A rapid finite element simulation method for electromagnetic field calculation of a voltage source driven permanent magnet synchronous motor

Abstract

This invention discloses a rapid finite element simulation method for the electromagnetic field of a voltage-source driven permanent magnet synchronous motor (PMSM). It constructs a time-step finite element simulation model of the electromagnetic field of the PSM with initial magnetic vector potential and current density of 0. To address the phenomenon of the stator flux linkage signal deviating from the ideal flux linkage signal during transient simulation calculations, voltage compensation is performed on the ideal voltage source signal in the drive circuit. This suppresses electromagnetic transients during simulation and effectively shortens the simulation time. While maintaining the accuracy of the finite element calculation of the electromagnetic field of the voltage-source driven PMSM, this invention effectively shortens the simulation time, saves computer resources, and reduces development costs.

Description

Technical Field

[0001] This invention relates to a finite element analysis method for the electromagnetic field of a permanent magnet synchronous motor. By adding an additional compensation voltage to the voltage source signal to reduce stator flux linkage error, a rapid finite element simulation calculation method for the electromagnetic field of a voltage source driven permanent magnet synchronous motor is achieved. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in industrial fields such as electric vehicles, home appliances, aerospace, and high-end CNC machine tools due to their advantages of small size, high power density, and simple control. Based on the installation method of the permanent magnets, PMSMs can generally be divided into surface-mounted and internal types. Surface-mounted PMSMs are characterized by simple structure, convenient manufacturing, and simple electromagnetic design; while internal PMSMs can utilize the reluctance effect to generate reluctance torque, thereby further improving the motor's electromagnetic torque. They are characterized by high torque density, complex manufacturing, and greater difficulty in electromagnetic design.

[0003] Electromagnetic design of permanent magnet synchronous motors (PMSMs) is one of the core technical challenges in motor design. Analytical methods and the finite element method (FEM) are two commonly used calculation methods for PMSM electromagnetic design. Analytical methods are convenient but have lower accuracy, making them suitable for surface-mounted PMSMs with simple topologies. The FEM, on the other hand, is complex to model but offers high accuracy, making it suitable for various types of PMSMs with complex topologies. In the FEM modeling and calculation of the electromagnetic field of PMSMs, to shorten the electromagnetic transient process during simulation and enable faster convergence to steady state, current source excitation is commonly used. Current source excitation effectively shortens the stator electromagnetic time constant and facilitates maximum torque-to-current ratio control. However, current source excitation modeling and simulation cannot consider the impact of stator current harmonics on the motor's electromagnetic performance and makes it difficult to examine the motor's electromagnetic performance under maximum torque-to-voltage ratio control.

[0004] Using voltage source excitation for finite element modeling and simulation of the electromagnetic field of a permanent magnet synchronous motor (PMSM) is one of the key technologies for solving the aforementioned core problems. However, modeling and simulating the electromagnetic field of a PMSM using voltage source excitation will induce electromagnetic transients in the stator windings, thus increasing the time for the simulation to converge to a steady state, which is detrimental to further optimization design of the PMSM. Therefore, it is necessary to explore a finite element modeling and simulation method for the electromagnetic field of a PMSM that can reduce electromagnetic transients and lower calculation time while maintaining calculation accuracy, in order to address the problem of excessively long electromagnetic transients in the finite element simulation of the electromagnetic field of a PMSM under voltage source excitation. Summary of the Invention

[0005] This invention addresses the problems of excessively long electromagnetic transients and slow calculation speed in finite element simulation of electromagnetic fields of permanent magnet synchronous motors under voltage source excitation. It provides a method for rapid finite element simulation of electromagnetic fields of voltage source-driven permanent magnet synchronous motors by adding an additional compensation voltage to the voltage source signal to weaken stator flux linkage errors and thus shorten the electromagnetic transients.

[0006] The present invention achieves the above objectives through the following technical solution, comprising the following steps:

[0007] A rapid finite element method for electromagnetic field simulation of a voltage source-driven permanent magnet synchronous motor includes the following steps:

[0008] (1) Establish a time-step finite element simulation model of the electromagnetic field of a voltage-source driven permanent magnet synchronous motor, and initialize the magnetic vector potential and current density to 0. In the time-step finite element calculation, the backward Euler method is used in the time direction. During the calculation, the stator flux linkage signal of the finite element simulation that varies with time t is output in real time as ψ. s，est (t), the ideal voltage source voltage signal u in the driving circuit s The expression for (t) changing with time t is:

[0009]

[0010] In the formula: Voltage amplitude; f is the initial phase angle; f is the frequency;

[0011] (2) The ideal voltage source voltage signal u from step (1) s Integrating (t) yields the ideal stator flux linkage signal ψ. s The expression for (t) changing with time t is:

[0012]

[0013] (3) Since the magnetic vector potential and current density are initialized to 0 in step (1), the ideal stator flux linkage signal ψ in step (2) is... s (t) There is no DC component, i.e., a constant term, and the ideal stator flux linkage signal ψ s The expression for (t) changing with time t can be further simplified to:

[0014]

[0015] (4) Based on the ideal stator flux linkage signal ψ in step (3) s (t) and the finite element simulation stator flux linkage signal ψ that can be calculated and obtained by the finite element simulation model in step (1). s，est (t), calculate the stator flux linkage error signal Δψ caused by the finite element simulation error. sThe expression for (t) changing with time t is:

[0016] Δψ s (t)=ψ s (t)-ψ s，est (t);

[0017] (5) Differentiate the stator flux linkage error signal caused by the finite element simulation error in step (4) to obtain the stator voltage error signal Δu caused by the finite element simulation error. s，FEM The expression for (t) changing with time t is:

[0018] Δu s，FEM (t)=2πft·Δψ s (t);

[0019] (6) Since the backward Euler method is used in the time direction of the time step finite element calculation in step (1), the stator flux linkage signal ψ in the finite element simulation in step (4) is therefore... s，est (t) There exists a lag of simulation step size Δt. The error caused by this lag is called the stator flux linkage error signal Δψ caused by the step size. s，step (t) is represented as:

[0020] Δψ s，step (t)=ψ s，est (t)-ψ s，est (t-1);

[0021] (7) In step (6), the stator flux linkage error signal Δψ caused by the step size s，step (t) can also be obtained by subtracting the ideal stator flux linkage signal at time t and time t-1, expressed as:

[0022]

[0023] (8) The stator flux linkage error signal Δψ caused by the step size in step (7) s，step Differentiating (t) yields the stator voltage error signal Δu caused by the step size. s，step The expression for (t) changing with time t is:

[0024] Δu s，step (t)=2πft·Δψ s，step (t);

[0025] (9) Based on the stator voltage error signal Δu caused by the finite element simulation error in step (5). s，FEM (t) and the stator voltage error signal Δu caused by the step size in step (8) s，step (t), the ideal voltage source voltage signal us(t) in the driving circuit in step (1) is compensated to obtain the total voltage source signal u.s，tot The expression for (t) is:

[0026] u s，tot (t)=u s (t)+Δu s，FEM (t-Δt)+Δu s，step (t);

[0027] (10) Solve the finite element model of the electromagnetic field of the permanent magnet synchronous motor driven by the voltage source after voltage compensation in step (9). After the finite element model reaches a stable state, obtain the main electromagnetic performance of the motor.

[0028] As a further optimization of the present invention, in step (1), the time-step finite element model is solved using a transient field solver.

[0029] As a further optimization of the present invention, in step (1), the initial phase angle It is the angle between the voltage space vector and the d-axis of the permanent magnet synchronous motor, and its size can be selected according to the specific load size.

[0030] As a further optimization of the present invention, in step (1), the stator flux linkage signal of the finite element simulation, which varies with time t, is output in real time during the finite element calculation process as ψ. s，est (t), whose calculation expression is: (This formula is from the reference: Yan Jingwen, Di Chong, Bao Xiaohua, Zhu Qinglong. Analysis and calculation of T-type equivalent circuit parameters of induction motor based on two-dimensional finite element method [J]. Proceedings of the Chinese Society for Electrical Engineering, 2021, 41(S1):294-302.), where: N s I is the number of turns in series per phase; s (t) represents the stator phase current; A z (t) represents the axial component of the magnetic vector position; J z (t) represents the axial component of the current density; V represents the volume region where the stator winding is located.

[0031] As a further optimization of the present invention, in step (6), the simulation step size Δt ranges from 1 / 200 to 1 / 40 of the simulation electric period T = 1 / f.

[0032] As a further optimization of the present invention, in step (10), the time range of the steady state solution of the finite element model of the voltage source driven permanent magnet synchronous motor after voltage compensation is 2 to 4 simulation electric cycles T; the steady state is defined as the maximum error of the average electromagnetic torque, current and flux linkage waveform of the motor calculated by the finite element simulation within ±2% in any two adjacent electric cycles.

[0033] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0034] This invention, while maintaining the accuracy of finite element simulation of the electromagnetic field of permanent magnet synchronous motors (PMSMs), effectively shortens the electromagnetic transients caused by voltage source power supply, enabling the model to converge quickly to a stable state and thus reducing the finite element simulation time. Furthermore, compared to existing finite element simulation techniques for voltage source-driven PMSMs, this invention does not require additional solutions for the physical quantities of the initial state, thus reducing the complexity of the solution and eliminating the need for an additional finite element solver. Simultaneously, compared to finite element simulation techniques for current source-driven PMSMs, this invention can consider the impact of stator current harmonics on the motor's electromagnetic performance. In summary, this invention provides a complete and systematic approach for rapid finite element simulation of the electromagnetic field of voltage source-driven PMSMs.

[0035] The underlying mechanism is as follows: First, a time-step finite element simulation model of the electromagnetic field of a voltage-source driven permanent magnet synchronous motor is established, and the magnetic vector potential and current density are initialized to 0. Based on the ideal voltage source voltage signal in the drive circuit, the ideal stator flux linkage signal is obtained. Combining the finite element simulation stator flux linkage signal, the stator flux linkage error signal caused by the finite element simulation error is further solved, and thus the stator voltage error signal caused by the finite element simulation error is obtained. Based on the signal hysteresis characteristics caused by the backward Euler method, the stator flux linkage error signal caused by the step size is obtained, and thus the stator voltage error signal caused by the step size is obtained. Based on the above two types of voltage error signals, the ideal voltage source voltage signal in the drive circuit is compensated, and the simulation calculation reaches a steady state, realizing the rapid finite element simulation of the electromagnetic field of the voltage-source driven permanent magnet synchronous motor. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the finite element method for rapid simulation calculation of electromagnetic field of a voltage source driven permanent magnet synchronous motor according to the present invention.

[0037] Figure 2 A comparison of the average electromagnetic torque over time calculated using the model proposed in this invention and the voltage source drive model without voltage compensation;

[0038] Figure 3 A comparison of the U-phase current versus time calculated by the model proposed in this invention and the voltage source drive model without voltage compensation;

[0039] Figure 4 This is a comparison chart showing the change of U-phase flux over time calculated by the model proposed in this invention and the voltage source drive model without voltage compensation. Detailed Implementation

[0040] To clearly illustrate the objectives, technical solutions, and advantages of the embodiments of the present invention, the present invention will be described completely and clearly below with reference to the accompanying drawings. However, the embodiments described herein are only a part of the embodiments of the present invention, not all of them. The description of the embodiments is merely to help understand the core ideas of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should be included within the scope of protection claimed by the present invention.

[0041] like Figure 1 As shown, this invention discloses an embodiment of a rapid finite element simulation calculation method for the electromagnetic field of a voltage source-driven permanent magnet synchronous motor, comprising the following steps:

[0042] (1) In the Altair Flux electromagnetic field finite element simulation software, a time-stepping finite element simulation model of a three-phase permanent magnet synchronous motor driven by a 36-slot, 4-pole, 1500rpm, 50Hz voltage source was established. The magnetic vector potential and current density were initialized to 0. In the time-stepping finite element calculation, the backward Euler method was used in the time direction. During the calculation, the finite element simulation stator flux linkage signal that varies with time t was output in real time as ψ. s，set (t), simulation step size Δt=0.0002s; the voltage signal parameters of the UVW three-phase ideal voltage source in the drive circuit are: voltage amplitude Initial phase angle Frequency f = 50Hz, voltage signal u of a three-phase ideal voltage source s，U (t), u s，v (t) and u s，w The expression for (t) changing with time t is:

[0043]

[0044] (2) The three-phase ideal voltage source voltage signal u from step (1) s，U (t), u s，V (t) and u s，W Integrating (t) yields the three-phase ideal stator flux linkage signal ψ. s，U (t), ψ s，V (t) and ψ s，W The expression for (t) changing with time t is:

[0045]

[0046] (3) Since the magnetic vector potential and current density are initialized to 0 in step (1), the three-phase ideal stator flux linkage signal ψ in step (2) is... s，U (t), ψ s，V (t) and ψ s，W(t) There is no DC component, i.e., a constant term, and the three-phase ideal stator flux linkage signal ψ s，U (t), ψ s，V (t) and ψ s，W (t) can be further simplified to:

[0047]

[0048] (4) Based on the three-phase ideal stator flux linkage signal ψ in step (3) s，U (t), ψ s，V (t) and ψ s，W (t) and the three-phase finite element simulation stator flux linkage signal ψ that can be calculated and obtained by the finite element simulation model in step (1). s，est，U (t), ψ s，set，V (t) and ψ s，est，W (t), calculate the three-phase stator flux linkage error signal ψ caused by the finite element simulation error. s，U (t), ψ s，V (t) and Δψ s，W The expression for (t) changing with time t is:

[0049]

[0050] (5) The three-phase stator flux linkage error signal ψ caused by the finite element simulation error in step (4) s，U (t), Δψ s，V (t) and Δψ s，W Differentiating (t) yields the three-phase stator voltage error signal Δψ caused by the finite element simulation error. s，FEM，U (t), Δu s，FEM，V (t) and Δu s，FEM，W The expression for (t) changing with time t is:

[0051]

[0052] (6) Since the backward Euler method is used in the time direction of the time step finite element calculation in step (1), the stator flux linkage signal ψ in the three-phase finite element simulation in step (4) is therefore... s，est，U (t), ψ s，est，V (t) and ψ s，est，W (t) There exists a lag of simulation step size Δt = 0.0002s. The error caused by this signal lag is called the three-phase stator flux linkage error signal Δψ caused by the step size. s，step，U (t), Δψ s，step，V (t) and Δψ s，step，W (t) is represented as:

[0053]

[0054] (7) In step (6), the three-phase stator flux linkage error signal Δψ caused by the step size s，step，U (t), Δψ s，step，V (t) and Δψ s，step，W (t) can also be obtained by subtracting the three-phase ideal stator flux linkage signals at time t and time t-1, expressed as:

[0055]

[0056] (8) The three-phase stator flux linkage error signal Δψ caused by the step size in step (7) s，step，U (t), Δψ s，step，V (t) and Δψ s，step，W Differentiating (t) yields the three-phase stator voltage error signal Δu caused by the step size. s，step，U (t), Δu s，step，V (t) and Δu s，step，W The expression for (t) changing with time t is:

[0057]

[0058] (9) Based on the three-phase stator voltage error signal Δu caused by the finite element simulation error in step (5). s，FEM，U (t), Δu s，FEM，V (t) and Δu s，FEM，W (t) and the three-phase stator voltage error signal Δu caused by the step size in step (8) s，step，U (t), Δu s，step，V (t) and Δu s，step，W (t), for the three-phase ideal voltage source voltage signal u in the drive circuit in step (1). s，U (t), u s，V (t) and u s，W (t) is compensated to obtain the total three-phase voltage source signal u. s，tot，U (t), u s，tot，V (t) and u s，tot，W The expression for (t) is:

[0059]

[0060] (10) Solve the finite element model of the electromagnetic field of the permanent magnet synchronous motor driven by the voltage source after voltage compensation in step (9). After the finite element model reaches a stable state, obtain the main electromagnetic performance of the motor. Figure 2 This is a comparison chart showing the time-varying average electromagnetic torque calculated using the model proposed in this invention and a voltage source drive model without voltage compensation. The average electromagnetic torque is defined as the average value of the electromagnetic torque over the preceding electrical cycle from the calculated time point. Figure 2The average electromagnetic torque is displayed starting from 0.02s after the first electrical cycle. Figure 2 The voltage source drive model without voltage compensation reached steady state in 0.18s, with a total of 9 simulation cycles and a step size of 900 steps. The model proposed in this invention reached steady state in 0.04s, with a total of 2 simulation cycles and a step size of 200 steps. The average electromagnetic torques calculated by the voltage source drive model without voltage compensation and the model proposed in this invention were 22.47 Nm and 22.05 Nm, respectively, with an error of -1.87%.

[0061] Figure 3 This chart compares the U-phase current versus time calculated by the model proposed in this invention and the voltage source drive model without voltage compensation. The voltage source drive model without voltage compensation reaches steady state in 0.14s, with a total of 7 simulation cycles and a step size of 700 steps; the model proposed in this invention reaches steady state in 0.04s, with a total of 2 simulation cycles and a step size of 200 steps. The effective current values ​​calculated by the voltage source drive model without voltage compensation and the model proposed in this invention are 70.72A and 68.93A, respectively, with an error of -2.53%.

[0062] Figure 4 This is a comparison of the U-phase flux linkage over time calculated by the model proposed in this invention and the voltage source drive model without voltage compensation. The voltage source drive model without voltage compensation reaches a steady state in 0.14s, with a total of 7 simulation cycles and a step size of 700 steps; the model proposed in this invention reaches a steady state in 0.04s, with a total of 2 simulation cycles and a step size of 200 steps. The current flux linkage amplitudes calculated by the voltage source drive model without voltage compensation and the model proposed in this invention are 0.353Wb and 0.351Wb, respectively, with an error of -0.57%.

[0063] In step (1), the time-step finite element model is solved using a transient field solver. The example uses the Transient Magnetic transient field solver in the Altair Flux electromagnetic field finite element simulation software.

[0064] In step (1), the initial phase angle The initial phase angle is the angle between the voltage space vector and the d-axis of the permanent magnet synchronous motor, and its magnitude can be selected according to the specific load. 170.74° is equivalent to 2.98 rad in electrical degrees.

[0065] In step (1), the stator flux linkage signal of the finite element simulation, which varies with time t, is output in real time during the finite element calculation process as ψ. s，est (t), whose calculation expression is: Where: N sI is the number of turns in series per phase; s (t) represents the stator phase current; A z (t) represents the axial component of the magnetic vector position; J z (t) represents the axial component of the current density; V represents the volume region where the stator winding is located.

[0066] In step (6), the simulation step size Δt ranges from 1 / 200 to 1 / 40 of the simulation electrical period T = 1 / f. In this embodiment, the simulation electrical period T = 0.02s, and the simulation step size Δt is 1 / 100 of the simulation electrical period T, which is 0.0002s.

[0067] In step (10), the solution time to steady state of the finite element model of the electromagnetic field of the voltage source-driven permanent magnet synchronous motor ranges from 2 to 4 simulation electrical cycles T. In this embodiment, in order to compare with the voltage source-driven model without voltage compensation, the solution time in the finite element model is 0.3s, a total of 15 simulation electrical cycles. The method proposed in this invention reaches steady state in 0.04s, that is, the solution time to steady state is 2 simulation electrical cycles T. And starting from the second simulation electrical cycle, the maximum error of the average electromagnetic torque, current and flux linkage waveform of the motor calculated by the finite element simulation is ±1.6% in any two adjacent electrical cycles.

Claims

1. A fast simulation method of electromagnetic field of permanent magnet synchronous motor driven by voltage source, characterized in that, Comprising the following steps: (1) Establish the time-stepped finite element simulation model of the electromagnetic field of the permanent magnet synchronous motor driven by the voltage source, and initialize the magnetic vector potential and the current density to 0. In the time-stepped finite element calculation, the backward Euler method is used in the time direction, and the finite element simulation stator flux linkage signal varying with time t is output in real time during the calculation process as ψ s，est (t). (2) The expression of the ideal voltage source voltage signal u s (t) varying with time t in the drive circuit is: wherein: is the voltage amplitude; is the initial phase angle; f is the frequency; (2) the ideal voltage source voltage signal u s (t) is obtained by integrating the ideal stator flux linkage signal ψ s (t) is given by the expression (3) Since the magnetic vector potential and the current density are initialized to zero in step (1), the ideal stator flux linkage signal ψ s (t) does not have a constant term, i.e. a direct current component, the ideal stator flux linkage signal ψ s (t) is further simplified to the expression which varies with time t: (4) The ideal stator flux linkage signal ψ s (t) according to step (3) and the finite element simulation stator flux linkage signal ψ s，est (t) that can be calculated by the finite element simulation model in step (1), the stator flux linkage error signal Δψ s (t) caused by the finite element simulation error is calculated. The expression of the stator flux linkage error signal Δψ s (t) changing with time t is: Δψ s (t) = ψ s (t) - ψ s，est (t); (5) Differentiating the stator flux error signal caused by the finite element simulation error in step (4) to obtain a stator voltage error signal Δu caused by the finite element simulation error s，FEM (t) is expressed as a function of time t: Δu s，FEM (t) = 2πft· Δψ s (t) = 2πft· Δψ (6) Since backward Euler method is used in time direction in the time-stepped finite element calculation in step (1), the finite element simulation stator flux linkage signal ψ s，est (t) in step (1) is given by: (t) where Δψ s，step (t) is the step-size induced stator flux linkage error signal. Δψ s，step (t) = ψ s，est (t) - ψ s，est (t - 1); (7) In step (6), the step-induced stator flux linkage error signal Δψ s，step (t) can also be obtained by subtracting the ideal stator flux linkage signal at time t-1 from that at time t, and is expressed as: (8) a step (7) step length induced stator flux error signal Δψ s，step (t) is differentiated to obtain a step length induced stator voltage error signal Δu s，step (t) is expressed as a function of time t: Δu s，step (t) = 2πft· Δψ s，step (t) = 2πft· Δψ (9) The stator voltage error signal Δu caused by the finite element simulation error in step (5) s，FEM (t) and the step size in step (8) s，step (t), the total voltage source signal u s (t) is compensated for the ideal voltage source signal u s，tot (t) in the drive circuit in step (1) to obtain the total voltage source signal u (t) is expressed as: u s，tot (t) = u s (t) + Δu s，FEM (t - Δt) + Δu s，step (t); (10) solving the voltage source drive permanent magnet synchronous motor electromagnetic field finite element model after voltage compensation in step (9), and obtaining the main electromagnetic performance of the motor after the finite element model reaches a steady state.

2. The fast electromagnetic field finite element simulation method of permanent magnet synchronous motor driven by voltage source according to claim 1, characterized in that: In step (1), the time step finite element model is solved by using a transient field solver.

3. The fast electromagnetic field finite element simulation method of permanent magnet synchronous motor driven by voltage source according to claim 1, characterized in that: In the step (1), the initial phase angle is the included angle between the voltage space vector and the d-axis of the permanent magnet synchronous motor, and its size can be selected according to the specific load size.

4. The fast electromagnetic field finite element simulation method of permanent magnet synchronous motor driven by voltage source according to claim 1, characterized in that: In the step (1), the finite element simulation stator flux linkage signal varying with time t is output in real time in the finite element calculation process as ψ s，est (t), and the calculation expression is In the formula, N s is the number of turns in series per phase; I s (t) is the stator phase current; A z (t) is the axial component of the magnetic potential; J z (t) is the axial component of the current density; V is the body domain where the stator winding is located.

5. The fast electromagnetic field finite element simulation method of permanent magnet synchronous motor driven by voltage source according to claim 1, characterized in that: In step (6), the simulation step Δt is in the range of 1 / 200 to 1 / 40 of the simulation electrical period T=1 / f.

6. The fast electromagnetic field finite element simulation method of permanent magnet synchronous motor driven by voltage source according to claim 1, characterized in that: In step (10), the voltage source drive permanent magnet synchronous motor finite element model after voltage compensation is solved to a steady state for a time in the range of 2 to 4 simulation electrical periods T; the steady state is defined as the maximum error of the motor average electromagnetic torque, current and flux linkage waveforms in any two adjacent electrical periods being kept within ±2%.

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