AC Operation of Magnetic Circuits

AC Operation of Magnetic Circuits

For establishing a magnetic field, energy must be spent, though to energy is required to maintain it. Consider an electromagnet’s energising coils as an example. The energy that is supplied to it is used in two different ways: I part of it goes to meet I2R loss and is permanently lost; (ii) part of it goes to create flux and is stored as potential energy in the magnetic field, similar to the potential energy of a raised weight; for example, when a mass M is raised through a height of H, the potential energy that is stored in it is mgh. This mass must be raised, but after reaching a certain height, work is done. It can remain in that position without requiring any additional energy expenditure.

It is possible to recover the electrical energy that was stored in a magnetic field along with the mechanical potential energy. Every change in the current flowing through an inductive coil as it is gradually increased from zero to the maximum value is resisted by the self-induced emf. resulted from this modification. In order to defeat this opposition, energy is required. This energy is captured in the coil’s magnetic field and later released when the field collapses.

The magnetic circuits are excited by the ac supply in many applications and machines, including transformers and a.c. machines. Even in steady state operation, inductance is crucial in this operation even though in direct current it acts as a short circuit. In this scenario, the applied a.c voltage and frequency determine the flux, so the exciting current must adjust to the flux in order for the B-H relationship to always be satisfied.

Consider a coil having N turns wound on iron core as shown in fig

The coil carries an alternating current i varying sinusoidally. Thus the flux produced by the exciting current I is also sinusoidally varying with time.

ϕm = Maximum value of flux in core

ω = 2πf where f is frequency in Hz

According to Faraday’s law as flux changes with respect to coil, the e.m.f. gets induced in the coil given by,

According to Len’s law, the induced e.m.f’s sign must be determined in opposition to changes in the flux. Since current immediately causes flux, the current and flux are in phase. Now that induced emf is a cosine term, it pushes flux and current aside. Given that it opposes the applied voltage, this is known as back e.m.f. Most electromagnetic devices neglect the very small and unnoticeable resistance drops.

Energy stored under AC Operation

The instantaneous electric power input into the magnetic circuit through the coil terminals is given by,

The power is rate of change of energy hence energy input which gets stored in the magnetic field during the interval t1 to t2 is,

Thus Wf is the increase in the field energy as the flux linkages of the coil change from l1 to l2 during the interval t1 to t2 is,

The flux density of the core is changing from B1 to B2 as the flux linkage change from  l1 to l2

Thus is the field energy in terms of field quantities.

This is called fields energy density.