Transformers

Primary and Secondary Windings A two-winding transformer consists of two windings interlinked by a mutual magnetic field. Primary winding – energized by connecting it to an input source Secondary winding – winding to which an electrical load is connected and from which output energy is drawn. Primary winding Secondary winding

In instantaneous quantities Ideal Transformers An ideal transformer is a lossless device with an input winding and an output winding. fM The relationships between the input voltage and the output voltage, and between the input current and the output current, are given by the following equations. In instantaneous quantities

Ideal Transformers Np: Number of turns on the primary winding In rms quantities Np: Number of turns on the primary winding Ns: Number of turns on the secondary winding vp(t): voltage applied to the primary side vs(t): voltage at the secondary side a: turns ratio ip(t): current flowing into the primary side is(t): current flowing into the secondary side

Derivation of the Relationship …………….. (1) …………….. (2) Dividing (1) by (2) ………………......……….. (3) From Ampere’s law …………………..……….. (4) Equating (3) and (4) ………………….. (5)

Impedance Transformation through a Transformer ZL Is Ip Vp Vs Impedance of the load: ZL = Vs/Is The impedance of the primary circuit: Z’L = Vp/Ip = (aVs)/(Is /a) = a2 (Vs / Is ) = a2 ZL Ip Vp Z’L Is Vs

Example 1 A 100-kVA, 2400/240-V, 60-Hz step-down transformer (ideal) is used between a transmission line and a distribution system. Determine turns ratio. What secondary load impedance will cause the transformer to be fully loaded, and what is the corresponding primary current? Find the load impedance referred to the primary.

Solution to Example 1 Turns ratio, a = 2400 / 240 = 10 b) Is= 100,000/240 = 416.67 A Ip = Is /a = 416.67 / 10 = 41.67 A Magnitude of the load impedance = Vs/Is = 240/416.7 = 0.576 ohm Load impedance referred to the primary = a2*0.576 = 57.6 ohm