This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy
This chapter is to discuss certain aspects of the theory of magnetically-coupled circuits, with emphasis on transformer action.
The static transformer is not an energy conversion device, but an indispensable component in many energy conversion systems.
It is a significant component in ac power systems:
Electric generation at the most economical generator voltage
Power transfer at the most economical transmission voltage
Power utilization at the most voltage for the particular utilization device
It is widely used in low-power, low-current electronic and control circuits:
Matching the impedances of a source and its load for maximum power transfer
Isolating one circuit from another
Isolating direct current while maintaining ac continuity between two circuits
The transformer is one of the simpler devices comprising two or more electric circuits coupled by a common magnetic circuit.
Its analysis involves many of the principles essential to the study of electric machinery.
§2.1 Introduction to Transformers
Essentially, a transformer consists of two or more windings coupled by mutual magnetic flux.
One of these windings, the primary, is connected to an alternating-voltage.
An alternating flux will be produced whose magnitude will depend on the primary voltage, the frequency of the applied voltage, and the number of turns.
The mutual flux will link the other winding, the secondary, and will induce a voltage in it whose value will depend on the number of secondary turns as well as the magnitude of the mutual flux and the frequency.
By properly proportioning the number of primary and secondary turns, almost any desired voltage ratio, or ratio of transformation, can be obtained.
The essence of transformer action requires only the existence of time-varying mutual flux linking two windings.
Iron-core transformer: coupling between the windings can be made much more effectively using a core of iron or other ferromagnetic material.
The magnetic circuit usually consists of a stack of thin laminations.
Silicon steel has the desirable properties of low cost, low core loss, and high permeability at high flux densities (1.0 to 1.5 T).
Silicon-steel laminations 0.014 in thick are generally used for transformers operating at frequencies below a few hundred hertz.
Two common types of construction: core type and shell type (Fig. 2.1).
Figure 2.1 Schematic views of (a) core-type and (b) shell-type transformers.
Most of the flux is confined to the core and therefore links both windings.
Leakage flux links one winding without linking the other.
Leakage flux is a small fraction of the total flux.
Leakage flux is reduced by subdividing the windings into sections and by placing them as close together as possible.
§2.2 No-Load Conditions
Figure 2.4 shows in schematic form a transformer with its secondary circuit open and an alternating voltage
applied to its primary terminals.
