Electrical Machines
Electrical II/II
Tutorial 2
Transformers
1. A 30 kva sinle phase transformer has 500 primary turns and 30 secondary turns.
Theprimary is connected to a 3300 V, 50 hz supply. Calculate a. maximum flux in the
core b. secondary e.m.f c. primary and secondary current. (ans: 29.7, 198, 9.09, 151.5)
2. A 230/460V transformer has a primary resistance of 0.2Ω and reactance of 0.5Ω and
corresponding values on secondary are 0.75Ω and 1.8Ω. Find the secondary terminal
voltage when supplying a. 10 A at 0.8 pf lagging and b. 10 A at 0.8 pf leading. Obtain the
result using actual phasor equation and approximate voltage equations. (ans: 424.8V,
470.4V )
3. A 50 kVA 2400:240V, 60 Hz distribution transformer has a leakage impedance of
0.72+0.92j in high voltage wining and 0.0070+ 0.009j ohms in low voltage winding. At
rated voltage and frequency the impedance of shunt branch (equal to the impedance of
𝑅0 , 𝑗𝑋0 in parallel) is 6.32 + 43.7j when viewed from low voltage side. Draw the
equivalent circuit referred to:
a
High voltage side
b
Low voltage side and label the impedances numerically
4. The transformer mentioned in problem 3 is used to step down voltage at load end of
the feeder whose impedance is 0.3 + j1.60 Ω. The voltage at the sending end of feeder is
2400 V. Find the voltage at the secondary terminal of the transformer when the load
connected to its secondary draws rated current from the transformer and the power
factor of the load is 0.8 lagging and 0.8 leading. (Ans: 233V, 239 V)
5. Using the instruments in high voltage side and the low voltage side is short circuited,
the short circuit test readings for the 50 kVA 2400: 240 V transformer mentioned in
example 4 are 48 V, 20.8 A, 617 W. An Open circuit test with the low voltage side
energized gives instrument readings on that side of 240 V, 5.42A and 186 W. Determine
the efficiency and the voltage regulation at full load, 0.8 power factor lagging. (Ans: 98
%, 1.92 %)
6. The primary of a transformer is rated at 10 A and 1000V. On open circuit the ratingsare
V1 = 1000V , v2 = 500V I = 0.42A and Poc = 100W. On short circuit, readings are: V = 126
V, I = 10A and Psc = 400W. Draw the equivalent circuit and determine parameters.
Predict output voltage if ZL = 19 + j12Ω (ans: 449.65∠− 4.55V )
7. Calculate the efficiency at half load, full load and 25% overload for a 100 kva
transformer at power factor (a) unity (b) 0.8. The core loss is 1000W and full load
copper loss is
1000W (ans: 0.976, 0.98, 0.98, 0.97, 0.976, 0.975 )
8. A 15 KVA 2300/230 V, 50 Hz single phase transformer has following test data
O.C test : V = 2300V, I= 0.21 A, W = 50 W
S.C test : V = 47V , I = 6 A, W = 160W
(a) Find the equivalent circuit referred to primary side.
(b) Calculate the full load voltage regulation at 0.8 pf lagging awhen the load voltageis
held at 220 V.(2.3 %)
(c) What is the efficiency at half the rated load at unity power factor. (98.7)
(d) Find the maximum efficiency and corresponding output power.
(98.7)
9. A 200 KVA transformer has an efficiency of 98 % at full load if the maixmum
efficiencyoccures at three quarters of full load , calculate efficiency at half load . Assume
negligible magnetising current and 0.8 pf at all loads. (97)
10. The daily variation of load on a 100 kva transformer is given below:
8-1 : 65 kw, 35 kvar
1-6 : 80 kw, 50 kvar
6-1 : 30 kw, 30 kvar
1-8 : No load
No load core loss is 270 W and full load copper loss is 1200 W. Calculate all day
efficiency.(ans: 98.26) Note: copper loss proportion to kva2
11. A 100 kva single phase transformer gave following test data:
O.C test(secondary winding open): primary volts 1000, secondary volts 100, power input
975W
S.C test (secondary winding open): primary volts 22, full load current (100 A), power
input 1050 W
Find (a) percentage impedance, resistance and leakage reactance, (b) efficiency ate 75%
load 0.8 lag (c) full load regulation at 0.9 pf lag. (ans: 2.2%,1.05%,1.933%, 97.4%, 1.7%)
12. A 11500/2300 V transformer is rated at 100 kva as a two winding transformer. If the
two winding connected in series to form an auto transformer, what will be the voltage
ratio and output. (ans: 13.8/11.5 kv, 600kva, 13.8/2.3 kv, 120 kva)
13. Three single phase 10 kva, 460/120 V ,60 Hz transformer are connected to a three
phase460/208 V transformer bank. the equivalent impedance of each referred to hv
side is 10 + j 2.0 Ω. Transformer delivers 20 kw at 0.8 pf lead. Draw diagram, find
transformer current, primary induced voltage and voltage regulation. (ans: 18.1A,
452.7V, -1.57%)
14. Three single phase 50 kVA, 2400:240 V transformer, each having following parameters
are connected 𝑌 − Δ in a three phase 150 kVA bank to step down the voltage ath the
load end of a feeder whose impedance is 0.15+1j Ω/phase. The voltage at the sending
end of the feeder is 4160 V line to line. On their secondary sides, the transformers
supply a balanced three phase load through a feeder whose impedance is 0.0005 + j
0.002 Ω/𝑝ℎ𝑎𝑠𝑒 . Find the line-to-line voltage at the load when the load draws rated
current from the transformers at the power factor of 0.8 lagging.
Parameters: R1 +jX1 = 0.72+0.92j , R2+jX2 = 0.0070+ 0.009j ohms (Ans: 233V)
15. What will happen if the three-transformer mentioned in problem 14 are connected in
Δ − Δ connection.
16. Represent the transformer mentioned in problem 2 in per unit system.
17. A three phase load is supplied from a 2.4 kV: 460 V, 250 kVA transformer whose
equivalent series impedance is 0.026 + 0.12 j per unit on its own base. The load voltage
is observed to be 438 V line to line and it is drawing 95 kW at unity power factor.
Calculate the voltage the high voltage side of the transformer. Perform the calculations
on a 460 V, 100 kVA base. (Ans: 2313 V)
18. Observe a three-phase transformer nearby your home. Gather the detail of the
transformer with connection, load, voltage level. Discuss on the importance of the
transformer and write an essay on your perception as an engineering student.