Electric Machine Transformers By Dr. Shorouk Ossama

References Stephen J. Chapman, “Electric Machinery Fundamentals”, 5th Edition, 2012.

Introduction A Transformer is a device that changes ac electric power at one frequency and voltage level to ac electric power at the same frequency and another voltage level through the action of a Magnetic Field.

It consists of two or more coils of wire wrapped around a common ferromagnetic core. These coils are (usually) not directly connected. The only connection between the coils is the common magnetic flux present within the core.

Load Input Winding Output Winding Magnetic Flux Primary Secondary Connected To a Source Of Ac Electric Power The Winding Connected To The Loads Input Winding Output Winding

Why Transformers Are Important To Modern Life? A transformer ideally changes one ac voltage level to another voltage level without affecting the actual power supplied. voltage stepped up for transmission over long distances at very low losses, and its voltage stepped down again for final use.

Types of Transformers Power Transformers are given a variety of different names, depending on their use in power systems. A transformer connected to the output of a generator and used to step its voltage up to transmission levels (110+ KV) is sometimes called a Unit Transformer.

The transformer at the other end of the transmission line, which steps the voltage down from transmission levels to distribution levels (from 2.3 to 34.5 Kv), is called a Substation Transformer. the transformer that takes the distribution voltage and steps it down to the final voltage at which the power is actually used (110, 208, 220 V, etc.) is called a Distribution Transformer.

Transformers Construction Power transformers are constructed on one of two types of cores. Core Type: simple rectangular laminated piece of steel with the transformer windings wrapped around two sides of the rectangle.

Shell Type: consists of a three-legged laminated core with the windings wrapped around the center leg. In either case, the core is constructed of thin laminations electrically isolated from each other in order to minimize eddy currents.

Circuit Diagram Symbol For Transformer

Transformer Principle of Operation an alternating voltage V1 is applied to the primary winding small current called the no-load current I0 magnetic flux in the core alternating flux links with both primary and secondary coils induces in them e.m.f.'s of E1 and E2

The induced e.m.f (E) in a coil of N turns is given by: E = - N (dϕ/dt) volts Where: dϕ/dt is the rate of change of flux In an ideal transformer, the rate of change of flux is the same for both primary and secondary and thus E1/N1 = E2/N2

The Ideal Transformer An ideal transformer is a lossless device with an input winding and an output winding. (V1/V2) is called the voltage ratio (N1/N2) the turns ratio

If N2 is less than N1 then V2 is less than V1 and the device is termed a step-down transformer. If N2 is greater than N1 then V2 is greater than V1 and the device is termed a step-up transformer. When a load is connected across the secondary winding, a current I2 flows.

Input Power = Output Power V1I1 = V2I2 i. e Input Power = Output Power V1I1 = V2I2 i.e. in an ideal transformer, the primary and secondary ampere turns are equal.

For an ideal transformer, voltage ratio = turns ratio Example 1: A transformer has 500 primary turns and 3000 secondary turns. If the primary voltage is 240 V, determine the secondary voltage, assuming an ideal transformer. Solution For an ideal transformer, voltage ratio = turns ratio V1/V2 = N1/N2 = a 240/V2 = 500/3000, V2 = 1440V

Example 2: An ideal transformer with turns ratio of 2:7 is fed from a 240V supply. Determine its output voltage.   Solution A turns ratio of 2:7 means that the transformer has 2 turns on the primary for every 7 turns on the secondary (i.e. a step-up transformer); thus a = (N1/N2) = (2/7). For an ideal transformer, voltage ratio = turns ratio V1/V2 = N1/N2 = a V2 = 7 × 240 /2 =840V

Example 3: A 5 KVA single-phase transformer has a turn ratio of 10 : 1 and is fed from a 2.5 KV supply. Neglecting losses, determine: The full-load secondary current, Minimum load resistance which can be connected across the secondary winding to give full load KVA. The primary current at full load KVA

Turns ratio a = N1/N2 = 10/1 and V1 = 2.5KV =2500 V. Since N1/N2 = V1/V2 V2 = V1 (N2/N1)= 250V The transformer rating in volt-amperes=V2I2(at full load) i.e. 5000 = 250I2 Hence full load secondary current: I2 = (5000/250) =20A.

Minimum value of load resistance, RL = V2/I2 = 250/20 = 12.5Ω The primary current, N1 / N2 = I2 / I1 I1 = I2(N2 / N1) = 20×0.1 = 2A

Thanks