A Transformerless Single-Phase Current Source Inverter Topology and Control for Photovoltaic Applications

Abstract

Low power grid-tied photovoltaic (PV) generation systems increasingly use transformerless inverters. The elimination of the transformer allows smaller, lighter and cheaper systems, and improves the total efficiency. However, a leakage current may appear, flowing from the grid to the PV panels through the existing parasitic capacitance between them, since there is no galvanic isolation. As a result, electromagnetic interferences and security issues arise. This paper presents a novel transformerless single-phase Current Source Inverter (CSI) topology with a reduced inductor, compared to conventional CSIs. This topology directly connects the neutral line of the grid to the negative terminal of the PV system, referred as common mode configuration, eliminating this way, theoretically, the possibility of any leakage current through this terminal. The switches control is based on a hysteresis current controller together with a combinational logic circuitry and it is implemented in a digital platform based on National Instruments Technology. Results that validate the proposal, based on both simulations and tests of a low voltage low power prototype, are presented.

1. Introduction

Low-frequency transformers (50–60 Hz) between the conversion stage and the grid are often included in grid-tied photovoltaic (PV) systems. For security reasons, the grid neutral line and the chassis of the PV panel must be grounded. The transformer ensures that no leakage current flows between the grounded PV panels and the grounded grid neutral line. It also provides galvanic isolation and guarantees the absence of direct current (DC) injected from the PV system into the grid. However, the low-frequency transformer results in bulkier, heavier, and more expensive systems compared to transformerless ones. Finally, it also reduces the total efficiency of the system [1,2,3,4]. In order to eliminate these drawbacks, it can be used transformerless inverters. Unfortunately, in this case, a direct electrical connection between the PV panels ground and the grounded grid neutral line appears, due to the existing parasitic capacitances of the PV panels to ground. If a varying common-mode (CM) voltage, V_CM, is generated by the conversion stage, a leakage current, or common-mode currents (i_cm), flows through the resulting equivalent circuit. This circuit is formed by the inverter and its output filter, the existing ground impedance Z_GcGg and the parasitic capacitance C_PVg between the PV panel and ground, as shown in Figure 1 [2,3,5]. This leakage current affects system efficiency, deteriorates the distortion of the grid current and the electromagnetic compatibility (EMC), and may cause security issues [5,6,7,8,9,10,11,12,13,14,15,16,17].

According to [2,3], V_CM is defined as:

$$v_{CM}=\frac{v_{1N}+v_{2N}}{2}+\left(v_{1N}-v_{2N}\right)\frac{L_2-L_1}{2\left(L_1+L_2\right)}$$

(1)

where v_1N is the voltage difference between points “1” and “N”, v_2N is the voltage difference between points “2” and “N” and, L₁ and L₂ are the output filter inductors.

Thus, the value of the leakage current mainly depends on the value of the parasitic capacitance of the PV system and the common-mode voltage, V_CM, which is closely related to the inverter modulation strategy [6,7]. The PV panel and its frame structure, the surface and the distance between cells, the ambient conditions or the converter EMC filter are, among others, factors that affect to the value of the parasitic capacitance [8].

In order to minimize the generation of variable V_CM voltages in transformerless PV systems, several solutions have been proposed: in [18], a review of several modulation strategies to suppress leakage currents is presented. Modulation techniques that do not produce a variable V_CM, such us Bipolar Sinusoidal Pulse Width Modulation (BSPWM), are a possible solution [18]. Another option is isolating the PV system from the grid when V_CM varies. Topologies such us H5, H6, HERIC and those shown in [19,20,21], have been proposed following this principle. Finally, other solutions propose the direct connection of the negative terminal of PV to the neutral line of the grid, referred here as common mode (CM). Such a configuration is proposed in [22]. It is worth mentioning that all these topologies are voltage source inverters (VSI).

Another option for a transformerless PV inverter is the Current Source Inverter (CSI). The voltage and current waveforms of this kind of inverters make them suitable for high power applications and adjustable speed drives. They also presents low EMC issues, low torque pulsations, and reduced stress on motors insulation. Fuel cells and wind turbine farms connected to the grid also uses CSI converters, since they present boost capability and permits parallel operation [23].

The CSI is also a natural candidate for transformerless PV inverters since they keep constant the value of the current at a defined set-point. In PV systems it is always desirable to have a Maximum Power Point Tracking (MPPT) algorithm in order to optimize the energy obtained from the PV panels. The PV panel current is one of the variables usually needed to implement an MPPT algorithm, so that the optimum value of the PV panel current can be used as the CSI current set-point.

Few CSI topologies for transformerless PV systems can be found in the literature. The Flying Inductor topology (FI), also known as the Karschny inverter, has the negative PV array connected directly to the neutral terminal of the grid, behaving almost as a CSI inverter in common mode configuration [24]. For this converter, the input voltage must be higher than the AC mains. Very recently, a modified FI with buck-boost capabilities has been presented [25]. The FI topology demands a high low-frequency input-current ripple from the PV panel, although it can be reduced with the appropriate design of the input capacitor placed in parallel with the PV panel. Recently, some CSI proposals for leakage current reduction have appeared in the literature. A transformerless CSI with low leakage current, based on the VSC H5 topology, is presented in [26]. In the same way, two transformerless three-phase CSI, based on the VSC H7 topology, are presented in [27,28]. These schemes are based on traditional differential mode inverters.

Following this trend, this paper presents a novel CSI topology with low leakage current, that could be considered a modified FI topology. It features low switching dv/dt and reliable protection against over-currents and short-circuits. The presented topology uses the common mode configuration, so the neutral line of the grid is connected directly to the negative terminal of the PV system, unlike the existing proposals. This connection maintains its voltage constant and negligible leakage current is generated, ideally zero. Another characteristic of this topology is that it allows the use of a smaller inductor L, compared to those usually found in conventional CSIs.

2. Proposed Topology

The circuit diagram of the proposed inverter is shown in Figure 2. It a based on a CSI in which, as mentioned before, the neutral line of the grid is connected directly to the negative terminal of the PV system. The output of the inverter is coupled to the grid through a CLC filter. It is composed of six power Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFET) switches (S₁, S₂, S₃, S₄, S₅ and S₆) with a diode in series each, two capacitors (C_f and C_fout) and two inductors (L and L_f). Only two of the MOSFETs are conducting in each switching state.

2.1. Analysis of the CSI Converter

In order to analyze the topology, an equivalent subcircuit is obtained for each switching state of the inverter, depending on what switches are On or Off simultaneously. The proposed CSI can be in one of five states, as summarized in

Table 1. Switching states.

Switch	Subcircuit 1 (+)	Subcircuit 2 (−)	Subcircuit 3 (0)	Subcircuit 4 (0)	Subcircuit 5 (0)
S1	On	Off	On	Off	Off
S2	Off	On	On	Off	Off
S3	Off	On	Off	Off	On
S4	On	Off	Off	Off	On
S5	Off	Off	Off	On	Off
S6	Off	Off	Off	On	Off

.

The equivalent subcircuits for each state are depicted in Figure 3.

2.1.1. Subcircuit 1

This subcircuit is defined by S₁ and S₄ turned on, and all other switches turned off (Figure 3a) This subcircuit generates the current for the positive half cycle of the output waveform. The inductor current i_L increases in this stage if PV panel input voltage V_in is greater than filter capacitor voltage V_Cf. At the same time, V_Cf increases depending on the sign of i_L − i_Lf, and filter current i_Lf increases if voltage V_Cf is greater than grid voltage V_out. Otherwise, all of them decrease. The state equations are:

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=\frac{V_{in}-V_{Cf}}{L}$$

(2)

$$\frac{\mathrm{d}}{\mathrm{d}t}{V}_{Cf}=\frac{i_L-i_{Lf}}{C_f}$$

(3)

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_{Lf}=\frac{V_{Cf}-V_{out}}{L_f}$$

(4)

2.1.2. Subcircuit 2

This subcircuit is defined by S₂ and S₃ turned on, and all other switches turned off (Figure 3b) This subcircuit generates the current for the negative half cycle of the output waveform. The inductor current i_L increases in this stage if V_Cf is positive, otherwise decreases; filter capacitor voltage V_Cf decreases depending on the sign of i_L + i_Lf, and filter current i_Lf increases if V_Cf is greater than V_out, otherwise decreases. The state equations are Equation (4) and:

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=\frac{V_{Cf}}{L}$$

(5)

$$\frac{\mathrm{d}}{\mathrm{d}t}{V}_{Cf}=-\frac{i_L+i_{Lf}}{C_f}$$

(6)

2.1.3. Subcircuit 3

In this subcircuit, the switches S₁ and S₂ are turned on, and all other switches are turned off (Figure 3c). The inductor current i_L increases and the filter capacitor voltage V_Cf decreases. The filter current i_Lf only increases if V_Cf is greater than V_out; if not, it decreases. No output current is generated in this stage. The state equations are Equation (4) and:

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=\frac{V_{in}}{L}$$

(7)

$$\frac{\mathrm{d}}{\mathrm{d}t}{V}_{Cf}=-\frac{i_{Lf}}{C_f}$$

(8)

2.1.4. Subcircuit 4

In this subcircuit, the switches S₅ and S₆ are turned on, and all other switches are turned off (Figure 3d). The inductor current i_L and the filter capacitor voltage V_Cf decreases. The filter current i_Lf only increases if V_Cf is greater than V_out; if not, it decreases. No output current is generated in this stage. The state equations are Equations (4) and (8):

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=-\frac{V_{in}}{L}$$

(9)

2.1.5. Subcircuit 5

In this subcircuit, the switches S₃ and S₄ are turned on, and all other switches are turned off (Figure 3e). Ideally, the inductor current i_L remains constant and the filter capacitor voltage V_Cf decreases. The filter current i_Lf only increases if V_Cf is greater than V_out; if not, it decreases. No output current is generated in this stage. The state equations are Equations (4) and (8):

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=0$$

(10)

Table 2. Voltages and currents behavior.

Variable	Subcircuit 1	Subcircuit 2	Subcircuit 3	Subcircuit 4	Subcircuit 5
iL	Increases if Vin is greater than VCf otherwise decreases	Increases if VCf is positive otherwise decreases	Increases	Decreases	No change
VCf	Depends on the value of iL − iLf	Depends on the value of iL + iLf	Decreases	Decreases	Decreases
iLf	Increases if VCf is greater than Vout otherwise decreases	Increases if VCf is greater than Vout otherwise decreases	Increases if VCf is greater than Vout otherwise decreases	Increases if VCf is greater than Vout otherwise decreases	Increases if VCf is greater than Vout otherwise decreases

summarizes the significant voltages and currents for each subcircuit. It indicates under which conditions their values increase or decrease.

2.2. Model of the CSI Converter

In order to obtain a model of the converter, we define U₁, U₂, and U₅ as the control laws for switches S₁, S₂, S₃, S₄, S₅ and S₆, according to Figure 2.

$$U_1=\{\begin{array}{c} 1 \mathrm{if} S_1 \mathrm{is} \mathrm{on}, \mathrm{but} S_3 \mathrm{is} \mathrm{off}\\ 0 \mathrm{if} S_3 \mathrm{is} \mathrm{on}, \mathrm{but} S_1 \mathrm{is} \mathrm{off}\end{array}$$

(11)

$$U_2=\{\begin{array}{c}0 \mathrm{if} S_2 \mathrm{is} \mathrm{on}, \mathrm{but} S_4 \mathrm{is} \mathrm{off}\\ 0 \mathrm{if} S_4 \mathrm{is} \mathrm{on}, \mathrm{but} S_2 \mathrm{is} \mathrm{off}\end{array}$$

(12)

$$U_5=\{\begin{array}{c}1 \mathrm{if} S_5 \mathrm{and} S_6 \mathrm{are} \mathrm{on}\\ 0 \mathrm{if} S_5 \mathrm{and} S_6 \mathrm{are} \mathrm{off}\end{array}$$

(13)

The model is obtained considering Equation (2) through Equation (13), as follows:

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_L=\frac{V_{in }\left(U_1-U_5-U_1{U}_5\right)-V_{Cf}\left(U_5-1\right)\left(U_1-U_2\right)}{L}$$

(14)

$$\frac{\mathrm{d}}{\mathrm{d}t}{V}_{Cf}=-\frac{i_L\left(U_5-1\right)\left(U_1-U_2\right)+i_{Lf}}{C_f}$$

(15)

$$\frac{\mathrm{d}}{\mathrm{d}t}{i}_{Lf}=\frac{V_{Cf}-V_{out}}{L_f}$$

(16)

The capacitor C_out is not a state variable since it is at the same voltage as the grid.

2.3. Proposed Controller of the CSI Converter

For the modulation strategy of the proposed converter, Unipolar Sinusoidal Pulse Width Modulation (USPWM) has been chosen [18]. To do so, a sinusoidal modulator signal is compared with two symmetrical triangular carrier signals. Then, comparing the sinusoidal modulator signal with the upper triangular carrier, the auxiliary control signal A is obtained. In the same way, the auxiliary control signal B is obtained comparing the sinusoidal modulator signal with the lower triangular carrier.

Both signals A and B at a logic high level correspond to subcircuit 1, indicating that the output current i_out will be positive. Both signals A and B at a low logic level correspond to subcircuit 2, indicating that the output current i_out will be negative. Finally, both signals A and B at different logic levels correspond to any of the subcircuits 3, 4 or 5, indicating a zero output current i_out. Subcircuits 1 and 2 increase or decrease the inductor current i_L respectively. In order to maintain the i_L current constant, as in any CSI converter, the controller has to select the appropriate subcircuit 3, 4 or 5.

So, subcircuits 1 and 2 are in charge of providing the output current i_out, while subcircuits 3, 4 and 5 are responsible for keeping constant the inductance current i_L.

All these waveforms are shown in Figure 4. Note that two low-frequency triangular carrier signals have been used only to better illustrate the operation.

2.3.1. Inductor Current Control

The current controller consists of a hysteresis controller along with a zero output current selector subcircuit. For the hysteresis controller, it has to be defined a value for the current hysteresis band, around the constant value of the inductor current i_L. When the current i_L is higher or lower than desired, a high logic level signal PE or NE is generated respectively, by means of two comparators. These signals together with a signal $\overline{\mathrm{Q}}$, coming for the zero output current subcircuit selector, generates signal F. This signal will be used as an input to select the appropriate zero output current subcircuit 3 or 4, in order to increase or decrease current i_L. The hysteresis controller associated circuitry is shown in Figure 5.

It has to be noticed that although the hysteresis controller is a frequency variable control, its output signal F is the input to a bi-stable of the zero output current selector subcircuit which is clocked by the Sinusoidal Pulse Width Modulation (SPWM) signal, resulting, then, in a constant switching frequency.

The zero output current selector subcircuit detects any zero output current i_pwm state. To do so, an XOR function of signals A and B is performed, obtaining an auxiliary output signal C. This signal is at a high logic level at any zero output current i_pwm and is also used as the CLK input to a D-type positive edge triggered flip-flop, which will divide the frequency of C by half. The input of the D-type flip-flop is signal F, coming from the hysteresis controller. The output signal Q allows differentiating two cases for the zero output current state. Signal Q at a high logic level indicates that subcircuit 3 must be used, and signal Q at a low logic level indicates that subcircuit 4 must be used.

Therefore, this current controller allows to increase and decrease the current i_L during the zero output current sates in order to keep i_L constant. These signals and the associated logic circuit are shown in Figure 6 (a low-frequency signal was used to illustrate the operation).

It has to be noticed that the selection of the appropriate zero output current i_pwm state depends on changes of signals A and B. During the sinusoidal output current zero crossing, both signals A and B do not change in an interval. During this interval, it is not possible to change the state of charge or discharge of the inductance L, so the current i_L will remain increasing or decreasing according to the last zero output current state selected. This may cause an overcurrent, as seen in Figure 7. The length of this interval depends mainly on the frequency of the SPWM carrier signal and to a lesser extent on the amplitude modulation index. This drawback can be overcame increasing the SPWM carrier signal frequency, at a higher cost in switching losses; increasing the value of the inductance L to limit the maximum current i_L, at a higher cost in size and weight of this inductance; or oversizing the nominal current of the switches. Alternatively, a new control with an independent second hysteresis band can be designed, at a higher cost in control complexity.

A combinational logic circuit is employed to determine the drive signals of the switches, for which signals A, B, Q and the states of Table 1 are considered. The truth tables for each switch are shown in Figure 8.

2.4. CSI Converter Synthesis

The design criteria for the different components of the converter are detailed. A low voltage low power prototype has been built and tested following these design guidelines. Since the main purpose is to validate the topology and the proposed control, it is not an optimized design in terms of efficiency, size, and weight.

2.4.1. Inductor

It is desirable to have the minimum possible inductor L. It has to be large enough to store energy to maintain an average constant value of the i_L current, and to limit its excursion as close as possible to the hysteresis band. Its design has to take into account the worst case of operation, corresponding to a change from subcircuit 3 to subcircuit 1, in which the inductor current i_L increases, as shown in Figure 9. Equations (17) and (18) determine the necessary inductance Ls₃ and Ls₁ to limit the maximum value of the increment of i_L (Δi_L) at each stage, derived from Equations (2) and (7), respectively:

$$L_{S3}=\frac{V_{in}\Delta t_1}{\Delta i_L}$$

(17)

$$L_{S1}=\frac{\left(V_{in}-V_{out}\right)\Delta t_2}{\Delta i_L}$$

(18)

where Δt₁ and Δt₂ are the duration of subcircuits 3 and 1 respectively. These stages are consecutive, both contribute to Δi_L, so the necessary L is obtained by adding Equations (17) and (18), resulting in Equation (19):

$$L=\frac{V_{in}\Delta t_1+\left(V_{in}-V_{out}\right)\Delta t_2}{\Delta i_L}$$

(19)

It can be observed that the contribution of subcircuit 3 to i_L is higher than the contribution of subcircuit 1. The time Δt₁ is maximum at the peak of the sinusoidal modulator signal and depends on the modulation index of the SPWM. At low modulation indexes, subcircuit 3 stage is longer than at high modulation indexes. A conservative value of 0.5 for the modulation index can be taken as design criteria.

For an input voltage V_in = 200 V, average current i_L = 22 A, hysteresis band of 0.02 A, switching frequency f_sw = 60 kHz, modulation signal f_grid = 60 Hz and modulation index of 0.5; a value of Δt₁ ≈ Δt₂ = 10 μs is obtained by simulation. With a Δi_L = 0.5 A (2.5% of i_L) results in an inductance of approximately 5 mH.

As mentioned in Section 2.3.1, during the sinusoidal output current i_out zero crossing an overcurrent may occur. For the proposed values, the overcurrent interval lasts up to 50 μs, the value was obtained by simulation, and an overcurrent of Δi_L ≈ 2.5 A may be expected.

An alternative criteria design for inductance L is to limit this maximum current i_L. A worst case would be subcircuit 3, Equation (17), with the aforementioned value of Δt₁ ≈ 50 μs obtained by simulation, resulting in an inductance L of approximately 10 mH.

2.4.2. Output Filter

For reducing current ripple provoked by PWM high-frequency switching and improve Total Harmonic Distortion (THD) of the output current i_out, it is necessary an output filter. A CLC filter has been implemented. It consists of a conventional CL filter plus an additional capacitor C_out on the grid side. This configuration shows better performance with smaller size and capacity compared to a CL filter. A detailed analysis and calculation method, including filter resonance, damping methods, and grid inductance influence can be found in [29]. As a simplified approach, a CL filter can be first calculated [30]. Equations (20) and (21) are the current function transfer G_CL and cut-off frequency f_coff, respectively, for an ideal non-dumped filter, although a small series dumping effect is always present due to capacitors ESR and inductance winding resistance:

$$G_{CL}=\frac{1}{{\left(j\omega \right)}^2{C}_f{L}_f+1}$$

(20)

$$f_{coff}=\frac{1}{2\mathsf{\pi }\sqrt{C_f{L}_f}}$$

(21)

For a switching frequency of f_sw = 60 kHz, a cut-off frequency f_coff = 1.5 kHz, and selecting a C_f = 5 μF film capacitor, an inductance L_f = 2 mH is obtained. A C_out = 0.1 μF capacitor is then added, taking into account that the two resonance frequencies of a CLC filter are related to all components values of the filter (C_f, L_f, C_out and grid variable inductance) [29]. These values are validated by simulation.

2.4.3. Semiconductors Selection

In CSI converters, the semiconductors for the switches must be unidirectional in current, so if MOSFETs are selected, a series diode must be included. Another option is the use of single Insulated Gate Bipolar Transistors (IGBT) as switches (without anti-parallel diode), reducing the number of components and increasing system reliability since no series diodes are needed. Regarding efficiency, it should be evaluated if two low loss semiconductors in series, such as SiC MOSFETs and SiC diodes, offer a better performance than a single IGBT.

In the prototype developed, Si MOSFETs and diodes have been used because of the availability of these components. For the currents and voltages expected, <5 A and <230 V respectively, an IRF840 MOSFET (8 A, 500 V, R_DS = 0.85 Ω, Fairchild Semiconductor Corporation, Sunnyvale, CA, USA) and a MUR840 diode (8 A, 400 V, Fairchild Semiconductor Corporation, Sunnyvale, CA, USA) have been selected.

2.4.4. Comparison with Other CSI Schemes

Comparing the proposed converter with other CSI topologies, it can be found that a significant reduction in the inductor L is achieved. A general classification of CSI can be found in [31]. For Multilevel Paralleled CSI, the design criteria for the inductor is the energy stored in order to maintain the output current, resulting in large inductors of 400 mH for inductor currents of 0.5 A [31]. The Multilevel Two-stages CSI uses two inductors, the input and the balanced inductor, of 600 mH and 60 mH respectively, for currents of 2 A. These inductors can be reduced at higher currents, but its value still remains high [32]. The Embedded Multilevel CSI uses two balance inductors of 45 mH each, and an input inductor of 105 mH for a total current of 18 A [33]. The PWM CSI has values of 80 mH for inductor currents of 10 A [34]. A modified PWM CSI topology allows reductions of the inductor up to 7 mH for inductor currents of 91 A [35]. Also, the reduction can be obtained by means of the switching strategies, resulting in inductors of 30 mH for 9 A currents [36].

Note that for the same current of the PWM CSI of [34] and keeping Δi_L = 2.5% of i_L, and approximately inductance of 750 μH results. Also note that none of these topologies deal with leakage current reduction. Recently, some proposals for leakage current reduction have appeared. A transformerless CSI with low leakage current, based on the VSC H5 topology, is presented in [26], with an inductor of 8 mH for inductor currents of 8 A. It concludes that for an inductor reduction, higher switching frequencies should be achieved by means of SiC devices, and then the leakage current may be an important issue. In the same way, two transformerless three-phase CSI, based on the VSC H7 topology, are presented in [27,28]. A reduced inductor of 2 mH, but without information regarding the inductor current, is used in [27]. Two different modulation strategies are presented in [28], with an inductor of 2 mH for inductor currents of 8 A.

Table 3. CSI topologies comparison, including inductor values.

Converter	Semiconductors			Passive Components		Other Characteristics
	Voltage Stress	Switches	Diodes	Ls	Cs	Inductor Value	Inductor Current	Leakage Current	Output Waveform	Efficiency
Reference [31]	Vpk	8	8	2	1	400 mH	500 mA	High	Multilevel	Not available
Reference [32]	Vpk	6	6	2	1	60 mH	2 A	High	Multilevel	>90%
Reference [34]	Vpk	4	4	1	1	80 mH	10 A	High	Unipolar	Not available
Reference [33]	> Vpk	8	8	2	1	45 mH	18 A	High	Multilevel	Not available
Reference [26]	Vpk	5	5	2	1	8 mH	8 A	24.7 mA	Unipolar	Not available
Reference [36]	Vpk	6	6	1	3	30 mH	9 A	High	Unipolar, 3-phase	Not available
Reference [35]	Vpk	7	7	1	3	7 mH	91 A	High	Unipolar, 3-phase	Not available
Reference [27]	Vpk	7	7	1	3	2 mH	Not available	26 mA	Unipolar, 3-phase	>90%
Reference [28]	Vpk	7	7	1	3	2 mH	8 A	Low	Unipolar, 3-phase	>90%
Proposed	Vpk	6	6	1	1	5 mH, 150 uH	1 A, 100 A	<10 mA	Unipolar	>90%

V_pk is the peak of the grid voltage.

summarizes the significant values of the CSI schemes compared.

As it can be observed in the table, the proposed topology offers the best leakage current reduction since it uses the common mode configuration. Some of the other schemes also have low values for leakage currents, but not as low as the proposed one, since they all are based on traditional differential mode inverters.

3. Simulation and Prototype Test Results

The proposed system was first numerically simulated and then tested in a low power prototype, in order to confirm the feasibility of the proposed system.

3.1. Simulations Results

A simulation using PSIM^© (Version 11.1, Powersim Inc., Rockville, MD, USA) was performed for the circuit of Figure 2, in which the CSI inverter is connected to the grid. Parameter values for the simulation are shown in

Table 4. Simulation parameters.

Parameter	Symbol	Value	Parameter	Symbol	Value
Input voltage	Vin	200 V	RMS output voltage	Vout	127 V
Inductor	L	5 mH	Inductor current	iL	22 A
Filter capacitor	Cf	5 μF	Current hysteresis	Hysteresis	0.04 A
Filter inductor	Lf	2 mH	Grid frequency	fgrid	60 Hz
Output capacitor	Cout	0.1 μF	Switching frequency	fsw	60 kHz

.

The operation of the proposed hysteresis controller shown in Figure 10. Figure 10a shows several periods of auxiliary control signals A and B, the resulting output current before de CLC filter, i_pwm, and the inductor current i_L, in order to illustrate the steady state operation of the system. Figure 10b shows a zoom of the rounded area in Figure 10a. It can be observed that the system operates as expected. The signals V_out, i_out, and i_L are shown in Figure 11. As it can be observed, the current of the inductor L is controlled around the desired level by means of the hysteresis band, except during the sinusoidal output current i_out zero crossing, where an overcurrent occurs, although always within acceptable limits. The voltage and the current are operated with a CLC filter. The output signals can be viewed clearly sinusoidal and in phase. The THD of the output current at steady state is 1.8%.

The leakage current in the solar panel is under 15 mA for a conservative value of the parasitic capacitance C_PVg = 5 nF every 200 W, that makes a total of 25 nF for an array of panels of 1 kW, as it can be seen in Figure 12.

3.2. Prototype Test

The proposed system was designed and built. The controller was implemented on an electronic board based on the National Instruments technology. The platform considered was the General Purpose Inverter Controller (GPIC), together with the LabVIEW visual programming software. The protections have been also programmed.

3.2.1. Controller Stage

The first component of the implemented controller in the LabVIEW software (2016 version, National Instruments Corporation, Austin, TX, USA) is the input/output block. The grid voltage V_line and the inductor current i_L are sensed by means of the LEM LV25-P and LTS 25-NP voltage and current sensors, respectively. These signals are read by the GPIC. Also, the output signal for driving the switches are implemented. The current reference, free of distortions and synchronized with the grid, was generated by means of a Second Order Generalized Integrator-Frequency Looked Loop (SOGI-FLL). The amplitude was normalized, in order to avoid the dependency from the input voltage variations, and a measurements offset elimination stage was also added. A soft-start has also been implemented, to avoid high currents at the start-up of the power stage. It consists of an AC mains zero crossing detector that triggers the start-up of the converter. The switches control signals are generated following a USPWM pattern. The sinusoidal signal reference, synchronized with the grid, comes from de SOGI-FL, and the triangular carrier signals are at a frequency of 60 kHz. As it was mentioned before, a combinational circuit and a hysteresis controller is employed to regulate the current of the inductor L, i_L, selecting the appropriate subcircuit according to the Table 2. SPWM, the hysteresis controller, the control signals A, B, F and Q, subcircuit switches selection and overlapping time are generated by logic blocks implemented on the GPIC platform. One of the main advantages of using LabVIEW is that a friendly-user interface can be easily implemented. It allows to fix the converter control parameters, such as the current protection, the desired inductor current i_L level (set point), the width of the hysteresis band or the soft-start operation; and also some signals can be shown, to monitor the status of the converter. A diagram of the blocks of the controller is shown in Figure 13.

3.2.2. Experimental Test

A low power prototype was implemented, just to illustrate the operation of the proposed topology and control. A PV panel simulator E4361A from Agilent Technologies was used to generate the input voltage V_in. This simulator generates a maximum output voltage of 60 V and a maximum output current of 4.25 A, so maximum available voltage and power are bounded.

Parameter values for the prototype are shown in

Table 5. Prototype parameters.

Parameter	Symbol	Value	Parameter	Symbol	Value
Input voltage	Vin	35 V	Load resistance	R	24 Ω and 8 Ω
RMS output voltage	Vout	12.5 V	Inductor current	iL	1–3 A
Inductor	L	5 mH	Hysteresis band	Hysteresis	0.2 A
Filter capacitor	Cf	5 μF	Grid frequency	fgrid	60 Hz
Filter inductor	Lf	2 mH	Switching frequency	fsw	60 kHz
Output capacitor	Cout	0.1 μF	-	-	-

.

First, the prototype was tested with a resistive load. Figure 14 and Figure 15 show the main waveforms and output current i_out distortion, for an inductance current i_L of 1 A and 3 A, respectively. A hysteresis band of 0.2 A was selected. The THD of the output current was measured with a 1735 Power Logger Analyst (FLUKE, Everett, WA, USA). As it can be seen, the converter operates as expected. At this low voltage, overcurrents in i_L are negligible. A THD of 2.8% was obtained for the last test.

The performance of the converter under a sudden change in the set point of the inductor current i_L is illustrated in Figure 16. A step from 1 A to 3 A and viceversa is forced. A hysteresis band of 0.2 A was selected. The settling time was 784 μs and 260 μs respectively.

The prototype was also tested connected to the grid, as shown in Figure 2. A sudden change in the set point of the inductor current i_L was conducted. Figure 17 shows the output current and the grid voltage during this test.

It has to be noted that there is no direct control of the output current i_out, so the THD can be high when connected to the grid. Additional control strategies may be proposed to reduce the output current distortion.

3.2.3. Power Losses Estimation

The conduction losses of the power stage can be determined considering the simplified circuit is shown in Figure 18. This is possible since there are always two switches conducting at the same time, and the inductor current i_L is kept constant (the ripple is disregarded). The switches have been implemented with a MOSFET and a diode in series. If an IGBT without diode in anti-parallel is considered, the series diode should be removed.

The power losses, including the switching losses, are determined by:

$$P_l=i_L\left\{r_L{i}_L+2\left[V_D+r_{DSon}{i}_L+f_{sw}{V}_{DS}\left(t_r+t_f\right)\right]\right\}$$

(22)

where r_L is the parasitic resistance of the inductor L; V_D is the diode forward voltage; r_DSon is the MOSFET ON resistance; V_DS is the MOSFET Drain-Source voltage; t_r and t_f are the rise and fall time of the main semiconductors, respectively; and f_sw is the switching frequency.

The measured r_L is 0.4 Ω. Τhe components selected are Si semiconductors, with V_D = 1.1 V, V_DS = 35 V, r_DSon = 850 mΩ t_r = 35 ns, t_f = 30 ns, and f_sw = 60 kHz, the estimated power losses are 4.57 W. However, changing V_DS = 200 V, the losses are incremented to 5.86 W and considering a grid voltage of 127 V, the resulting estimated efficiency is 88.45%.

With equivalent SiC semiconductors, the values are now V_D = 0.8 V, V_DS = 35 V, r_DSon = 16 mΩ, t_r = 11 ns, t_f = 10 ns and f_sw = 60 kHz, the estimated power losses are 2.41 W. And, considering V_DS = 200 V, the losses are incremented to 2.82 W, if the grid voltage is 127 V, the resulting estimated efficiency is 94.08% respectively. Figure 19 shows an estimated loss breakdown figures for both Si and SiC semiconductors for these last conditions.

As it can be seen, the losses in the diodes are the main contributor to total losses, so, as mentioned in Section 2.4.3, a solution with an IGBT switches without antiparallel diode should be considered for a practical implementation. It has been taken into account that, as mentioned in Section 3.2.2.

4. Conclusions

There are many works on topologies of transformerless PV converters, trying to reduce the leakage current at the ground connection. One of the most successful technique is the common mode configuration, in which the neutral line of the grid directly connects to the negative terminal of the PV system. However, most of them are based on VSI converters. This paper proposes a new topology for a CSI converter with reduced leakage currents in common mode configuration. A complete analysis, design, and operation were presented. A new controller has been also designed and implemented. A 1 kW system simulation has been carried out, but also a low power prototype has been built and tested in order to confirm the feasibility of the proposed system. The system has a leakage current under 15 mA and low output current THD, <3%. Efficiency has been estimated, with reasonable numbers, although converter design was intended to test the topology proposed and the control, and it was not optimized for reduced losses. Finally, the inductor L is smaller than those usually found in conventional CSIs. The obtained results show that this proposal is suitable for PV converters connected to the AC mains.