Analysis and classification of Non-isolated inverter leakage currents for photovoltaic systems

. In the past few years, there has been a growing concern about the pollution caused by fossil fuels, leading to a significant interest in photovoltaic power generation due to its clean and environmentally friendly features. However, suppressing leakage currents is a major problem for Non-isolated PV inverters. This paper focuses on the leakage current suppression methods, summarises three main leakage current suppression paths and systematically analyses and classifies the DC-bypass topology, the H5 topology and the Neutral Point Clamped (NPC) three-level topology. In order to address the issue mentioned above, several approaches can be taken. Firstly, a suitable sinusoidal pulse width modulation strategy is implemented. Additionally, alterations are made to the common mode impedance Z. Furthermore, efforts are made to ensure a proper match of circuit parameters. The analyses in this paper are all carried out based on bridge-type inverters to provide a reference for the study of leakage current suppression in Non-isolated Inverter. Future studies will be more efficient when similar issues arise.


Introduction
With mankind's increasing demand for energy, photovoltaic power generation, which is rich in reserves and clean and pollution-free, has received increasing attention and interest.Photovoltaic power generation has extensive applications in various aspects of life, and China currently holds the title of the world's fastestgrowing country in terms of installed photovoltaic capacity [1].The transformerless PV grid-connected inverter structure, with its high efficiency and low cost, is the best choice.However, the transformerless construction of grid-connected PV inverters still poses a safety problem due to the fact that common mode currents can increase significantly when establishing an electrical connection between the power supply and the grid.Consequently, the primary focus must be on effectively mitigating leakage currents [2].
In this paper, a simplified model of leakage current in full-bridge topology is established, the causes of leakage current are analysed from the source of its generation, and three ways of leakage current suppression are analysed and summarised.Furthermore, based on the three pathways for suppressing leakage current, the leakage current suppression effects of several mainstream bridge-type non-isolated inverter topologies are analysed and categorised.The analyses in this paper are all based on bridge inverters and provide a detailed analysis of leakage currents.Several major bridge topologies are analysed and categorised according to the leakage current suppression mechanism to provide a reference for the study of leakage current suppression in non-isolated inverters.

Current situation and structural analysis of photovoltaic systems 2.1 Current status of photovoltaic power generation
Photovoltaic power generation has a wide range of application scenarios in life.Small-scale photovoltaic power generation is mainly used for residential electricity in remote areas, with a power generation power of 10-100W; 3-5KW family rooftop photovoltaic grid-connected power generation system; traffic/railway signal lights, highway/railway wireless telephone booths and other transportation areas; the establishment of car park charging stations in cities, 10KW-50MW independent photovoltaic power stations [3,4].
Figure1 below illustrates the timeline for the development of grid-connected PV installations in China, taking into account the current situation of PV power generation.According to the official website of the National Energy Administration, the cumulative installed capacity of photovoltaic power generation in China reaches 253 million kilowatts in 2020, an increase of 23.5% year-onyear [5].In 2021, the total installed capacity of gridconnected photovoltaic power generation surpassed 300 million kilowatts, reaching 306 million kilowatts.This achievement solidifies China's position as the global leader for seven consecutive years.The new gridconnected capacity for photovoltaic power generation reached approximately 53 million kilowatts, maintaining its dominance for the ninth consecutive year [6].Looking ahead to 2022, China is expected to continue its robust growth in the photovoltaic sector.The total installed capacity of grid-connected PV is expected to reach approximately 39,000 GWh, an increase of 28.1% year-on-year.In addition, the new installed capacity of grid-connected PV is estimated at approximately 87.41 GWh, a significant increase of 60.3% year-on-year [7].By the end of April 2023, China is anticipated to have installed an impressive 440 million kilowatts of PV power generation capacity.Importantly, the country has added 48.31 million kilowatts of new PV power generation capacity during this period [8].

Structure of the photovoltaic system
The PV system consists of PV panels, PV gridconnected inverters and various common loads, the main structure of which is shown in Figure 2   The PV inverter is the most important component of the total process of grid-connecting PV.An apparatus that changes the DC power generated by solar panels into AC power is known as a PV grid-connected inverter.The PV inverter is one of the important balancing systems in a PV array system.PV grid-connected inverters can be divided into three types according to whether they contain a transformer: frequency isolated, high frequency isolated and non-isolated.The initial two systems guarantee the isolation of electricity between the grid and the PV system, thereby ensuring the safety of equipment and individuals.However, all have disadvantages to varying degrees.The industrial frequency isolated inverters are large, expensive and costly and are generally suitable for high-power applications.High-frequency isolated inverters have several stages of power change circuits and more complex control, making the system less efficient.The Non-isolated grid-connected inverter configuration without a transformer offers the benefits of high efficiency and low cost, especially the single-stage Nonisolated version with a maximum efficiency of 98.8%.Hence, opting for a Non-isolated grid-connected inverter is unquestionably a wise decision.Transformerless grid-connected photovoltaic inverter consist of five components: the PV panel, the DC filter, the PV inverter, the AC inverter and the grid.In Nonisolated systems, the absence of galvanic isolation results in the formation of a common mode loop, leading to the generation of common mode voltages.The common mode voltage interacts with the PV panel and parasitic capacitance to generate leakage current [9].Therefore, in a transformerless photovoltaic grid-connected inverter, the generation of leakage currents is inevitable.In the following, the leakage current will be modelled and analysed.

Energy efficiency
A model of a single-phase full-bridge grid-connected inverter is illustrated in Figure 4 [10].Fig. 4. Non-isolated system schematic [10] CPV is the parasitic capacitor, Cdc is the voltage regulator capacitance, C is the parasitic capacitance of the collector of the IGBT to ground, Cy is the common mode capacitance, CX is the filter differential mode capacitance, Zline is the transmission line impedance and ZG is the ground impedance of the grounding point enclosure.The reference point for the panel N is the negative end, while the outputs are the midpoints 1 and 2 of the two bridge arms.The definitions of UCM and UDM enable us to determine the common mode voltage and differential mode voltage.
From the variation of expressions ( 1) and (2) can get Using Thévenin's Theorem to simplify and combining expressions (3) and ( 4), this can be reduced to    5) it can be concluded that suppressing the common mode voltage UCM is the most effective way to reduce the leakage current ICM.Tang proposes a minimalist unified common mode equivalent circuit for a bridge-like inverter topology based on the variable, controllable nature of Z and CPV, as shown in Figure 6 below [11].Fig. 6.Simplest unified common mode equivalent circuit of single-phase bridge-type grid-connected inverter [11] Since the common mode voltage UCM usually changes at high frequency in the form of a square wave, if the impedance Z when the UCM is high (or low) is infinite, the high frequency leakage current can also be eliminated theoretically.Based on the above analysis, three leakage current suppression paths can be obtained for three Non-isolated inverters: (1) using a suitable sinusoidal pulse width modulation (SPWM) strategy to make Ucm a constant value (provided the circuit parameters are symmetrical); (2) making the sum of Ucm and Ucm-dm a constant value by matching the circuit parameters; (3) varying the common mode impedance Z so that Z remains high impedance when Ucm varies at high frequencies (provided the circuit parameters are symmetrical).

Analysis of the effect of Non-isolated inverter topology on leakage current suppression 4.1 The common mode voltage UCM
The basic principle of SPWM is to adjust the width and frequency of the output pulses by comparing the phase of the reference sine wave signal and the triangular wave signal, thus controlling the on/off of the switching devices in the inverter circuit.In modulation, unipolar modulation and bipolar modulation are commonly used.The effect of each type of modulation in a non-isolated topology will be discussed below.A full-bridge topology model, shown in Figure 7, is built to verify the different modulation theories.

4.1.1.Effect of unipolar modulation on leakage current
In unipolar modulation, the delta carrier has only one polarity for half the operating cycle of the modulating waveform, and the output waveform has only one polarity.As there is an output filter inductor in the topology, the output current lags behind the voltage, so there are cases where the output current is greater than zero and cases where the output current is less than zero when the output voltage is positive.
During the positive half-cycle of the output voltage, the switching tube S1 is always on, the switching tube S2 is always off, and the switching tubes S3 and S4 are alternately on and off at high frequencies.In the negative half-cycle of the output voltage, the switching tube S2 is always on, the switching tube S1 is always off, and the switching tubes S3 and S4 are alternately on and off at high frequencies [12].Figure 8 displays the waveforms of the common mode voltage Ucm and the drain current Ilk that can be obtained in unipolar modulation with a dc voltage input of 400 V.The common mode voltage shifts between (Udc/2, Udc) during the first half-cycle and between (0, Udc/2) during the second half-cycle, resulting in a large leakage current in the system.It can be seen that the common mode voltage UCM for unipolar modulation shifts between (0, Udc, Udc/2).The variation of the leakage current, as indicated by equation ( 5), is directly linked to the common mode voltage and is therefore detectable when employing single pole modulation.However, because the unipolar modulation output has three level voltages, the system losses are small and the grid current quality and efficiency are high.

Effect of bipolar modulation on leakage current
In bipolar modulation, the delta carrier is not unipolar as before for half the operating cycle of the modulating waveform, but positively and negatively transformed, so that the output waveform has both positive and negative polarities.
Throughout the positive half-cycle of the output voltage, switching tubes S1 and S4 remain continuously activated, while switching tubes S2 and S3 remain continuously deactivated.In the negative half-cycle, the opposite is true. Figure 9 illustrates the waveforms of the common mode voltage Ucm and the drain current Ilk that can be obtained in bipolar modulation with an input dc voltage of 400V.As depicted, the common mode voltage remains constant at Udc/2 throughout the cycle [12].

Fig. 9. Common mode voltage and leakage current for bipolar modulation [12]
The common mode voltage Ucm for bipolar modulation is always proportional to the constant value Udc/2.The leakage current is very modest and practically nonexistent, as shown by equation ( 5).Bipolar modulation involves switching all four switching tubes at high frequencies, which causes significant switching losses.Additionally, because the output voltage is two-level and the switching sub-voltage ripple is significant, a filter with a high sense value is needed, increasing the cost and switching losses.
The above comparison between unipolar and bipolar modulation shows that although the leakage current is almost non-existent with bipolar modulation, unipolar modulation is more efficient and requires less filtering.Therefore, the modulation method for grid-connected inverters is generally chosen to be unipolar modulation.The Non-isolated topology circuit is the topology shown in Figure 10 below [13].Fig. 10. Circuit diagram of DC-bypass topology [13] This topology can be referred to as the DC-bypass topology.This topology adds two switching tubes S5 and S6 to the full bridge circuit.The DC-bypass topology uses unipolar modulation.During the renewal phase, S1 to S4 are on, S5 and S6 are off, and diodes D1 and D2 are used to keep the common mode voltage constant to suppress leakage current by grounding the midpoint of the renewal branch and fixing the midpoint voltage of the capacitor at Udc/2.
The DC-bypass topology is fed with a DC voltage of 250 V at the input and obtains a maximum leakage current of 192 mA.According to DIN VDE 0126-1-1 the leakage current is controlled to less than 300 mA and the topology complies with the leakage current standard [14].

Match the parameters of the circuit
A full bridge topology is modelled and verified using unipolar modulation as shown in Figure 7.The equation for Z1 can be obtained by applying the "Davinan's Theorem" to the variation 'Δ→Y' and then simplifying it as follows: Similarly, the formula for Z2 can be obtained as follows: The formula for Z3 is as follows: Applying "Thévenin's Theorem", two equivalent resistances ZA and ZB are established with the following expressions: The amount of operating level of the full-bridge inverter with unipolar modulation is obtained as shown in Table 1 below.Where the expressions for a and b are as follows: The expressions for c and d are as follows: There is no such thing as constructing a unipolar modulated full-bridge inverter with filter inductors L1 and L2 and values C1 and C2 so that UCM+UCM-DM equals a constant to prevent leakage currents [10].Compared to a full-bridge inverter, the half-bridge inverter requires electrolytic capacitors that can handle higher voltage as its input voltage is twice as high.Furthermore, the half-bridge inverter possesses the ability to clamp and sustain a steady common mode voltage UCM.This feature gives the half-bridge gridconnected inverter the ability to suppress leakage current to a certain extent.
Akira Nabae, a professor at Nagaoka University of Science and Technology in Japan, first suggested the NPC three-level topology at the IAS annual meeting in 1980.It was employed in real-world industrial applications for high voltage inverters in the early 1990s.The NPC three-level architecture employs a unipolar modulated half-bridge topology, as seen in Figure 11 below.The NPC three-level topology consists of four switching tubes S1, S2, S3 and S4 and two clamp diodes D1 and D2.The NPC three-level topology has five operating states, which are three normal operating states: positive half-cycle power transfer operating state P, renewal operating state 0, negative half-cycle power transfer operating state N and two dead zone operating states.As shown in Table 2 below, the NPC three-level topology is in positive half-cycle power transfer operation (P) when switching tubes S1 and S2 are on; in renewal operation (0) when switching tubes S2 and S3 are on; and in negative half-cycle power transfer operation (N) when switching tubes S3 and S4 are on [15].The duration of the three operating states (P, O, N) depends on the switching frequency of the device and is relatively long; the duration of the two dead zone operating states depends on the switching delay and the commutation time of the switching tubes.
The levels of the operating phases of the NPC threelevel topology are shown in Table 3 below.As can be seen from the diagram, the sum of the three different normal operating states UCM + UCM-DM is a constant value Udc/2, for the purpose of leakage current suppression.

4.3.Changing the common mode impedance Z to keep it high
The H5 topology is a patented topology proposed by SMA solar GmbH, Germany, which uses unipolar modulation and adds a switching tube to the full-bridge circuit, switching it off during the renewal phase and providing a new renewal circuit, which is equivalent to putting a high impedance in series with the common mode circuit to suppress the leakage current.An H5 topology model is created as shown in Figure 12.The H5 topology has two half-cycles, positive and negative, and both common mode voltages are Udc/2.In the positive half cycle, there exists a normal operating state as shown in Figure 13 (a) and a renewal operating state as shown in Figure 13 (b) [16].In the negative half cycle, there is a normal operating state as shown in Figure 14 (a) and a renewal operating state as shown in Figure 14 (b).In the H5 topology, when the input voltage is 400V, the common mode voltage is 200V (half of the input voltage) and the common mode current does not exceed 0.05A.The grid-connected current and grid voltage are in phase, indicating that the H5 topology successfully suppresses the common mode current [17].

Conclusion
By adjusting the common mode impedance Z, employing a suitable sinusoidal pulse width modulation method, and matching the circuit parameters, leakage current can be suppressed.Bipolar modulation causes a big switching sub-voltage ripple, which necessitates a high inductance value in the filter, increasing costs and losses while decreasing efficiency.The switching subvoltage ripple is lower and more effective than unipolar modulation.Therefore, unipolar modulation is typically used as the modulation technique for grid-connected inverters.Three typical topologies are individually examined in this work.One of these is the full-bridge topology known as the DC-bypass topology, which uses unipolar modulation and a common mode voltage UCM that is maintained at a constant value of Udc/2 to reduce leakage currents.A half-bridge topology with unipolar modulation, the NPC three-level topology keeps the sum of UCM + UCM-DM at a constant value of Udc/2 during the operating cycle, suppressing leakage current.Theoretically, high frequency leakage currents are fully eliminated by this topology.The H5 topology is a unipolar modulated full bridge topology.The suppression path is to vary the common mode impedance Z so that it remains high to suppress the leakage current.However, this topology has high losses in the energy transfer phase as the current flows through the four switching tubes.

Fig. 1 .
Fig. 1.Timeline for the development of grid-connected PV installations (Photo/Picture credit: Original) below.

Fig. 2 .
Fig. 2. The main structure of the PV system (Photo/Picture credit: Original)

Figure 3
Figure 3 below shows a simplified diagram of a transformerless grid-connected PV inverter.

Figure 5
Figure 5 below, where Z is the common mode impedance due to other non-ideal factors.

Fig. 5 .
Fig. 5. Minimal equivalent circuit for single-phase gridconnected inverters (Photo/Picture credit: Original) The common mode current through the parasitic capacitor is

Fig. 8 .
Fig. 8. common mode voltage and leakage current for unipolar modulation (Photo/Picture credit: Original)

Table 1 .
The amount of operating level of the full-bridge inverter

Table 2 .
Operating state of the NPC three-level topology.

Table 3 .
Level quantities in the operating phase of the NPC three-level topology.