High-precision prediction method and system for high-frequency frequency domain characteristics and time domain waveforms of electromagnetic equipment system

Abstract

The application discloses a kind of high-frequency frequency domain characteristics and time-domain waveform high-precision prediction method and system of electromagnetic equipment system, including steps: (1) cable, electromagnetic equipment winding is divided into cascaded multi-conductor minimum unit;(2) establish cable, electromagnetic equipment winding high-precision multi-conductor minimum circuit unit model;(3) finite element simulation calculation parasitic parameter, setting minimum circuit unit model parameter;(4) the transmission matrix calculation of minimum circuit unit, cable, electromagnetic equipment winding system;(5) according to the connection form of electromagnetic equipment winding end and high-frequency characteristic measurement, calculate high-frequency frequency domain characteristics;(6) the spectrum analysis of inverter output PWM voltage, predict high-frequency time-domain waveform.The application can quickly and accurately predict the high-frequency frequency domain and time-domain characteristics of electromagnetic equipment system at the design stage or online operation, which is of great significance for improving the reliability of electromagnetic equipment system driven by power electronic converter.

Description

Technical Field

[0001] This invention belongs to the field of power electronics and electromagnetic equipment system modeling and prediction technology, and relates to a method and system for high-precision prediction of high-frequency frequency domain characteristics and time domain waveforms of electromagnetic equipment systems. Background Technology

[0002] With the rapid development of power electronics technology, power electronic converters based on PWM (Pulse-Width Modulation) technology have been widely used in various electromagnetic equipment systems such as motors, transformers, reactors, and inductors. To improve system power density and efficiency, the switching frequency of power electronic converters is constantly increasing. However, this higher frequency also brings negative effects such as high voltage spikes, high common-mode current, and high EMI (Electromagnetic Interference), significantly reducing the reliability of electromagnetic equipment systems.

[0003] The essence of the negative effects of high-frequency power electronic converters lies in the strong coupling of internal parasitic parameters of electromagnetic equipment and its connecting lines under high-frequency PWM excitation, inducing undesirable resonances. For example, in a system driven by an inverter via a long cable, the high-voltage slew rate PWM voltage can generate significantly amplified high-frequency voltage spikes at the first turn of the winding, the neutral point, or other equivalent nodes, causing excessive voltage stress on the winding insulation. When this stress exceeds the PDIV (Partial Discharge Inception Voltage), partial discharge occurs, and as the discharge accumulates, the PDIV decreases, partial discharge intensifies, and ultimately accelerates insulation degradation and shortens equipment life. Therefore, the first turn of the winding, the neutral point, or the equivalent neutral node are usually weak points in voltage stress and should be given special attention.

[0004] The voltage spike oscillation frequencies at different nodes typically correspond to the resonant frequencies of the system's common-mode / differential-mode impedance. Reference 1 (M. Memon, M. Diab, and X. Yuan, "Mitigation of Machine Neutral Point Overvoltage in SiC Motor Drives by Controlling Antiresonance Frequency and Switching Frequency," IEEE Journal of Emerging and Selected Topics in PowerElectronics, vol. 13, no. 2, pp. 1514-1527, 2025) indicates that when the common-mode impedance resonant frequency of the system composed of cables and electromagnetic equipment approaches the converter's switching frequency, a spike up to six times the bus voltage may appear at the neutral point. Therefore, accurately and quickly predicting the high-frequency domain characteristics and time-domain waveforms of electromagnetic equipment driven by power electronic converters during the design phase or online operation is of great significance for assessing the high-frequency negative impacts of the electromagnetic equipment system caused by the power electronic converter and for taking targeted optimization measures.

[0005] Existing high-precision prediction methods are mainly based on time-domain simulation of refined multi-conductor transmission line circuit models. Circuit simulation software can predict system impedance curves, first-turn / neutral point voltage spikes, and common-mode currents during the design phase (see reference 2, S. Sundeep, J. Wang, and A. Griffo, "Holistic Modeling of High-Frequency Behavior of Inverter-Fed Machine Winding, Considering MutualCouplings in Time Domain," IEEE Transactions on Industry Applications, vol.57, no. 6, pp. 6044-6057, 2021). However, these methods involve complex modeling, require frequency-varying parameter fitting, and often have long simulation times. The calculation time increases significantly with cable length and the number of winding turns. For long cables or multi-turn winding systems, the simulation time may reach days or weeks, making it difficult to meet the rapid evaluation needs during the design phase or online operation. This affects the optimization design of high-frequency matching, dv / dt filters, and the implementation of reliable online operation and maintenance. Summary of the Invention

[0006] The technical problem to be solved by this invention is to propose a general and efficient method for high-precision prediction of the high-frequency characteristics and time-domain waveforms of electromagnetic equipment systems driven by power electronic converters. The electromagnetic equipment includes, but is not limited to, electromagnetic devices with windings or multi-conductor structures such as motors, transformers, reactors, and inductors. This method enables rapid and accurate prediction of the frequency and time-domain high-frequency characteristics of the electromagnetic equipment system during the design phase or online operation, including but not limited to common-mode impedance curves, differential-mode impedance curves, first-turn voltage spikes of windings, neutral point voltage spikes, and common-mode currents. This provides a basis for high-frequency matching of the system, dv / dt filter design, insulation design, and online status monitoring of the system.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] First, this invention discloses a high-precision prediction method for the high-frequency domain characteristics and time-domain waveforms of an electromagnetic equipment system driven by a power electronic converter. The electromagnetic equipment system consists of an m-phase power electronic converter, an m-phase n-core cable (n≥m), and m-phase electromagnetic equipment. The electromagnetic equipment is a device with multi-turn windings or multi-conductor structures, including but not limited to motors, transformers, reactors, and inductors. The main steps of this method are as follows:

[0009] (1) Divide the windings of the cable and the electromagnetic equipment into N sections respectively. c 1 and N s A system composed of cascaded multi-conductor minimum units;

[0010] (2) Establish high-precision multi-conductor minimum circuit unit models for cables and electromagnetic equipment respectively;

[0011] (3) Based on the impedance and capacitance parameters of the unit length cable and electromagnetic equipment winding in the key frequency band, and according to the actual cable and winding conductor length corresponding to the multi-conductor minimum unit model, the parameters such as self impedance, mutual impedance, capacitance to ground, phase-to-phase capacitance and mutual capacitance in the multi-conductor minimum circuit unit model of the cable and electromagnetic equipment winding are calculated proportionally.

[0012] (4) Based on the multi-conductor minimum circuit unit model and its quantity of cable and electromagnetic equipment respectively, calculate the transmission matrix corresponding to the minimum circuit unit model of cable and electromagnetic equipment;

[0013] (5) Determine the equation relationship between input / output voltage and current based on the winding end of the electromagnetic equipment and the circuit connection form when measuring different high-frequency characteristics. Use circuit principles and matrix operations to solve for the high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter.

[0014] (6) Harmonic decomposition is performed on the PWM pulse voltage output by the power electronic converter. Based on the harmonic amplitude and phase of the PWM pulse voltage and the high frequency domain characteristics of the system, the high frequency time domain waveforms such as the first turn voltage spike of the winding, the neutral point voltage spike and the common mode current of the electromagnetic equipment under the action of the PWM pulse voltage of the power electronic converter are predicted.

[0015] The minimum number of multi-conductor units N in the above-mentioned cables c The determination method is as follows: First, based on the rise time t of the PWM pulse voltage output by the power electronic converter... r The upper limit frequency f of the effective spectrum of the PWM pulse output voltage is calculated. max Then the upper limit frequency f max Converted to the minimum wavelength λ corresponding to the upper limit frequency of PWM voltage min Furthermore, based on the lumped parameter circuit assumption, the actual cable length l corresponding to the smallest circuit unit of the cable is calculated. c =M λ min (0 < M ≤ 0.1, in practice M is usually taken as 0.05). Determine l c Then, use the total cable length L c Divide by l c That is, the total number N of the smallest cable units is obtained. c .

[0016] The minimum number of multi-conductor units N in the above-mentioned electromagnetic equipment s The method for determining the number N of each phase winding of the electromagnetic equipment is as follows: w and the number of turns N of each winding t Multiplying them together gives the minimum number of circuit units N for the electromagnetic equipment. s .

[0017] The high-precision multi-conductor minimum circuit unit model of the above cable is a 2n-terminal network containing n input ports and n output ports. It is composed of m-phase self-impedance, nm core ground self-impedance, m-phase mutual impedance, m-phase-to-ground mutual impedance, m-phase-to-ground capacitance, m-phase-to-phase capacitance, and nm core ground mutual capacitance. Its connection structure is as follows: each input port and output port is connected in series by the self-impedance of the corresponding phase of the port, the mutual impedance of the phase to other phases, and the mutual impedance of the phase to ground; between each output port, it is composed of the phase-to-phase capacitance and the phase-to-ground capacitance.

[0018] The high-precision multi-conductor minimum circuit unit model of the aforementioned electromagnetic equipment is a two-port network representing an actual single-turn winding. It consists of the self-inductance, self-resistance, capacitance to ground, and mutual capacitance with the next turn winding of the single-turn winding. Its connection structure is as follows: each input port and output port is connected in series by the self-impedance of the turn and the mutual impedance between the turn and other turns, and then connected in parallel with the mutual capacitance of the next turn winding; the input port is connected to ground by the half-turn capacitance of the turn; the output port is connected to ground by the half-turn capacitance of the turn.

[0019] The two-port network structure of the high-precision multi-conductor minimum circuit unit model of the above electromagnetic equipment, when m≥2, i.e. for electromagnetic equipment with multi-phase windings, in order to facilitate subsequent matrix operations, connect the ground wires of the two-port networks corresponding to the single-turn windings of different phases to obtain a 2(m+1)-terminal network, which constitutes the high-precision multi-conductor minimum circuit unit model of the electromagnetic equipment.

[0020] The steps for obtaining the impedance and capacitance parameters of the cable and electromagnetic equipment windings within the aforementioned key frequency bands are as follows: Finite element electromagnetic simulation models of the cable and electromagnetic equipment are established respectively. The built-in electrostatic field simulator and eddy current field simulator are used to calculate and obtain the impedance and capacitance parameters per unit length of the cable and electromagnetic equipment windings, including self-impedance, mutual impedance, capacitance to ground, phase-to-phase capacitance, and mutual capacitance. The key frequency band setting should include the main resonant frequencies of the cable and electromagnetic equipment, generally set to 100kHz to 100MHz.

[0021] The calculation steps for the transmission matrix corresponding to the minimum circuit unit model of the cable and electromagnetic equipment are as follows: First, based on the multi-conductor minimum circuit unit model of the cable and electromagnetic equipment, obtain the vectors representing the input and output voltages [U]. i U o ] and input / output current [I i , I o The admittance matrix representing the relationship between [U] is then used to perform matrix operations, converting the admittance matrix into a vector representing the input voltage and current [U]. i , I i ] and output voltage and current [U o , I o The transmission matrix of the relationship between [] is used to obtain the transmission matrices of the multi-conductor minimum circuit unit model of cables and electromagnetic equipment, respectively T. c and T s Then, based on the minimum number of units N... c and N s The power operation yields the transmission matrices for the cable and electromagnetic equipment, respectively (T). c ) Nc and (T) s ) Ns ;

[0022] The specific steps for solving the high-frequency domain characteristics of the aforementioned electromagnetic equipment system are as follows: Determine the input and output voltage and current U based on the transfer matrix. i U o , I i , I o The two equations relating the four quantities determine the final output voltage and current U based on the connection configuration at the ends of the electromagnetic equipment windings. o , I o The equations are then used to determine the voltage and current relationships for different circuit connections during high-frequency characteristic measurements. Finally, the equations for U under different input voltage excitations are obtained using circuit principles and matrix operations. i The input current I of the system under (s) i (s), Output voltage and current U o (s), I o (s), and the voltage U of key nodes such as the first turn of the winding and the neutral point. p ( ), where s is the complex frequency; then... Substituting (j is the imaginary unit, f is the frequency) yields the high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter.

[0023] The high-frequency domain characteristics of the electromagnetic equipment system driven by the aforementioned power electronic converter include: the common-mode impedance curve and differential-mode impedance curve of the cable, the electromagnetic equipment winding, and the system composed of the cable and the electromagnetic equipment; the transfer function of the first-turn voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter; and the transfer function of the neutral point of the electromagnetic equipment winding relative to the output voltage of the power electronic converter. The input voltage U is obtained by solving for each impedance curve based on its corresponding measurement circuit connection. i ( ) / divided by the input current I i ( The node voltage U is obtained by solving various transfer functions based on their corresponding measurement circuit connections. p ( Divide by the input current U i ( )get.

[0024] The neutral point of the aforementioned electromagnetic equipment winding refers to: the common connection point of a star- or Y-connected winding, or the midpoint of a delta-connected winding or a single-phase winding.

[0025] The high-frequency time-domain characteristics of the electromagnetic equipment winding first-turn voltage spike, neutral point voltage spike, and common-mode current under the action of the aforementioned power electronic converter PWM pulse voltage are predicted using the following steps: First, the inverter output voltage is Fourier decomposed, with the AC component of the switching frequency as the fundamental wave and the upper limit of the equivalent effective bandwidth of the PWM pulse voltage as the highest harmonic, to obtain the amplitude and phase of the PWM pulse voltage harmonics of each frequency; then, based on the previously obtained transfer function of the electromagnetic equipment winding first-turn voltage relative to the power electronic converter output voltage, the voltage... The high-frequency domain characteristics, such as the transfer function of the neutral voltage of the magnetic equipment winding relative to the output voltage of the power electronic converter and the common-mode impedance curve, are obtained. The frequency domain responses of the first-turn voltage, neutral point voltage, and common-mode current of the electromagnetic equipment winding under the action of each harmonic of the PWM pulse voltage of the power electronic converter are calculated. Finally, the results of each harmonic action are added together, and the frequency domain response waveform is transformed back to the time domain using inverse Fourier transform, thus obtaining the high-frequency time domain waveforms of the first-turn voltage spike of the electromagnetic equipment winding, the neutral point voltage spike of the motor, and the common-mode current driven by the power electronic converter.

[0026] Furthermore, the present invention also proposes an electronic system comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the method described in the present invention.

[0027] The present invention adopts the above technical solution and has the following technical effects compared with the prior art:

[0028] (1) The system is modeled as a cascade of transmission matrices of the smallest unit of multiple conductors, which avoids the complicated process of fitting the vector of frequency-varying parameters and performing large-scale time-domain simulation in circuit simulation software, and effectively reduces the implementation complexity.

[0029] (2) While ensuring high accuracy, the calculation efficiency has been significantly improved. The calculation time for predicting the high frequency domain characteristics and time domain waveforms of electromagnetic equipment has been greatly reduced from hours / days in the traditional method to seconds. It is particularly suitable for the rapid evaluation of electromagnetic equipment systems with long cables or multi-turn windings.

[0030] (3) The method is highly versatile and applicable to the prediction of frequency and time domain high-frequency characteristics of various electromagnetic equipment such as cables, motors, inductors, and transformers and their cascaded systems.

[0031] (4) It can be used in the design stage for high frequency matching, dv / dt filter and insulation design, and can also be used for online prediction of system high frequency domain characteristics and time domain waveforms, which is of great significance for improving the reliability of electromagnetic equipment systems driven by power electronic converters. Attached Figure Description

[0032] Figure 1 This is a flowchart of the high-precision prediction method for high-frequency frequency domain characteristics and time domain waveforms of the electromagnetic equipment system of the present invention.

[0033] Figure 2 This is a schematic diagram of the multi-conductor minimum circuit cascade model and the simplest cascade model of the electromagnetic equipment system constructed in this invention (taking a three-phase four-core cable connecting a three-phase motor as an example).

[0034] Figure 3 This is a schematic diagram of the smallest circuit unit model of the cable in this invention (taking a three-phase four-core cable as an example).

[0035] Figure 4 This is a schematic diagram of the smallest circuit unit model of the winding of the electromagnetic equipment in this invention (taking a three-phase motor as an example).

[0036] Figure 5 This is a finite element model for obtaining the minimum circuit element impedance and capacitance parameters of cables and electromagnetic equipment in this invention (taking a three-phase four-core cable and a three-phase motor as examples).

[0037] Figure 6 This paper compares the amplitude and phase results of the prediction of common-mode impedance of electromagnetic equipment using the present invention and existing methods (taking a 2.5m three-phase four-core cable as an example).

[0038] Figure 7 The time-domain waveform diagrams for predicting the first-turn voltage of the electromagnetic equipment winding and the neutral point voltage of the motor in this invention are shown (taking a three-phase motor connected by a 2.5m three-phase four-core cable as an example).

[0039] Figure 8 This is a comparison of the calculation time for predicting voltage spikes between the present invention and existing methods (taking a three-phase motor connected by a 2.5m three-phase four-core cable as an example). Detailed Implementation

[0040] The present invention will now be described in further detail with reference to the accompanying drawings. The following embodiments are for illustrative purposes only and do not constitute a limitation thereof.

[0041] Example 1: The flowchart of the high-precision prediction method for frequency domain characteristics and high-frequency time domain waveforms of an electromagnetic equipment system disclosed in this invention is as follows. Figure 1 As shown, there are 6 main steps. In this embodiment, the power electronic converter is a three-phase two-level inverter, the cable is a 2.5m three-phase four-core cable, and the electromagnetic equipment is a three-phase motor (8 windings per phase, 11 turns per winding), i.e., m=3, n=4. The specific implementation steps are described below:

[0042] First step, such as Figure 2 As shown, the cable and motor windings are divided into N sections respectively. c =25 and N s=A system composed of 88 cascaded multi-conductor minimum units. In Figure 2 In the diagram, i1~i3 are the cable signal line input terminals, and o1~o3 are the cable signal line output terminals, which are also the motor three-phase signal line input terminals; i4 is the cable protective earth (PE) wire input terminal, and o4 is the cable PE wire output terminal. Since the motor casing is connected to the protective earth output, o4 is also the motor casing; N1 is the motor winding neutral point. c and N s The specific steps for determining this are as follows:

[0043] (1) Based on the minimum rise time t of the PWM pulse voltage output by the power electronic converter r The upper limit frequency f of the effective spectrum of the PWM pulse output voltage is calculated. max Then the upper limit frequency f max Converted to the minimum wavelength λ corresponding to the upper limit frequency of PWM voltage min Furthermore, based on the lumped parameter circuit assumption, the actual cable length l corresponding to the smallest circuit unit of the cable is calculated. c =M λ min =0.1m. Determine l c Then, divide the total cable length of 2.5m by l. c That is, to obtain the total number N of the smallest cable units. c =25.

[0044] (2) The electromagnetic equipment is a three-phase motor with 8 windings per phase, 11 turns per winding, and Y-connected. Therefore, multiplying the number of windings per phase and the number of turns per winding gives the minimum number of circuit units N of the motor. s =88.

[0045] The second step, as Figure 3 and Figure 4 As shown, high-precision multi-conductor minimum circuit unit models are established for cable and electromagnetic equipment windings respectively:

[0046] (1) The smallest unit circuit model of the cable is as follows Figure 3 As shown, this includes the self-impedance Z of each phase cable. 11 Z 22 Z 33 and PE line self-impedance Z 44 The mutual impedance Z of each phase cable 12 Z 13 Z 21 Z 23 Z 31 Z 32 and the mutual impedance Z of each phase cable to the PE line 14 Z 24 Z 34 Z 41Z 42 Z 43 The capacitance C between each phase cable 21 C 32 C 31 and the capacitance C of each phase cable to the PE line 11 C 22 C 33 .

[0047] (2) The minimum circuit unit model of the winding of a three-phase motor is as follows: Figure 4 As shown, this is a network constructed by connecting the ground wires of each phase's single-turn two-port network. Nodes 1-3 represent the beginnings of the three-phase signal lines, and nodes 5-7 represent the ends. The connection method of the beginnings and ends is determined according to whether the motor is Y-connected or delta-connected. Nodes 4 and 8 represent the motor casing. Specifically, the single-turn two-port network includes the equivalent self-impedance Z of the k-th turn. k The capacitance C of the kth turn to reference ground k0 The mutual capacitance C between the k-th turn and the (k+1)-th turn k_k+1 The induced voltage on the remaining turns Z mutual I represents the equivalent mutual impedance of the k-th turn to the remaining turns. i This represents the current flowing through the i-th turn of the coil, and N is the total number of turns in the winding; nodes a and b represent the input ports of the single-turn two-port network, and nodes c and d represent the output ports of the single-turn two-port network; in the motor, the reference ground is the motor housing.

[0048] The above-mentioned minimum circuit unit model can accurately characterize the electromagnetic coupling relationship within the cable and motor stator winding in the range of 100kHz~100MHz, ensuring the high accuracy of the model.

[0049] The third step is to use finite element simulation to calculate parasitic parameters and tune the parameters of the minimum circuit unit model:

[0050] like Figure 5 As shown, cable and motor stator models were established in finite element software such as ANSYS Maxwell. In the cable model, conductors A, B, and C correspond to the three-phase cable, and the PE conductor corresponds to the cable's protective ground wire. In the motor model, T1 to T11 correspond to turns 1 to 11 of each coil in the motor. Using the built-in electrostatic field simulator and eddy current field simulator, and multiplying by the ratio of the cable / motor winding conductor length to the unit length, impedance and capacitance parameters such as self-impedance, mutual impedance, capacitance to ground, phase-to-phase capacitance, and mutual capacitance of the cable and motor windings from 100kHz to 100MHz were obtained. Figure 3 and Figure 4 The parameters of the minimum circuit unit model are given in equations (1) and (2). Taking a 1MHz cable as an example, equations (1) and (2) give all the impedance Z and capacitance parameters C in the obtained minimum circuit model.

[0051] (1)

[0052] (2)

[0053] Where j represents the imaginary unit, Ω is the resistance unit ohm, pF is the capacitance unit picofarad, and m is the unit meter;

[0054] Step 4: Calculation of the transmission matrix for the smallest circuit unit, cable, and electromagnetic equipment winding system:

[0055] according to Figure 3 The cable multi-conductor minimum unit circuit model shown has an admittance matrix Y. c This represents the output voltage vector [U] i U o ] and input / output current [I i , I o The relationship between ], that is:

[0056] (3)

[0057] Where vector U i , I i The voltages and currents U1~U4 and I1~I4 at the input ports of the smallest circuit unit of the cable are respectively composed of vector U. o , I o These are composed of the output ports U5~U8 and I5~I8 of the minimum circuit unit of the cable, respectively. Based on the impedance and capacitance matrices Z and C obtained earlier, the admittance matrix Y can be calculated according to circuit principles. c Similarly, taking a 1MHz cable as an example, its minimum circuit model admittance matrix is ​​calculated as follows:

[0058] (4)

[0059] Transmission Matrix T c Represents the input voltage and current vector [U] i , I i ] and output voltage and current [U o , I o The relationship between ], that is:

[0060] (5)

[0061] Therefore, the admittance matrix can be converted into a transmission matrix using matrix operations. Taking a 1MHz cable as an example, the calculated transmission matrix for the minimum circuit unit model of a multi-conductor cable is as follows:

[0062] (6)

[0063] Similarly, the transfer matrix T of the multi-conductor minimum circuit unit model of the motor can be calculated. s Then, based on the minimum number of units N... c and N s Exponentiation, such as Figure 2 As shown, the transmission matrices for the entire cable and the entire motor can be further obtained as (T) c ) Nc and (T) s ) Ns .

[0064] The fifth step involves calculating the common-mode / differential-mode impedance curves, voltage transfer functions, and other high-frequency domain characteristics based on the different circuit connection forms at the ends of the electromagnetic equipment windings and during high-frequency characteristic measurements. The specific steps are as follows:

[0065] Determine the input and output voltage and current U based on the transfer matrix. i U o , I i , I o The two equations relating the four quantities determine the final output voltage and current U based on the connection configuration at the ends of the electromagnetic equipment windings. o , I o Based on the equation relationships, and according to the transfer functions of common-mode, differential-mode, and motor winding first-turn voltage relative to the power electronic converter output voltage, and the transfer function of electromagnetic equipment winding neutral point relative to the power electronic converter output voltage, voltage and current equation relationships are written for different circuit connection forms during high-frequency characteristic measurements. Using circuit principles and matrix operations, the U under different input voltage excitation conditions is obtained. i The input current I of the system under (s) i (s), Output voltage and current U o (s), I o (s), and the voltage U at different nodes p (s), then Substituting (f is the frequency), we obtain the high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter: the various impedance curves are obtained by solving for the input voltage U based on the corresponding measurement circuit connections. i ( Divide by the input current I i ( The node voltage U is obtained by solving various transfer functions based on their corresponding measurement circuit connections. p ( Divide by the input voltage U i ( )get.

[0066] Step 6: Perform spectrum analysis on the inverter output PWM voltage to predict high-frequency time-domain waveforms such as the first turn of the winding, neutral point voltage spike, and common-mode current.

[0067] First, Fourier decomposition is performed on the inverter output voltage. Using the AC component of the switching frequency as the fundamental frequency and the upper limit of the effective bandwidth of the PWM pulse voltage as the highest harmonic, the amplitude and phase of the PWM pulse voltage harmonics at each frequency are obtained. Then, based on the previously obtained transfer functions of the first-turn voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter, the transfer function of the neutral voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter, and the common-mode impedance curve, the frequency domain responses of the first-turn voltage of the electromagnetic equipment winding, the neutral point voltage, and the common-mode current under the action of each harmonic of the PWM pulse voltage of the power electronic converter are calculated. Finally, the results of each harmonic action are summed, and the frequency domain response waveform is transformed back to the time domain using inverse Fourier transform, thus obtaining the high-frequency time domain waveforms of the first-turn voltage spike of the electromagnetic equipment winding, the neutral point voltage spike of the motor, and the common-mode current driven by the power electronic converter.

[0068] Figure 6 The prediction results of the common-mode impedance of a 2.5m three-phase four-core cable by the present invention and the time-domain simulation method based on refined multi-conductor transmission line modeling are presented. It can be seen that the common-mode impedance prediction results of the two are basically the same, and both can accurately capture the common-mode resonance point of the cable, which verifies the high accuracy of the present invention in predicting the high-frequency domain characteristics of variable frequency motor systems.

[0069] Figure 7 The present invention provides time-domain waveforms of the predicted first-turn voltage and neutral point voltage of a three-phase motor winding connected to a 2.5m three-phase four-core cable. The cable input voltage (i.e., command voltage) is a pulse signal with a slew rate of 27.5V / ns and an amplitude of 550V. It can be seen that the present invention can effectively predict the voltage spike of the first turn and the voltage spike of the neutral point of the motor, thus verifying the effectiveness of the present invention for high-frequency time-domain waveform prediction of variable frequency motor systems.

[0070] Figure 8 A comparison is presented between the calculation time of this invention and an existing method (time-domain simulation based on refined multi-conductor transmission line modeling) for predicting voltage spikes in the windings of a three-phase motor connected by a 2.5m three-phase four-core cable. It can be seen that, in this embodiment, the present invention reduces the calculation time from hours to less than one second. Furthermore, the calculation time of the time-domain simulation method based on refined multi-conductor transmission line modeling increases significantly with increasing cable length, while the calculation time of the present invention remains essentially unchanged with increasing cable length, indicating that the present invention has extremely high computational efficiency.

[0071] Furthermore, as can be seen from the embodiments of the present invention, the present invention avoids complex frequency-varying parameter vector fitting and tedious modeling operations in circuit simulation software. It is simple and easy to implement and can achieve high-precision and rapid prediction of the high-frequency domain characteristics and time-domain waveforms of electromagnetic equipment systems during the design stage or online operation.

[0072] Example 2: This example proposes an electronic system, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the method described in this invention.

[0073] It should be noted that the electronic system can use terminal devices such as desktop computers, laptops, or cloud servers. Furthermore, terminal devices include, but are not limited to, processors and memory. For example, terminal devices can also include input / output devices, network access devices, and buses.

[0074] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0075] Furthermore, the memory can be an internal storage unit of the terminal device, such as the hard disk or RAM of the terminal device, or an external storage device of the terminal device, such as a plug-in hard disk, smart memory card (SMC), secure digital card (SD), or flash memory card (FC) equipped on the terminal device. In addition, the memory can also be a combination of the internal storage unit and the external storage device of the terminal device. The memory is used to store computer programs and other programs and data required by the terminal device. The memory can also be used to temporarily store data that has been output or will be output. This application does not limit this.

[0076] Furthermore, through this electronic system, any one of the methods described in the above embodiments can be stored in the memory of the electronic system and loaded and executed on the processor of the terminal device for convenient use.

[0077] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. A method for high-precision prediction of high-frequency frequency domain characteristics and time domain waveforms of an electromagnetic equipment system, characterized in that, Including the following steps: The cable and electromagnetic equipment windings are divided into N sections respectively. c 1 and N s A system composed of cascaded multi-conductor minimum units; High-precision multi-conductor minimum circuit unit models were established for cables and electromagnetic equipment, respectively. Based on the impedance and capacitance parameters of the cable and electromagnetic equipment windings within the key frequency band, and according to the actual cable and winding conductor lengths corresponding to the multi-conductor minimum circuit unit model, the parameters in the multi-conductor minimum circuit unit model of the cable and electromagnetic equipment windings are calculated proportionally, including self-impedance, mutual impedance, capacitance to ground, phase-to-phase capacitance, and mutual capacitance. Based on the multi-conductor minimum circuit unit models and their quantities for cables and electromagnetic equipment, respectively, calculate the transmission matrices corresponding to the minimum circuit unit models for cables and electromagnetic equipment. The equation relationship between input / output voltage and current is determined based on the circuit connection form at the end of the electromagnetic equipment winding and during different high-frequency characteristic measurements. The high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter are obtained by using circuit principles and matrix operations. Harmonic decomposition is performed on the PWM pulse voltage output by the power electronic converter. Based on the harmonic amplitude and phase of the PWM pulse voltage and the high-frequency frequency domain characteristics of the system, the high-frequency time domain waveform of the electromagnetic equipment under the action of the PWM pulse voltage of the power electronic converter is predicted, including: the voltage spike of the first turn of the winding, the voltage spike of the neutral point, and the common-mode current. The calculation steps for the transmission matrix corresponding to the minimum circuit unit model of the cable and electromagnetic equipment are as follows: First, based on the multi-conductor minimum circuit unit model of the cable and electromagnetic equipment, respectively, obtain the input and output voltage vectors [U]. i U o ] and input / output current [I i , I o The admittance matrix representing the relationship between [U] is then used to perform matrix operations, converting the admittance matrix into a vector representing the input voltage and current [U]. i , I i ] and output voltage and current [U o , I o The transmission matrix of the relationship between [] is used to obtain the transmission matrices of the multi-conductor minimum circuit unit model of cables and electromagnetic equipment, respectively T. c and T s Then, based on the minimum number of units N... c and N s The power operation yields the transmission matrices for the cable and electromagnetic equipment, respectively (T). c ) Nc and (T) s ) Ns ; The specific steps for predicting the high-frequency time-domain waveform of electromagnetic equipment under the action of PWM pulse voltage from a power electronic converter are as follows: First, Fourier decomposition is performed on the inverter output voltage. The AC component of the switching frequency is taken as the fundamental wave, and the upper limit of the effective bandwidth of the PWM pulse voltage is taken as the highest harmonic. The amplitude and phase of the PWM pulse voltage harmonics of each frequency are obtained. Subsequently, based on the obtained transfer function of the first turn voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter, the transfer function of the neutral voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter, and the common-mode impedance curve, the frequency domain response of the first turn voltage, neutral point voltage, and common-mode current of the electromagnetic equipment winding under the action of each harmonic of the PWM pulse voltage of the power electronic converter is calculated. Finally, the results of each harmonic effect are summed, and the frequency domain response waveform is transformed back to the time domain using inverse Fourier transform, thus obtaining the high-frequency time domain waveforms of the first-turn voltage spike, neutral point voltage spike, and common-mode current of the electromagnetic equipment driven by the power electronic converter.

2. The method according to claim 1, characterized in that, The high-precision multi-conductor minimum circuit unit model of the cable is a 2n-terminal network containing n input ports and n output ports. It is composed of m-phase self-impedance, nm core ground self-impedance, m-phase mutual impedance, m-phase-to-ground mutual impedance, m-phase-to-ground capacitance, m-phase-to-phase capacitance, and nm core ground mutual capacitance. Its connection structure is as follows: each input port and output port is connected in series by the self-impedance of the corresponding phase of the port, the mutual impedance of the phase to other phases, and the mutual impedance of the phase to ground; between each output port, it is composed of the phase-to-phase capacitance and the phase-to-ground capacitance.

3. The method according to claim 2, characterized in that, The high-precision multi-conductor minimum circuit unit model of electromagnetic equipment is a two-port network structure representing an actual single-turn winding. It consists of the self-inductance, self-resistance, capacitance to ground, and mutual capacitance with the next turn winding of the single-turn winding. Its connection structure is as follows: each input port and output port is connected in series by the self-impedance of the turn and the mutual impedance between the turn and other turns, and then connected in parallel with the mutual capacitance of the next turn winding; the input port is connected to ground by the half-turn capacitance of the turn; the output port is connected to ground by the other half-turn capacitance of the turn.

4. The method according to claim 3, characterized in that, The two-port network structure, when m≥2, i.e. for electromagnetic equipment with multi-phase windings, connects the ground wires of the two-port networks corresponding to the single-turn windings of different phases to obtain a 2(m+1)-terminal network, which constitutes a high-precision multi-conductor minimum circuit unit model of the electromagnetic equipment.

5. The method according to claim 1, characterized in that, The impedance and capacitance parameters of the unit length cable and electromagnetic equipment windings within the key frequency band are obtained through the following steps: finite element electromagnetic simulation models of the cable and electromagnetic equipment are established respectively. The self-impedance, mutual impedance, capacitance to ground, phase-to-phase capacitance, and mutual capacitance of the unit length cable and electromagnetic equipment windings are calculated using the built-in electrostatic field simulator and eddy current field simulator. The key frequency band setting should include the main resonant frequencies of the cable and electromagnetic equipment, with a setting range of 100kHz to 100MHz.

6. The method according to claim 1, characterized in that, The specific steps for solving the high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter are as follows: Determine the input and output voltage and current U based on the transfer matrix. i U o , I i , I o The two equations between them determine the terminal output voltage and current U based on the connection configuration of the winding ends of the electromagnetic equipment. o , I o The equation relationship; Based on the different circuit connection configurations for high-frequency characteristic measurements, voltage and current equations are written, and the different input voltages U are obtained by solving them using circuit principles and matrix operations. i (s) Input current I of the system under excitation i (s), Output voltage and current U o (s), I o (s), and the voltage U of the key node. p ( s ), where s is the complex frequency; Then Substituting the values, we obtain the high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter. f is the imaginary unit, and f is the frequency.

7. The method according to claim 6, characterized in that, The high-frequency domain characteristics of the electromagnetic equipment system driven by the power electronic converter include: the common-mode impedance curve and differential-mode impedance curve of the cable, the electromagnetic equipment winding, and the system composed of the cable and the electromagnetic equipment; the transfer function of the first-turn voltage of the electromagnetic equipment winding relative to the output voltage of the power electronic converter; the transfer function of the neutral point of the electromagnetic equipment winding relative to the output voltage of the power electronic converter; and the input voltage U obtained by solving the various impedance curves based on their corresponding measurement circuit connections. i ( Divide by the input current I i ( The node voltage U is obtained by solving various transfer functions based on their corresponding measurement circuit connections. p ( Divide by the input voltage U i ( )get.

8. An electronic system comprising: At least one processor; And a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, characterized in that the instructions are executed by the at least one processor to enable the at least one processor to perform the method steps of any one of claims 1-7.

Images