Open-circuit fault three-harmonic current injection fault-tolerant control strategy for five-phase permanent magnet synchronous motor

Abstract

The five-phase permanent magnet synchronous motor open-circuit fault three times harmonic current injection fault-tolerant control strategy belongs to the motor field, and aims to solve the problem of torque fluctuation rising of the five-phase permanent magnet synchronous motor under winding open-circuit fault. The strategy includes the following aspects: adjusting the residual phase current to suppress the torque fluctuation rising caused by the winding open-circuit fault, and the residual phase current is determined according to the fault-tolerant control current; the obtaining process of the residual phase winding fault-tolerant control current is as follows: the relationship between the output torque and the residual phase winding fault-tolerant control current of the motor under the fault-tolerant state of the winding open-circuit fault is established according to the no-load back electromotive force, and then the relationship between the constant torque component of the output torque, the second torque fluctuation amplitude and the fourth torque fluctuation amplitude and the residual phase winding fault-tolerant control current is established; the multi-objective particle swarm algorithm is used for solving to obtain the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the second and fourth torque fluctuation amplitudes.

Description

Technical Field

[0001] This invention relates to a fault-tolerant control technology for windings of a multiphase permanent magnet synchronous motor, belonging to the field of motors. Background Technology

[0002] Compared to three-phase permanent magnet synchronous motor systems, five-phase permanent magnet synchronous motor systems, due to the increased number of phases, offer improved fault tolerance and control flexibility. Therefore, five-phase permanent magnet synchronous motor systems have broad application prospects in fields such as national defense and transportation, where high reliability and stability are required. Open-circuit faults in the windings of five-phase permanent magnet synchronous motors can be caused by factors such as vibration, overload, corrosion, or open circuits in the inverter's IGBTs. After an open-circuit fault occurs in a five-phase motor, the imbalance caused by the missing phase prevents the remaining phase currents from synthesizing a circular rotating magnetomotive force. This results in a significant increase in torque fluctuations and a decrease in torque output quality during operation. Traditional fault-tolerance strategies can only suppress torque fluctuations generated by the interaction between the fundamental back EMF and the fundamental current, and therefore cannot achieve ideal fault-tolerance effects for some five-phase motors with high back EMF harmonic content. Summary of the Invention

[0003] To address the issue of increased torque fluctuation in a five-phase permanent magnet synchronous motor under open-circuit fault conditions, this invention provides a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor.

[0004] The fault-tolerant control strategy for third harmonic current injection in a five-phase permanent magnet synchronous motor with open circuit faults described in this invention includes fault-tolerant control strategies for open circuit faults in any one phase, any two phases, or any three phases of the winding:

[0005] The remaining normal phase winding current is adjusted to suppress the increase in torque fluctuation caused by the winding open circuit fault. The remaining normal phase winding current is determined based on the fault-tolerant control current.

[0006] The process for obtaining the fault-tolerant control current of the remaining phase winding is as follows:

[0007] Based on the no-load back EMF, establish the relationship between the output torque of the motor under the fault-tolerant state of the winding open circuit fault and the fault-tolerant control current of the remaining phase winding. Then, establish the relationship between the constant torque component, the amplitude of the second torque fluctuation and the amplitude of the fourth torque fluctuation and the fault-tolerant control current of the remaining phase winding.

[0008] The multi-objective particle swarm optimization algorithm is used to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations.

[0009] The beneficial effects of this invention are as follows: This invention discloses a fault-tolerant control strategy for open-circuit fault harmonic current injection in a five-phase permanent magnet synchronous motor based on a multi-objective particle swarm optimization algorithm. This strategy not only considers the influence of the fundamental no-load back EMF on fault-tolerant control, but also suppresses the additional torque fluctuations caused by the third and fifth harmonics of the no-load back EMF during the fault-tolerant control process. For some five-phase permanent magnet synchronous motors with high no-load back EMF harmonic content, it can achieve good fault-tolerant control effects and reduce torque fluctuations during fault-tolerant operation. The effective value of the fault-tolerant control current for the remaining normal phase given by this strategy is the same as the effective value of the motor phase current under normal operation. When the motor is operated under fault tolerance using this strategy, the copper loss of the remaining normal phase winding is the same as under normal operation. Therefore, the copper loss of the remaining normal phase winding will not increase during fault-tolerant operation. In addition, this strategy uses a multi-objective particle swarm optimization algorithm to assist in solving the phase angle of the fault-tolerant control current and the harmonic current injection rate, avoiding the limitations caused by the difficulty in solving equations when the torque fluctuation is zero or the magnetomotive force fluctuation component is zero, and shortening the time required to solve the phase angle of the fault-tolerant control current and the harmonic current injection rate. Attached Figure Description

[0010] Figure 1 This is a comparison of torque waveforms before and after applying the proposed fault-tolerant control strategy for a single-phase winding open-circuit fault-tolerant control of the motor.

[0011] Figure 2 This is a comparison of torque waveforms before and after applying the proposed fault-tolerant control strategy to perform fault-tolerant control for open-circuit faults in two adjacent phase windings of the motor.

[0012] Figure 3 This is a comparison of torque waveforms before and after applying the proposed fault-tolerant control strategy to perform fault-tolerant control for open-circuit faults in two phases of the motor windings.

[0013] Figure 4 This is a comparison of torque waveforms before and after applying the proposed fault-tolerant control strategy to perform fault-tolerant control for open-circuit faults in adjacent three-phase windings of the motor.

[0014] Figure 5 This is a comparison of torque waveforms before and after applying the proposed fault-tolerant control strategy for open-circuit fault control of the motor's three-phase windings;

[0015] Figure 6 It is the Pareto front solution obtained by running the multi-objective particle swarm optimization algorithm when solving the proposed fault-tolerant strategy for open-circuit faults in a single-phase winding;

[0016] Figure 7 This is a flowchart of the process for solving the fault-tolerant control current in Implementation Method 2;

[0017] Figure 8 This is a flowchart of the process for solving the fault-tolerant control current in implementation methods three to six. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0020] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0021] Specific Implementation Method 1: The fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor described in this implementation method includes fault-tolerant control strategies for open-circuit faults in any one phase, any two phases, or any three phases of the winding:

[0022] The remaining normal phase winding current is adjusted to suppress the increase in torque fluctuation caused by the winding open circuit fault. The remaining normal phase winding current is determined based on the fault-tolerant control current.

[0023] The process for obtaining the fault-tolerant control current of the remaining phase winding is as follows:

[0024] Based on the no-load back EMF, establish the relationship between the output torque of the motor under the fault-tolerant state of the winding open circuit fault and the fault-tolerant control current of the remaining phase winding. Then, establish the relationship between the constant torque component, the amplitude of the second torque fluctuation and the amplitude of the fourth torque fluctuation and the fault-tolerant control current of the remaining phase winding.

[0025] The multi-objective particle swarm optimization algorithm is used to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations.

[0026] The open-circuit faults described in this embodiment include open circuits in any one phase, any two phases, or any three phases of the winding. Taking an open-circuit fault in phase A as an example, the handling method for open circuits in other phases is the same. An open circuit in any two phases includes open circuits in adjacent phases and open circuits in phases separated by one phase. An open circuit in adjacent phases is illustrated using an open circuit fault in phases A and B as an example, while an open circuit fault in phases separated by one phase is illustrated using an open circuit fault in phases A and C as an example. An open circuit in any three phases of the winding includes open circuits in adjacent three phases and open circuits in phases separated by one phase. An open circuit in adjacent three phases is illustrated using an open circuit fault in phases A, B, and C as an example, while an open circuit fault in phases separated by one phase is illustrated using an open circuit fault in phases A, B, and D as an example.

[0027] In this embodiment, the motor is driven by a five-phase full-bridge inverter or a five-phase six-bridge inverter, with independent power supply to each phase winding. When an open-circuit fault occurs, the current of the remaining normal phase winding is adjusted to suppress the torque fluctuation caused by the open-circuit fault. However, adjusting the current of the remaining normal phase winding involves modifying the current of the remaining normal phase winding according to the fault-tolerant control current. Therefore, the focus of this embodiment is to solve for the fault-tolerant control current.

[0028] The fault-tolerant control current mainly consists of two parts: amplitude and phase angle. Specifically, it includes the phase angles of the fundamental and third harmonic fault-tolerant control currents, and the amplitudes I1 and I3 of the fundamental and third harmonic fault-tolerant control currents. When different phases experience open-circuit faults, the phase angles of the remaining phases will differ. For example, if phase A is open-circuited, the remaining phases are phases B, C, D, and E. Therefore, the phase angles of the remaining phase fault-tolerant control currents include information from all four phases (B, C, D, and E). The phase angles of the fundamental and third harmonic fault-tolerant control currents in phase B are θ. B1 and θ B3 Similarly, the phase angles of the fundamental and third harmonic fault-tolerant control currents of phases C, D, and E are θ, respectively. C1 and θ C3 θ D1 and θ D3 θ E1 and θ E3 In this implementation, the fundamental frequency, third harmonic amplitude, and phase angle of the fault-tolerant control current are solved using a multi-objective particle swarm optimization algorithm, which requires the construction of the following various relationships:

[0029] Calculate the output torque of the motor winding under fault-tolerant state with open-circuit fault based on the fault-tolerant control current of the remaining phase winding and the no-load back EMF.

[0030] Construct the constant torque component T of the output torque c The relationship is related to the fundamental back EMF E1 and the fundamental fault-tolerant control current, the third harmonic back EMF E3 and the third harmonic fault-tolerant control current.

[0031] A formula for the amplitude of the second-order torque fluctuation is constructed. This formula is related to the fundamental back EMF E1 and the fundamental fault-tolerant control current, the third harmonic back EMF E3 and the fundamental fault-tolerant control current, the fundamental back EMF E1 and the third harmonic fault-tolerant control current, and the fifth harmonic back EMF E5 and the third harmonic fault-tolerant control current.

[0032] A fourth-order torque fluctuation amplitude relationship is constructed, which is related to the third harmonic back EMF E3 and the fundamental fault-tolerant control current, the fifth harmonic back EMF E5 and the fundamental fault-tolerant control current, and the fundamental back EMF E1 and the third harmonic fault-tolerant control current.

[0033] It can be seen that all the above relationships are related to the fault-tolerant control current. Taking an open-circuit fault in phase A as an example, the variables to be solved in the fault-tolerant control current include: θ B1 θ B3 θ C1 θ C3 θ D1 θ D3 θ E1 θ E3 I1 and I3; This implementation uses a multi-objective particle swarm optimization algorithm to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations. After solving for each variable of the fault-tolerant control current, the remaining corresponding adjustment values ​​can be obtained so that the fault-tolerant control current of the remaining normal phase winding can be independently controlled by the controller, without being constrained by the neutral point current being zero.

[0034] Specific Implementation Method Two: The following is combined with... Figure 1 , Figure 6 and Figure 7 This embodiment describes a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor. This strategy includes a fault-tolerant control strategy for any one phase winding being open-circuited.

[0035] When the motor is operating normally, i.e., without a winding open-circuit fault, the current in each phase is:

[0036] i A =15cos(ω e t)

[0037]

[0038]

[0039]

[0040]

[0041] Among them, i A i B i C i D i E These represent the winding currents of phases A, B, C, D, and E under normal operating conditions, ω. e Let be the electric angular velocity of the motor.

[0042] Taking an open-circuit fault occurring in phase A as an example, and combining this with a specific instance of a 45-slot, 12-pole five-phase permanent magnet synchronous motor with open windings, the amplitude of the motor phase current under normal operating conditions is I = 15A. When an open-circuit fault occurs in the phase A winding of the five-phase permanent magnet synchronous motor, the currents of the remaining normal phases, namely phases B, C, D, and E, are adjusted as follows:

[0043]

[0044] To perform the operation, the torque fluctuation caused by an open-circuit fault in one phase winding is suppressed; where ω e The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where θ B1 and θ B3 θ C1 and θ C3 θ D1 and θ D3 θ E1 and θ E3 I1 and I3 are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phases B, C, D, and E, respectively; I1 and I3 are the amplitudes of the remaining phase fundamental and third harmonic fault-tolerant control currents, respectively, and I1 and I3 satisfy the following relationship:

[0045]

[0046] In the formula, a is the third harmonic current injection rate, and I is the amplitude of the motor phase current under normal operating conditions, I = 15A;

[0047] The no-load back EMF of phases B, C, D, and E is given as follows:

[0048]

[0049] Where E 2k+1 The amplitude of the (2k+1)th reverse EMF harmonic;

[0050] The output torque of the motor under fault-tolerant conditions with an open-circuit fault in one phase winding is calculated based on the fault-tolerant control current of phases B, C, D, and E and the no-load back EMF.

[0051] The constant torque component T of the output torque c It is generated by the interaction of the fundamental back EMF E1 and the fundamental fault-tolerant control current, and the third harmonic back EMF E3 and the third harmonic fault-tolerant control current, as shown in the following equation:

[0052]

[0053] ω m This refers to the mechanical angular velocity of the motor.

[0054] Secondary torque ripple is generated by the interaction of the fundamental back EMF E1 and the fundamental fault-tolerant control current, the third harmonic back EMF E3 and the fundamental fault-tolerant control current, the fundamental back EMF E1 and the third harmonic fault-tolerant control current, and the fifth harmonic back EMF E5 and the third harmonic fault-tolerant control current. The amplitude of secondary torque ripple is T. 2f As shown in the following formula:

[0055]

[0056] Where K1, K2, K3, K4, K5, K6, K7, and K8 are coefficients related to the phase angle of the fault-tolerant control current in the secondary torque ripple, as shown in the following formula:

[0057]

[0058] The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF E3 and the fundamental fault-tolerant control current, the fifth harmonic back EMF E5 and the fundamental fault-tolerant control current, and the fundamental back EMF E1 and the third harmonic fault-tolerant control current. Since the amplitude of the seventh harmonic back EMF is relatively low, the fourth-order torque ripple generated by the seventh harmonic back EMF and the third harmonic fault-tolerant control current is ignored. The amplitude of the fourth-order torque ripple is T. 4f As shown in the following formula:

[0059]

[0060] Where Q1, Q2, Q3, Q4, Q5, and Q6 are coefficients related to the phase angle of the fault-tolerant control current in the four torque ripples, as shown in the following formula:

[0061]

[0062] The variables to be solved in the fault-tolerant control current include: θ B1 θ B3 θ C1 θ C3 θ D1 θ D3 θ E1 θ E3 I1 and I3; see also Figure 7 The solution process is as follows:

[0063] First, determine the amplitude E of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. 2k+1 and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component T of the motor after applying the fault-tolerant control current is calculated. c Secondary torque fluctuation amplitude T 2f and the amplitude of the fourth torque fluctuation T 4f The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation:

[0064]

[0065] The Pareto front solution obtained after running the multi-objective particle swarm optimization algorithm is as follows: Figure 6 As shown, the specific steps of the multi-objective particle swarm optimization algorithm include: 1) Determining the range of values ​​for the variable to be solved, and treating the variable as a movable particle with velocity and position attributes. The position of the particle represents the value of the variable to be solved, and determining the maximum moving velocity of the particle based on the range of values ​​of the variable to be solved; 2) Initializing the particle position using Latin hypercube sampling; 3) Utilizing the particle position combined with T c T 2f and T 4f The expression calculates the value of the constant torque component corresponding to the particle, the sum of the amplitudes of the second and fourth torque fluctuations, determines the individual optimal solution of the particle in the evolution process, further calculates the dominance and crowding of the particle swarm, and obtains the Pareto front solution and the global optimal solution; 4) Allow the particle to iterate its position and velocity according to the evolution formula of the multi-objective particle swarm algorithm; 5) Repeat the iteration process until the upper limit is reached; 6) Obtain the Pareto front solution after completing all iterations; 7) Select a set of solutions from the Pareto front solution as the phase angle and amplitude of the final fault-tolerant control current. This solution enables the second and fourth torque fluctuations to obtain low values ​​simultaneously, thereby reducing the overall torque fluctuation of the motor. The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current, as shown in the following formula:

[0066] i B =14.73cos(ω) e t-1.24)+2.86cos(3ω e t-1.32)

[0067] i C =14.73cos(ω) e t-2.72)+2.86cos(3ω e t-4.55)

[0068] i D =14.73cos(ω) e t+2.72)+2.86cos(3ω e t+4.55)

[0069] i E =14.73cos(ω) e t+1.24)+2.86cos(3ω e t+1.32)

[0070] Figure 1The figure shows a comparison of the torque waveforms of the motor under normal operation, when one phase winding is open-circuited and uncontrolled, and when the proposed fault-tolerant control strategy is applied. It can be seen from the figure that after applying the proposed fault-tolerant control strategy, the torque fluctuation of the motor is reduced compared with the uncontrolled fault situation. This proves that the proposed fault-tolerant control strategy can effectively suppress the increase in motor torque fluctuation caused by the fault and improve the torque output quality of the motor during fault-tolerant operation.

[0071] Specific Implementation Method Three: The following is combined with... Figure 2 and Figure 8 This embodiment describes a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor. This strategy includes a fault-tolerant control strategy for any two adjacent phase windings being open-circuited.

[0072] When the motor is operating normally, i.e., without a winding open-circuit fault, the current in each phase is:

[0073] i A =15cos(ω e t)

[0074]

[0075]

[0076]

[0077]

[0078] Among them, i A i B i C i D i E These represent the winding currents of phases A, B, C, D, and E under normal operating conditions, ω. e Let be the electric angular velocity of the motor.

[0079] Taking an open-circuit fault occurring in phases A and B as an example, and combining this with a specific instance of a 45-slot, 12-pole five-phase permanent magnet synchronous motor with open windings, the amplitude of the motor phase current under normal operating conditions is I = 15A. When an open-circuit fault occurs in the windings of adjacent phases A and B of the five-phase permanent magnet synchronous motor, the remaining normal phases, i.e., the winding currents of phases C, D, and E, are adjusted according to the fault-tolerant control current:

[0080]

[0081] This is done to suppress the increase in torque fluctuation caused by an open-circuit fault in two adjacent phase windings; where ω e The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where θ C1 and θ C3θ D1 and θ D3 θ E1 and θ E3 I1 and I3 are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phases C, D, and E, respectively; I1 and I3 are the amplitudes of the remaining phase fundamental and third harmonic fault-tolerant control currents, respectively, and I1 and I3 satisfy the following relationship:

[0082]

[0083] In the formula, a is the third harmonic current injection rate, and I is the amplitude of the motor phase current under normal operating conditions, I = 15A;

[0084] The no-load back EMF of phases C, D, and E is given as follows:

[0085]

[0086] Where E 2k+1 The amplitude of the (2k+1)th reverse EMF harmonic;

[0087] The output torque of the motor under fault-tolerant state with open circuit fault in two adjacent phase windings is calculated based on the fault-tolerant control current of the C, D, and E phase windings and the no-load back EMF.

[0088] The constant torque component T of the output torque c It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation:

[0089]

[0090] ω m This refers to the mechanical angular velocity of the motor.

[0091] Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple is T. 2f As shown in the following formula:

[0092]

[0093] Where K1, K2, K3, K4, K5, K6, K7, and K8 are coefficients related to the phase angle of the fault-tolerant control current in the secondary torque ripple, as shown in the following formula:

[0094]

[0095] The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. Since the amplitude of the seventh harmonic back EMF is relatively low, the fourth-order torque ripple generated by the seventh harmonic back EMF and the third harmonic fault-tolerant control current is ignored. The amplitude T of the fourth-order torque ripple is... 4f As shown in the following formula:

[0096]

[0097] Where Q1, Q2, Q3, Q4, Q5, and Q6 are coefficients related to the phase angle of the fault-tolerant control current in the four torque ripples, as shown in the following formula:

[0098]

[0099] The variables to be solved in the fault-tolerant control current include: θ C1 θ C3 θ D1 θ D3 θ E1 θ E3 I1 and I3; see also Figure 8 The solution process is as follows:

[0100] First, determine the amplitude E of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. 2k+1 and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component T of the motor after applying the fault-tolerant control current is calculated. c Secondary torque fluctuation amplitude T 2f and the amplitude of the fourth torque fluctuation T 4f The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation:

[0101] [Max(T c Min(T) 2f +T 4f )]

[0102] The specific steps of the multi-objective particle swarm optimization algorithm include: 1) Determining the range of values ​​for the variable to be solved, and treating the variable as a movable particle with velocity and position attributes. The position of the particle represents the value of the variable to be solved, and determining the maximum moving velocity of the particle based on the range of values ​​of the variable to be solved; 2) Initializing the particle position using Latin hypercube sampling; 3) Utilizing the particle position combined with T c T 2f and T 4fThe expression calculates the value of the constant torque component corresponding to the particle, the sum of the amplitudes of the second and fourth torque fluctuations, determines the individual optimal solution of the particle in the evolution process, further calculates the dominance and crowding of the particle swarm, and obtains the Pareto front solution and the global optimal solution; 4) Allow the particle to iterate its position and velocity according to the evolution formula of the multi-objective particle swarm algorithm; 5) Repeat the iteration process until the upper limit is reached; 6) Obtain the Pareto front solution after completing all iterations; 7) Select a set of solutions from the Pareto front solution as the phase angle and amplitude of the final fault-tolerant control current. This solution enables the second and fourth torque fluctuations to obtain low values ​​simultaneously, thereby reducing the overall torque fluctuation of the motor. The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current, as shown in the following formula:

[0103] i C =14.86cos(ω) e t-2.68)+2.06cos(3ω e t-5.32)

[0104] i D =14.86cos(ω) e t-3.67)+2.06cos(3ω e t-2.64)

[0105] i E =14.86cos(ω) e t-4.63)+2.06cos(3ω e t-5.07)

[0106] Figure 2 The figure shows a comparison of the torque waveforms of the motor during normal operation, when there is an open-circuit fault in two adjacent phase windings, and when the proposed fault-tolerant control strategy is applied. It can be seen from the figure that after applying the proposed fault-tolerant control strategy, the torque fluctuation of the motor is reduced compared with the case of an open-circuit fault. This proves that the proposed fault-tolerant control strategy can effectively suppress the increase in motor torque fluctuation caused by the fault and improve the torque output quality of the motor during fault-tolerant operation.

[0107] Specific Implementation Method Four: The following is combined with... Figure 3 and Figure 8 This embodiment describes a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor. This strategy includes a fault-tolerant control strategy for open-circuit faults in any two-phase windings:

[0108] When the motor is operating normally, i.e., without a winding open-circuit fault, the current in each phase is:

[0109] i A =15cos(ω e t)

[0110]

[0111]

[0112]

[0113]

[0114] Among them, i A i B i C i D i E These represent the winding currents of phases A, B, C, D, and E under normal operating conditions, ω. e Let be the electric angular velocity of the motor.

[0115] Taking an open-circuit fault occurring in phases A and C as an example, and combining this with a specific instance of a 45-slot, 12-pole five-phase permanent magnet synchronous motor using an open winding configuration, the amplitude of the motor phase current under normal operating conditions is I = 15A. When a two-phase open-circuit fault occurs in the five-phase permanent magnet synchronous motor, assuming the open-circuit fault occurs in phases A and C, the current of the remaining normal phases, i.e., phases B, D, and E, is adjusted as follows:

[0116]

[0117] This is done to suppress the increase in torque fluctuation caused by an open-circuit fault in two phases of the winding; where ω e The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where θ B1 and θ B3 θ D1 and θ D3 θ E1 and θ E3 I1 and I3 are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phases B, D, and E, respectively; I1 and I3 are the amplitudes of the remaining phase fundamental and third harmonic fault-tolerant control currents, respectively, and I1 and I3 satisfy the following relationship:

[0118]

[0119] In the formula, a is the third harmonic current injection rate, and I is the amplitude of the motor phase current under normal operating conditions, I = 15A;

[0120] The no-load back EMF of phases B, D, and E is given as follows:

[0121]

[0122] Where E 2k+1 The amplitude of the (2k+1)th reverse EMF harmonic;

[0123] The output torque of the motor under fault-tolerant state with open circuit fault in two phases of windings is calculated based on the fault-tolerant control current of phases B, D, and E and the no-load back EMF.

[0124] The constant torque component T of the output torque c It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation:

[0125]

[0126] ω m This refers to the mechanical angular velocity of the motor.

[0127] Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple is T. 2f As shown in the following formula:

[0128]

[0129] Where K1, K2, K3, K4, K5, K6, K7, and K8 are coefficients related to the phase angle of the fault-tolerant control current in the secondary torque ripple, as shown in the following formula:

[0130]

[0131] The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. Since the amplitude of the seventh harmonic back EMF is relatively low, the fourth-order torque ripple generated by the seventh harmonic back EMF and the third harmonic fault-tolerant control current is ignored. The amplitude T of the fourth-order torque ripple is... 4f As shown in the following formula:

[0132]

[0133] Where Q1, Q2, Q3, Q4, Q5, and Q6 are coefficients related to the phase angle of the fault-tolerant control current in the four torque ripples, as shown in the following formula:

[0134]

[0135] The variables to be solved in the fault-tolerant control current include: θ B1 θ B3 θ D1 θ D3 θ E1 θ E3I1 and I3; see also Figure 8 The solution process is as follows:

[0136] First, determine the amplitude E of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. 2k+1 and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component T of the motor after applying the fault-tolerant control current is calculated. c Secondary torque fluctuation amplitude T 2f and the amplitude of the fourth torque fluctuation T 4f The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation:

[0137] [Max(T c Min(T) 2f +T 4f )]

[0138] The specific steps of the multi-objective particle swarm optimization algorithm include: 1) Determining the range of values ​​for the variable to be solved, and treating the variable as a movable particle with velocity and position attributes. The position of the particle represents the value of the variable to be solved, and determining the maximum moving velocity of the particle based on the range of values ​​of the variable to be solved; 2) Initializing the particle position using Latin hypercube sampling; 3) Utilizing the particle position combined with T c T 2f and T 4f The expression calculates the value of the constant torque component corresponding to the particle, the sum of the amplitudes of the second and fourth torque fluctuations, determines the individual optimal solution of the particle in the evolution process, further calculates the dominance and crowding of the particle swarm, and obtains the Pareto front solution and the global optimal solution; 4) Allow the particle to iterate its position and velocity according to the evolution formula of the multi-objective particle swarm algorithm; 5) Repeat the iteration process until the upper limit is reached; 6) Obtain the Pareto front solution after completing all iterations; 7) Select a set of solutions from the Pareto front solution as the phase angle and amplitude of the final fault-tolerant control current. This solution enables the second and fourth torque fluctuations to obtain low values ​​simultaneously, thereby reducing the overall torque fluctuation of the motor. The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current, as shown in the following formula:

[0139] i B =14.46cos(ω) e t-1.23)+3.98cos(3ω e t-0.62)

[0140] i D =14.46cos(ω) et-3.59)+3.98cos(3ω e t-2.54)

[0141] i E =14.46cos(ω) e t-5.19)+3.98cos(3ω e t-4.85)

[0142] Figure 3 The figure shows a comparison of the torque waveforms of the motor under normal operation, under an uncontrolled open-circuit fault in two phases of the winding, and under the proposed fault-tolerant control strategy. It can be seen from the figure that after applying the proposed fault-tolerant control strategy, the torque fluctuation of the motor is reduced compared to the uncontrolled fault situation. This proves that the proposed fault-tolerant control strategy can effectively suppress the increase in motor torque fluctuation caused by the fault and improve the torque output quality of the motor under fault-tolerant operation.

[0143] Specific Implementation Method Five: The following is combined with... Figure 4 and Figure 8 This embodiment describes a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor. This strategy includes a fault-tolerant control strategy for open-circuit faults in any three adjacent phase windings.

[0144] When the motor is operating normally, i.e., without a winding open-circuit fault, the current in each phase is:

[0145] i A =15cos(ω e t)

[0146]

[0147]

[0148]

[0149]

[0150] Among them, i A i B i C i D i E These represent the winding currents of phases A, B, C, D, and E under normal operating conditions, ω. e Let be the electric angular velocity of the motor.

[0151] Taking an open-circuit fault occurring in phases A, B, and C as an example, and combining this with a specific instance of a 45-slot, 12-pole five-phase permanent magnet synchronous motor using an open winding configuration, the amplitude of the motor phase current under normal operating conditions is I = 15A. When an open-circuit fault occurs in three adjacent phases of the five-phase permanent magnet synchronous motor, assuming the open-circuit fault occurs in phases A, B, and C, the current of the remaining normal phases, i.e., phases D and E, is adjusted as follows:

[0152]

[0153] This is done to suppress the increase in torque fluctuation caused by an open-circuit fault in adjacent three-phase windings; where ω e The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where θ D1 and θ D3 θ E1 and θ E3 I1 and I3 are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phases D and E, respectively; I1 and I3 are the amplitudes of the remaining phase fundamental and third harmonic fault-tolerant control currents, respectively, and I1 and I3 satisfy the following relationship:

[0154]

[0155] In the formula, a is the third harmonic current injection rate, and I is the amplitude of the motor phase current under normal operating conditions, I = 15A;

[0156] The no-load back EMF of phases D and E is given as follows:

[0157]

[0158] Where E 2k+1 The amplitude of the (2k+1)th reverse EMF harmonic;

[0159] The output torque of the motor under fault-tolerant state with open circuit fault in adjacent three-phase windings is calculated based on the fault-tolerant control current of the D and E phase windings and the no-load back EMF.

[0160] The constant torque component T of the output torque c It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation:

[0161]

[0162] ω m This refers to the mechanical angular velocity of the motor.

[0163] Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple is T. 2f As shown in the following formula:

[0164]

[0165] Where K1, K2, K3, K4, K5, K6, K7, and K8 are coefficients related to the phase angle of the fault-tolerant control current in the secondary torque ripple, as shown in the following formula:

[0166]

[0167] The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. Since the amplitude of the seventh harmonic back EMF is relatively low, the fourth-order torque ripple generated by the seventh harmonic back EMF and the third harmonic fault-tolerant control current is ignored. The amplitude T of the fourth-order torque ripple is... 4f As shown in the following formula:

[0168]

[0169] Where Q1, Q2, Q3, Q4, Q5, and Q6 are coefficients related to the phase angle of the fault-tolerant control current in the four torque ripples, as shown in the following formula:

[0170]

[0171] The variables to be solved in the fault-tolerant control current include: θ D1 θ D3 θ E1 θ E3 I1 and I3; see also Figure 8 The solution process is as follows:

[0172] First, determine the amplitude E of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. 2k+1 and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component T of the motor after applying the fault-tolerant control current is calculated. c Secondary torque fluctuation amplitude T 2f and the amplitude of the fourth torque fluctuation T 4f The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation:

[0173] [Max(Tc Min(T) 2f +T 4f )]

[0174] The specific steps of the multi-objective particle swarm optimization algorithm include: 1) Determining the range of values ​​for the variable to be solved, and treating the variable as a movable particle with velocity and position attributes. The position of the particle represents the value of the variable to be solved, and determining the maximum moving velocity of the particle based on the range of values ​​of the variable to be solved; 2) Initializing the particle position using Latin hypercube sampling; 3) Utilizing the particle position combined with T c T 2f and T 4f The expression calculates the value of the constant torque component corresponding to the particle, the sum of the amplitudes of the second and fourth torque fluctuations, determines the individual optimal solution of the particle in the evolution process, further calculates the dominance and crowding of the particle swarm, and obtains the Pareto front solution and the global optimal solution; 4) Allow the particle to iterate its position and velocity according to the evolution formula of the multi-objective particle swarm algorithm; 5) Repeat the iteration process until the upper limit is reached; 6) Obtain the Pareto front solution after completing all iterations; 7) Select a set of solutions from the Pareto front solution as the phase angle and amplitude of the final fault-tolerant control current. This solution enables the second and fourth torque fluctuations to obtain low values ​​simultaneously, thereby reducing the overall torque fluctuation of the motor. The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current, as shown in the following formula:

[0175] i D =14.76cos(ω) e t-3.79)+2.67cos(3ω e t-3.93)

[0176] i E =14.76cos(ω) e t-5.21)+2.67cos(3ω e t-4.04)

[0177] Figure 4 The figure shows a comparison of the torque waveforms of the motor under normal operation, when there is an open circuit fault in the adjacent three-phase windings, and when the proposed fault-tolerant control strategy is applied. It can be seen from the figure that after applying the proposed fault-tolerant control strategy, the torque fluctuation of the motor is reduced compared with the case of an open circuit fault. This proves that the proposed fault-tolerant control strategy can effectively suppress the increase in motor torque fluctuation caused by the fault and improve the torque output quality of the motor during fault-tolerant operation.

[0178] Specific Implementation Method Six: The following is combined with... Figure 5 and Figure 8This embodiment describes a fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor. This strategy includes a fault-tolerant control strategy for open-circuit faults in any three-phase windings spaced apart.

[0179] When the motor is operating normally, i.e., without a winding open-circuit fault, the current in each phase is:

[0180] i A =15cos(ω e t)

[0181]

[0182]

[0183]

[0184]

[0185] Among them, i A i B i C i D i E These represent the winding currents of phases A, B, C, D, and E under normal operating conditions, ω. e Let be the electric angular velocity of the motor.

[0186] Taking an open-circuit fault occurring in phases A, B, and D as an example, and combining this with a specific instance of a 45-slot, 12-pole five-phase permanent magnet synchronous motor using an open winding configuration, the amplitude of the motor phase current under normal operating conditions is I = 15A. When a three-phase open-circuit fault occurs in the five-phase permanent magnet synchronous motor, assuming the open-circuit fault occurs in phases A, B, and D, the current of the remaining normal phases, i.e., phases C and E, is adjusted as follows:

[0187]

[0188] To suppress the increase in torque fluctuation caused by open-circuit faults in three phase windings; where ω e The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where θ C1 and θ C3 θ E1 and θ E3 I1 and I3 are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phase C and phase E, respectively; I1 and I3 are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively, and I1 and I3 satisfy the following relationship:

[0189]

[0190] In the formula, a is the third harmonic current injection rate, and I is the amplitude of the motor phase current under normal operating conditions, I = 15A;

[0191] The no-load back EMF of phase C and phase E windings is given as follows:

[0192]

[0193] Where E 2k+1 The amplitude of the (2k+1)th reverse EMF harmonic;

[0194] The output torque of the motor under fault-tolerant state with open circuit fault in three phase-separated windings is calculated based on the fault-tolerant control current of the C and E phase windings and the no-load back EMF.

[0195] The constant torque component T of the output torque c It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation:

[0196]

[0197] Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple is T. 2f As shown in the following formula:

[0198]

[0199] Where K1, K2, K3, K4, K5, K6, K7, and K8 are coefficients related to the phase angle of the fault-tolerant control current in the secondary torque ripple, as shown in the following formula:

[0200]

[0201] The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. Since the amplitude of the seventh harmonic back EMF is relatively low, the fourth-order torque ripple generated by the seventh harmonic back EMF and the third harmonic fault-tolerant control current is ignored. The amplitude T of the fourth-order torque ripple is... 4f As shown in the following formula:

[0202]

[0203] Where Q1, Q2, Q3, Q4, Q5, and Q6 are coefficients related to the phase angle of the fault-tolerant control current in the four torque ripples, as shown in the following formula:

[0204]

[0205] The variables to be solved in the fault-tolerant control current include: θ C1 θ C3 θ E1 θ E3 I1 and I3; see also Figure 8 The solution process is as follows:

[0206] First, determine the amplitude E of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. 2k+1 and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component T of the motor after applying the fault-tolerant control current is calculated. c Secondary torque fluctuation amplitude T 2f and the amplitude of the fourth torque fluctuation T 4f The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation:

[0207] [Max(T c Min(T) 2f +T 4f )]

[0208] The specific steps of the multi-objective particle swarm optimization algorithm include: 1) Determining the range of values ​​for the variable to be solved, and treating the variable as a movable particle with velocity and position attributes. The position of the particle represents the value of the variable to be solved, and determining the maximum moving velocity of the particle based on the range of values ​​of the variable to be solved; 2) Initializing the particle position using Latin hypercube sampling; 3) Utilizing the particle position combined with T c T 2f and T 4f The expression calculates the value of the constant torque component corresponding to the particle, the sum of the amplitudes of the second and fourth torque fluctuations, determines the individual optimal solution of the particle in the evolution process, further calculates the dominance and crowding of the particle swarm, and obtains the Pareto front solution and the global optimal solution; 4) Allow the particle to iterate its position and velocity according to the evolution formula of the multi-objective particle swarm algorithm; 5) Repeat the iteration process until the upper limit is reached; 6) Obtain the Pareto front solution after completing all iterations; 7) Select a set of solutions from the Pareto front solution as the phase angle and amplitude of the final fault-tolerant control current. This solution enables the second and fourth torque fluctuations to obtain low values ​​simultaneously, thereby reducing the overall torque fluctuation of the motor. The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current, as shown in the following formula:

[0209] i C =14.49cos(ω) et-2.90)+3.89cos(3ω e t-4.27)

[0210] i E =14.49cos(ω) e t-4.63)+3.89cos(3ω e t-5.73)

[0211] Figure 5 The figure shows a comparison of the torque waveforms of the motor under normal operation, under an uncontrolled three-phase open-circuit fault, and under the proposed fault-tolerant control strategy. It can be seen from the figure that after applying the proposed fault-tolerant control strategy, the torque fluctuation of the motor is reduced compared to the uncontrolled fault situation. This proves that the proposed fault-tolerant control strategy can effectively suppress the increase in motor torque fluctuation caused by the fault and improve the torque output quality of the motor under fault-tolerant operation.

[0212] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims.

Claims

1. A fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor, characterized in that: This strategy is applicable to open-circuit faults in any phase winding. When an open-circuit fault occurs in any phase winding, this strategy adjusts the current of the remaining normal phase winding to suppress the torque fluctuation caused by the open-circuit fault. The remaining normal phase winding current is determined based on the fault-tolerant control current. The process for obtaining the fault-tolerant control current of the remaining normal phase winding is as follows: Based on the no-load back EMF, establish the relationship between the output torque of the motor under the fault-tolerant state of the winding open circuit fault and the fault-tolerant control current of the remaining phase winding. Then, establish the relationship between the constant torque component, the amplitude of the second torque fluctuation and the amplitude of the fourth torque fluctuation and the fault-tolerant control current of the remaining phase winding. The multi-objective particle swarm optimization algorithm is used to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations. The fault-tolerant control strategy for any phase winding being open is as follows: When an open circuit occurs in phase A winding, the remaining normal phases, i.e., the winding currents of phases B, C, D, and E, are adjusted according to the fault-tolerant control current: This is done to suppress the increase in torque fluctuation caused by an open-circuit fault in one phase winding; where, The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where... and , and , and , and These are the phase angles of the fundamental and third harmonic fault-tolerant control currents for phases B, C, D, and E, respectively. and These are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively. and The following relationship is satisfied: In the formula, The third harmonic current injection rate, This represents the amplitude of the motor phase current under normal operating conditions. The no-load back EMF of phases B, C, D, and E is: in, for The amplitude of the second back EMF harmonic; The output torque of the motor under fault-tolerant conditions with an open-circuit fault in one phase winding is calculated based on the fault-tolerant control current of phases B, C, D, and E and the no-load back EMF. The constant torque component of the output torque From the fundamental back potential and fundamental fault-tolerant control current, third harmonic back EMF It is generated by the interaction with the third harmonic fault-tolerant control current, as shown in the following equation: This refers to the mechanical angular velocity of the motor. Secondary torque ripple is caused by the fundamental back EMF and fundamental fault-tolerant control current, third harmonic back EMF and fundamental fault-tolerant control current, fundamental back EMF And third harmonic fault-tolerant control current, fifth harmonic back EMF The second torque ripple amplitude is generated by the interaction with the third harmonic fault-tolerant control current. As shown in the following formula: in , , , , , , and The coefficient related to the phase angle of the fault-tolerant control current in the secondary torque ripple is shown in the following formula: The fourth torque ripple is caused by the third harmonic back electromotive force. and fundamental fault-tolerant control current, fifth harmonic back EMF and fundamental fault-tolerant control current, fundamental back EMF The fourth torque ripple amplitude is generated by the interaction with the third harmonic fault-tolerant control current. As shown in the following formula: in: , , , , , The coefficient related to the phase angle of the fault-tolerant control current in the four torque ripples is shown in the following formula: The variables to be solved in the fault-tolerant control current include: , , , , , , , , and The solution process is as follows: First, determine the amplitude of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component of the motor after applying the fault-tolerant control current is calculated. Secondary torque fluctuation amplitude and the amplitude of the fourth torque fluctuation The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation: The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current.

2. A fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor, characterized in that: This strategy is applicable to open-circuit faults in any two-phase windings, including open-circuit faults in any two adjacent windings and open-circuit faults in any two windings separated by any phase. When an open-circuit fault occurs in any two phases of the winding, this strategy adjusts the current of the remaining normal phase winding to suppress the increase in torque fluctuation caused by the open-circuit fault. The current of the remaining normal phase winding is determined based on the fault-tolerant control current. The process for obtaining the fault-tolerant control current of the remaining normal phase winding is as follows: Based on the no-load back EMF, establish the relationship between the output torque of the motor under the fault-tolerant state of the winding open circuit fault and the fault-tolerant control current of the remaining phase winding. Then, establish the relationship between the constant torque component, the amplitude of the second torque fluctuation and the amplitude of the fourth torque fluctuation and the fault-tolerant control current of the remaining phase winding. The multi-objective particle swarm optimization algorithm is used to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations. The fault-tolerant control strategy for any two adjacent phase windings being open is as follows: When an open-circuit fault occurs in phases A and B, the remaining normal phases, i.e., the winding currents of phases C, D, and E, are adjusted according to the fault-tolerant control current: This is done to suppress the increase in torque fluctuation caused by open-circuit faults in two adjacent phase windings; where, The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where... and , and , and These are the phase angles of the fundamental and third harmonic fault-tolerant control currents for phases C, D, and E, respectively. and These are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively. and The following relationship is satisfied: In the formula, The third harmonic current injection rate, This represents the amplitude of the motor phase current under normal operating conditions. The no-load back EMF of phases C, D, and E windings is: in, for The amplitude of the second back EMF harmonic; The output torque of the motor under fault-tolerant state with open circuit fault in two adjacent phase windings is calculated based on the fault-tolerant control current of the C, D, and E phase windings and the no-load back EMF. The constant torque component of the output torque It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation: This refers to the mechanical angular velocity of the motor. Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple... As shown in the following formula: in , , , , , , and The coefficient related to the phase angle of the fault-tolerant control current in the secondary torque ripple is shown in the following formula: The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. The amplitude of the fourth-order torque ripple... As shown in the following formula: in: , , , , , The coefficient related to the phase angle of the fault-tolerant control current in the four torque ripples is shown in the following formula: The variables to be solved in the fault-tolerant control current include: , , , , , , and The solution process is as follows: First, determine the amplitude of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component of the motor after applying the fault-tolerant control current is calculated. Secondary torque fluctuation amplitude and the amplitude of the fourth torque fluctuation The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation: The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current.

3. The fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor according to claim 2, characterized in that, The fault-tolerant control strategy for open-circuit faults in any two phases of the winding is as follows: When an open-circuit fault occurs in phases A and C, the remaining normal phases are adjusted according to the fault-tolerant control current, i.e., the winding currents of phases B, D, and E are adjusted as follows: This is done to suppress the increase in torque fluctuation caused by an open-circuit fault in two phases of the winding; where, The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where... and , and , and These are the phase angles of the fundamental and third harmonic fault-tolerant control currents for phases B, D, and E, respectively. and These are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively. and The following relationship is satisfied: In the formula, The third harmonic current injection rate, This represents the amplitude of the motor phase current under normal operating conditions. The no-load back EMF of phases B, D, and E windings is: in, for The amplitude of the second back EMF harmonic; The output torque of the motor under fault-tolerant state with open circuit fault in two phases of windings is calculated based on the fault-tolerant control current of phases B, D, and E and the no-load back EMF. The constant torque component of the output torque It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation: This refers to the mechanical angular velocity of the motor. Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple... As shown in the following formula: in , , , , , , and The coefficient related to the phase angle of the fault-tolerant control current in the secondary torque ripple is shown in the following formula: The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. The amplitude of the fourth-order torque ripple... As shown in the following formula: in: , , , , , The coefficient related to the phase angle of the fault-tolerant control current in the four torque ripples is shown in the following formula: The variables to be solved in the fault-tolerant control current include: , , , , , , and The solution process is as follows: First, determine the amplitude of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component of the motor after applying the fault-tolerant control current is calculated. Secondary torque fluctuation amplitude and the amplitude of the fourth torque fluctuation The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation: The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current.

4. A fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor, characterized in that... This strategy is applicable to any three-phase winding open-circuit fault, which includes any adjacent three-phase winding open-circuit fault and any three-phase winding open-circuit fault separated by any phase. When any three-phase winding open-circuit fault occurs, this strategy adjusts the remaining normal phase winding current to suppress the torque fluctuation increase caused by the winding open-circuit fault. The remaining normal phase winding current is determined based on the fault-tolerant control current. The process for obtaining the fault-tolerant control current of the remaining normal phase winding is as follows: Based on the no-load back EMF, establish the relationship between the output torque of the motor under the fault-tolerant state of the winding open circuit fault and the fault-tolerant control current of the remaining phase winding. Then, establish the relationship between the constant torque component, the amplitude of the second torque fluctuation and the amplitude of the fourth torque fluctuation and the fault-tolerant control current of the remaining phase winding. The multi-objective particle swarm optimization algorithm is used to solve for the fault-tolerant control current under the condition of maximizing the constant torque component and minimizing the sum of the amplitudes of the second and fourth torque fluctuations. The fault-tolerant control strategy for any two adjacent three-phase winding open-circuit faults is as follows: When an open-circuit fault occurs in phases A, B, and C, the remaining normal phases, i.e., the winding currents of phases D and E, are adjusted according to the fault-tolerant control current: The operation is performed to suppress the increase in torque fluctuation caused by an open-circuit fault in adjacent three-phase windings; where, The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where... and , and These are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phase D and phase E, respectively. and These are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively. and The following relationship is satisfied: In the formula, The third harmonic current injection rate, This represents the amplitude of the motor phase current under normal operating conditions. The no-load back EMF of phase D and E windings is: in, for The amplitude of the second back EMF harmonic; The output torque of the motor under fault-tolerant state with open circuit fault in adjacent three-phase windings is calculated based on the fault-tolerant control current of the D and E phase windings and the no-load back EMF. The constant torque component of the output torque It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation: This refers to the mechanical angular velocity of the motor. Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple... As shown in the following formula: in , , , , , , and The coefficient related to the phase angle of the fault-tolerant control current in the secondary torque ripple is shown in the following formula: The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. The amplitude of the fourth-order torque ripple... As shown in the following formula: in: , , , , , The coefficient related to the phase angle of the fault-tolerant control current in the four torque ripples is shown in the following formula: The variables to be solved in the fault-tolerant control current include: , , , , and The solution process is as follows: First, determine the amplitude of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component of the motor after applying the fault-tolerant control current is calculated. Secondary torque fluctuation amplitude and the amplitude of the fourth torque fluctuation The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation: The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current.

5. The fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor according to claim 4, characterized in that, The fault-tolerant control strategy for open-circuit faults in any three-phase windings with arbitrary spacing is as follows: When an open-circuit fault occurs in phases A, B, and D, the remaining normal phases, i.e., the winding currents of phases C and E, are adjusted according to the fault-tolerant control current: This is done to suppress the increase in torque fluctuation caused by open-circuit faults in three-phase windings; where, The electric angular velocity of the motor; the fault-tolerant control current includes two parts: amplitude and phase angle, where... and , and These are the phase angles of the fundamental and third harmonic fault-tolerant control currents of phase C and phase E, respectively. and These are the amplitudes of the residual phase fundamental and third harmonic fault-tolerant control currents, respectively. and The following relationship is satisfied: In the formula, The third harmonic current injection rate, This represents the amplitude of the motor phase current under normal operating conditions. The no-load back EMF of phase C and phase E windings is: in, for The amplitude of the second back EMF harmonic; The output torque of the motor under fault-tolerant state with open circuit fault in three phase windings is calculated based on the fault-tolerant control current of the C and E phase windings and the no-load back EMF. The constant torque component of the output torque It is generated by the interaction of the fundamental back EMF and the fundamental fault-tolerant control current, and the third harmonic back EMF and the third harmonic fault-tolerant control current, as shown in the following equation: Secondary torque ripple is generated by the interaction of the fundamental back EMF and fundamental fault-tolerant control current, the third harmonic back EMF and fundamental fault-tolerant control current, the fundamental back EMF and third harmonic fault-tolerant control current, and the fifth harmonic back EMF and third harmonic fault-tolerant control current. The amplitude of secondary torque ripple... As shown in the following formula: in , , , , , , and The coefficient related to the phase angle of the fault-tolerant control current in the secondary torque ripple is shown in the following formula: The fourth-order torque ripple is generated by the interaction of the third harmonic back EMF and the fundamental fault-tolerant control current, the fifth harmonic back EMF and the fundamental fault-tolerant control current, and the fundamental back EMF and the third harmonic fault-tolerant control current. The amplitude of the fourth-order torque ripple... As shown in the following formula: in: , , , , , The coefficient related to the phase angle of the fault-tolerant control current in the four torque ripples is shown in the following formula: The variables to be solved in the fault-tolerant control current include: , , , , and The solution process is as follows: First, determine the amplitude of each harmonic of the no-load back EMF of the five-phase permanent magnet synchronous motor. and the effective value of the remaining normal phase-tolerance control current. The effective value of this current is determined by the heat dissipation conditions of the motor windings; then, the constant torque component of the motor after applying the fault-tolerant control current is calculated. Secondary torque fluctuation amplitude and the amplitude of the fourth torque fluctuation The fault-tolerant control current that maximizes the constant torque component and minimizes the sum of the amplitudes of the second and fourth torque fluctuations can be solved using the multi-objective particle swarm optimization algorithm, as shown in the following equation: The remaining normal phase winding current during an open-circuit fault is determined based on the solved fault-tolerant control current.

6. The fault-tolerant control strategy for third harmonic current injection during open-circuit faults in a five-phase permanent magnet synchronous motor according to claim 1, 2, 3, 4, or 5, is characterized in that... Five-phase full-bridge or five-phase six-bridge inverters are used to power the five-phase permanent magnet synchronous motor.

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