3 +1-phase permanent magnet synchronous motor sensorless control system and method
By monitoring the reactance change in the 3+1 phase permanent magnet synchronous motor and outputting the control voltage, the problem of zero-speed full torque start and full speed range control in the prior art is solved, and stable control and simplified control of the full speed range are achieved.
Patent Information
- Application Number
- CN202411818548.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-11
- Publication Date
- 2025-03-14
AI Technical Summary
The prior art methods of high-frequency voltage injection + observer cannot achieve zero-speed full torque start and full speed range control.
By setting N-phase wiring in the 3+1 phase permanent magnet synchronous motor, the reactance change is monitored and the control voltage is output, the full speed range control is achieved. The specific steps include obtaining the three-phase stator voltage, using SVPWM phase shift technology, monitoring the reactance change, determining the voltage vector, and injecting the control signal through the SVPWM phase shift.
Starting from any speed, including zero speed, full torque, ensures stable operation of the full speed range in sensorless state, simplifies control procedures and improves control effects.
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Figure CN119628500A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of permanent magnet synchronous motor control, and in particular to a sensorless control system and method for a 3+1-phase permanent magnet synchronous motor. Background Art
[0002] With the development of power electronics technology, the control strategy of AC speed regulation system has been rapidly developed. The AC permanent magnet synchronous motor vector control system proposed in the 1970s has brought the application of asynchronous permanent magnet synchronous motors in industry to a new level. As a type of AC permanent magnet synchronous motor, permanent magnet synchronous motors have been widely used in recent years. Compared with traditional asynchronous permanent magnet synchronous motors, permanent magnet synchronous motors have the following characteristics: 1) High efficiency and high power factor: Since permanent magnet synchronous motors use permanent magnets instead of electric excitation, they do not require reactive excitation current, so the power factor is significantly improved. In addition, the stator and rotor of permanent magnet synchronous motors are synchronized, and there is no iron core loss in the rotor. The efficiency of permanent magnet synchronous motors is also higher than that of asynchronous permanent magnet synchronous motors; 2) High dynamic response performance and stable speed; small size and light weight: With the continuous application of high-performance permanent magnet materials, the power density of permanent magnet synchronous motors has been greatly improved. Compared with asynchronous permanent magnet synchronous motors of the same capacity, their volume and weight have been greatly reduced.
[0003] In the vector control of permanent magnet synchronous motors, traditional mechanical sensors such as photoelectric encoders are often used for speed identification. However, installing mechanical sensors will not only increase the size of the permanent magnet synchronous motor, but also increase the manufacturing cost of the permanent magnet synchronous motor. In addition, mechanical sensors are easily affected by the ambient temperature and vibration, causing damage, and are difficult to repair and have poor reliability. Therefore, the use of speed sensorless control methods instead of traditional mechanical sensors to identify and estimate the rotor position and speed can not only improve the stability of the permanent magnet synchronous motor, but also reduce the manufacturing cost of the permanent magnet synchronous motor.
[0004] At present, there are many speed sensorless control methods, which can be roughly divided into methods suitable for high speed and low speed. The existing technology uses observer + high-frequency injection to control the motor. The high-frequency frequency is several to dozens of times the PWM frequency, between 0.5 and 3KHz, and is a single-frequency sound. The high-frequency voltage injection + observer method can be applied to occasions when the permanent magnet synchronous motor is running at low speed. It mainly estimates the position information of the rotor by detecting the salient polarity of the permanent magnet synchronous motor. However, the observation error of the observer cannot start at zero speed and full torque, and cannot achieve full speed range control.
[0005] The published Chinese patent, with the publication number CN110061670A, discloses a permanent magnet synchronous motor control method, including adjusting the difference between the preset speed and the rotor tracker, outputting the torque current after the sliding mode speed controller adjusts, the comparison difference between the torque current and the torque current feedback quantity passes through the PI regulator to output the voltage uq; and the comparison difference between the deviation of the excitation current feedback quantity and the excitation current quantity passes through the current PI regulator to output the voltage ud, and the torque voltage uq and the excitation voltage ud are transformed by Park inverse transformation to obtain the two-phase control voltage; SVPWM modulation is performed according to the two-phase control voltage to generate a PWM modulation wave. The three-phase inverter switch device is controlled by the PWM modulation wave to obtain the required three-phase voltage, thereby controlling the permanent magnet synchronous motor.
[0006] The above-mentioned patent disclosure requires taking the current for bandpass filtering and synchronous axis filtering to finally obtain the phase. This method of control procedure is relatively complicated and prone to errors, which affects the control effect on the motor. Summary of the invention
[0007] In view of the shortcomings of the prior art mentioned above, the object of the present invention is to provide a 3+1-phase permanent magnet synchronous motor sensorless control system and method, which is used to solve the problems in the prior art of controlling the motor by high-frequency voltage injection + observer that the motor cannot be started at zero speed with full torque and cannot achieve full speed range control.
[0008] To achieve the above-mentioned object and other related objects, the present invention provides a 3+1-phase permanent magnet synchronous motor sensorless control system, comprising a permanent magnet synchronous motor and an electronic control module, wherein the permanent magnet synchronous motor comprises a central axis and a U-phase winding, a V-phase winding, and a W-phase winding arranged around the outside of the central axis and at intervals of 120°;
[0009] The electric control module is provided with U-phase wiring, V-phase wiring and W-phase wiring, the U-phase wiring is connected to the U-phase winding, the V-phase wiring is connected to the V-phase winding, and the W-phase wiring is connected to the W-phase winding;
[0010] The electronic control module is also provided with an N-phase connection, which is connected to the shaft head of the central shaft of the permanent magnet synchronous motor. It is used to monitor the actual change in the reactance of the permanent magnet synchronous motor as the permanent magnet electrical angle changes, and output the corresponding control voltage to control the permanent magnet synchronous motor over the full speed range.
[0011] In one embodiment of the present invention, the U-phase winding, the V-phase winding, and the W-phase winding all have an inductor L and a resistor R distributed in series.
[0012] In one embodiment of the present invention, the calculation formula for the change in the reactance of the permanent magnet synchronous motor as the permanent magnet electrical angle changes is Z=R+jωL, and the meanings of the parameters in the formula are as follows:
[0013] R: represents the real part of resistance;
[0014] j: represents the imaginary unit, used to represent the phase change in the circuit;
[0015] ω: represents angular frequency, which is a physical quantity that describes the speed of change of alternating current, and its unit is radians per second (rad / s). L: represents the phase line alternating inductance, which is a component that stores magnetic field energy in the circuit.
[0016] A sensorless control method for a 3+1-phase permanent magnet synchronous motor, including the sensorless control system of the 3+1-phase permanent magnet synchronous motor, comprises the following steps:
[0017] S1. Obtain the three-phase stator voltages Vu, Vv, and Vw of the permanent magnet synchronous motor through the electronic control module;
[0018] S2. Use SVPWM phase shifting technology to shift the phase of the three-phase stator voltage Vu, Vv, and Vw of the permanent magnet synchronous motor, so that the voltage vector of the permanent magnet synchronous motor remains unchanged but the waveform moves, meeting the requirements of voltage vector synchronization point sampling;
[0019] S3. After the three-phase stator voltages Vu, Vv, and Vw are phase-shifted, the voltage value of the center point N can be obtained at UV→W, UW→V, and U→VW, that is, the actual reactance change of the permanent magnet synchronous motor as the electrical angle of the permanent magnet synchronous motor changes is monitored by the center point N of the permanent magnet synchronous motor, and then the permanent magnet control angle of the permanent magnet synchronous motor is obtained;
[0020] S4. The control module determines the voltage vector to be applied based on the comparison result between the torque and flux given value and the actual value of the permanent magnet synchronous motor itself and the permanent magnet control angle; for example, if the torque needs to be increased and the position of the flux is determined based on the permanent magnet control angle, a voltage vector that can increase the torque is selected.
[0021] S5. The control module converts the selected voltage vector into a control signal and injects it into the permanent magnet synchronous motor through SVPWM phase shifting to control the operation of the permanent magnet synchronous motor.
[0022] In one embodiment of the present invention, the three-phase inductance of the permanent magnet synchronous motor and the mutual inductance between the three phases change with the position of the permanent magnet synchronous motor magnetic steel as follows:
[0023] L u = l s +l g 0-l g 2*cos 2θ
[0024]
[0025] Among them, l s is the leakage inductance of the permanent magnet synchronous motor, i.e., the leakage flux;
[0026] l g 0 is the DC component of the permanent magnet synchronous motor inductance, i.e. the main magnetic flux;
[0027] l g 2 is the alternating component of the permanent magnet synchronous motor inductance, that is, the salient pole flux.
[0028] In one embodiment of the present invention, the SVPWM phase-shift modulation technology combines the SVPWM modulation method and the phase-shift technology, and realizes precise control of the inverter system through the selection and phase-shift control of the voltage vector.
[0029] As described above, the 3+1 phase permanent magnet synchronous motor sensorless control system and method of the present invention has the following beneficial effects:
[0030] The present invention uses the permanent magnet synchronous motor center point N (N is 1 in "3+1 phases") to actually monitor the actual change of the reactance Z=R+jωL of the permanent magnet synchronous motor phase line as the electrical angle of the permanent magnet synchronous motor changes, thereby obtaining the permanent magnet control angle of the permanent magnet synchronous motor, and can achieve starting at any speed including zero speed with full torque, and achieve stable operation of the permanent magnet synchronous motor in the full speed range under the sensorless state; the present invention takes the voltage after high-frequency injection, and compared with the comparative technology that needs to take the current for bandpass filtering and synchronous shaft filtering to finally obtain the phase, the control program is simple and direct, and the control effect is good. BRIEF DESCRIPTION OF THE DRAWINGS
[0031] Figure 1 Shown is a schematic structural diagram of a 3+1-phase permanent magnet synchronous motor sensorless control system disclosed in an embodiment.
[0032] Figure 2 It is a schematic diagram showing the generation of N poles and S poles by the three-phase winding of the permanent magnet synchronous motor in Example 1.
[0033] Figure 3 The figure shows a sinusoidal waveform of the motor inductance changing with the motor multiple period in Example 1.
[0034] Figure 4 The display is a seven-segment voltage space vector PWM waveform diagram in Example 2.
[0035] Figure 5 and Figure 6 It shows a schematic diagram of SVPWM phase shift in Example 2.
[0036] Figure 7 It shows the three-phase inductance distribution diagram in Example 2.
[0037] Figure 8The diagram shows the change in divided voltage of each reactance at the center point obtained when the phase-shifted PWM carrier drive is performed in Example 2 as the electrical angle of the motor changes.
[0038] Component number description
[0039] Permanent magnet synchronous motor 1; electronic control module 2; central shaft 3; U-phase winding 4; V-phase winding 5; W-phase winding 6; U-phase wiring 7; V-phase wiring 8; W-phase wiring 9; N-phase wiring 10. DETAILED DESCRIPTION
[0040] The following is a description of the implementation of the present invention by means of specific embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification.
[0041] See also Figures 1 to 8 It should be noted that the structures, proportions, sizes, etc. illustrated in the drawings in this specification are only used to match the contents disclosed in the specification for people familiar with this technology to understand and read, and are not used to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any structural modification, change in proportion or adjustment of size should still fall within the scope of the technical contents disclosed in the present invention without affecting the effects and purposes that can be achieved by the present invention.
[0042] Example 1, please refer to Figure 1-Figure 4 , This embodiment provides a 3+1 phase permanent magnet synchronous motor sensorless control system, including a permanent magnet synchronous motor 1 and an electric control module 2, wherein the permanent magnet synchronous motor 1 includes a central axis 3 and a U-phase winding 4, a V-phase winding 5, and a W-phase winding 6 arranged around the outside of the central axis 3 and at an interval of 120°, wherein the winding with a high voltage generates an N pole, and the winding with a low voltage generates an S pole; the electric control module 2 is provided with a U-phase connection 7, a V-phase connection 8, and a W-phase connection 9, wherein the U-phase connection 7 is connected to the U-phase winding 4, the V-phase connection 8 is connected to the V-phase winding 5, and the W-phase connection 9 is connected to the W-phase winding 6; the U-phase winding 4, the V-phase winding 5, and the W-phase winding 6 are all provided with an inductance L and a resistance R distributed in series, and the calculation formula for the actual change in the reactance of the permanent magnet synchronous motor 1 as the permanent magnet electric angle changes is Z=R+jωL, and the meanings of the parameters in the formula are as follows:
[0043] R: represents the real part of resistance;
[0044] j: represents the imaginary unit, used to represent the phase change in the circuit;
[0045] ω: represents angular frequency, which is a physical quantity that describes the speed of change of alternating current, and its unit is radians per second (rad / s);
[0046] L: stands for inductance, which is a component that stores magnetic field energy in the circuit;
[0047] The formula Z = R + jωL describes the complex form of impedance in an AC circuit; impedance is a complex number that describes the circuit's resistance to sinusoidal current, including resistance and reactance. The resistance part R represents the actual resistance to current, while the reactance part jωL represents the shift in the current phase. When ωL>0, the circuit is inductive; when ωL<0, the circuit is capacitive.
[0048] The electric control module 2 is also provided with an N-phase connection 10, which is connected to the shaft head of the central shaft 3 of the permanent magnet synchronous motor 1, and is used to monitor the actual change in the reactance of the permanent magnet synchronous motor 1 as the permanent magnet electric angle changes, and output a corresponding control voltage to control the permanent magnet synchronous motor 1 over the full speed range.
[0049] The present invention uses the center point N of the permanent magnet synchronous motor 1 (N is 1 in "3+1 phases") to actually monitor the change in the reactance Z=R+jωL of the phase line of the permanent magnet synchronous motor 1 as the electrical angle of the permanent magnet permanent magnet synchronous motor 1 changes, thereby obtaining the permanent magnet control angle of the permanent magnet synchronous motor 1, and can achieve starting at any speed including zero speed with full torque, and achieve stable operation of the permanent magnet synchronous motor 1 in the full speed range under the sensorless state; the present invention takes the voltage after high-frequency injection, and compared with the comparative technology that needs to take the current for bandpass filtering and synchronous shaft filtering to finally obtain the phase, the control procedure is simple and direct, and the control effect is good.
[0050] Example 2, please refer to Figure 5-Figure 8 This embodiment provides a sensorless control method for a 3+1-phase permanent magnet synchronous motor 1, including the sensorless control system of the 3+1-phase permanent magnet synchronous motor 1 described in Embodiment 1, including the following steps:
[0051] S1. Obtain the three-phase stator voltages Vu, Vv, and Vw of the permanent magnet synchronous motor 1 through the electronic control module 2
[0052] S2. Use SVPWM phase shifting technology to shift the phase of the three-phase stator voltage Vu, Vv, and Vw of the permanent magnet synchronous motor 1, so that the voltage vector of the permanent magnet synchronous motor 1 remains unchanged but the waveform moves, meeting the requirements of voltage vector synchronization point sampling;
[0053] S3. After the three-phase stator voltages Vu, Vv and Vw are phase-shifted, the voltage value of the center point N can be obtained at UV→W, UW→V and U→VW, that is, the center point N of the permanent magnet synchronous motor 1 is used to monitor the actual reactance change of the permanent magnet synchronous motor 1 as the electrical angle of the permanent magnet synchronous motor 1 changes, and then the permanent magnet control angle of the permanent magnet synchronous motor 1 is obtained;
[0054] S4. The control module determines the voltage vector to be applied based on the comparison result between the torque and flux given value and the actual value of the permanent magnet synchronous motor 1 itself and the permanent magnet control angle; for example, if the torque needs to be increased and the position of the flux is determined based on the permanent magnet control angle, a voltage vector that can increase the torque is selected.
[0055] S5. The control module converts the selected voltage vector into a control signal and injects it into the permanent magnet synchronous motor 1 through the SVPWM phase shift to control the operation of the permanent magnet synchronous motor 1; the SVPWM phase shift modulation (Space Vector Pulse Width Modulation with Phase Shift) is a modulation technology used in a cascaded multi-level inverter system. It combines the SVPWM modulation method and the phase shift technology, and realizes precise control of the inverter system through the selection and phase shift control of the voltage vector; in the cascaded multi-level inverter system, the selection and calculation become complicated due to the large number of voltage vectors. The SVPWM phase shift modulation method combines the SVPWM modulation method and the phase shift technology, and uses a digital signal processor and a field programmable logic device FPGA to realize vector control of the system. This method reduces the computational complexity through the phase shift technology and ensures the stability and efficiency of the system.
[0056] VPWM phase shift is to solve the problem that the voltage vector synchronization point cannot sample the required analog quantity and make the change of the vector constant waveform movement. After phase shift, the divided voltage value of each reactance at the center point can be obtained when the PWM carrier drives UV->W, UW->V, VW->U and W->UV, V->UW, U->VW, that is, the actual change of the reactance Z=R+jωL of the motor with the change of the permanent magnet motor electrical angle is actually monitored by the motor center point N (N is 1 in "3+1 phase"), and the permanent magnet control angle of the motor is obtained.
[0057] The three-phase inductance of the permanent magnet synchronous motor 1 and the mutual inductance between the three phases change with the position of the magnetic steel of the permanent magnet synchronous motor 1 as follows:
[0058] L u = l s +l g 0-l g 2*cos 2θ
[0059]
[0060] Among them, l s is the leakage inductance of the permanent magnet synchronous motor 1, i.e., the leakage flux;
[0061] l g 0 is the DC component of the inductance of the permanent magnet synchronous motor 1, i.e., the main magnetic flux;
[0062] l g 2 is the alternating component of the inductance of the permanent magnet synchronous motor 1, i.e., the salient pole flux;
[0063] Depend on Ignore leakage inductance s The three-phase reactance is
[0064]
[0065] Then, when phase-shift PWM carrier driving is performed, the divided voltage values of each reactance at the center point are obtained as follows:
[0066] UV->W, the center voltage is
[0067] UW->V, the center voltage is
[0068] VW->U, the center voltage is
[0069] as well as:
[0070] W->UV, the center voltage is
[0071] XV->UW, the center voltage is
[0072] U->VW, the center voltage is
[0073] From the above values, it can be seen that the inductance of the motor changes with the change of the magnetic field. When the high-frequency voltage is injected with PWM at the same frequency, the position of the magnetic field can be obtained by obtaining the ratio of the three-phase UVW of the inductance; in order to verify the voltage division of the inductance of the five-segment or seven-segment SVPWM after injecting the high-frequency voltage of the same frequency as PWM under the condition of phase shift, it is proved that the voltage at point N is different.
[0074] Assume l g 0=0.18mH,l g 2=0.07mH, then the three-phase inductance distribution is as follows Figure 8As shown, the horizontal axis is the motor electrical angle (0-359°), and the vertical axis is the electrical three-phase inductance Lu, Lv, and Lw. Then, when the phase-shifted PWM carrier drive is performed, the divided voltage of each reactance at the center point that changes with the motor electrical angle is obtained (when the power supply voltage Vcc=15V), where the divided voltages of UV->W and W->UV, UW->V and V->UW, and VW->U and U->VW are all symmetrical around Vcc / 2. Finally, the motor control angle can be calculated in reverse by collecting the divided voltages of each reactance at the center point that changes with the motor electrical angle when the phase-shifted PWM carrier drive is driven, and the closed-loop control of the motor is formed from the motor angle to the motor drive and then to the motor drive to the motor angle.
[0075] Embodiment 3, this embodiment provides a modeling matrix of a permanent magnet synchronous motor:
[0076]
[0077] Among them, λ is the magnetic flux, λ=L*R, L is taken out and verified, L UVW and M UVW They are all alternating, that is, the inductance is alternating and changes with the change of the permanent magnetic field. The current magnetic field position is obtained by comparing the size of the inductance L.
[0078] In summary, the present invention monitors the actual change of the U, V, and W three-phase reactances of the permanent magnet synchronous motor 1 phase line as the electrical angle of the permanent magnet synchronous motor 1 changes by the center point N of the permanent magnet synchronous motor 1, thereby obtaining the permanent magnet control angle of the permanent magnet synchronous motor 1 and controlling the permanent magnet synchronous motor 1 to work stably in the full speed range in the sensorless state. Therefore, the present invention effectively overcomes various shortcomings in the prior art and has a high industrial utilization value.
[0079] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.
Claims
1. A 3+1 phase permanent magnet synchronous motor sensorless control system, comprising a permanent magnet synchronous motor and an electronic control module, wherein the permanent magnet synchronous motor comprises a central axis and a U-phase winding, a V-phase winding, and a W-phase winding arranged around the outside of the central axis and spaced 120° apart, wherein the winding with a high voltage generates an N pole, and the winding with a low voltage generates an S pole; The electric control module is provided with U-phase wiring, V-phase wiring and W-phase wiring, the U-phase wiring is connected to the U-phase winding, the V-phase wiring is connected to the V-phase winding, and the W-phase wiring is connected to the W-phase winding; Features: The electronic control module is also provided with an N-phase connection, which is connected to the shaft head of the central shaft of the permanent magnet synchronous motor. It is used to monitor the actual change in the reactance of the permanent magnet synchronous motor as the permanent magnet electrical angle changes, and output the corresponding control voltage to control the permanent magnet synchronous motor over the full speed range.
2. The 3+1 phase permanent magnet synchronous motor sensorless control system according to claim 1 is characterized in that: The U-phase winding, the V-phase winding, and the W-phase winding all have inductors L and resistors R distributed in series.
3. The 3+1 phase permanent magnet synchronous motor sensorless control system according to claim 1 is characterized in that: The calculation formula for the actual change in the reactance of the permanent magnet synchronous motor as the permanent magnet electric angle changes is Z=R+jωL, and the meanings of the parameters in the formula are as follows: R: represents the real part of resistance; j: represents the imaginary unit, used to represent the phase change in the circuit; ω: represents angular frequency, which is a physical quantity that describes the speed of change of alternating current, and its unit is radians per second (rad / s); L: represents the phase line alternating inductance, which is the element that stores magnetic field energy in the circuit.
4. A sensorless control method for a 3+1-phase permanent magnet synchronous motor, comprising the sensorless control system for a 3+1-phase permanent magnet synchronous motor according to any one of claims 1 to 3, characterized in that: The steps include: S1. Obtain the three-phase stator voltages Vu, Vv, and Vw of the permanent magnet synchronous motor through the electronic control module; S2. Use SVPWM phase shifting technology to shift the phase of the three-phase stator voltage Vu, Vv, and Vw of the permanent magnet synchronous motor, so that the voltage vector of the permanent magnet synchronous motor remains unchanged but the waveform moves, meeting the requirements of voltage vector synchronization point sampling; S3. After the three-phase stator voltages Vu, Vv, and Vw are phase-shifted, the voltage value of the motor winding center point N can be obtained at UV→W, UW→V, and U→VW, that is, the actual reactance change of the permanent magnet synchronous motor as the electrical angle of the permanent magnet synchronous motor changes is monitored by the center point N of the permanent magnet synchronous motor, and then the permanent magnet control angle of the permanent magnet synchronous motor is obtained; S4, the control module determines the voltage vector to be applied according to the comparison result between the torque and flux given value of the permanent magnet synchronous motor and the actual value, combined with the permanent magnet control angle; S5. The control module converts the selected voltage vector into a control signal and injects it into the permanent magnet synchronous motor through the phase-shifted wave of SVPWM to control the operation of the permanent magnet synchronous motor.
5. The sensorless control method of a 3+1 phase permanent magnet synchronous motor according to claim 4 is characterized in that: The three-phase inductance of the permanent magnet synchronous motor and the mutual inductance between the three phases change with the position of the permanent magnet synchronous motor magnetic steel as follows: L u =l s +l g 0-l g 2*cos 2θ Among them, l s is the leakage inductance of the permanent magnet synchronous motor, i.e., the leakage flux; l g 0 is the DC component of the permanent magnet synchronous motor inductance, i.e. the main magnetic flux; l g 2 is the alternating component of the permanent magnet synchronous motor inductance, that is, the salient pole flux.
6. The sensorless control method of a 3+1 phase permanent magnet synchronous motor according to claim 4, characterized in that: The SVPWM phase-shift modulation technology combines the SVPWM modulation method and the phase-shift technology, and realizes precise control of the synchronous position of the inverter system through the selection and phase-shift control of the voltage vector.
Citation Information
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