#### Systematic analysis model of leakage current in bridge inverter topology

At present, a large number of photovoltaic power generation systems are used in homes and other roofs, and the power is usually 1~50kW. When the photovoltaic grid-connected system does not contain a transformer, the distributed capacitance of the solar panel to the ground provides a low-impedance loop for the common-mode current (Figure 1), where i_{CM} and i_{DM} represent common-mode and differential-mode currents, respectively. From the spectrum point of view, the common mode current i_{CM} includes the fundamental frequency component (50Hz or 60Hz), the intermediate frequency component at the switching frequency (generally 10k-100kHz) and the high-frequency component (generally 150kHz-30MHz).

The common-mode current of non-isolated photovoltaic grid-connected inverters must be suppressed in an effective way. The suppression methods and allowable amplitudes of common-mode currents in different frequency bands are different. The low-frequency common-mode current mainly flows through the parasitic capacitance of the photovoltaic panel and the grid ground loop. In the case of low-power and low-voltage grid-connected inverters, due to the large common-mode loop impedance and low grid voltage amplitude, the low-frequency common-mode current is small (generally less than 0.5mA), so special suppression measures may not be taken. However, in high-power and high-voltage grid-connected applications, the low-frequency common-mode current increases rapidly due to the increase in parasitic capacitance of large-area photovoltaic panels and the high grid voltage amplitude. A low-frequency isolation transformer is usually used to increase the low-frequency common-mode current loop impedance and match the battery string voltage and the grid voltage; the high-frequency common-mode current mainly flows through the parasitic capacitance of the solar panel and the parasitic capacitance of the inverter to the ground, and then returns through the capacitance path of the EMI (Electro Magnetic Interference) filter. In order to meet international standards, such as 1EC61000, EMI filters are usually used to suppress high-ton common-mode noise: the intermediate frequency common-mode current near the switching frequency is the most concerned common-mode current component for non-isolated grid-connected inverter applications, and is usually referred to as “leakage current” and “ground current.” Its flow path includes the parasitic capacitance of the photovoltaic panel, the parasitic capacitance of the inverter to the ground, the parasitic capacitance of the EMI filter and the ground loop of the power grid. In order to ensure the safety of personnel and equipment, the leakage current of the photovoltaic grid-connected inverter must be suppressed to a certain amplitude range. The suppression of the leakage current of the photovoltaic grid-connected inverter is generally achieved by adopting an improved converter structure and switching modulation strategy.

In order to correctly and comprehensively understand the leakage current generation mechanism and seek leakage current suppression measures, the following will establish a unified analysis model of the leakage current of the bridge inverter topology. The single-phase non-isolated grid-connected inverter circuit considering parasitic parameters is shown in Figure 2. If the bridge arms 1 and 2 are both power tubes, it is a full-bridge circuit: If one of the bridge arms is a capacitor branch, it is a half-bridge circuit; in addition, if the half-bridge circuit has a midpoint box structure, it is a three-level NPC circuit.

In Figure 2, U_{dc} is the output voltage of the photovoltaic panel; C_{dc} is the DC side decoupling capacitor: L_{i1} and L_{i2} are filter inductors. Differential mode capacitors C_{X}_{1}, C_{X}_{2}, differential mode inductance L_{DM}, common mode capacitors C_{Y1}, C_{Y2}, and common mode inductance L_{CM} form an EMI filter that suppresses high-frequency electromagnetic interference. In addition, C_{PV1} and C_{PV2} are the parasitic capacitances of the positive and negative terminals of the battery panel to the ground, and their size mainly depends on the composition, area, installation environment and installation method of the battery panel, etc.: C_{1}, C_{2} are the parasitic capacitances of point 1 and point 2 to the ground; Z_{Line1} and Z_{Line2} are line transmission impedances, which are mainly inductive: Z_{g} is the ground impedance between the grid grounding point and the inverter chassis grounding point.

Taking the negative terminal N of the battery board as the reference point, and the midpoints 1 and 2 of the two bridge arms as the output terminals, it can be obtained by the definition of differential mode and common mode voltage:

Further from formula (1.1) and formula (1.2), we can get:

Use the variable C_{PV} to represent the total parasitic capacitance of the solar panel to the ground:

C_{PV} = C_{PV1}+ C_{PV2} (1.5)

In order to derive the common-mode equivalent circuit, replace the bridge arm circuit in Figure 2 with equations (1.3) and (1.4). Based on the superposition principle, the differential mode loop and components can be omitted, and only the common mode loop and components are retained. For the high frequency (switching frequency and multiple times) common mode equivalent circuit, the grid voltage source can be short-circuited, and the equivalent circuit shown in Figure 3 can be obtained.

Figure 3 can be split into the circuit shown in Figure 4. The dashed frame parts A and B form a differential mode branch, where the common mode inductor L_{CM} can be moved out of the A branch to the common mode loop (its suppression of differential mode current is zero). The Thevenin equivalent can be used to derive the contribution of the differential-mode voltage source to the common-mode current, thereby completing the derivation of the common-mode equivalent model of the A.B branch. Among them, branch A needs two △→Y transformations before applying Thevenin’s theorem. The process is shown in Figure 5. The B branch can be directly transformed by Thevenin’s theorem, so that the common mode equivalent model 3 can be obtained, as shown in Figure 6.

In Figure 5,

In Figure 6,

Applying Thevenin’s theorem to Figure 6 again can derive a simplified form of the common-mode equivalent circuit of a single-phase grid-connected inverter, as shown in Figure 7, where,