Abstract
In this chapter, an equivalent circuit model is derived for analysis of the torque-slip characteristics and efficiency of induction machines. This model is not intended for transient dynamic analysis. A more representative model for dynamic analysis will be developed in the next chapter.
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Notes
- 1.
Connection of the illustrated three-phase winding gives rise to a single pole-pair electric machine. However, three-phase motors are commonly configured with multiple pole pairs.
- 2.
Three phases can be connected in either a Y or \(\varDelta \) manner. Y connection is more widely used in automotive and is adopted in this book, but \(\varDelta \) connection also has its applications as it can produce a rather high power and starting torque.
- 3.
Clockwise or anticlockwise rotation of the magnetic field depends on the configuration of phase winding arrangement. If two phases are swopped in space, or if the phase current excitation sequence is changed to ACB instead of ABC, the magnetic field will rotates in a clockwise direction.
- 4.
This principle is generic for AC machines.
- 5.
The notation of \(\omega _{r}\) is also often used in this book for simplicity sake.
- 6.
Hereinafter, the stator speed is referred to as the stator flux rotating speed in this book.
- 7.
Flux is the result of MMF and the magnetic reluctance of the corresponding magnetic path.
- 8.
Here \(\omega _{re}\) is referred to as the electrical rotating speed of the rotor. \(\omega _{re} = N_p\omega _{r}\) as defined by Eq. (2.1).
- 9.
The notations of I and \(I^*_r\) as the rotor current at the stator side will be used exchangeably in this section. It is also called the torque current later on.
- 10.
This is only valid in the relatively high frequency range. Extra voltage is required to compensate the stator resistance loss (and etc.) to maintain the desired magnetic strength, and the therefore constant machine torque.
- 11.
In this case, the maximum torque is achieved with the optimal slip under the constant phase voltage.
- 12.
This method of boosting the phase voltage has an issue when the stator frequency is at or very close to zero. At that range, offset compensation is more effective than scaling compensation.
- 13.
This is a rms value, which shall not be confused with the peak value used in the vector torque control in Chap. 6.
- 14.
By the voltage control alone, the air-gap flux and torque current are coupled to derive the demanded machine torque. By contrast, the vector control decouples the air-gap flux and torque current to regulate torque.
- 15.
Due to the numerical errors, the continuous current is not truly constant in the constant power region.
- 16.
The use of the equivalent model as in Fig. 2.15 for phase diagram analysis is not recommended.
- 17.
When using the magnitude instead of the rms value, the torque is given as \(T_{em}=3/2N_p \overline{\varPsi }_m \overline{I_r^*} \sin (\delta )\).
- 18.
\(\times \) is the cross-product operation for vectors.
- 19.
The copper loss here refers to the conductor loss irrespective of copper or aluminum rotor cage.
- 20.
\({\displaystyle \langle \cdot ,\cdot \rangle }\) is the inner product operation for vectors.
- 21.
IM motors have good efficiency at high speeds, attributed to a low core loss compared to the PM motors.
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Shen, S., Chen, Qz. (2024). Equivalent Circuit Modelling and Analysis. In: Practical Control of Electric Machines for EV/HEVs . Lecture Notes in Electrical Engineering, vol 1064. Springer, Cham. https://doi.org/10.1007/978-3-031-38161-4_2
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