Long cable motor overvoltage suppression circuit based on active filter and control method

By installing the active DV/DT filter between the inverter output side and the long cable, using voltage clamp switching and continuous flow diode and other components to form two steps to offset the reflex voltage, solve the overvoltage of the long cable motor motor, The problem has achieved efficient overvoltage suppression and low loss.

CN119340926AActive Publication Date: 2025-01-21GUANGZHOU INSTITUTE OF TECHNOLOY XIDIAN UNIVERSITY
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Patent Information

Application Number
CN202411691031.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-25
Publication Date
2025-01-21
Estimated Expiration
2044-11-25

AI Technical Summary

Technical Problem

When the inverter and the motor are connected through a long cable, overvoltage problems are prone to occur at the end of the motor, and traditional passive dv/dt filters have problems with large size and high losses.

Method used

A long cable motor overvoltage suppression circuit based on an active filter is used. By combining the power circuit and the drive signal circuit, and using components such as voltage clamp switches and freewheeling diodes, the circuit is used to suppress the rising and falling edges of the inverter output voltage. The voltage is clamped to zero level, forming a two-stage staircase wave to cancel the reflected voltage.

Benefits of technology

Effectively suppress the reflex voltage of the motor side, reduce the overvoltage of the motor winding, and reduce the current stress of the voltage clamp switch, and improve the overall efficiency.

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Abstract

The invention provides a long cable motor overvoltage suppression circuit based on an active filter and a control method. The circuit comprises a power circuit and a driving signal circuit. The power circuit comprises a bus capacitor, a voltage clamping switch, a fly-wheel diode and an energy storage inductor; the driving signal circuit comprises a divider resistor, a comparator, a trigger circuit and a driving circuit; the power circuit is connected in series between the output side of the inverter and the long cable, meanwhile, the output voltage of the inverter is connected with the input end of the driving signal circuit, the output end of the driving signal circuit is connected with the power circuit of the active dv / dt filter, and the working mode of the power circuit is controlled. According to the invention, through the active dv / dt filter, the output voltage is forcibly clamped to the zero level, so that the reflection voltage of the first-stage step wave and the reflection voltage of the second-stage step wave are mutually offset, and the reflection voltage of the motor end is inhibited.
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Description

Technical Field

[0001] The invention relates to the technical field of motor control, and in particular to an overvoltage suppression circuit and a control method for a long cable motor based on an active filter. Background Art

[0002] In applications where the inverter and motor are far apart, the two need to be connected by a long cable, such as Figure 1 As shown. Usually the inverter output voltage waveform has a high dv / dt characteristic, such as Figure 2 As shown. Due to the mismatch between the cable impedance and the motor impedance, the high dv / dt characteristics of the output voltage lead to a transmission line effect in the cable, which in turn generates a reflected voltage at the motor end, causing overvoltage in the motor winding, such as Figure 3 As shown. The voltage at the motor end is U mot =(1+Γ L ) in , where Umot is the motor terminal voltage, Uin is the inverter output voltage, Γ L is the reflection coefficient;

[0003]

[0004] Z L is the motor impedance, Zc is the cable impedance, usually, Z L >>Zc, so Γ L ≈1.

[0005] The traditional method of suppressing motor overvoltage is to use a passive dv / dt filter. Figure 4 As shown in the figure. The principle is to use LCR devices to slow down the rising and falling edges of the inverter output voltage, thereby reducing the overvoltage at the motor end. However, the passive dv / dt filter is large in size and has high losses. Especially the resistance loss, which is proportional to the switching frequency of the inverter. The faster the inverter switching frequency, the higher the loss. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide an active filter-based long cable motor overvoltage suppression circuit and a control method to solve the problem of motor load overvoltage in the active filter-based long cable motor overvoltage suppression circuit mentioned in the background technology.

[0007] To solve the above technical problems, an embodiment of the present invention provides the following technical solutions: an active dv / dt filter circuit for suppressing overvoltage of a long cable motor, the circuit comprising a power circuit and a drive signal circuit; the power circuit comprises a bus capacitor, a voltage clamp switch, a freewheeling diode and an energy storage inductor; the drive signal circuit comprises a voltage dividing resistor, a comparator, a trigger circuit and a drive circuit; the power circuit is connected in series between the output side of the inverter and the long cable, and at the same time, the inverter output voltage is connected to the input end of the drive signal circuit, and the output end of the drive signal circuit is connected to the power circuit of the active dv / dt filter to control the working mode of the power circuit;

[0008] The power circuit of the active dv / dt filter includes a first bus capacitor C1, a second bus capacitor C2, a first voltage clamp switch T1, a second voltage clamp switch T2, a first freewheeling diode D1, a second freewheeling diode D2 and an energy storage inductor L1, wherein:

[0009] The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide a zero level for the active dv / dt filter;

[0010] The first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in reverse series, and at each rising edge and falling edge of the inverter output voltage, the voltage is clamped to zero level, so as to realize the output voltage in the form of a two-level step wave;

[0011] The first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction, and when the voltage clamp switch is not working, the energy storage inductor L1 is freewheeling;

[0012] The energy storage inductor L1 is composed of a power inductor. When the first voltage clamp switch T1 and the second voltage clamp switch T2 are actuated, a portion of energy is stored to reduce the current stress of the voltage clamp switch.

[0013] Furthermore, the drive signal circuit includes a voltage-dividing resistor, a comparator, a trigger circuit and a drive circuit, wherein the voltage-dividing resistor includes a first voltage-dividing resistor R11 and a second voltage-dividing resistor R12, wherein one end of the first voltage-dividing resistor R11 is connected to the output side of the inverter, the other end of the first voltage-dividing resistor R11 is connected to one end of the second voltage-dividing resistor R12 and the same-phase input end of the comparator, the inverting input end of the comparator is connected to the positive electrode of a DC power supply, the other end of the second voltage-dividing resistor R12 and the negative electrode of the DC power supply are both grounded, the output end of the comparator is connected to the input end of the trigger circuit, the output of the trigger circuit is connected to the input end of the drive circuit, and the output end of the drive circuit is connected to the gates of the first voltage clamping switch T1 and the second voltage clamping switch T2.

[0014] Furthermore, the input end of the energy storage inductor L1 is connected to the output end of the inverter, and the output end of the energy storage inductor L1 is connected to the long cable; the two ends of the first bus capacitor C1 and the second bus capacitor C2 connected in series are respectively connected to the inverter bus voltage output end.

[0015] Furthermore, each phase output end of the inverter is correspondingly connected to the power circuit and the drive signal circuit.

[0016] Furthermore, the first voltage clamping switch T1 and the second voltage clamping switch T2 are switch tubes, wherein the drain of the first voltage clamping switch T1 is connected to the connection end of the first bus capacitor C1 and the second bus capacitor C2, the source of the first voltage clamping switch T1 is connected to the source of the second voltage clamping switch T2, the drain of the second voltage clamping switch T2 is connected to the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2, the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2 is also connected to the output end of the energy storage inductor L1, and the two ends of the first freewheeling diode D1 and the second freewheeling diode D2 after being connected in series are respectively connected to the inverter bus voltage output end.

[0017] The present invention also provides a control method for the active dv / dt filter circuit as described above, comprising:

[0018] The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide zero level for the active dv / dt filter at the same time; the first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in series in reverse order to clamp the voltage to zero level at each rising edge and falling edge of the inverter output voltage, so that the output voltage forms a two-stage step wave form, and the reflected voltage of the first stage step wave and the reflected voltage of the second stage step wave cancel each other out; the first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction to provide freewheeling for the energy storage inductor L1 when the voltage clamp switch is not working; the energy storage inductor L1 stores a part of energy when the first voltage clamp switch T1 and the second voltage clamp switch T2 are in action to reduce the current stress of the voltage clamp switch.

[0019] Furthermore, the trigger controls the on-time of the voltage clamp switch, and the on-time td of the voltage clamp switch is twice the cable transmission time t t ,in:

[0020]

[0021] l ca is the cable length, v ca The transmission speed of the cable.

[0022] The beneficial effects of the above technical solution of the present invention are as follows:

[0023] The present invention uses an active dv / dt filter to force the output voltage to be clamped to zero level at each rising edge and falling edge of the inverter output voltage, so that the output voltage forms a two-stage step wave form. The reflected voltage of the first-stage step wave and the reflected voltage of the second-stage step wave offset each other, thereby suppressing the reflected voltage at the motor end. In specific control, the microprocessor controls the on-time of the voltage clamp switch, and the on-time td of the voltage clamp switch is twice the cable transmission time t t ,in:

[0024]

[0025] Among them, l ca is the cable length, v ca is the transmission speed of the cable. d =2t t When the voltage is higher than the rated voltage, the reflected voltages at the motor end can cancel each other out, thus suppressing the overvoltage at the motor end. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0027] Figure 1 This is a circuit schematic diagram of a traditional inverter connected to a motor via a long cable;

[0028] Figure 2 This is a typical inverter output voltage waveform;

[0029] Figure 3 This is a waveform diagram of the inverter output voltage waveform after it passes through a long cable and the transmission line effect appears in the cable;

[0030] Figure 4 The schematic diagram of the passive dv / dt filter circuit used in the traditional method of suppressing motor overvoltage;

[0031] Figure 5 The active dv / dt filter circuit used in the present invention is a schematic diagram for suppressing motor overvoltage;

[0032] Figure 6 The active dv / dt filter circuit schematic diagram used in the present invention;

[0033] Figure 7 The schematic diagram of the signal driving circuit used in the present invention;

[0034] Figure 8 The output voltage waveform diagram after being filtered by an active dv / dt filter of the present invention;

[0035] Fig. 9 This is the waveform diagram of the motor end after being filtered by the active dv / dt filter and passing through the long-line cable. DETAILED DESCRIPTION

[0036] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0037] In applications where the inverter and motor are far apart, the two need to be connected by a long cable, such as Figure 1 As shown. Usually the inverter output voltage waveform has a high dv / dt characteristic, such as Figure 2 As shown. Due to the mismatch between the cable impedance and the motor impedance, the high dv / dt characteristics of the output voltage lead to a transmission line effect in the cable, which in turn generates a reflected voltage at the motor end, causing overvoltage in the motor winding, such as Figure 3 shown.

[0038] The voltage at the motor end is

[0039] U mot =(1+Γ L ) in

[0040] Among them, Umot is the motor terminal voltage, Ui n is the inverter output voltage, Γ L is the reflection coefficient;

[0041]

[0042] Z L is the motor impedance, Zc is the cable impedance, usually, Z L >>Zc, so Γ L ≈1

[0043] The traditional method of suppressing motor overvoltage is to use a passive dv / dt filter. Figure 4 The principle is to use LCR devices to slow down the rising and falling edges of the inverter output voltage, thereby reducing the overvoltage at the motor end.

[0044] However, passive dv / dt filters are large in size and have high losses, especially resistance losses, which are proportional to the switching frequency of the inverter. The faster the switching frequency of the inverter, the higher the loss.

[0045] like Figure 5 As shown, the present invention proposes an active dv / dt filter circuit for suppressing overvoltage of a long cable motor, the circuit comprising a power circuit and a drive signal circuit; the power circuit comprises a bus capacitor, a voltage clamp switch, a freewheeling diode and an energy storage inductor; the drive signal circuit comprises a voltage dividing resistor, a comparator, a trigger circuit and a drive circuit; the power circuit is connected in series between the output side of the inverter and the long cable, and at the same time, the inverter output voltage is connected to the input end of the drive signal circuit, and the output end of the drive signal circuit is connected to the power circuit of the active dv / dt filter to control the working mode of the power circuit;

[0046] The power circuit of the active dv / dt filter includes a first bus capacitor C1, a second bus capacitor C2, a first voltage clamp switch T1, a second voltage clamp switch T2, a first freewheeling diode D1, a second freewheeling diode D2 and an energy storage inductor L1, wherein:

[0047] The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide a zero level for the active dv / dt filter;

[0048] The first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in reverse series, and at each rising edge and falling edge of the inverter output voltage, the voltage is clamped to zero level, so as to realize the output voltage in the form of a two-level step wave;

[0049] The first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction, and when the voltage clamp switch is not working, they are used to freewheel the energy storage inductor L1;

[0050] The energy storage inductor L1 is composed of a power inductor. When the first voltage clamp switch T1 and the second voltage clamp switch T2 are actuated, a portion of energy is stored to reduce the current stress of the voltage clamp switch.

[0051] In this embodiment, the drive signal circuit includes a voltage-dividing resistor, a comparator, a trigger circuit and a drive circuit. The voltage-dividing resistor includes a first voltage-dividing resistor R11 and a second voltage-dividing resistor R12, wherein one end of the first voltage-dividing resistor R11 is connected to the output side of the inverter, the other end of the first voltage-dividing resistor R11 is connected to one end of the second voltage-dividing resistor R12 and the non-inverting input end of the comparator, the inverting input end of the comparator is connected to the positive electrode of a DC power supply, the other end of the second voltage-dividing resistor R12 and the negative electrode of the DC power supply are both grounded, the output end of the comparator is connected to the input end of the trigger circuit, the output of the trigger circuit is connected to the input end of the drive circuit, and the output end of the drive circuit is connected to the gates of the first voltage clamping switch T1 and the second voltage clamping switch T2.

[0052] In this embodiment, the input end of the energy storage inductor L1 is connected to the output end of the inverter, and the output end of the energy storage inductor L1 is connected to the long cable; the two ends of the first bus capacitor C1 and the second bus capacitor C2 connected in series are respectively connected to the inverter bus voltage output end.

[0053] In this embodiment, each phase output terminal of the inverter is correspondingly connected to a power circuit and a drive signal circuit.

[0054] In this embodiment, the first voltage clamping switch T1 and the second voltage clamping switch T2 are switch tubes, which can be traditional silicon-based MOS, Si C MOS, or GaN devices; wherein the drain of the first voltage clamping switch T1 is connected to the connection end of the first bus capacitor C1 and the second bus capacitor C2, the source of the first voltage clamping switch T1 is connected to the source of the second voltage clamping switch T2, the drain of the second voltage clamping switch T2 is connected to the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2, the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2 is also connected to the output end of the energy storage inductor L1, and the two ends of the first freewheeling diode D1 and the second freewheeling diode D2 after being connected in series are respectively connected to the inverter bus voltage output end.

[0055] The present invention also provides a control method for the active dv / dt filter circuit as described above, comprising:

[0056] The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide zero level for the active dv / dt filter at the same time; the first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in series in reverse order to clamp the voltage to zero level at each rising edge and falling edge of the inverter output voltage, so that the output voltage forms a two-stage step wave form, and the reflected voltage of the first stage step wave and the reflected voltage of the second stage step wave cancel each other out; the first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction to provide freewheeling for the energy storage inductor L1 when the voltage clamp switch is not working; the energy storage inductor L1 stores a part of energy when the first voltage clamp switch T1 and the second voltage clamp switch T2 are in action to reduce the current stress of the voltage clamp switch.

[0057] In this embodiment, the trigger controls the on-time of the voltage clamp switch, and the on-time td of the voltage clamp switch is twice the cable transmission time t t ,in:

[0058]

[0059] l ca is the cable length, v ca The transmission speed of the cable.

[0060] The above design uses an active dv / dt filter to force the output voltage to be clamped to zero level at each rising and falling edge of the inverter output voltage, so that the output voltage forms a two-step wave form. The reflected voltage of the first-step wave and the reflected voltage of the second-step wave cancel each other out, thereby suppressing the reflected voltage at the motor end.

[0061] The active dv / dt filter proposed in the present invention is installed between the inverter output side and the long cable. Figure 5 Taking the U phase as an example, the circuit of the active dv / dt filter includes bus capacitors (C1, C2), voltage clamp switches (T1, T2), freewheeling diodes (D1, D2) and energy storage inductors (L1), as shown in Figure 6 As shown. The bus capacitor is composed of two capacitors connected in series, which provide voltage for the active dv / dt filter. At the same time, the two bus capacitors provide zero level for the active dv / dt filter. The voltage clamp switch is composed of two power devices connected in series in reverse order. Its function is to clamp the voltage to zero level at each rising and falling edge of the inverter output voltage, thereby realizing the output voltage in the form of a two-stage ladder wave. The freewheeling diode is composed of two diodes connected in series. Its function is to provide freewheeling in the energy storage inductor when the voltage clamp switch is not working. The energy storage inductor is composed of power inductors. Its function is to store part of the energy when the voltage clamp switch is in action, thereby reducing the current stress of the voltage clamp switch.

[0062] Connection method: U in of the energy storage inductor is connected to the output end of the inverter, and U out of the energy storage inductor is connected to the long cable; both ends of the bus capacitor are respectively connected to the inverter bus voltage.

[0063] like Figure 7 As shown, the schematic diagram of the signal driving circuit used in the present invention includes an operational amplifier, a trigger circuit and a driving circuit connected in sequence. The voltage-dividing resistors R11 and R12 are used to divide the high voltage of the inverter to obtain a smaller voltage. The divided voltage is compared with the DC power supply to eliminate the influence of the oscillation of the rising and falling edges of the inverter output voltage on the subsequent output. The output voltage of the comparator passes through the trigger circuit to generate the required control signal, and then the driving circuit drives the voltage clamp switch in the power circuit.

[0064] Then, after the active dv / dt filter, the output voltage waveform is as follows Figure 8 As shown, each rising edge and falling edge becomes a two-step wave form.

[0065] Among them, the voltage clamp switch conduction time td should be twice the cable transmission time tt;

[0066]

[0067] Among them, l ca is the cable length, v ca is the transmission speed of the cable;

[0068] When t d =2t t When the reflected voltages at the motor end can cancel each other out, thus suppressing the overvoltage at the motor end. The waveform is as follows: Fig. 9 shown.

[0069] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. Long cable motor overvoltage suppression circuit based on active filter, characterized in that: The circuit includes a power circuit and a drive signal circuit; the power circuit includes a bus capacitor, a voltage clamp switch, a freewheeling diode and an energy storage inductor; the drive signal circuit includes a voltage dividing resistor, a comparator, a trigger circuit and a drive circuit; the power circuit is connected in series between the output side of the inverter and the long cable, and at the same time, the inverter output voltage is connected to the input end of the drive signal circuit, and the output end of the drive signal circuit is connected to the power circuit of the active dv / dt filter to control the working mode of the power circuit; The power circuit of the active dv / dt filter includes a first bus capacitor C1, a second bus capacitor C2, a first voltage clamp switch T1, a second voltage clamp switch T2, a first freewheeling diode D1, a second freewheeling diode D2 and an energy storage inductor L1, wherein: The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide a zero level for the active dv / dt filter; The first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in reverse series, and at each rising edge and falling edge of the inverter output voltage, the voltage is clamped to zero level, so as to realize the output voltage in the form of a two-level step wave; The first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction, and when the voltage clamp switch is not working, the energy storage inductor L1 is freewheeling; The energy storage inductor L1 is composed of a power inductor. When the first voltage clamp switch T1 and the second voltage clamp switch T2 are actuated, a portion of energy is stored to reduce the current stress of the voltage clamp switch.

2. The long cable motor overvoltage suppression circuit based on active filter according to claim 1 is characterized in that: The driving signal circuit includes a voltage-dividing resistor, a comparator, a trigger circuit and a driving circuit. The voltage-dividing resistor includes a first voltage-dividing resistor R11 and a second voltage-dividing resistor R12, wherein one end of the first voltage-dividing resistor R11 is connected to the output side of the inverter, the other end of the first voltage-dividing resistor R11 is connected to one end of the second voltage-dividing resistor R12 and the non-inverting input end of the comparator, the inverting input end of the comparator is connected to the positive electrode of a DC power supply, the other end of the second voltage-dividing resistor R12 and the negative electrode of the DC power supply are both grounded, the output end of the comparator is connected to the input end of the trigger circuit, the output of the trigger circuit is connected to the input end of the driving circuit, and the output end of the driving circuit is connected to the gates of the first voltage clamping switch T1 and the second voltage clamping switch T2.

3. The long cable motor overvoltage suppression circuit based on active filter according to claim 1 is characterized in that: The input end of the energy storage inductor L1 is connected to the output end of the inverter, and the output end of the energy storage inductor L1 is connected to the long cable; the two ends of the first bus capacitor C1 and the second bus capacitor C2 connected in series are respectively connected to the inverter bus voltage output end.

4. The long cable motor overvoltage suppression circuit based on active filter according to claim 1 is characterized in that: Each phase output end of the inverter is correspondingly connected to the power circuit and the drive signal circuit.

5. The long cable motor overvoltage suppression circuit based on active filter according to claim 1 is characterized in that: The first voltage clamp switch T1 and the second voltage clamp switch T2 are switch tubes, wherein the drain of the first voltage clamp switch T1 is connected to the connection end of the first bus capacitor C1 and the second bus capacitor C2, the source of the first voltage clamp switch T1 is connected to the source of the second voltage clamp switch T2, the drain of the second voltage clamp switch T2 is connected to the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2, the series connection end of the first freewheeling diode D1 and the second freewheeling diode D2 is also connected to the output end of the energy storage inductor L1, and the two ends of the first freewheeling diode D1 and the second freewheeling diode D2 after being connected in series are respectively connected to the inverter bus voltage output end.

6. A control method for a long cable motor overvoltage suppression circuit based on an active filter as claimed in any one of claims 1 to 5, characterized in that: include: The first bus capacitor C1 and the second bus capacitor C2 are connected in series to provide voltage for the active dv / dt filter and provide a zero level for the active dv / dt filter; The first voltage clamp switch T1 and the second voltage clamp switch T2 are connected in series in reverse direction. When each rising edge and falling edge of the inverter output voltage arrives, the voltage is clamped to zero level, so that the output voltage forms a two-step wave form, and the reflected voltage of the first step wave and the reflected voltage of the second step wave cancel each other out; the first freewheeling diode D1 and the second freewheeling diode D2 are connected in series in the same direction. When the voltage clamp switch is not working, they continue the current for the energy storage inductor L1; when the first voltage clamp switch T1 and the second voltage clamp switch T2 are in operation, the energy storage inductor L1 stores a part of the energy to reduce the current stress of the voltage clamp switch.

7. The control method of the long cable motor overvoltage suppression circuit based on active filter according to claim 6 is characterized in that: The trigger controls the on-time of the voltage clamp switch, and the on-time td of the voltage clamp switch is twice the cable transmission time. ,in: ; l ca is the cable length, v ca The transmission speed of the cable.

Citation Information

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