Electrical Machines · Fundamentals

AC Excitation in Magnetic Circuits

Dr. Mithun Mondal BITS Pilani, Hyderabad Campus Electrical Machines

Demonstrative Video

SECTION 01

AC Excitation in Magnetic Circuits

  • To magnetise the magnetic circuits of electrical devices such as transformers, AC machines, electromagnetic relays, etc., AC supply is used.

  • The magnetisation of magnetic circuits is called their excitation.

magnetic core
Magnetic Core

  • The magnetic circuits are never excited by DC supply, because in case of DC excitation the steady-state current is determined by the impressed voltage and resistance of the circuit.

  • \(L_{coil}\) comes into picture only during transient period i.e., when the current is building-up or decaying during switching (ON or OFF) instants.

Key Concepts

  • \(\phi\) adjusts itself in accordance with \(I_{\text{steady-state}}\) so that the relationship imposed by magnetisation (B-H) curve in satisfied.

  • However, with AC excitation, inductance comes into picture even at steady-state condition.

  • As a result for most of the magnetic circuits (not for all) the flux is determined by the impressed voltage and frequency.

  • Then the magnetisation current adjusts itself in accordance with this flux so that the relationship imposed by the magnetisation (B-H) curve is satisfied

  • Usually, for economic reasons, the normal working \(B\) is kept beyond the linear portion of the magnetisation curve thus accurate analysis cannot be predicted for determining self inductance.

  • However, for all practical purposes the parameters of the magnetic circuit are considered to be constant.

Key Concepts
\[\begin{aligned} e&=N \frac{d \phi}{d t} \\ \phi&=\phi_{m} \sin \omega t=\phi_{m} \sin 2 \pi f t \quad \ldots(i) \\ e&=N \frac{d \phi}{d t}=N \frac{d}{d t}\left(\phi_{m} \sin 2 \pi f t\right) \\ &=2 \pi f N \phi_{m} \cos 2 \pi f t=2 \pi f N \phi_{m} \sin \left(2 \pi f t+\frac{\pi}{2}\right) \ldots(i i) \\ E_{m}&=2 \pi f N \phi_{m} \\ E_{r m s}&=\frac{E_{m}}{\sqrt{2}}=\frac{2 \pi f N \phi_{m}}{\sqrt{2}}=4 \cdot 44 f N \phi_{m} \end{aligned}\]

  • Eqs. (i) and (ii) reveal that the induced emf leads the flux and hence the exciting current by \(\frac{\pi}{2}\) radian or \(90^{\circ} .\)

  • Induced emf & coil resistance drop oppose the applied \(V\).

  • In electrical machines, usually the drop in \(R\) is only a few percent of \(V\) and therefore, neglected

  • \(E\) and \(V\) may be considered equal in magnitude.