A simplified prediction method for inter-turn short-circuit fault current in fault-tolerant permanent magnet synchronous motors

Abstract

This invention discloses a simplified prediction method for inter-turn short-circuit fault current in a fault-tolerant permanent magnet synchronous motor (PMSM). The method includes the following steps: Step 1: Based on the fault dynamic model and Kirchhoff's voltage law, obtain the expression for the inter-turn short-circuit fault current of the PMSM; Step 2: Considering the very low inter-phase mutual inductance of the fault-tolerant PMSM, simplify the expression for the inter-turn short-circuit fault current; Step 3: Assuming the motor operates under steady-state conditions, derive the expression for the fault current in the time domain based on the simplified expression in Step 2 and the inverse Laplace transform; Step 4: Treat the fault current in Step 3 as a superposition of a cosine component and a sine component, and derive the expression for the magnitude of the fault current based on trigonometric functions. This invention significantly reduces cost and computational burden compared to traditional methods based on finite element analysis and closed-loop simulation, while maintaining high prediction accuracy.

Description

Technical Field

[0001] This invention belongs to the field of inter-turn short-circuit faults in permanent magnet synchronous motors, and relates to an offline fault current prediction method, specifically a simplified prediction method for inter-turn short-circuit fault currents in fault-tolerant permanent magnet synchronous motors. Background Technology

[0002] Fault-tolerant permanent magnet synchronous motors have been widely used in industrial fields. Among the common fault types in motor systems, inter-turn short-circuit faults are characterized by their high degree of concealment and severe damage. Generally, any diagnosis or fault-tolerance-related research on inter-turn short-circuit faults requires prior offline prediction of the fault current magnitude of the target motor under different fault conditions, reference speeds, and load conditions. Predicting the fault current in advance is beneficial for ensuring system safety, classifying fault levels, and assessing the motor's fault tolerance capability. In previous studies, fault current prediction typically relied on fault dynamic models, obtaining predicted fault current values ​​through finite element analysis or closed-loop simulation. However, when the motor type, motor structure, and operating conditions change, methods based on finite element analysis and closed-loop simulation usually require reconstructing the fault model, which incurs significant workload and computational burden. However, research on how to mitigate the computational burden of fault current prediction is limited. Summary of the Invention

[0003] To address the high cost and computational burden of offline fault current prediction and improve the efficiency of short-circuit current amplitude prediction, this invention provides a simplified prediction method for inter-turn short-circuit fault current in fault-tolerant permanent magnet synchronous motors. This method is simple and computationally inexpensive, showing promising application prospects in aerospace, electric vehicles, and high-reliability fields.

[0004] The objective of this invention is achieved through the following technical solution:

[0005] A simplified prediction method for inter-turn short-circuit fault current in a fault-tolerant permanent magnet synchronous motor includes the following steps:

[0006] Step 1: Based on the fault dynamic model and according to Kirchhoff's voltage law, the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor is obtained:

[0007]

[0008] In the formula, i f R represents the fault current in the time domain. Af ω is the short-circuit turn resistance; j is the imaginary part in units; ω is the electric angular velocity; μ is the short-circuit turns ratio; L A For phase A self-inductance; M AfX The mutual inductance between the short-circuit turn and the healthy phase X; i A e is the phase current of phase A; f R is the short-circuit turn electromotive force;f For fault resistor; L Af For short-circuit turn self-inductance;

[0009] Step 2: Considering the very low inter-phase mutual inductance of the fault-tolerant permanent magnet synchronous motor, the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor is simplified as follows:

[0010]

[0011] Step 3: Assuming the motor operates under steady-state conditions, based on the simplified expression in Step 2, and using the inverse Laplace transform, derive the expression for the fault current in the time domain:

[0012]

[0013] In the formula, ψ PM K represents the amplitude of the fundamental frequency component of the permanent magnet flux linkage, s is a complex operator; c and K s These are two constants related to the motor's operating conditions and fault conditions;

[0014] Step 4: Consider the fault current in Step 3 as a superposition of a cosine component and a sine component. Based on trigonometric relationships, derive the expression for the fault current amplitude:

[0015]

[0016] In the formula, I f Let be the magnitude of the fault current. The above formula is a simplified prediction result of the fault current.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention provides a fault current amplitude prediction method based on Laplace transform, which significantly reduces cost and computational burden compared with traditional methods based on finite element analysis and closed-loop simulation, while maintaining high prediction accuracy. Attached Figure Description

[0019] Figure 1 This is a schematic diagram for fault current prediction.

[0020] Figure 2 The results of short-circuit current experiments under different operating conditions are shown in (a) fault condition one and (b) fault condition two. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0022] This invention provides a simplified prediction method for inter-turn short-circuit fault current in a fault-tolerant permanent magnet synchronous motor, such as... Figure 1 As shown, the method includes the following steps:

[0023] 1. Based on the fault dynamic model and according to Kirchhoff's voltage law, the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor is obtained:

[0024]

[0025] In the formula, i f R represents the fault current in the time domain. Af ω is the short-circuit turn resistance; j is the imaginary part in units; ω is the electric angular velocity; μ is the short-circuit turns ratio; L A For phase A self-inductance; M AfX The mutual inductance between the short-circuit turn and the healthy phase X; i A e is the phase current of phase A; f R is the short-circuit turn electromotive force; f For fault resistor; L Af It is a short-circuit turn self-inductance.

[0026] 2. Due to the very low interphase magnetic coupling of the fault-tolerant permanent magnet synchronous motor, the mutual inductance between the short-circuited turn and the healthy phase X is minimal. Therefore, the expression for the fault current can be simplified to:

[0027]

[0028] 3. Assuming the motor operates under steady-state conditions, by performing an inverse Laplace transform on equation (2), we can obtain the expression for the fault current in the time domain:

[0029]

[0030] In the formula, ψ PM K represents the amplitude of the fundamental frequency component of the permanent magnet flux linkage, s is a complex operator; c and K s These are two constants related to the motor's operating conditions and fault conditions.

[0031] 4. As shown in equation (3), the fault current can be considered as the superposition of a sine component and a cosine component. Therefore, the amplitude of the fault current can be expressed as:

[0032]

[0033] Equation (4) is the simplified prediction result of the fault current proposed in this invention.

[0034] 5. Substitute the parameters such as the rotational speed, load current, short-circuit turns ratio, and fault resistance that you want to predict into equation (4) to obtain the predicted fault current amplitude.

[0035] To verify the effectiveness of the invention, a 12-slot, 10-pole symmetrical six-phase permanent magnet synchronous motor was used as a prototype for experimentation. The basic parameters of the prototype are shown in Table 1. The fault conditions selected in the experiment were: a relatively low fault condition "Fault Condition One" (fault resistance 0.13Ω, short-circuit turns ratio 12.5%) and a relatively high fault condition "Fault Condition Two" (fault resistance 0.04Ω, short-circuit turns ratio 25%). The experimental results of the fault current under different operating conditions and the predicted results of the present invention are compared as follows: Figure 2 As shown in the figure. Experimental results demonstrate that the present invention has high prediction accuracy.

[0036] Table 1 Basic Parameters of Motor

[0037]

[0038] The total cost and burden of fault pre-analysis includes preparation and computation. Generally, finite element analysis typically requires more modeling and computation time than closed-loop simulation. Therefore, to verify the computational advantage of this invention, in the closed-loop simulation, the motor was accelerated from rest, then immediately loaded, and the simulation was stopped immediately after reaching steady state. Under the condition of obtaining one set of data, the computation time of this invention in Mathematica software was 0.0000167s, while the computation time of the closed-loop simulation was 2.291s. The computation time results show that the computation time of this invention is significantly lower than that of the closed-loop simulation, thus resulting in lower computational costs.

Claims

1. A simplified prediction method for inter-turn short-circuit fault current in a fault-tolerant permanent magnet synchronous motor, characterized in that... The method includes the following steps: Step 1: Based on the fault dynamic model and Kirchhoff's voltage law, obtain the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor. Step 2: Considering that the fault-tolerant permanent magnet synchronous motor has very low inter-phase mutual inductance, the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor is simplified. Step 3: Assuming the motor is operating under steady-state conditions, based on the simplified expression in Step 2, and using the inverse Laplace transform, derive the expression for the fault current in the time domain. Step 4: Treat the fault current in Step 3 as a superposition of a cosine component and a sine component. Based on the trigonometric function relationship, derive the expression for the magnitude of the fault current. This expression is the simplified prediction result of the fault current.

2. The simplified prediction method for inter-turn short-circuit fault current of a fault-tolerant permanent magnet synchronous motor according to claim 1, characterized in that... In step 1, the expression for the inter-turn short-circuit fault current of the permanent magnet synchronous motor is: In the formula, i f R represents the fault current in the time domain. Af ω is the short-circuit turn resistance; j is the imaginary part in units; ω is the electric angular velocity; μ is the short-circuit turns ratio; L A For phase A self-inductance; M AfX The mutual inductance between the short-circuit turn and the healthy phase X; i A e is the phase current of phase A; f R is the short-circuit turn electromotive force; f For fault resistor; L Af It is a short-circuit turn self-inductance.

3. The simplified prediction method for inter-turn short-circuit fault current of a fault-tolerant permanent magnet synchronous motor according to claim 2, characterized in that... In step 2, the expression simplifies to:

4. The simplified prediction method for inter-turn short-circuit fault current of a fault-tolerant permanent magnet synchronous motor according to claim 3, characterized in that... In step 3, the expression for the fault current in the time domain is: In the formula, ψ PM K represents the amplitude of the fundamental frequency component of the permanent magnet flux linkage, s is a complex operator; c and K s These are two constants related to the motor's operating conditions and fault conditions.

5. The simplified prediction method for inter-turn short-circuit fault current of a fault-tolerant permanent magnet synchronous motor according to claim 4, characterized in that... In step 4, the expression for the fault current amplitude is: In the formula, I f This represents the magnitude of the fault current.

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