A method for suppressing beat frequency in a permanent magnet synchronous motor traction system for high-speed trains based on self-disturbance rejection.

Abstract

This invention provides a beat frequency suppression method for a permanent magnet synchronous motor (PMSM) traction system in a high-speed train based on self-disturbance rejection. The method includes: transforming the three-phase current and voltage of the PMSM to a synchronous rotating coordinate system to construct a mathematical model of the PMSM; constructing a resonant expansion state observer based on the mathematical model to observe second-harmonic disturbances and low-frequency disturbances in the system; generating d- and q-axis reference voltage adjustment values ​​through a proportional controller based on the errors of the d- and q-axis current setpoints and feedback currents; and superimposing the observed disturbances with the output of the proportional controller to obtain the final d- and q-axis reference voltages, thereby achieving beat frequency suppression of the PMSM traction system in the high-speed train. Compared with existing control technologies, this invention, by eliminating the LC resonant circuit, suppresses the beat frequency current through a proposed control algorithm, while compensating for other disturbances, reducing torque ripple, and improving the system's anti-disturbance capability.

Description

Technical Field

[0001] This invention belongs to the field of high-speed trains, specifically relating to a beat frequency suppression method for a permanent magnet synchronous motor traction system of a high-speed train based on self-disturbance rejection. Background Technology

[0002] Because the traction drive system of the EMU uses a single-phase rectifier topology, the input power varies AC with twice the grid frequency, resulting in DC bus voltage fluctuations at twice the grid-side voltage frequency. This pulsating intermediate DC bus voltage further couples with the motor-side inverter, causing significant frequency beating in the traction motor, leading to pulsations in motor torque and current. This frequency beating problem not only degrades the performance of the traction converter but also severely impacts the safety, reliability, and efficiency of the EMU operation.

[0003] Currently, all high-speed trains operating in my country use induction motor traction systems. Permanent magnet motors, on the other hand, have many advantages such as high efficiency, low energy consumption, lightweight, good starting characteristics, low noise, and good maintainability. With the continuous increase in high-speed rail capacity and the increasing number of high-speed trains, the development of high-speed EMUs with efficient and energy-saving permanent magnet motor traction systems has become a development trend.

[0004] To address the frequency beat phenomenon in EMU traction systems, existing technologies mainly include hardware and software solutions. Hardware solutions primarily reduce voltage fluctuations by connecting an LC resonant circuit in parallel with the intermediate DC link or increasing the DC bus capacitance. While simple and effective, this method results in large LC resonant circuits, increasing costs and hindering vehicle lightweighting. Software solutions, without adding any hardware, compensate for output voltage harmonics caused by DC voltage fluctuations through control algorithms. This approach reduces costs, has significant practical value, and is a hot research topic. Existing frequency beat suppression algorithms are mostly designed for induction motor traction systems and do not consider the influence of other disturbances present in the system. In practical systems, the effectiveness of these algorithms is affected, resulting in poor anti-interference capabilities. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and propose a beat frequency suppression method for a permanent magnet synchronous motor traction system of a high-speed train based on self-disturbance rejection. This method can effectively reduce low-frequency beat frequency current and torque fluctuations under asynchronous modulation, synchronous modulation and square wave control, while also compensating for other low-frequency disturbances in the system and improving the system's anti-disturbance capability.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] First, the three-phase current and voltage signals of the permanent magnet synchronous motor collected by the sensors are transformed into a synchronous rotating coordinate system to construct a mathematical model of the permanent magnet synchronous motor. Based on the mathematical model, a resonant expansion state observer is constructed to observe the second harmonic disturbance and low-frequency disturbance in the system. Based on the error of the d-axis current setpoint and feedback current, the d-axis and q-axis reference voltage adjustment values ​​are generated by a proportional controller. The observed disturbance is fed forward and compensated, and then superimposed with the output of the proportional controller to obtain the final d-axis and q-axis reference voltage. The generated reference voltage is processed by a PWM circuit to ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0008] This invention includes the following steps:

[0009] Step 1: The three-phase current and voltage signals of the permanent magnet motor collected by the sensor are transformed into a synchronous rotating coordinate system to construct a mathematical model of the permanent magnet synchronous linear motor.

[0010] Due to inherent problems with single-phase rectifiers, the DC-side voltage exhibits second-harmonic fluctuations, which can be approximated as:

[0011]

[0012] Among them, u dc U is the DC side voltage. dc The average value of the DC voltage, ΔU dc ω represents the voltage fluctuation amplitude. g For the power grid frequency, This is the initial phase.

[0013] The voltage command modulation signal for each phase of the three-phase inverter is defined in cosine form as follows:

[0014] u i =Mcos(ω e t+θ i (2)

[0015] In the formula, M is the modulation depth, i = a, b, c represent the three phases a, b, and c of the motor, respectively, and u a u b u c These represent the three-phase modulation signals, θ a θ b θ c These represent the initial phases of the modulated waves, with a phase difference of 2π / 3, ω. e To modulate the angular frequency of the wave.

[0016] Ignoring the high-order switching harmonics caused by the pulse width modulation stage, the phase voltage of the inverter in the stationary coordinate system is expressed as:

[0017]

[0018] The secondary pulsating component of the DC bus voltage couples with the modulation signal, generating a frequency of ω. e +2ω g and frequency ω e -2ω g High and low beat frequency voltage components.

[0019] The constant amplitude transformation is shown below:

[0020]

[0021] Where θ is the electrical angle.

[0022] The mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system can be expressed as:

[0023]

[0024] Among them, u d u q Let i be the d-axis and q-axis voltages. d i q Let L be the d-axis and q-axis currents. d L q R represents the d-axis and q-axis currents. s For the stator resistance, ω e Let ψ be the angular velocity of the motor. f Let p be the flux linkage of the permanent magnet and p be the differential operator.

[0025] Because there is ω in the motor voltage e -2ω g The low-frequency fluctuation components, in the rotating coordinate system, exhibit second harmonic components and other components in the d-axis and q-axis voltages, specifically as follows:

[0026]

[0027] Where u d0 u q0 U is the fundamental voltage along the d and q axes. h The amplitude of the second harmonic voltage. For the second harmonic voltage phase, u df u qf The remaining voltage components.

[0028] Step 2: Construct a resonant expansion state observer based on the mathematical model, and observe the second harmonic disturbance and other low-frequency disturbances in the system based on the constructed observer.

[0029] First, transform the expression into the form of a differential equation:

[0030]

[0031] in, This represents the second harmonic voltage. It can be seen that the presence of second harmonic voltage is the direct cause of the motor current beat frequency. If the harmonic voltage can be observed and compensated, the beat frequency current can be suppressed.

[0032] The resonant controller can operate at a single frequency ω n To achieve steady-state error-free tracking of AC signals, a high gain is generated at a certain frequency, but significant attenuation occurs for other frequency signals, resulting in an excessively narrow controller bandwidth. Furthermore, the presence of harmonics in the traction power grid reduces the anti-interference capability of the control system. Therefore, a quasi-resonant controller is employed to improve system stability. Simultaneously, to compensate for the phase lag in the system, a quasi-resonant controller with delay compensation is used, whose transfer function is:

[0033]

[0034] Where, ω n ω is the resonant frequency. c For the bandwidth of the quasi-resonant controller, θ n Let s be the phase lag angle present in the control system, and let s be a complex variable.

[0035] To observe the second harmonic voltage waves along the d and q axes, a resonant frequency of 2ω was used. g Based on the differential equation, the quasi-resonant controller can be used to construct the following resonant extended state observer:

[0036]

[0037] Where β1 and β2 are the observer coefficients, For the observed d-axis and q-axis currents, ε d , ε q For d-axis and q-axis current deviations, For the observed d and q second harmonic voltage perturbations, For the remaining disturbances along the d and q axes, the second harmonic disturbance and the remaining disturbances can be observed by adjusting the observer coefficients.

[0038] Step 3: Generate d-axis and q-axis reference voltage adjustment values ​​using a proportional controller based on the given d-axis and q-axis currents and the d-axis and q-axis current errors.

[0039] First, design a low-pass filter to filter out i d i q The second harmonic component and other high-frequency components are present in the filter. The transfer function of the first-order low-pass filter is:

[0040]

[0041] Where, ω f =2πf c f c This is the cutoff frequency of the low-pass filter.

[0042] The filtered d-axis and q-axis currents are proportionally controlled to obtain the d-axis and q-axis voltage adjustment values, calculated as follows:

[0043]

[0044] Where, k p For proportional controller coefficients, Given the d-axis and q-axis currents, i dLPF i qLPF U represents the d-axis and q-axis currents after passing through a low-pass filter. dP u qP This is the output of the proportional controller. By adjusting the controller's coefficients, tracking of the base frequency current can be achieved.

[0045] Step 4: Feedforward compensation is applied to the observed disturbance, and the result is superimposed on the output of the proportional controller to obtain the final d-axis and q-axis reference voltages.

[0046] The fundamental current is tracked by a proportional controller, and the second harmonic voltage and other disturbances are observed by a resonant extended state observer. The final reference voltage is obtained by superimposing the outputs of the two, as calculated below:

[0047]

[0048] Among them, u d u q This is the final reference voltage.

[0049] By substituting the expression into the expression, it can be simplified to:

[0050]

[0051] Therefore, by adding an observer and performing disturbance feedforward compensation, the fundamental current can be tracked simply by adjusting the coefficient of the proportional controller, while beat frequency suppression and disturbance compensation can also be achieved.

[0052] Step 5: The generated reference voltage is processed through a PWM circuit to ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0053] Based on the generated reference voltage and the acquired DC-side voltage, the modulation ratio and angle are calculated as follows:

[0054]

[0055] Among them, u dck is the DC-side bus voltage. v and θ v These are the modulation ratio and the angle, respectively.

[0056] Asynchronous modulation, synchronous modulation, and square wave modulation are achieved based on modulation ratio, angle, and frequency to generate PWM signals, control the on / off state of the switching transistors, and ultimately suppress beat frequency in the permanent magnet synchronous motor traction system of the EMU.

[0057] Beneficial effects:

[0058] The beat frequency suppression method for permanent magnet synchronous motor traction systems of EMUs proposed in this invention differs from the traditional method of using DC-side pulsating voltage for open-loop compensation. This scheme obtains the required compensation voltage through a resonant extended state observer, which can more effectively suppress beat frequency current and pulsating torque. It is applicable to various modulation strategies such as asynchronous modulation, synchronous modulation, and square wave control. Attached Figure Description

[0059] Figure 1 This is a control block diagram of the beat frequency suppression method described in this invention.

[0060] Figure 2 This is a block diagram of the d-axis quasi-resonant extended state observer described in this invention.

[0061] Figure 3 This is a block diagram of the q-axis quasi-resonant extended state observer described in this invention.

[0062] Figure 4 The waveforms of motor current, torque, and line voltage under asynchronous modulation without beat frequency suppression algorithm are shown.

[0063] Figure 5 The waveforms of motor current, torque, and line voltage under asynchronous modulation conditions using the beat frequency suppression algorithm of this application.

[0064] Figure 6 The waveforms of motor current, torque, and line voltage under synchronous modulation without beat frequency suppression algorithm are shown.

[0065] Figure 7 The waveforms of motor current, torque, and line voltage using the beat frequency suppression algorithm of this application under synchronous modulation conditions are shown.

[0066] Figure 8 The waveforms of motor current, torque, and line voltage under square wave modulation without beat frequency suppression algorithm are shown.

[0067] Figure 9 The waveforms of motor current, torque, and line voltage using the beat frequency suppression algorithm of this application under square wave modulation are shown. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0069] The control block diagram of the beat frequency suppression algorithm of the present invention is as follows: Figure 1 As shown, the d-axis and q-axis quasi-resonant extended state observers are respectively as follows: Figure 2 and Figure 3 As shown, the three-phase current and voltage signals of the permanent magnet motor collected by the sensors are first transformed into a synchronous rotating coordinate system to construct a mathematical model of the permanent magnet synchronous linear motor. Based on the mathematical model, a resonant expansion state observer is constructed to observe the second harmonic disturbance and other low-frequency disturbances in the system. Based on the given d-axis and q-axis currents and their errors, a proportional controller generates d-axis and q-axis reference voltage adjustment values. The observed disturbances are then fed forward and compensated, and superimposed with the output of the proportional controller to obtain the final d-axis and q-axis reference voltages. The generated reference voltages are then processed through a PWM circuit to ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0070] The specific embodiments of the present invention include the following steps:

[0071] Step 1: Transform the three-phase current and voltage signals of the permanent magnet motor collected by the sensor into a synchronous rotating coordinate system to construct a mathematical model of the permanent magnet synchronous linear motor.

[0072] Due to inherent problems with single-phase rectifiers, the DC-side voltage exhibits second-harmonic fluctuations, which can be approximated as:

[0073]

[0074] Among them, u dc U is the DC side voltage. dc The average value of the DC voltage, ΔU dc ω represents the voltage fluctuation amplitude. g For the power grid frequency, This is the initial phase.

[0075] The voltage command modulation signal for each phase of the three-phase inverter is defined in cosine form as follows:

[0076] u i =Mcos(ω e t+θ i (2)

[0077] In the formula, M is the modulation depth, i = a, b, c represent the three phases a, b, and c of the motor, respectively, and u a u b u c These represent the three-phase modulation signals, θ a θ b θ c These represent the initial phases of the modulated waves, with a phase difference of 2π / 3, ω. e To modulate the angular frequency of the wave.

[0078] Ignoring the high-order switching harmonics caused by the pulse width modulation stage, the phase voltage of the inverter in the stationary coordinate system is expressed as:

[0079]

[0080] The secondary pulsating component of the DC bus voltage couples with the modulation signal, generating a frequency of ω. e +2ω g and frequency ω e -2ω g High and low beat frequency voltage components.

[0081] The constant amplitude transformation is shown below:

[0082]

[0083] Where θ is the electrical angle.

[0084] The mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system can be expressed as:

[0085]

[0086] Among them, u d u q Let i be the d-axis and q-axis voltages. d i q Let L be the d-axis and q-axis currents. d L q R represents the d-axis and q-axis currents. s For the stator resistance, ω e Let ψ be the angular velocity of the motor. f Let p be the flux linkage of the permanent magnet and p be the differential operator.

[0087] Because there is ω in the motor voltage e -2ω g The low-frequency fluctuation components, in the rotating coordinate system, exhibit second harmonic components and other components in the d-axis and q-axis voltages, specifically as follows:

[0088]

[0089] Where u d0 uq0 U is the fundamental voltage along the d and q axes. h The amplitude of the second harmonic voltage. For the second harmonic voltage phase, u df u qf The remaining voltage components.

[0090] Step 2: Construct a resonant extended state observer based on the mathematical model, and observe the second harmonic disturbance and other low-frequency disturbances in the system based on the constructed resonant extended state observer.

[0091] First, transform the expression into the form of a differential equation:

[0092]

[0093] in, This represents the second harmonic voltage. It can be seen that the presence of second harmonic voltage is the direct cause of the motor current beat frequency. If the harmonic voltage can be observed and compensated, the beat frequency current can be suppressed.

[0094] The resonant controller can operate at a single frequency ω n To achieve steady-state error-free tracking of AC signals, a high gain is generated at a certain frequency, but significant attenuation occurs for other frequency signals, resulting in an excessively narrow controller bandwidth. Furthermore, the presence of harmonics in the traction power grid reduces the anti-interference capability of the control system. Therefore, a quasi-resonant controller is employed to improve system stability. Simultaneously, to compensate for the phase lag in the system, a quasi-resonant controller with delay compensation is used, whose transfer function is:

[0095]

[0096] Where, ω n ω is the resonant frequency. c For the bandwidth of the quasi-resonant controller, θ n Let s be the phase lag angle present in the control system, and let s be a complex variable.

[0097] To observe the second harmonic voltage waves along the d and q axes, a resonant frequency of 2ω was used. g Based on the differential equation, the quasi-resonant controller can be used to construct the following quasi-resonant extended state observer:

[0098]

[0099] Where β1 and β2 are the observer coefficients, For the observed d-axis and q-axis currents, ε d , ε q For d-axis and q-axis current deviations, For the observed d and q second harmonic voltage perturbations, To observe the remaining disturbances along the d and q axes, the quasi-resonant extended state observer is digitally discretized. By adjusting the observer coefficients, once the observer converges, the second harmonic disturbance and other disturbances can be observed. The block diagram of the d- and q-axis quasi-resonant extended state observer is shown below. Figure 2 and Figure 3 As shown, the implementation process can be explained more clearly.

[0100] Step 3: Generate d-axis and q-axis reference voltage adjustment values ​​using a proportional controller based on the given d-axis and q-axis currents and the d-axis and q-axis current errors.

[0101] First, design a low-pass filter to filter out i d i q The second harmonic component and other high-frequency components are present in the filter. The transfer function of the first-order low-pass filter is:

[0102]

[0103] Where ω f =2πf c f c This is the cutoff frequency of the low-pass filter.

[0104] The filtered d-axis and q-axis currents are proportionally controlled to obtain the d-axis and q-axis voltage adjustment values, calculated as follows:

[0105]

[0106] Where, k p For proportional controller coefficients, Given the d-axis and q-axis currents, i dLPF i qLPF U represents the d-axis and q-axis currents after passing through a low-pass filter. dP u qP This is the output of the proportional controller. By adjusting the controller's coefficients, tracking of the base frequency current can be achieved.

[0107] Step 4: Feedforward compensation is applied to the observed disturbance, and the result is superimposed on the output of the proportional controller to obtain the final d-axis and q-axis reference voltages.

[0108] The fundamental current is tracked by a proportional controller, and the second harmonic voltage and other disturbances are observed by a resonant extended state observer. The final reference voltage is obtained by superimposing the outputs of the two, as calculated below:

[0109]

[0110] Among them, u d u q This is the final reference voltage.

[0111] By substituting the expression into the equation, it can be simplified to:

[0112]

[0113] Therefore, by adding an observer and performing disturbance feedforward compensation, the fundamental current can be tracked simply by adjusting the coefficient of the proportional controller, while beat frequency suppression and disturbance compensation can also be achieved.

[0114] Step 5: The generated reference voltage passes through the PWM circuit to ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0115] Based on the generated reference voltage and the acquired DC-side voltage, the modulation ratio and angle are calculated as follows:

[0116]

[0117] Among them, u dc k is the DC-side bus voltage. v and θ v These are the modulation ratio and the angle, respectively.

[0118] Different modulation algorithms (asynchronous modulation, synchronous modulation, square wave modulation) are implemented based on the modulation ratio, angle, and frequency to generate PWM signals, control the switching transistors, and ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0119] As an embodiment of this application, the beat frequency suppression algorithm without current and the beat frequency suppression algorithm of this application were verified under the same traction power supply voltage and load conditions in three cases: asynchronous modulation, synchronous modulation, and square wave modulation. The results of motor A-phase current, output torque, and line voltage are shown in the example of the beat frequency suppression algorithm without current under asynchronous modulation. Figure 4 In asynchronous modulation cases, the beat frequency suppression algorithm of this application is used. Figure 5 No beat frequency suppression algorithm under synchronous modulation Figure 6 In the case of synchronous modulation, the beat frequency suppression algorithm of this application is used. Figure 7 No beat frequency suppression algorithm in the case of square wave modulation Figure 8 In the case of square wave modulation, the beat frequency suppression algorithm of this application is used. Figure 9 As shown in Table 1, the comparison results of the fundamental amplitude of the motor phase current, the beat frequency current amplitude, the average torque, and the second harmonic torque are as follows. It can be seen that the method of this application has a good beat frequency suppression effect.

[0120] Table 1. Motor phase current fundamental amplitude, beat frequency current amplitude, average torque, and second harmonic torque under different operating conditions.

[0121] Operating conditions Phase current fundamental amplitude (A) Beat frequency current amplitude (A) Average torque (Nm) Second harmonic torque (Nm) Asynchronous modulation beat frequency suppression 366 57.4 1912 318 Asynchronous modulation employs beat frequency suppression 366 3.1 1912 43.7 Synchronous modulation without beat frequency suppression 366 54.4 1914 305 Synchronization modulation employs beat frequency suppression 366 3.1 1916 42.5 Square wave modulation without beat frequency suppression 453 172.8 1790 1163 Square wave modulation employs beat frequency suppression 453 14.4 1815 55.1

[0122] Therefore, the beat frequency suppression method for permanent magnet synchronous motor traction systems of EMUs provided in this application example introduces a quasi-resonant extended state observer into the current closed-loop control strategy of permanent magnet synchronous motor based on a rotating coordinate system. This method can effectively eliminate low-frequency harmonics in the three-phase current of the motor due to the presence of secondary ripple in the DC voltage of the single-phase rectifier, suppress torque second harmonic pulsation, compensate for system disturbances, and improve the anti-interference performance of the system.

[0123] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing beat frequency in a permanent magnet synchronous motor traction system for high-speed trains based on self-disturbance rejection, characterized in that, Includes the following steps: Step 1: Transform the three-phase current and voltage signals of the permanent magnet synchronous motor collected by the sensor into a synchronous rotating coordinate system to construct a mathematical model of the permanent magnet synchronous motor; Step 2: Construct a resonant extended state observer based on the mathematical model, and observe the second harmonic disturbance and low-frequency disturbance in the traction system based on the constructed resonant extended state observer; The mathematical model of the permanent magnet synchronous motor in the synchronous rotating coordinate system is transformed into the form of differential equations: (7) in, For the d-axis and q-axis fundamental voltages, The phase of the second harmonic voltage. For the remaining voltage components, For d-axis and q-axis currents, For d-axis and q-axis inductance, For stator resistance, The angular velocity of the motor. It is a permanent magnet flux linkage. , representing the second harmonic voltage; This represents the amplitude of the second harmonic voltage. The resonant frequency; It is a differential operator; To observe the second harmonic voltage frequencies along the d and q axes, a resonant frequency of [frequency value missing] was used. The quasi-resonant controller has the following transfer function: (8) in, The resonant frequency, For the bandwidth of the quasi-resonant controller, The lag phase angle present in the system. It is a complex variable; Based on the differential equation, the following resonant extended state observer is constructed: (9) in, For observer coefficients, For the observed d-axis and q-axis currents, For d-axis and q-axis current deviations, For the observed d and q second harmonic voltage perturbations, For the remaining perturbations along the d and q axes observed; Step 3: Based on the given d-axis and q-axis currents and the d-axis and q-axis current samples after first-order low-pass filtering, generate the d-axis and q-axis reference voltage adjustment values ​​through a proportional controller; Step 4: Feedforward compensation is applied to the observed disturbance, and the result is superimposed on the output of the proportional controller to obtain the final d-axis and q-axis reference voltages; Step 5: The generated reference voltage is processed through a PWM circuit to ultimately suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

2. The beat frequency suppression method according to claim 1, characterized in that, In step 1, the presence of second-harmonic frequency fluctuations in the DC-side voltage is represented as follows: (1) in, DC side voltage This is the average value of the DC voltage. This refers to the voltage fluctuation amplitude. For the power grid frequency, This is the initial phase; The voltage command modulation signal for each phase of the three-phase inverter is defined in cosine form as follows: (2) In the formula, M is the modulation depth. These represent the three phases a, b, and c of the motor, respectively. These represent the three-phase modulation signals, These represent the initial phases of the modulated wave, and their mutual differences are... , For the modulation wave angular frequency; Ignoring the high-order switching harmonics caused by the pulse width modulation stage, the phase voltage of the inverter in the stationary coordinate system is expressed as: (3) The secondary pulsating component of the DC bus voltage couples with the modulation signal, generating a frequency of... and frequency High and low beat frequency voltage components; The mathematical model of a permanent magnet synchronous motor in a synchronous rotating coordinate system is expressed as follows: (5) in, For d-axis and q-axis voltages, For d-axis and q-axis currents, For d-axis and q-axis inductance, For stator resistance, The angular velocity of the motor. It is a permanent magnet flux linkage. It is a differential operator; Because there is a frequency in the motor voltage. and frequency The fluctuation components, in the rotating coordinate system, have second harmonic components and other components in the d-axis and q-axis voltages, specifically: (6) in For the d-axis and q-axis fundamental voltages, The amplitude of the second harmonic voltage. The phase of the second harmonic voltage. The remaining voltage components.

3. The beat frequency suppression method according to claim 2, characterized in that, In step 3, the transfer function of the first-order low-pass filter is: (10) in, , This is the cutoff frequency of the low-pass filter; The filtered d-axis and q-axis currents are proportionally controlled to obtain the d-axis and q-axis voltage adjustment values, calculated as follows: (11) in, For proportional controller coefficients, Given the d-axis and q-axis currents, These are the d-axis and q-axis currents after passing through a low-pass filter. This is the output of the proportional controller.

4. The beat frequency suppression method according to claim 3, characterized in that, In step 4, the proportional controller from step 3 is used to track the fundamental current, and the quasi-resonant extended state observer from step 2 is used to observe the second harmonic voltage and low-frequency disturbance. The outputs of the two are superimposed to obtain the final reference voltage, calculated as follows: (12) in, This is the final reference voltage; For proportional controller coefficients, This is the output of the proportional controller; For d-axis and q-axis currents, For d-axis and q-axis inductance, For stator resistance, The angular velocity of the motor. For permanent magnet flux linkage; For the observed d and q second harmonic voltage perturbations, The remaining perturbations on the d and q axes are observed.

5. The beat frequency suppression method according to claim 4, characterized in that, In step 5: based on the generated reference voltage and the acquired DC-side voltage, the modulation ratio and angle are calculated as follows: (13) in, This is the DC-side bus voltage. and These are the modulation ratio and the angle, respectively. Asynchronous modulation, synchronous modulation, and square wave modulation are achieved based on modulation ratio, angle, and frequency to generate PWM signals, control the on / off state of the switching transistors, and ultimately suppress beat frequency in the permanent magnet synchronous motor traction system of the EMU.

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