The voltage space phasor pulse width control technology of the three-phase four-leg inverter, namely the three-phase four-leg VSV-PWM inverter, will be introduced.

The main circuit of the three-phase four-arm inverter is shown in Figure 1. It is composed of a three-phase half-bridge inverter and a bridge arm formed by a neutral point (composed of switch tubes S7 and S8). Switch tubes S1, S4 and switch tubes S7, S8 form an A-phase full-bridge inverter; switch tubes S3, S6 and switch tubes S7, S8 form a B-phase full-bridge inverter; switch tubes S3, S2 and switch tubes S7, S8 constitutes a C-phase full-bridge inverter. Since S7 and S8 are the common bridge arms that form the neutral point, the drive of the inverter switches of the three bridge arms of A, B and C and the excitation of the output current will be restrained on the common bridge arm, and the space phasor control technology is adopted. This restraint can be completely lifted.

**1 .The voltage space phasor of the three-phase four-leg inverter**For the main circuit shown in Figure 1, if the neutral line inductance Lf0 is ignored, it can be simplified to the equivalent circuit shown in Figure 2. Each of the bridge arms has two working modes. There are 24=16 working modes for the 4 bridge arms.

The three-phase three-arm inverter has 23=8 switching modes, and there are also 8 voltage space phasors. Among them, 2 are zero-voltage space phasors, and 6 are non-zero-voltage space phasors. Therefore, it can be represented by two-dimensional α-β plane rectangular coordinates. The three-phase four-leg inverter has 24=16 switching modes, which is 8 more switching modes than the three-leg inverter. Therefore, its voltage space phasor must be represented by three-dimensional α-β-γ three-dimensional orthogonal coordinates . Using the 16 switching modes in Table 1, the corresponding three-dimensional space voltage phasors Ù_{α}, Ù_{β} and Ù_{γ} can be calculated by the following equations, namely

The values of Ù_{α}, Ù_{β} and Ù_{γ} can also be obtained by using U_{AO}, U_{BO }and U_{CO }as follows, namely

In this way, the calculation results of Ù_{α}, Ù_{β} and Ù_{γ} can be obtained with the above two algorithms.

Taking the space phasor Ù_{x} (Ù_{α}, Ù_{β} and Ù_{γ}) as a function of the switching mode of each bridge arm, the three-dimensional space of the four-leg inverter α-β-γ represented by the switching mode M_{x} (S_{A}, S_{B}, S_{C}, S_{0}) The voltage phasors are shown in Figure 3. The projection of the 16 space voltage phasors on the α-β plane coordinates is a regular hexagon, as shown in Figure 4. The phasor projection length is Hua. Among them, Ù_{1}(100-)~Ù_{6}(101-) are the projections of the two phasors in Figure 3, respectively. For example, Ù_{1}(100-) is the projection of Ù_{8}(1000) and Ù_{9}(1001). This projection relationship shows the relationship between the three-phase four-leg inverter and the three-phase three-leg inverter space voltage phasors. The three phase voltages U_{AO}, U_{BO} and U_{CO} are in the α-β plane, with Ù_{AO}+Ù_{BO}+Ù_{CO}=0, and the γ-axis represents the zero-sequence component axis.

**2. Space phasor control of three-phase four-leg inverter**The space phasor control is realized by tracking the trajectory of the reference phasor in time with the motion trajectory of the space phasor, so it is very important to find the trajectory of the reference phasor.

1) Steady-state reference phasor

In the steady state, the trajectory of the reference voltage phasor of the three-phase three-leg inverter on the α-β plane is a circle with a rotation speed of ω. For a three-phase four-leg inverter, at steady state, the reference voltage [U_{AO}, U_{BO}, U_{CO} ]T can be obtained with the circuit model shown in Figure 5, where the load is represented by a current source.

In Figure 5, the voltage and DC current of the inverter are

In the formula, d_{AO}, d_{BO}, d_{CO} are the duty ratios; the current source l_{in} is used for the AC power supply and the diode rectifier bridge. Indicates; l_{aL}, I_{bL}, I_{cL} are load currents.

In steady state, the voltages U_{AO}, U_{BO}, U_{CO} can be expressed as

The first term in the formula is the positive-sequence reference voltage caused by the positive-sequence load current, namely

The second term in equation (4) is the negative sequence reference voltage caused by the negative sequence load current, namely

The third term in equation (4) is the zero-sequence reference voltage caused by the zero-sequence load current, namely

The reference voltage [Ù_{α},Ù_{β}.Ù_{γ}]T can be obtained by transforming [U_{AO}, U_{BO}, U_{CO} ]T to α-β-γ coordinates by formula (8). The projection Ù_{γ} of the reference voltage on the γ-axis is dominated by only the zero-sequence reference voltage, and the projection of the reference voltage on the α-β plane is caused by the positive-sequence and negative-sequence reference voltages, namely

When the load is symmetrical, there is neither zero-sequence load current nor negative-sequence load current. Similar to the three-arm inverter, the reference voltage phasor rotates at the speed ω on the α-β plane, and the depicted reference voltage The trajectory is a circle.

When the three-phase load is asymmetric (such as l_{ao}=l∠0°, I_{bo}=l∠120°, I_{co}=l∠240°), the trajectory depicted by the reference voltage phasor in space is an oblique ellipse, as shown in Figure 6 shown.

The projection of the reference voltage phasor on the a-β plane is an ellipse as shown in Figure 7. The major radius of the ellipse is equal to the sum of the positive sequence reference voltage given by equation (5) and the negative sequence reference voltage given by equation (6). The short radius of the ellipse is equal to the difference between the two. It can be seen from this that the negative sequence reference voltage caused by the negative sequence load current has a great influence on the selection of the DC power supply voltage.

2) Static phasor control

The task of space phasor control is to use the switching phasor shown in Figure 4 to synthesize the trajectory of the reference voltage phasor, as shown in Figure 6. The space phasor control can be divided into two steps: the first step is to select the switching phasors and calculate the duration of each switching phasor; the second step is to determine the sequence of the reference switching phasors.

(1) Selection of practical switching phasors

The chosen condition is to eliminate the small loops created by the trace and reduce the harmonics of the inductor current. For the three-phase three-arm inverter, the reference voltage phasor synthesized by two adjacent non-zero phasors and zero phasors can meet the above requirements. For the three-phase four-leg inverter, the adjacent phasors must be distinguished and found first. As shown in Figure 8, in a 60° region, there are 6 non-zero phasors and two zero phasors that can be for selection. For this purpose, four adjacent phasor tetrahedra as shown in Figure 9 can be analyzed in this 60° region, each tetrahedron is composed of three adjacent non-zero phasors (the triangle formed by its top end is the base) and two (tetrahedral pyramid) composed of zero phasors (with the point as the top). This tetrahedron is in turn determined by the adjacent switching phasors. The duration of each practical switching phasor can also be calculated in the same way as for the three-leg inverter. Assuming that the reference voltage phasor used is in the tetrahedron /, the selected switching phasors are Ù1 (1000), Ù2 (1001), Ù3 (1101), Ù0 (11l1), Ù0 (0000), and the corresponding duration can be derived from the following formula, namely

(2) Selection of switching phasor sequence

For the three-phase three-leg inverter, in order to prevent the trajectory from generating small loops, the conditions for reducing the number of switching operations, reducing the switching loss, and reducing the output voltage THDi are to alternately select the conversion sequence of adjacent phasors. For the four-leg inverter, the sequence of switching phasors is also selected according to this condition. Figure 10 shows three sequential selection schemes: scheme 1 is the order of symmetry selection; scheme 2 is the order of selection according to high instantaneous value current not turned on to reduce switching loss; scheme 3 is selected according to zero phasor alternate work Order. After a detailed study of these three schemes, the results shown in Figure 11, Figure 12 and Table 2 were obtained. Option 1 can be selected if THDi is desired to be small. When option 1 is selected, the simulation test is carried out under the symmetrical load and the asymmetrical load, and the waveforms of the output voltage, output current and neutral line current obtained are shown in Figure 13. When the load is symmetrical, the THDi of the output voltage is 2.3%; when the load is asymmetric, the THDi of the output voltage is 4.8%.

**3. Instantaneous space current phasor control method using hysteresis comparator**The instantaneous space current phasor control method using the hysteresis comparator is formed by adding the α-β-γ space phasor link on the basis of the current tracking control of the hysteresis comparator.

1) Two-state current tracking control using hysteresis comparator

Figure 14 shows the current tracking control principle of the three-phase four-leg inverter using the hysteresis comparator. The main circuit of the three-phase four-arm inverter is shown in Figure 1. Here, the A-phase bridge arm is used as an example for introduction. As shown in Figure 14 , the deviation ira to iaL between the reference current ira and the load current iaL is used as the input of the two-state comparator with hysteresis characteristics, and the on-off of S1 and S4 is controlled by its output. For example, the conduction of S1 increases the current ira; the conduction of S4 reduces iaL, causing the current iaL to track back and forth between ira+h and ira-h with a deviation of h. The characteristics of this control method are: the hardware is very simple; the response speed of the current control is very fast; compared with other methods, at the same switching frequency, the output current contains more harmonics; the spectrum of the output voltage does not contain specific frequencies component; the waveform of the output voltage is bipolar.

2) Instantaneous space current phasor control method

The circuit block diagram of the α-β-γ three-state (four-state) current hysteresis PWM regulator using the instantaneous space current phasor control method for the three-phase four-bridge inverter is shown in Figure 15. It is formed on the basis of the circuit in Figure 14, after adding the α-β-γ space phasor link. The central idea is to use the one-to-one correspondence between the α-β-γ space voltage phasors given in Table 1 and the switching mode M_{x} (S_{A,} S_{B}, S_{C}, S_{0}) to determine the switching mode of each bridge arm, which removes the The pinning effect of the neutral point bridge arm. In the figure, i_{ra}, i_{rb}, and i_{rc} are the given fundamental currents, and the three given currents can be transformed into given currents i_{rα}, i_{rβ}, i_{rγ} in α-β-γ orthogonal coordinates in three-dimensional space by equation (10) ,Right now

The output currents i_{aL}, i_{bL}, i_{cL}, io of each bridge arm of the inverter are measured by the current transformer, and can be transformed into the feedback current i_{α}, i_{β}, i_{γ} of the three-dimensional α-β-γ space orthogonal coordinates by the following formula, namely

Figure 15. The switch tables (such as M_{x} and Ù_{x} in Table 1) stored in the EPROM are shown in Tables 3 and 4. The switching modes of the four bridge arms can be determined according to the output electrical signals d_{α}, d_{β}, and d_{γ} of the three current hysteresis loops.

The working process of the circuit is as follows: compare the current, irα, i_{rβ}, i_{rγ} with the feedback current i_{α}, i_{β}, i_{γ}, and obtain the error signals Δiα, Δiβ, Δiγ. These three error signals are respectively compared with the three-state current hysteresis comparator. After comparing the hysteresis widths of , the output signals d_{α}, d_{β}, d_{γ} determine Ù’_{k} according to the values of d_{α}, d_{β} and Table 3, and then determine Ù_{x }(Ù_{α}, Ù_{β}, Ù_{γ}), =~. From the one-to-one correspondence between the phasors Ùx (Ùα, Ùβ, Ùγ) and the switching mode M_{x} (S_{A}, S_{B}, S_{C}, S_{0}) shown in Table 1, the switching mode M_{x }(S_{A}, S_{B}, S_{C}, S_{0}) that the inverter should have can be determined.(S_{A} , S_{B}.S_{C}, S_{0}), which also determines the switching modes S_{A}, S_{B}.S_{C}, S_{0} of each bridge arm of the inverter.

The circuit shown in Figure 15 is a three-state α-β-γ space phasor current hysteresis control circuit, which uses three three-state current hysteresis comparators (the output is -1, 0, +1 three levels ). If the top three-state current hysteresis loop is replaced with a four-state current hysteresis loop (the output is -2, -1, 1, 2 four levels), the four-state α-β-γ space phasor control can be obtained circuit. Its working principle and working process are the same as the three-state control circuit, but the switch table stored in the EPROM can be changed from Table 3 to Table 5. First use dα, dβ and Table 5 to determine U’_{k}, then use U’_{k,} dγ and Table 4 to determine U_{x} (U_{α}, U_{β}, U_{γ}), and finally determine U_{x} (U_{α}, U_{β}, U_{γ}) and Table 1 The switching mode of each bridge arm of the inverter.

3) Comparison of two-state and multi-state current hysteresis controllers

Using three-state or four-state current hysteresis for control can reduce the switching frequency of the inverter. A comparison of switching times for two-state, three-state, and four-state regulators is shown in Figure 16. Figure 17 shows the projections of two-state, three-state, and four-state switching phasors on the α-β plane. As can be seen from Figure 17,

Three-state can select adjacent phasors for control more times than two-state, and all four-states select adjacent phasors, so the number of switching can be reduced. In addition, the use of three-state or four-state can make the output voltage PWM waveform of the inverter be a unipolar waveform.

The disadvantage of using three-state or four-state is that the circuit is complicated.

Figures 18 to 20 show the simulation results of the PWM waveforms of the output current, output voltage, switching phasor trajectory and inverter output voltage for two-state, three-state and four-state control for reference.

4) Dual-loop tri-state current hysteresis voltage regulator

The so-called double-loop voltage regulator is to add a voltage outer loop on the basis of the current mode control method. The given voltage is compared with the output feedback voltage, and the difference is used as the given signal of the current regulator (inner loop) to control, so that it can better adapt to the requirements of load changes. Therefore, a two-loop three-state current hysteresis voltage regulator can be constructed by adding a voltage outer loop based on the current regulator in Figure 14 . The block diagram of phase A of its load current feedforward voltage regulator is shown in Figure 21. The voltage outer loop adopts a Pl regulator, and the A-phase of the inverter is given a voltage uar. Compare with the A-phase output feedback voltage uao’, and send the error signal to the PI regulator. PI regulator output. As a given signal for the current regulator (inner loop). Comparing ira with the A-phase output current iaL, through the original A-phase current regulator (inner loop), the A-phase switching method can be obtained to control the inverter switch tubes S1 and S4 like the current regulator in Figure 14. open, so as to achieve the purpose of voltage regulation.

In order to eliminate the “static difference” of the output voltage when the load changes, in addition to adding a PI regulator, a current positive feedback iao’f and a given voltage are added. The micro-branch path will be iao’f and uar. of the differential signal with the output of the PI regulator. ira are added together to form a load current feed-forward voltage regulator. Since the transfer function of this regulator is constant, its characteristics are independent of load changes, so there is no more static output voltage difference.