A method for suppressing beat frequency in the traction system of permanent magnet synchronous motors for high-speed trains

Abstract

This invention provides a method for suppressing beat frequency in the traction system of a permanent magnet synchronous motor (PMSM) in a high-speed train. The method includes: obtaining the d-axis and q-axis currents in a synchronous rotating coordinate system based on the three-phase currents of the PMSM collected by sensors; generating d-axis and q-axis reference voltage adjustment values ​​using a PI controller based on the given d-axis and q-axis current values ​​and their errors; suppressing the second harmonic frequency fluctuations of the power grid in the d-axis and q-axis currents using a preset quasi-resonant controller; superimposing the outputs of the PI controller and the quasi-resonant controller to obtain the final d-axis and q-axis reference voltages; and finally, passing the generated reference voltages through a PWM circuit to suppress the beat frequency in the PMSM traction system of the high-speed train. Compared with existing control technologies, this invention, by eliminating the LC resonant circuit and using a proposed control algorithm to suppress the beat frequency current, reduces torque ripple and improves system stability.

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 in high-speed trains. 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 skipping phenomenon in the traction system of high-speed trains, 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 weight reduction. 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.

[0005] Existing beat frequency suppression algorithms are mostly designed for induction motor traction systems. The patent document "A beat frequency suppression system and method for electric transmission system of EMU" (CN112311292A) achieves beat frequency suppression by extracting the second harmonic fluctuation component of the bus voltage signal and performing frequency and phase compensation through a beat frequency suppression controller. Essentially, it is an open-loop algorithm that relies on the extracted bus voltage fluctuation component. The patent document "Motor beat frequency suppression method and system, electric transmission control system, storage medium" (CN112751519B) compensates for the given torque or the given slip corresponding to the given torque based on static compensation coefficient and dynamic compensation coefficient, but its implementation is relatively complex. The beat frequency suppression method for permanent magnet synchronous motor traction system of EMU can meet the needs of future high-speed EMUs. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and propose a beat frequency suppression method for the traction system of permanent magnet synchronous motors in high-speed trains, which can effectively reduce low-frequency beat frequency current and torque fluctuations under asynchronous modulation, synchronous modulation and square wave control.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] First, the three-phase current of the permanent magnet motor collected by the current sensor is transformed to obtain the d-axis and q-axis currents in the synchronous rotating coordinate system. Based on the given d-axis and q-axis currents and their errors, a PI controller is used to generate d-axis and q-axis reference voltage adjustment values. A preset quasi-resonant controller is applied to suppress the second harmonic frequency fluctuations of the power grid in the d-axis and q-axis currents. The outputs of the PI controller and the quasi-resonant controller are superimposed 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.

[0009] This invention includes the following steps:

[0010] Step 1: Transform the three-phase motor current collected by the current sensor into a rotating coordinate system.

[0011] Due to inherent problems with single-phase rectifiers, the DC-side voltage exhibits second-harmonic fluctuations, which will generate a Wo in the motor current. e -2w g The low-frequency current fluctuation component and w e +2w g Ignoring high-frequency harmonics, the high-frequency current fluctuation component of the motor can be expressed as:

[0012]

[0013] Among them, i a i b i c The current is the three-phase current of the motor, and t is the time. e w is the angular velocity of the motor. g For the power grid frequency, I s and I h These are the amplitudes of the fundamental current and the fluctuating current, respectively. The phases of the low-frequency and high-frequency fluctuation components;

[0014] The constant amplitude transformation is shown below:

[0015]

[0016] Where θ is the electrical angle.

[0017] Combining equations (1) and (2), the d-axis and q-axis currents in the rotating coordinate system can be obtained as follows:

[0018]

[0019] Among them, i d i q Let i be the d-axis and q-axis currents. d0 i q0 As can be seen from the fundamental currents of the d and q axes, in the rotating coordinate system, the currents of the d and q axes have second harmonic components.

[0020] Step 2: Perform PI control based on the d and q current setpoints and the d and q axis currents after low-pass filtering to output d and q axis voltage adjustment values.

[0021] 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:

[0022]

[0023] Among them, w f =2πf c f c Let be the cutoff frequency of the low-pass filter, and s be a complex variable.

[0024] The filtered d-axis and q-axis currents are subjected to proportional-integral control to obtain the d-axis and q-axis voltage regulation values, calculated as follows:

[0025]

[0026]

[0027] Where, k p k i For PI 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. dPI u qPI This is the output of the PI controller. By adjusting the coefficients of the PI controller, good tracking of the fundamental frequency current can be achieved.

[0028] Step 3: Design a quasi-resonant controller for the second harmonic components of the d-axis and q-axis currents to suppress beat frequency current.

[0029] The resonant controller can operate at a single frequency w nTo 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 control system, a quasi-resonant controller with delay compensation is used, with the transfer function as follows:

[0030]

[0031] Among them, w n For the resonant frequency, w c For the bandwidth of the quasi-resonant controller, θ n This refers to the lag phase angle present in the control system.

[0032] To suppress the second harmonic components of the d-axis and q-axis currents, a resonant frequency of 2ω was used. g The quasi-resonant controller is calculated as follows:

[0033]

[0034] Among them, u dQRSC u qQRSC For the output of the quasi-resonant controller, k r The coefficients of the quasi-resonant controller are determined by adjusting k. r This allows for the suppression of beat frequency current.

[0035] Furthermore, the resonant controller will have a resonant point offset when it is digitally implemented. A bilinear transform with pre-distortion is used to discretize the transfer function of equation (6). The discretization method is as follows:

[0036]

[0037] Among them, T s Let z be the discrete step size and z be the complex variable of the discrete system. According to equations (6) and (8), the discrete quasi-resonant controller transfer function can be obtained as follows:

[0038]

[0039] Among them, a n1 a n2 b n0 b n1 b n2 The coefficient is:

[0040]

[0041] Step 4: Superimpose the outputs of the PI controller and the quasi-resonant controller to obtain the final d-axis and q-axis reference voltages.

[0042] The fundamental current is tracked using a PI controller, and the beat frequency current is suppressed using a quasi-resonant controller. By superimposing the outputs of the two controllers, the final reference voltage can be obtained, as calculated below:

[0043]

[0044] Among them, u d u q This is the final reference voltage.

[0045] 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.

[0046] Based on the generated reference voltage and the acquired DC-side voltage, the modulation ratio and angle are calculated as follows:

[0047]

[0048] Among them, u dc k is the DC-side bus voltage. v and θ v These are the modulation ratio and the angle, respectively.

[0049] 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.

[0050] Beneficial effects:

[0051] This invention patent application addresses the permanent magnet synchronous motor traction system of high-speed trains. With the goal of minimizing the output current pulsation component, the required compensation voltage is obtained through closed-loop control of a second-harmonic quasi-resonant controller. This approach can more effectively suppress beat frequency current and pulsating torque, and is simple to implement and easy to combine with other control strategies, thus meeting the needs of future high-speed trains. Attached Figure Description

[0052] Figure 1 This is a control block diagram of the beat frequency suppression method described in this invention.

[0053] Figure 2 This is a flowchart illustrating the beat frequency suppression method described in this invention.

[0054] Figure 3 Bode plots for the continuous quasi-resonant controller and the discrete quasi-resonant controller at a resonant frequency of 100 Hz.

[0055] Figure 4 The waveforms of motor current, torque, and line voltage under asynchronous modulation without beat frequency suppression algorithm are shown.

[0056] Figure 5 The waveforms of motor current, torque, and line voltage under asynchronous modulation conditions using the beat frequency suppression algorithm of this application.

[0057] Figure 6 The waveforms of motor current, torque, and line voltage under synchronous modulation without beat frequency suppression algorithm are shown.

[0058] 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.

[0059] Figure 8 The waveforms of motor current, torque, and line voltage without beat frequency suppression algorithm under square wave modulation are shown.

[0060] 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

[0061] 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.

[0062] The control block diagram of the beat frequency suppression algorithm of this invention is attached. Figure 1 As shown in the attached diagram, the implementation process of this invention is as follows. Figure 2 As shown, the three-phase current of the permanent magnet motor collected by the current sensor is first transformed to obtain the d-axis and q-axis currents in the synchronous rotating coordinate system. Based on the given d-axis and q-axis currents and the d-axis and q-axis current errors, the PI controller generates the d-axis and q-axis reference voltage adjustment. The preset quasi-resonant controller is used to suppress the second harmonic fluctuation of the power grid in the d-axis and q-axis currents. The outputs of the PI controller and the quasi-resonant controller are superimposed to obtain the final d-axis and q-axis reference voltages. The generated reference voltages are processed by the PWM stage to finally suppress the beat frequency of the permanent magnet synchronous motor traction system of the EMU.

[0063] The specific embodiments of the present invention include the following steps:

[0064] Step 1: Transform the three-phase motor current collected by the current sensor into a rotating coordinate system.

[0065] Due to inherent problems with single-phase rectifiers, the DC-side voltage exhibits second-harmonic fluctuations, which will generate a Wo in the motor current. e -2wg The low-frequency current fluctuation component and w e +2w g Ignoring high-frequency harmonics, the high-frequency current fluctuation component of the motor can be expressed as:

[0066]

[0067] Among them, i a i b i c The current is the three-phase current of the motor, t is time, and w is the current. e w is the angular velocity of the motor. g For the power grid frequency, I s and I h These are the amplitudes of the fundamental current and the fluctuating current, respectively. The phases of the low-frequency and high-frequency fluctuation components;

[0068] The constant amplitude transformation is shown below:

[0069]

[0070] Where θ is the electrical angle.

[0071] Combining equations (1) and (2), the d-axis and q-axis currents in the rotating coordinate system can be obtained as follows:

[0072]

[0073] Among them, i d i q Let i be the d-axis and q-axis currents. d0 i q0 As can be seen from the fundamental currents of the d and q axes, in the rotating coordinate system, the currents of the d and q axes have second harmonic components.

[0074] Step 2: Perform PI control based on the d-axis and q-axis current setpoints and the d-axis and q-axis currents after low-pass filtering to output d-axis and q-axis voltage adjustment values.

[0075] 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:

[0076]

[0077] Among them, w f =2πf c f c Let be the cutoff frequency of the low-pass filter, and s be a complex variable.

[0078] The filtered d-axis and q-axis currents are subjected to proportional-integral control to obtain the d-axis and q-axis voltage regulation values, calculated as follows:

[0079]

[0080] Where, k p k i For PI 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. dPI u qPI This is the output of the PI controller. By adjusting the coefficients of the PI controller, good tracking of the fundamental frequency current can be achieved.

[0081] Step 3: Design a quasi-resonant controller for the second harmonic components of the d-axis and q-axis currents to suppress beat frequency current.

[0082] The resonant controller can operate at a single frequency w 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 control system, a quasi-resonant controller with delay compensation is used, with the transfer function as follows:

[0083]

[0084] Among them, w n For the resonant frequency, w c For the bandwidth of the quasi-resonant controller, θ n This refers to the lag phase angle present in the control system.

[0085] To suppress the second harmonic components of the d-axis and q-axis currents, a resonant frequency of 2ω was used. g The quasi-resonant controller is calculated as follows:

[0086]

[0087] Among them, u dQRSC u qQRSC For the output of the quasi-resonant controller, k r The coefficients of the quasi-resonant controller are determined by adjusting k. r This allows for the suppression of beat frequency current.

[0088] Furthermore, the resonant controller will have a resonant point offset when it is digitally implemented. A bilinear transform with pre-distortion is used to discretize the transfer function of equation (6). The discretization method is as follows:

[0089]

[0090] Among them, T s Let z be the discrete step size and z be the complex variable of the discrete system. According to equations (6) and (8), the discrete quasi-resonant controller transfer function can be obtained as follows:

[0091]

[0092] Among them, a n1 a n2 b n0 b n1 b n2 The coefficient is:

[0093]

[0094] Figure 3 The Bode plots of the continuous quasi-resonant controller and the discrete quasi-resonant controller at a resonant frequency of 100Hz are basically the same, differing only near the Nyquist frequency, proving the correctness of the discretization method used in this invention.

[0095] Step 4: Superimpose the outputs of the PI controller and the quasi-resonant controller to obtain the final d-axis and q-axis reference voltages.

[0096] The fundamental current is tracked using a PI controller, and the beat frequency current is suppressed using a quasi-resonant controller. By superimposing the outputs of the two controllers, the final reference voltage can be obtained, as calculated below:

[0097]

[0098] Among them, u d u q This is the final reference voltage.

[0099] 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.

[0100] Based on the generated reference voltage and the acquired DC-side voltage, the modulation ratio and angle are calculated as follows:

[0101]

[0102] Among them, u dc k is the DC-side bus voltage. v and θv These are the modulation ratio and the angle, respectively.

[0103] 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.

[0104] 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.

[0105] Table 1. Motor phase current fundamental amplitude, beat frequency current amplitude, average torque, and second harmonic torque under different operating conditions.

[0106]

[0107]

[0108] Therefore, the beat frequency suppression method for permanent magnet synchronous motor traction systems in EMUs provided in this application example introduces a second-harmonic quasi-resonant controller into the current closed-loop control strategy of permanent magnet synchronous motor based on a rotating coordinate system. This not only achieves better dynamic response but also effectively eliminates 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, suppresses torque second-harmonic pulsation, and improves system stability.

[0109] 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 beat frequency suppression method for a multiple unit permanent magnet synchronous motor traction system, characterized in that, The method comprises the following steps: Step 1: transform the motor three-phase current collected by the current sensor into a rotating coordinate system; Step 2: perform PI control on the basis of the d-axis and q-axis current set values and the d-axis and q-axis currents after low-pass filtering to output d-axis and q-axis voltage adjustment values; Step 3: design a quasi-resonant controller for the d-axis and q-axis current double-frequency components to suppress the beat frequency current; The quasi-resonant controller with delay compensation is used to suppress the double-frequency components, and the transfer function is as follows: （6） wherein, is the resonant frequency, is the quasi-resonant controller bandwidth, is the phase lag present in the control system; is the complex variable; In order to suppress the d, q axis current double frequency components, a quasi-resonant controller with a resonant frequency of is used, and the following calculation is made: （7） wherein, is an output of the quasi-resonant controller, is a coefficient of the quasi-resonant controller, adjusted by to achieve suppression of the beat frequency current; are d, q-axis currents; is a grid frequency; Step 4: superimpose the outputs of the PI controller and the quasi-resonant controller to obtain the final d-axis and q-axis reference voltages; Step 5: generate the reference voltages through a PWM link to finally realize beat frequency suppression of the EMU permanent magnet synchronous motor traction system.

2. The method of beat suppression as claimed in claim 1, characterized in that In the step 1, ignoring the high frequency harmonic, the low frequency current fluctuation component and the high frequency current fluctuation component in the motor three-phase current are represented as: ​​ （1） wherein is the motor three-phase current, is the time, is the motor angular velocity, is the grid frequency, and are the fundamental current amplitude and the ripple current amplitude, respectively, is the low-frequency ripple component and the high-frequency ripple component phase; The equal-amplitude transformation is as follows: （2） wherein is the electrical angle; Combining equations (1) and (2), the d-axis and q-axis currents in the rotating coordinate system are obtained as follows: （3） wherein, is the d, q-axis current, is the d, q-axis fundamental current; In the rotating coordinate system, the d-axis and q-axis currents have double-frequency components.

3. The method of beat suppression as claimed in claim 2, characterized in that In step 2, the first-order low-pass filter transfer function is as follows: （4） wherein , is the cut-off frequency of the low-pass filter, is a complex variable; The filtered d-axis and q-axis currents are subjected to proportional-integral control to obtain the d-axis and q-axis voltage adjustment values, which are calculated as follows: （5） wherein, is a PI controller coefficient, is a d, q-axis current command, is a d, q-axis current after low pass filter, is an output of the PI controller.

4. The method of beat suppression as defined in claim 1, wherein, In step 3, the transfer function of equation (6) is discretized using the pre-distorted bilinear transformation method, and the discretization method is as follows: （8） wherein is the discrete step size, is the discrete complex variable, and according to equations (6) and (8), the discrete quasi-resonant controller transfer function is given as follows: （9） wherein are coefficients, in particular: （10）。 5. The method of beat suppression as defined in claim 4, wherein, In step 4, the PI controller of step 2 is used to track the fundamental frequency current, and the quasi-resonant controller of step 3 is used to suppress the beat frequency current. Superimposing the outputs of the two controllers can obtain the final reference voltage: （11） wherein, is the final reference voltage.

6. The method of beat suppression as defined in claim 5, wherein, Step 5 includes calculating the modulation ratio and angle as follows using the final reference voltage obtained in step 4 and the collected DC side voltage: （12） wherein is the DC side bus voltage, and are the modulation ratio and angle, respectively; According to the modulation ratio, angle and frequency, asynchronous modulation, synchronous modulation and square wave modulation are realized to generate PWM signals, control the on-off of the switching tube, and finally realize beat frequency suppression of the EMU permanent magnet synchronous motor traction system.

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