Abstract
In this chapter (which is mainly based on Novotny, Equivalent circuit steady state analysis of inverter driven electric machines, [30]), we will study a method for the fundamental harmonic modelling of inverter supplied rotating field machines. First, we derive fundamental harmonic equivalent circuits for the inverter. These fundamental harmonic circuits are then combined with the steady-state equivalent circuits of rotating field machines to derive the basic characteristics of these inverter-supplied machines. For the modelling of the inverters, the resistive voltage drop over the switches will not be taken into account. Commutation will also be simplified, as most transients will be disregarded.
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Notes
- 1.
This reactive current may be interpreted as corresponding to the short-circuit currents in the two phases that are shorted by the inverter, in each of the six modes.
- 2.
For a VSI switches are always used that can be turned off because a wrong commutation would result in a short circuit of the DC voltage source.
- 3.
For PWM-VSI, the effect is even lower due to the additional reduction factor \(a_{1}^{2}\) for the resistance.
- 4.
Indeed: \(6\cdot (1-s)\pi /3+6\cdot s\pi /3=2\pi \).
- 5.
In contrast, in a traditional (grid) voltage fed drive, the machine and load speed follow the frequency of the supply.
- 6.
When the stator resistance is zero or negligible, two scalar equivalent schemes exist but still no equivalent circuit for the complex phasor quantities exists.
- 7.
See Chap. 7: the voltage drop is equal to \(smfL_{k}I_{d}\) with \(s=2\) for a bridge.
- 8.
Prove that the corresponding resistance in the equivalent circuit is given by \(R_{kre}=\frac{\pi }{2}\omega _{n}L_{kr}\) and \(R_{kre}=\frac{\pi }{6}\omega _{n}L_{kr}\) for a load in delta or wye, respectively.
- 9.
This subtransient inductance is the very small equivalent inductance for a sudden short circuit of a synchronous machine (see Part 4).
- 10.
However, this resistance is dependent on the output frequency.
- 11.
Cf. the trapezoidal current wave form.
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Melkebeek, J.A. (2018). Modelling of Inverter Supplied Rotating Field Machines. In: Electrical Machines and Drives. Power Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-72730-1_16
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DOI: https://doi.org/10.1007/978-3-319-72730-1_16
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