reduced effectively.Some scholars proposed inverters which connect the PV array terminal with the grid terminal.The voltage between the PV array and the ground is clamped.Therefore, the leakage current can be reduced [28][29][30][31][32].
The two-stage power conversion would be complicated and have a low efficiency.An alternative solution is proposed using the current source inverter [33][34][35][36].However, the leakage current could not be well suppressed with the conventional current source inverter, which is the motivation of the paper in solving this problem.
The objective of the paper is to present a new single-phase transformerless current source inverter with leakage current reduction.Like the VH6 inverter [3], the proposed inverter only needs a bidirectional switch which in serial with the alternating current (AC) side.When the inverter works in zero switching states, the extra switch will work to isolate the PV array and the grid.The rest paper is organized as follows.Section 2 provides the theoretical analysis as to why the conventional single-phase current source inverter fails to reduce the leakage current.The new solution for the leakage current reduction is presented in Section 3. The simulation and experimental results are provided in Section 4.

Conventional Current Source Inverter
The conventional single-phase current source inverter is illustrated in Figure 1, which consists of four switches in an H-bridge format.Therefore, it is called a CH4 inverter.In order to evaluate the leakage current reduction capability, the common-mode loop model is established, as shown in Figure 2.
Energies 2018, 11, x 2 of 12 neutral point of the grid, and the voltages between the PV array and the ground are limited to a constant value.So, the leakage current can be reduced effectively.Some scholars proposed inverters which connect the PV array terminal with the grid terminal.The voltage between the PV array and the ground is clamped.Therefore, the leakage current can be reduced [28][29][30][31][32].The two-stage power conversion would be complicated and have a low efficiency.An alternative solution is proposed using the current source inverter [33][34][35][36].However, the leakage current could not be well suppressed with the conventional current source inverter, which is the motivation of the paper in solving this problem.
The objective of the paper is to present a new single-phase transformerless current source inverter with leakage current reduction.Like the VH6 inverter [3], the proposed inverter only needs a bidirectional switch which in serial with the alternating current (AC) side.When the inverter works in zero switching states, the extra switch will work to isolate the PV array and the grid.The rest paper is organized as follows.Section 2 provides the theoretical analysis as to why the conventional singlephase current source inverter fails to reduce the leakage current.The new solution for the leakage current reduction is presented in Section 3. The simulation and experimental results are provided in Section 4.

Conventional Current Source Inverter
The conventional single-phase current source inverter is illustrated in Figure 1, which consists of four switches in an H-bridge format.Therefore, it is called a CH4 inverter.In order to evaluate the leakage current reduction capability, the common-mode loop model is established, as shown in Figure 2. In Figure 2, Vpo and Vno represent the voltage between the positive or negative rail and the ground, respectively.They can be regarded as the controllable voltage sources, which are regulated by the switching states si (i = 1, 2, 3, 4).Lf1, Lf2, L1, and Lf2 are the input and output inductors, respectively.IL is the output inductor current.Vg is the grid voltage.Ia and Ib can be regarded as the controllable current sources, which are determined by the switching states si (i = 1, 2, 3, 4).neutral point of the grid, and the voltages between the PV array and the ground are limited to a constant value.So, the leakage current can be reduced effectively.Some scholars proposed inverters which connect the PV array terminal with the grid terminal.The voltage between the PV array and the ground is clamped.Therefore, the leakage current can be reduced [28][29][30][31][32].The two-stage power conversion would be complicated and have a low efficiency.An alternative solution is proposed using the current source inverter [33][34][35][36].However, the leakage current could not be well suppressed with the conventional current source inverter, which is the motivation of the paper in solving this problem.
The objective of the paper is to present a new single-phase transformerless current source inverter with leakage current reduction.Like the VH6 inverter [3], the proposed inverter only needs a bidirectional switch which in serial with the alternating current (AC) side.When the inverter works in zero switching states, the extra switch will work to isolate the PV array and the grid.The rest paper is organized as follows.Section 2 provides the theoretical analysis as to why the conventional singlephase current source inverter fails to reduce the leakage current.The new solution for the leakage current reduction is presented in Section 3. The simulation and experimental results are provided in Section 4.

Conventional Current Source Inverter
The conventional single-phase current source inverter is illustrated in Figure 1, which consists of four switches in an H-bridge format.Therefore, it is called a CH4 inverter.In order to evaluate the leakage current reduction capability, the common-mode loop model is established, as shown in Figure 2. In Figure 2, Vpo and Vno represent the voltage between the positive or negative rail and the ground, respectively.They can be regarded as the controllable voltage sources, which are regulated by the switching states si (i = 1, 2, 3, 4).Lf1, Lf2, L1, and Lf2 are the input and output inductors, respectively.IL is the output inductor current.Vg is the grid voltage.Ia and Ib can be regarded as the controllable current sources, which are determined by the switching states si (i = 1, 2, 3, 4).In Figure 2, V po and V no represent the voltage between the positive or negative rail and the ground, respectively.They can be regarded as the controllable voltage sources, which are regulated by the switching states s i (i = 1, 2, 3, 4).L f1 , L f2 , L 1 , and L f2 are the input and output inductors, respectively.
Energies 2018, 11, 1633 3 of 12 I L is the output inductor current.V g is the grid voltage.I a and I b can be regarded as the controllable current sources, which are determined by the switching states s i (i = 1, 2, 3, 4).
Note that the leakage current is mainly determined by the common-mode behavior of the inverter.Therefore, the differential-model variables, e.g., I a and I b , are neglected for simplicity.In this way, the simplified common-mode loop model can be obtained, as shown in Figure 3.Note that the leakage current is mainly determined by the common-mode behavior of the inverter.Therefore, the differential-model variables, e.g., Ia and Ib, are neglected for simplicity.In this way, the simplified common-mode loop model can be obtained, as shown in Figure 3.In Figure 3, the equivalent impedance Z and equivalent voltage Vm can be expressed as follows, according to Thevenin's theorem.
In Equation ( 2), the Vcm represents the CMV. () The Vm would be equal to Vcm on the condition that L1 and L2 have the identical inductances, which are generally designed the same in practical applications.
The voltage Vpo and Vno can be derived as follows: ) where: In the condition that L1 = L2 = L and Lf1 = Lf2 = Lf, Vm can be represented as follows: The leakage current Icm can be derived from Figure 3 as follows: Then, the common-mode current of Icm can be calculated by using Equations ( 6) and ( 7): From Equation (8), it can be observed that Icm is dependent on many factors, such as the parasitic capacitance CPV, the grid voltage Vg, input filter inductance L, output filter inductance Lf, and Simplified common-mode model of the CH4 inverter.
In Figure 3, the equivalent impedance Z and equivalent voltage V m can be expressed as follows, according to Thevenin's theorem.
In Equation ( 2), the V cm represents the CMV.
The V m would be equal to V cm on the condition that L 1 and L 2 have the identical inductances, which are generally designed the same in practical applications.
The voltage V po and V no can be derived as follows: where: In the condition that L 1 = L 2 = L and L f1 = L f2 = L f , V m can be represented as follows: The leakage current I cm can be derived from Figure 3 as follows: Then, the common-mode current of I cm can be calculated by using Equations ( 6) and ( 7): From Equation (8), it can be observed that I cm is dependent on many factors, such as the parasitic capacitance C PV , the grid voltage V g , input filter inductance L, output filter inductance L f , and switching states s i .In practice, the switching states vary at a high frequency, which will have an impact on the CMV.
According to the Equation ( 6), the switching states and the corresponding CMV is analyzed as follows.
When the switches S 1 and S 4 are ON, the CMV can be obtained as Equation (9).
When the switches S 1 and S 2 are ON, the CMV can be obtained.Considering the voltage drop across the inductor is much smaller than grid voltage, the CMV is approximately equal to the grid voltage as follows: When the switches S 2 and S 3 are ON, the CMV can be obtained as follows: When the switches S 3 and S 4 are ON, the CMV can be obtained.Note that the voltage drop across the inductor is much smaller than the grid voltage.Therefore, it can be neglected, and the CMV is approximately equal to zero as follows: Based on the above analysis, the switching states and the corresponding voltage are listed in Table 1.
Table 1.The switching states and their voltages.
From Table 1, it can be observed that the CMV varies with the switching states in a high-frequency way.That is the reason why the conventional CH4 inverter fails to reduce the leakage current.

New Current Source Inverter
As discussed in the previous section, the leakage current is not able to be reduced by the conventional current source inverter.In order to solve the problem, a new current source inverter is proposed in this paper.The idea of the proposed solution is based on the duality principle.Inspired by the voltage source inverter named VH6 [3], the new current source inverter is proposed.
In Figure 4, the VH6 inverter has two switches in parallel with the AC side to improve the common-mode behavior, in order to reduce the leakage current.According to the duality principle, the proposed inverter has an additional switch that is in serial with the upper or lower side of the AC.In the zero switching state, the new inverter would operate in the same way as the CH4 inverter, if the switch S5 is ON.However, when the switch S5 is OFF, the CH5 inverter would operate in a new mode, and the circuit model is shown in Figure 6.In this new mode, S1 and S2 are turned ON, and S3 and S4 are turned OFF.As shown in Figure 6, the voltages Vpo and Vno would be the same, as shown in Equation (13).Also, the CMV is half of the grid voltage, as shown in Equation (14).So, this operation mode can be used as the zero switching state of the inverter to keep the CMV over half of the grid voltage.As shown in Figure 5, different from the VH6 inverter, the proposed inverter only needs one extra switch.Thus, it is called CH5 inverter.In the zero switching state, the new inverter would operate in the same way as the CH4 inverter, if the switch S5 is ON.However, when the switch S5 is OFF, the CH5 inverter would operate in a new mode, and the circuit model is shown in Figure 6.In this new mode, S1 and S2 are turned ON, and S3 and S4 are turned OFF.As shown in Figure 6, the voltages Vpo and Vno would be the same, as shown in Equation (13).Also, the CMV is half of the grid voltage, as shown in Equation (14).So, this operation mode can be used as the zero switching state of the inverter to keep the CMV over half of the grid voltage.In order to demonstrate the leakage current reduction capability of the proposed inverter, the operation principle and common-mode behavior are presented in this section.Note that the new inverter in Figure 5 is similar to the original, and thus only the inverter shown in Figure 5a is discussed for simplicity.
In the zero switching state, the new inverter would operate in the same way as the CH4 inverter, if the switch S 5 is ON.However, when the switch S 5 is OFF, the CH5 inverter would operate in a new mode, and the circuit model is shown in Figure 6.In this new mode, S 1 and S 2 are turned ON, and S 3 and S 4 are turned OFF.In the zero switching state, the new inverter would operate in the same way as the CH4 inverter, if the switch S5 is ON.However, when the switch S5 is OFF, the CH5 inverter would operate in a new mode, and the circuit model is shown in Figure 6.In this new mode, S1 and S2 are turned ON, and S3 and S4 are turned OFF.As shown in Figure 6, the voltages Vpo and Vno would be the same, as shown in Equation ( 13).Also, the CMV is half of the grid voltage, as shown in Equation ( 14).So, this operation mode can be used as the zero switching state of the inverter to keep the CMV over half of the grid voltage.As shown in Figure 6, the voltages V po and V no would be the same, as shown in Equation ( 13).Also, the CMV is half of the grid voltage, as shown in Equation (14).So, this operation mode can be used as the zero switching state of the inverter to keep the CMV over half of the grid voltage.13) Based on the above analysis, the switching states and the corresponding voltage are listed in Table 2.
Table 2.The switching states and their voltages.
As shown in Table 2, it can be observed that the high-frequency CMV can be totally eliminated on the condition that the vectors of I 1 , I 2 , and I 5 are applied, leaving only the low-frequency grid voltage.It should be noted that the leakage current is mainly determined by the high-frequency components of CMV, and the low-frequency component has a slim impact on the leakage current.Therefore, the vectors of I 1 , I 2 and I 5 are used for controlling the proposed inverter.
The control structure of the proposed inverter is shown in Figure 7.
Energies 2018, 11, x 6 of 12 Based on the above analysis, the switching states and the corresponding voltage are listed in Table 2.
As shown in Table 2, it can be observed that the high-frequency CMV can be totally eliminated on the condition that the vectors of I1, I2, and I5 are applied, leaving only the low-frequency grid voltage.It should be noted that the leakage current is mainly determined by the high-frequency components of CMV, and the low-frequency component has a slim impact on the leakage current.Therefore, the vectors of I1, I2 and I5 are used for controlling the proposed inverter.
The control structure of the proposed inverter is shown in Figure 7.As shown in Figure 7, the zero crossing detection is used for the grid synchronization to provide the reference angle for the grid current.The proportional resonant (PR) controller [37] is used to regulate the grid current with zero-steady state error.The gating signals are generated by the modulation strategy.And the detailed modulation procedure is presented, as shown in Figure 8.As shown in Figure 7, the zero crossing detection is used for the grid synchronization to provide the reference angle for the grid current.The proportional resonant (PR) controller [37] is used  As shown in Figure 7, the zero crossing detection is used for the grid synchronization to provide the reference angle for the grid current.The proportional resonant (PR) controller [37] is used to regulate the grid current with zero-steady state error.The gating signals are generated by the modulation strategy.And the detailed modulation procedure is presented, as shown in Figure 8.In Figure 8a, during the positive half cycle, the reference vector Iref is synthesized by the active vector I1 and zero vector I5.While in the negative half cycle, the Iref is synthesized by active vector I2 and zero vector I5.The process of vector allocation is shown in Figure 8b.m represents the modulation index.t represents the operation time.Ts represents the switching period.T1 represents the dwell time of active vector.And T2 represents the dwell time of zero vector.a stands for the modulation signal which can be obtained from the output variable through the PR controller.As shown in Figure 8, the dwell time of vectors is allocated based on the modulation signal.
In the positive half cycle, the range of vector angle θ is from 0 to π. Iref can be represented as Equation (15).In the negative half cycle, the range of vector angle θ is from π to 2π.Iref can be represented as Equation (16).

Simulation and Experimental Results
The simulation and experimental tests are carried out to verify the effectiveness of the proposed solution.In the simulation test, the grid voltage is 220 V/50 Hz.The input current source is 12.5 A. The filter inductance is 2.5 mH.The filter capacitance is 9.4 uF.The switching frequency is 10 kHz.The grid current is 10 A. And the parasitic capacitance is 75 nF.
Figure 9 shows the simulation results of the conventional CH4 inverter and proposed CH5 inverter.As shown in Figure 9a, influenced by the leakage current, the grid current is superposed with the high-frequency harmonics.The CMV of the CH4 is shown in Figure 9g; it is obvious that CMV consists of high-frequency components, which results in the undesirable leakage current, as shown in Figure 9i.The amplitude of the leakage current is far beyond 300 mA, which fails to comply with VDE-0126-1-1 standard.On the right, it is the waveforms of proposed inverter that correspond to the CH4.As shown in Figure 9b, the high frequency harmonics of the grid current is significantly reduced, compared with Figure 9a.The CMV is free of any high-frequency harmonics, and thus the leakage current is significantly reduced well below 300 mA, which meet the VDE-0126-1-1 standard.
( , ) In Figure 8a, during the positive half cycle, the reference vector I ref is synthesized by the active vector I 1 and zero vector I 5 .While in the negative half cycle, the I ref is synthesized by active vector I 2 and zero vector I 5 .The process of vector allocation is shown in Figure 8b.m represents the modulation index.t represents the operation time.T s represents the switching period.T 1 represents the dwell time of active vector.And T 2 represents the dwell time of zero vector.a stands for the modulation signal which can be obtained from the output variable through the PR controller.As shown in Figure 8, the dwell time of vectors is allocated based on the modulation signal.
In the positive half cycle, the range of vector angle θ is from 0 to π.I ref can be represented as Equation (15).
In the negative half cycle, the range of vector angle θ is from π to 2π.I ref can be represented as Equation (16).

Simulation and Experimental Results
The simulation and experimental tests are carried out to verify the effectiveness of the proposed solution.In the simulation test, the grid voltage is 220 V/50 Hz.The input current source is 12.5 A. The filter inductance is 2.5 mH.The filter capacitance is 9.4 uF.The switching frequency is 10 kHz.The grid current is 10 A. And the parasitic capacitance is 75 nF.
Figure 9 shows the simulation results of the conventional CH4 inverter and proposed CH5 inverter.As shown in Figure 9a, influenced by the leakage current, the grid current is superposed with the high-frequency harmonics.The CMV of the CH4 is shown in Figure 9g; it is obvious that CMV consists of high-frequency components, which results in the undesirable leakage current, as shown in Figure 9i.The amplitude of the leakage current is far beyond 300 mA, which fails to comply with VDE-0126-1-1 standard.On the right, it is the waveforms of proposed inverter that correspond to the CH4.As shown in Figure 9b, the high frequency harmonics of the grid current is significantly reduced, compared with Figure 9a.The CMV is free of any high-frequency harmonics, and thus the leakage current is significantly reduced well below 300 mA, which meet the VDE-0126-1-1 standard.In order to further verify the effectiveness of the proposed solution.The experimental prototype is established.The experimental parameters are listed as follows.The input current source is 8 A. The filter inductance is 2.5 mH.The filter capacitance is 9.4 uF.The switching frequency is 10 kHz.The grid current is 10 A. And the parasitic capacitance is 75 nF.The control and modulation algorithm are implemented in the DSP (TMS20F28335, Texas Instruments, Dallas, TX, USA) plus FPGA (XC6SLX9 2TQG144, Xilinx, San Jose, CA, USA) digital control platform Figure 10 shows the experimental results of CH4 inverter and proposed CH5 inverter.It can be observed that the output currents are unipolar and sinusoidal before and after the filter as shown in  In order to further verify the effectiveness of the proposed solution.The experimental prototype is established.The experimental parameters are listed as follows.The input current source is 8 A. modulation.It operates as the CH5 inverter.The dynamic experimental results show that the leakage current with the CH5 inverter is much lower than that with the CH4 inverter, which again verifies the effectiveness of the proposed solution.

Conclusions
This paper has presented a new single-phase transformer-less current source inverter.It can achieve the leakage current reduction which is crucial for the PV inverter.The new current source inverter with the improved common mode behavior is established by the duality principle.The proposed solution only needs one extra switch to break the common-mode loop of the system for the leakage current reduction.Aside from that, a new one-dimensional space vector modulation is presented for eliminating the high-frequency common-mode voltage, so as to reduce the leakage current.The experimental results reveal that the leakage current can be significantly reduced from 1.2 to 0.19 A with the proposed solution.Therefore, it is an attractive solution for the single-phase transformerless PV systems.It should be noted that IGBT is used for the proposed inverter.There is a limitation regarding the switching frequency.With the rapid development of the wide-bandgap semiconductors such as the commercially available silicon carbide and GaN power device, the switching frequency would be high for a better techno-industrial level, which is the subject of our future research.

Figure 2 .
Figure 2. Circuit model of the CH4 inverter.

Figure 3 .
Figure 3. Simplified common-mode model of the CH4 inverter.

Figure 6 .
Figure 6. Circuit model of CH5 in new mode.

Figure 6 .
Figure 6. Circuit model of CH5 in new mode.

Figure 6 .
Figure 6. Circuit model of CH5 in new mode.

Figure 7 .
Figure 7.Control structure of the proposed inverter.

Figure 7 .
Figure 7.Control structure of the proposed inverter.
grid current with zero-steady state error.The gating signals are generated by the modulation strategy.And the detailed modulation procedure is presented, as shown in Figure8.

Figure 7 .
Figure 7.Control structure of the proposed inverter.

Figure 9 .
Figure 9. Simulation results of conventional CH4 inverter and proposed CH5 inverter.(a) Grid current of CH4; (b) Grid current of proposed one; (c) Vpo of CH4; (d) Vpo of proposed one; (e) Vno of CH4; (f) Vno of proposed one; (g) common-mode voltage (CMV) of CH4; (h) CMV of proposed one; (i) Leakage current of CH4; (j) Leakage current of proposed one.

Figure 9 .
Figure 9. Simulation results of conventional CH4 inverter and proposed CH5 inverter.(a) Grid current of CH4; (b) Grid current of proposed one; (c) V po of CH4; (d) V po of proposed one; (e) V no of CH4; (f) V no of proposed one; (g) common-mode voltage (CMV) of CH4; (h) CMV of proposed one; (i) Leakage current of CH4; (j) Leakage current of proposed one.

Figure 11 .
Figure 11.The dynamic experimental results from CH4 to CH5 inverter.(a) Vpo and Vno; (b) Leakage current and CMV.

Table 2 .
The switching states and their voltages.