A circuit form of a three-phase four-wire inverter is shown in Figure 1. This is a four-wire output inverter that uses the midpoint of the DC input supply voltage as the neutral point. For a balanced linear load, the neutral current is equal to zero; but for unbalanced and nonlinear loads, there is a zero-sequence current on the neutral through the center tap of the DC link filter capacitor. This zero sequence current is the fundamental frequency current caused by the asymmetrical load. The reactive power formed by it can cause the voltage U_{d} to be distorted.

The switching function analysis method mentioned above is also applicable to the three-phase four-wire inverter. The following uses this method to analyze the three-phase four-wire inverter.

**1. Unbalanced load and active filter compensation**On the DC side, the three-phase four-wire inverter circuit with active filter compensation is shown in Figure 2.

Assuming that the inverter is using an unbalanced load with “phase C off”, phase A and phase B loads being the same, and assuming that the load current is approximately sinusoidal, the input current to the inverter is

From formula (3), formula (2), when n=l, formula (1) can be written as

The value of the neutral current I_{o} is

Substitute equations (2) into equations (5) to get

Active filter 1 uses switch tubes S_{7}, S_{8} and inductor L_{1} to control the generated current L_{of }to eliminate l_{o}, and switch tubes S_{7} and S_{8} are controlled by SPWM, so there are

The induced current i_{of }is

By formula (6) and formula (8), it is determined that the condition for canceling io by the iof word is:

Therefore, as long as the above conditions are met, the fundamental frequency zero-sequence current caused by the use of “C-phase off” unbalanced loads in the neutral line will be eliminated. This compensation result will also be utilized in the following research. The derivation of the current i_{inf1} adopts the switching function method that has been said before, namely

Substitute equations (9) into equations (10) to get

Due to the action of active filter 1, the input current l_{inr} is

Substitute equations (4) and (11) into equations (12) to get

Equation (13) shows that the fundamental wave component in l_{in} is eliminated due to the action of active filter 1, so the synthetic current l_{inr} is composed of the DC component and the second harmonic component. To eliminate the second harmonic component in l_{inr} , a full-bridge active filter 2 composed of switches S_{9}~S_{12} and inductor L_{2} should be used. The method of elimination is to use the active filter 2 to generate a l_{inr2} with the same magnitude and opposite phase as the second harmonic component, so that the l_{inr2} and the second harmonic component are cancelled.

From the phasor and cosine theorem in Figure 2(b), we get

And by the law of sine

Therefore there is

Therefore, the sum of the last two second harmonics in equation (13) is

Substitute equation (18) into equation (13) to get

Therefore there is

From the formula (21), the condition for eliminating the second harmonic component in l_{inr} is obtained as

When the conditions of Equation (22) are satisfied, the second harmonic component in Equation (13) can be eliminated, so that the

The three-phase four-wire inverter must use two active filters, namely active filters 1 and 2. With the combined action of these two filters, the low-frequency pulsation caused by the unbalanced load in the DC link can be eliminated current and reactive power. At the same time, the current l_{of} in the neutral will also be eliminated. It can be seen from this that there will be no fundamental frequency zero-sequence current flowing through the DC link capacitor. As mentioned earlier, nonlinear loads and unbalanced loads have the same influence on the input current of the DC link, so the above method also compensates for the influence of nonlinear loads.

The control circuits of the half-bridge active filter 1 and the full-bridge active filter 2 in the three-phase four-wire inverter are shown in Figure 3. Figure (a) is the control circuit of the half-bridge active filter 1, and Figure (b) is the control circuit of the full-bridge active filter 2. Same as Figure 4, the control circuit shown in Figure 3 also adopts two-state hysteresis current tracking control. In Figure 3(a), l_{inr} is made to track l_{inr}=0 to eliminate the neutral current; in Figure 3(b), the second harmonic component in l_{i} is made to track l_{ref2}=0 to eliminate the second harmonic in l_{i} harmonic components.

**2. Simulation results**The three-phase four-wire inverter using half-bridge active filter 1, full-bridge active filter 2 and passive filter L

_{d}C

_{d}comprehensive filter compensation is simulated, and the results shown in Figure 5 to Figure 13 can be obtained. . Figure 5 shows the voltage and current waveforms of the three-phase four-wire inverter, in which Figure (a) is the waveform of the output voltage u

_{AO}, Figure (b) is the waveform of the line current i

_{a}, and Figure (c) is the line current i

_{b}waveform. Figure 6 shows the neutral current i of “C-phase open”. The current waveform of i

_{o}=i

_{a}+i

_{b}and its spectrum. Figure 7 shows the waveform of the input current iin and its frequency spectrum. Figure 8 shows the waveform of the active filter 1, in which Figure (a) is the waveform of the voltage u

_{of}, and Figure (b) is the waveform of the current i

_{of}. Figure 9 shows the waveform and spectrum of the synthesized neutral current i

_{or}=i

_{of}+i

_{o}. Figure 10 shows the waveform and spectrum of the current i

_{inf1}supplied to the active filter 1 by the DC link. Figure 11 is the waveform and spectrum of the DC link current i

_{inr}=i

_{in}+i

_{inf1}. Figure 12 shows the waveform of the current i

_{inf2}supplied to the active filter 2 by the DC link. Figure 13 shows the waveform of the synthesized input current i

_{i}and its frequency spectrum.