1. Project Background
In skew-slot squirrel-cage induction motors and salient-pole synchronous motors, insufficient insulation between the rotor bars leads to lateral leakage current through the core. This causes axial changes in the current distribution within the bars and core, affecting a range of electromagnetic and mechanical behaviors, including losses, torque, and temperature rise. Significant research has been conducted on the lateral leakage current of squirrel-cage induction motors.
The effects of lateral leakage current on the electromagnetic behavior of damping windings in salient-pole synchronous motors, the effects of lateral leakage current on rotor temperature rise, and the design theory of magnetic poles in salient-pole synchronous motors considering lateral leakage current factors still require further research.
2. The problems addressed and the significance of the paper
This paper summarizes the research findings on lateral leakage current in squirrel-cage induction motors, covering aspects such as generation mechanism, lateral contact resistance and its measurement methods, electromagnetic analysis models and algorithms, and its impact on motor performance. The causes of lateral leakage current in salient-pole synchronous motors and related case studies are introduced. Based on this, in-depth research on design improvements related to lateral leakage current is recommended.
3. Key Contents of the Paper
1) Generation of transverse leakage current
During operation, a squirrel-cage induction motor generates an induced electromotive force (EMF) in its rotor conductors under the influence of a time-varying magnetic field, resulting in a rotor current. Most of this rotor current flows in the conductor bars and end rings. However, in the absence of insulation between the conductor bars and the core, a portion of the current enters the laminations and flows through them into other conductor bars, forming a lateral leakage current. This lateral leakage current is particularly pronounced in induction motors using skewed slots. For certain special-purpose induction motors, if the end ring impedance is sufficiently high, even straight slots can produce a significant lateral leakage current.
2) Factors affecting contact resistivity
The contact resistance between the conductor bars and the core is a crucial factor affecting the lateral leakage current distribution, and the manufacturing process is the primary factor influencing the contact resistivity. The contact resistivity of pressure-cast aluminum conductor bars is generally significantly lower than that of centrifugally cast aluminum conductor bars, while the contact resistivity of welded rotors is generally higher than that of cast aluminum conductor bars. Some conventional processing techniques used in lamination, such as phosphating and oxidation, can improve the contact resistivity between the rotor slot inner surface and the conductor bars to some extent. Even with the same manufacturing process, random factors during production can still cause differences in contact resistivity.
In addition, the contact resistivity of cast aluminum rotors increases with increasing rotor operating temperature.
3) Methods for measuring contact resistance
Contact resistance measurements are generally performed on a squirrel cage that is either intact or has had its end rings removed.
① Complete Rat Cage Method
Figure 1 shows the experimental setup for measuring contact resistance on a complete squirrel cage. A low-voltage DC power supply is connected to a rotor with a shaft: one end is connected to the shaft; to ensure the current flows as evenly as possible into the conductors, the other end is connected to several equally spaced fan blades (four are selected in Figure 1, labeled I, II, III, and IV). The current forms a circuit through the end ring, conductors, core, and shaft.
Figure 1. Measuring the contact resistance between the conductor bar and the iron core on a complete squirrel cage.
The method of measuring contact resistance on a complete cage is relatively easy to implement, but assuming that each conductor is an equipotential body may introduce significant measurement errors. Furthermore, this method actually assumes that the total current is uniformly distributed across all conductors, and the measurement results cannot fully reflect the differences in contact resistance between different conductors.
② End-ring resection method
Figure 2 shows schematic diagrams of two typical end-loop removal methods for measuring contact resistance. The resistance value measured by the end-loop removal method is obtained by dividing the measured voltage by the measured current. This measured resistance has a certain mathematical relationship with the conductor resistance, contact resistance, and core resistance. It is generally believed that the core resistance is much smaller than the contact resistance and can be basically ignored. Therefore, the contact resistance value can be calculated from the measured resistance based on the above mathematical relationship.
Figure 2 shows the contact resistance between the conductor bar and the core after removing the end ring.
The end-ring removal method for measuring contact resistance is difficult to implement and is a destructive method for cast aluminum squirrel cages. However, for welded squirrel cages, it can be performed after the copper bars are installed and before the end rings are welded. Furthermore, because the end-ring removal method allows voltage to be applied to each pair of conductor bars individually, it can measure the differences in contact resistance between different conductor bars to some extent.
4) Calculation method for transverse leakage current
①Analytical method
In early research, analytical methods were developed based on various simplifications and assumptions, given the limited computing power of computers, resulting in limited accuracy. Nevertheless, the idea of multi-segment cascaded circuits laid the theoretical foundation for the later-developed, more practical and accurate multi-section field-circuit coupled two-dimensional time-stepping finite element method. Figure 3 shows a distributed analytical model of the transverse leakage current.
Figure 3 Distributed analytical model of transverse leakage current
② Three-dimensional finite element method
The axial changes in rotor current and magnetic field caused by lateral leakage current are quite complex. Considering the influence of the motor end magnetic field on the lateral leakage current, a three-dimensional finite element model is the most direct and accurate method for analyzing the electromagnetic behavior of lateral leakage current. However, to fully and accurately account for the electromagnetic effects of various time and space harmonics, especially the influence of cogging effect on lateral leakage current, a three-dimensional time-stepping finite element model that can reflect the rotor rotation process is needed.
However, the computational complexity of three-dimensional time-step finite element analysis is enormous for any personal computer today. Therefore, most three-dimensional finite element analyses of transverse leakage current use simplified models.
③ Multi-section two-dimensional finite element method
To avoid the enormous computational burden of the three-dimensional finite element method and to minimize the reduction in model accuracy, two-dimensional multi-section field-circuit coupled time-stepping finite element analysis has been widely applied. Specifically, the motor is divided into several layers along the axial direction, assuming that each layer contains straight slots and the magnetic field does not change with the axial direction. To simulate the skewed slot effect, the rotor portion of each layer is deflected around the motor axis by a certain angle. The magnetic field within each layer is coupled through a circuit that considers lateral leakage current. A squirrel-cage circuit model considering lateral leakage current in the multi-section field-circuit coupled finite element method is shown in Figure 4.
Figure 4 shows a multi-section squirrel-cage circuit model considering transverse leakage current.
④ Summary of various calculation methods
Table 1 summarizes the characteristics of the various calculation methods mentioned above. In the early stages of research on the transverse leakage current of asynchronous motors, analytical methods were used to establish some basic understandings of transverse leakage current. With the improvement of computer computing power, the finite element method, which can more completely reflect the electromagnetic phenomena related to transverse leakage current, has become an indispensable tool in related research.
Table 1. Calculation Method for Lateral Leakage Current of Asynchronous Motors
5) The effect of lateral leakage current
① Stray loss
A. When the contact resistance value approaches the order of magnitude of the conductor bar resistance or approaches the order of magnitude of the insulation resistance, the harmonic loss of the squirrel cage is relatively small, and even smaller under insulation conditions;
B. When the contact resistance value is between the two extreme cases mentioned above, the squirrel cage harmonic loss is quite sensitive to the change in contact resistance. As the contact resistance value increases, it shows a trend of first increasing and then decreasing, and reaches a peak value under a certain contact resistance value.
C. Under different rotor skew angle conditions, the squirrel cage harmonic loss shows the above trend with the change of contact resistance. Moreover, when the contact resistance value is between the two extreme cases, the larger the skew angle, the higher the squirrel cage harmonic loss.
D. The fundamental loss of the squirrel cage is less affected by contact resistance and skewness. The total squirrel cage loss obtained by adding the fundamental and harmonic components shows the same trend as the change in contact resistance and skewness as the squirrel cage harmonic loss.
② Torque
The starting torque of a squirrel-cage induction motor is smaller under conditions of good and poor rotor slot insulation. The effect of lateral leakage current on the starting torque is shown in Figure 5. Under conditions of low contact resistance, the contribution of each layer of the rotor to the starting torque is relatively average; under conditions of high contact resistance, the contributions of each layer of the rotor to the starting torque differ greatly, and even cancel each other out. This explains why the starting torque is smaller under conditions of good and poor rotor slot insulation.
Figure 5 shows the starting torque generated at various points along the rotor axis of the asynchronous motor under different contact resistance conditions (calculation results of a 5-layer multi-section finite element model).
6) Lateral leakage current problem in salient-pole synchronous motors
① Lateral leakage current phenomenon in salient pole synchronous motors
The damping winding of a salient-pole synchronous motor has a similar structure to the squirrel-cage rotor of an asynchronous motor. To suppress stator tooth harmonics, salient-pole synchronous motors often employ skewed slot technology, and lateral leakage current is often unavoidable in their damping windings. While the damping winding current is relatively small during normal operation of a typical synchronous motor, it becomes quite large and persists for extended periods under the following special conditions, requiring special attention.
A. Some low-speed hydro generators have very low rotational speeds, a large number of poles, and often small diameters, resulting in a small number of slots per pole and per phase. This can cause considerable damping winding tooth harmonic currents.
B. When a synchronous motor operates for an extended period under conditions such as eccentricity or asymmetrical load, the current generated in the damping winding cannot be ignored.
C. The damping winding current generated during transient processes such as low-frequency oscillations of synchronous generators and direct starting of synchronous motors should not be ignored.
② Abnormal local temperature rise of rotor caused by lateral leakage current
Due to the uneven air gap, the current in each damping bar of the salient pole synchronous motor is not equal. The lateral leakage current may exacerbate this uneven distribution (including the difference in current between different conductor bars, the difference in current at different axial positions of a single conductor bar, and the difference in lateral leakage current at different positions in the iron core), thereby causing local overheating of the rotor.
Figure 6 presents a typical case of a generator pole failure at a hydroelectric power station in North America. Uneven melting is observed around a damping bar, with more severe melting near the ends than in the middle. Public reports indicate that Hydro-Quebec, in monitoring the temperature of different poles of a skew-slot turbine generator, found significant differences in the temperature distribution across the surface of each pole, while no such difference was found in monitoring the temperature of a straight-slot turbine generator. These cases suggest that localized abnormal temperature rises in the rotor of a salient-pole synchronous motor may be related to lateral leakage current.
Figure 6. Local overheating fault of magnetic poles of a hydro-generator.
4. Outlook and Conclusion
Lateral leakage current is a significant factor affecting the operating performance of squirrel-cage induction motors. Future research requires in-depth analysis of the temperature rise of AC motor rotors under lateral leakage current conditions, particularly the localized abnormal temperature rise phenomena on the damping windings and pole surfaces of salient-pole synchronous motors. To address potential localized overheating faults in AC motor rotors, this research explores temperature rise analysis methods that consider lateral leakage current, aiming to improve traditional rotor structure design theories, especially the pole and damping winding design theories for salient-pole synchronous motors, and to enhance rotor reliability.
Citation information
Zhan Yang, Kong Kangkang, Xu Guorui, et al. A review and prospect of research on transverse leakage current between rotor bars of AC motor [J]. Proceedings of the CSEE, 2018, 38(7):2132-2143.
