UNIT - II

1. UNIT - II TRANSFORMERS Chetan Upadhyay

2. Introduction A transformer is a static machines. The word ‘transformer’ comes form the word ‘transform’. Transformer is not an energy conversion device, but is a device that changes AC electrical power at one voltage level into AC electrical power at another voltage level through the action of magnetic field, without a change in frequency. It can be either to step-up or step down. Transmission System Generation Station Distributions 33/13.5kV 13.5/6.6kV 6.6kV/415V Consumer Chetan Upadhyay

3. Transformer Construction • Two types of iron-core construction: • Core - type construction • Shell - type construction • Core - type construction Chetan Upadhyay

4. Transformer Construction • Shell - type construction Chetan Upadhyay

5. N1 : N2 I1 I2 V1 E1 E2 V2 Ideal Transformer • An ideal transformer is a transformer which has no loses, i.e. it’s winding has no ohmic resistance, no magnetic leakage, and therefore no I2 R and core loses. • However, it is impossible to realize such a transformer in practice. • Yet, the approximate characteristic of ideal transformer will be used in characterized the practical transformer. V1 – Primary Voltage V2 – Secondary Voltage E1 – Primary induced Voltage E2 – secondary induced Voltage N1:N2 – Transformer ratio Chetan Upadhyay

6. Transformer Equation Faraday’s Law states that, If the flux passes through a coil of wire, a voltage will be induced in the turns of wire. This voltage is directly proportional to the rate of change in the flux with respect of time. If we have N turns of wire, Lenz’s Law Chetan Upadhyay MZS FKEE, UMP

7. Transformer Equation For an ac sources, Let V(t) = Vm sint i(t) = im sint Since the flux is a sinusoidal function; Then: Therefore: Thus: Chetan Upadhyay MZS FKEE, UMP

8. Transformer Equation For an ideal transformer In the equilibrium condition, both the input power will be equaled to the output power, and this condition is said to ideal condition of a transformer. From the ideal transformer circuit, note that, Hence, substitute in (i) ………………… (i) Chetan Upadhyay MZS FKEE, UMP

9. Transformer Equation Where, ‘a’ is the Voltage Transformation Ratio; which will determine whether the transformer is going to be step-up or step-down E1 > E2 For a >1 For a <1 E1 < E2 Chetan Upadhyay MZS FKEE, UMP

10. Transformer Rating Transformer rating is normally written in terms of Apparent Power. Apparent power is actually the product of its rated current and rated voltage. • Where, • I1 and I2 = rated current on primary and secondary winding. • V1 and V2 = rated voltage on primary and secondary winding. • Rated currents are actually the full load currents in transformer Chetan Upadhyay MZS FKEE, UMP

11. Example 1.5kVA single phase transformer has rated voltage of 144/240 V. Finds its full load current. Solution Chetan Upadhyay MZS FKEE, UMP

12. X2 X1 I1’ I1 I2 R2 R1 Io N1: N2 Ic Im Load V1 V2 RC Xm E1 E2 Practical Transformer (Equivalent Circuit) V1 = primary supply voltage V2 = 2nd terminal (load) voltage E1 = primary winding voltage E2 = 2nd winding voltage I1 = primary supply current I2 = 2nd winding current I1’ = primary winding current Io = no load current V1 = primary supply voltage V2 = 2nd terminal (load) voltage E1 = primary winding voltage E2 = 2nd winding voltage I1 = primary supply current I2 = 2nd winding current I1’ = primary winding current Io = no load current Chetan Upadhyay

13. N1: N2 R1 X1 I2’ X2’ I1 I2 R2’ Io Ic Im Load V1 RC Xm E1 E2 V2 Single Phase Transformer (Referred to Primary)Actual Method Chetan Upadhyay

14. X1 N1: N2 I2’ R1 I1 R2’ X2’ I2 Io Im Ic Load V1 RC Xm E1 E2 V2 Single Phase Transformer (Referred to Primary ) Approximate Method Chetan Upadhyay

15. Example Problem 1. A 10 kVA single phase transformer 2000/440V has primary resistance and reactance of 5.5 and 12 respectively, while the resistance and reactance of secondary winding is 0.2 and 0.45  respectively. Calculate: • The parameter referred to high voltage side and draw the equivalent circuit • The approximate value of secondary voltage at full load of 0.8 lagging power factor, when primary supply is 2000V Chetan Upadhyay

16. Solution R1=5.5 , X1=j12  R2=0.2 , X2=j0.45  i) Refer to H.V side (primary) R2’=(4.55)2 (0.2) = 4.14, X2’=j(4.55)20.45 = j9.32  Therefore, R01=R1+R2’=5.5 + 4.13 = 9.64  X01=X1+X2’=j12 + j9. 32 = j21.32  R01 X01 I1 9.64 21.32 V1 aV2 Example 1 (Cont) Chetan Upadhyay

17. Solution ii) Secondary voltage p.f = 0.8 Cos  = 0.8  =36.87o Full load, From eqn Example 1 (Cont) Chetan Upadhyay

18. Transformer Losses • Generally, there are two types of losses; • Iron losses :- occur in core parameters • Copper losses :- occur in winding resistance • Iron Losses ii Copper Losses Chetan Upadhyay

19. Transformer Efficiency • To check the performance of the device, by comparing the output with respect to the input. • The higher the efficiency, the better the system. Where, if ½ load, hence n = ½ , ¼ load, n= ¼ , 90% of full load, n =0.9 Where Pcu = Psc Pc = Poc Chetan Upadhyay

20. Voltage Regulation • The purpose of voltage regulation is basically to determine the percentage of voltage drop between no load and full load. • Voltage Regulation can be determine based on 3 methods: a) Basic Defination b) Short – circuit Test c) Equivalent Circuit Chetan Upadhyay

21. Voltage Regulation (Basic Definition) • In this method, all parameter are being referred to primary or secondary side. • Can be represented in either • Down – voltage Regulation • Up – Voltage Regulation Chetan Upadhyay

22. Tap Changer A transformer tap is a connection point along a transformer winding that allows a certain number of turns to be selected. By this means, a transformer with a variable turns ratio is produced, enabling voltage regulation of the output. The tap selection is made via a tap changer mechanism. Chetan Upadhyay

23. Three Phase Transformers • 3 single phase transformers connected together 1.Star/Delta winding arrangements 2. Easy to replace failed units • Common core device 1. Lighter and cheaper than 3 individual units 2. 6 rather than 12 external connections 3. Whole transformer must be replaced if single winding fails . For both cases analysis procedure identical! Chetan Upadhyay

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