Single-Phase Transformer Questions 1 2 3 4 5 6 7 8 Draw the exact equivalent circuit diagram of a transformer under-load with a lagging power factor and also draw its corresponding phasor diagram. A non-sinusoidal voltage π = 150π ππ314π‘ − 75π ππ1570π‘ is applied to a 250 π‘π’ππ winding of a single phase transformer. Determine the flux as a function of time. A voltage π½ = ππππππππππ is applied to the transformer winding during a no-load test. The resulting π current was found to be π = π π¬π’π§ (ππππ − ) π¨. Find the core loss and the rms value of the exciting π current. A 100kVA single-phase transformer has 400 turns on the primary and 80 turns on the secondary. The primary and secondary resistances are 0.3 β¦ and 0.01 β¦ respectively, and the corresponding leakage reactances are 1.1 β¦ and 0.035 β¦ respectively. The supply voltage is 2200V. Calculate: (A) The equivalent impedance referred to the primary circuit (B)The voltage regulation and the secondary terminal voltage for full load having a power factor of (i) 0.8 lagging and (ii) 0.8 leading. (C) The percentage resistance and leakage reactance drops of the transformer. A 10-kVA, 2000/400-V, single-phase transformer at no-load has resistances and leakage reactances as follows: πΉπ = π. π π; πΉπ = π. π π & πΏπ = ππ π; πΏπ = π. ππ π. If the pf is 0.8 lagging, determine (A) the voltage regulation and the approximate value of the secondary voltage when the transformer is exposed to nameplate conditions. (B) Use p. u. to confirm your answers. The no-load current of a single-phase transformer is 1 π΄ at 0.4 power factor when connected across a 200 π, 50 π»π§ supply. The number of turns on the primary is twice that of the secondary. Find the primary current if a load taking 50 π΄ at a lagging power factor of 0.8 is now connected across the secondary. A 6600/400 π, single-phase transformer has emf per turn of 15 π and maximum flux density of 1.5 ππ/π2 , Find: (a) Suitable number of primary and secondary turns. (b) Cross-sectional area of the core. A 250/500-V, single-phase transformer gave the following test results: O.C.T: 250 π, 2 π΄, 80 π. S.C.T: 40 π 10 π΄ (Full-load) 120 π. Use a power factor of 0.8 lagging and determine: (A)The constant parameters of the transformer (B) The per unit secondary voltage and the load angle. −2.86 0 ). (c)The full-load efficiency. 9 The parameters of a 150 πππ΄, 2400/240 π, 50 π»π§, single-phase transformer are as follows: π 1 = 0.2 Ω, π 2 = 2 × 10−3 Ω, π1 = 0.45 Ω, π2 = 4.5 × 10−3 Ω π πΆ1 = 10 π Ω, ππ1 = 1.6 π Ω, Determine (A) the open circuit data when the LV-side is excited at rated voltage (B) The short circuit data when the LV-side is short-circuited. 10 A 10 πππ΄, 2000/400 π, 50π»π§, single-phase transformer has the following prameters: HV side: π = 5.5 Ω, ππΏ = 18 Ω. LV side: π = 0.5 Ω, ππΏ = 0.7 Ω If the AC source on the H.V. side, determine the full-load secondary voltage in per unit for a lagging power factor of 80%. 11 A 20-kVA, 4000/400-V, 50-Hz, single phase transformer has the following parameters: π―π½: πΉ = π π, πΏπ³ = π π, πΉπͺ = ππ ππ, πΏπ΄ = π ππ; π³π½: πΉ = π. ππ π, πΏπ³ = π. ππ π Determine; (11.1) per unit values of impedance referred to both sides (11.2) Voltage regulation for a lagging power factor of 0.8. 12 The full-load copper loss on the HV side of 1 300-kVA, 11000/550-V transformer is 1860-W and 1440-W on the LV-side. The reactance referred to the primary is 10-β¦. Calculate: (12.1) π 1 & π 2 (12.2) πππ»π & ) πππΏπ (12.3) Full-load terminal voltage at a pf 0.8 lagging. 13 A 23-kVA, 2300/230-V, 60-Hz, single-phase transformer with ππ = π + πππ π & ππ = π. ππ + ππ. ππ π. The transformer is operating at 75% of its rated load and uses 230-V terminal voltage. Determine the efficiency of the transformer if the load is operated at 0.886 lagging. 14 The primary and secondary windings of a 30 πππ΄, 5000/250 π, 50π»π§, single-phase transformer has a resistance of 10 Ω and 0.015 Ω respectively. The total reactance referred to the HV side is 25 Ω. Use a power factor of 0.85 lagging and determine: (a) The percentage regulation of the transformer when delivering full-load current. (b)The full-load secondary voltage. (c)The fullload copper loss. (d) The maximum efficiency at 85% of full-load. 15 Test data obtained on a 30-kVA, 3000/110-V, single-phase transformer is as follows: O.C.T: 3000-V 0.5-A 350-W S.C.T: 150-V 10-A 500-W Calculate: (15.1) The full-load efficiency of the transformer at 0.8 pf lagging. (15.2) The efficiency of the transformer at half-load, unity pf. (15.3) The kVA output at which the efficiency is maximum. 16 The following data refers to a single-phase transformer ratio 60:4; ππ = ππ + πππ π; ππ = π. ππ + ππ. ππ π; π°π = π. ππ π¨ and leads the flux by 60o. The secondary side delivers 200-A at a terminal voltage of 500-V with a pf 0.85 lagging. Find: (16.1) The primary voltage and pf (16.2) The machine efficiency. 17 A 10-kVA, 400/200-V, 50-Hz, single-phase transformer gave the following test results: O.C.T (H.V open): 200-V 13-A 120-W; S.C.T (LV short circuited): 22-V 30-A 200-W Determine the equivalent parameters referred to both sides. 18 A 20-kVA, 4000/400-V, single-phase transformer requires only 4.5% of the voltage to circulate full-load current on the low voltage side. If the core losses are 200-W, calculate (18.1) The voltage regulation for a load with 0.8 lagging pf. (18.2) Efficiency when supplying 18-kW load. 19 A 120-kVA, 2400/240-V, single-phase transformer has ππ = π. ππ + ππ. π π; ππ = π. ππ + ππ. ππ π. The transformer is designed to operate at maximum efficiency 0f 70% of its rated load with 0.8 lagging pf. Determine: (19.1) The base load at maximum efficiency. (19.2) Maximum efficiency. (19.3) Full-load efficiency. (19.4) RC. 20 A 50-kVA, 6360/240-V transformer is tested on open circuit and short circuited to obtain its efficiency; The results of the tests are as follows: πΆπͺπ»: π½π = ππππ π½, π°π = π π¨, π·ππ = π ππΎ πππ πΊπͺπ»: π½ππ = πππ π½, π°π = πππ π¨, π·ππ = π ππΎ. Find: (20.1) The equivalent parameters of the transformer referred to the high voltage side (20.2) The efficiency of the transformer when supplying full-load at a pf of 0.8 lagging. 21 The primary and secondary windings of a 30-kVA, 5000/250 –V transformer has resistances of 10 β¦ and 0.015 β¦ respectively. The total reactance referred to the primary is 25 β¦. Calculate: (21.1) The full-load regulation at pf of 0.8 lagging. (21.2) The secondary voltage for a leading pf of 0.6. (21.3) The full-load efficiency of the transformer for a lagging pf of 0.75 if the maximum efficiency occurs at 85% of full-load (21.4) The per unit equivalent resistance. 22 A 10-kVA, 250/100-V, 50-Hz, single-phase transformer gave the following test results: O.C.T: 250-V 2.6-A 0.3 pf and S.C.T: 18-V 100-A 240-W. Find: (22.1) The per unit impedance. (22.2) The voltage regulation for a leading power factor of 0.78. (22.3) The full-load efficiency at upf. (22.4) The load at which maximum efficiency occurs. (22.5) The value of the maximum efficiency at upf. 23 The maximum efficiency of 100-kVA, single-phase transformer is 98% and occurs at 80% of full-load at a power factor of 0.8 lagging. If the leakage reactance of the transformer is 5%, estimate the voltage regulation at rated voltage and a lagging pf of 0.8. 24 A 9.2-kVA, 230/115-V, 50-Hz transformer has the following parameters: ππ = π. πππ + ππ. πππ π; ππ = π. πππ + ππ. πππ π; βΆ πΉπͺ = πππ. ππ π; πΏµ = πππ. π. For a lagging pf 0.6, determine: (24.1) Voltage regulation and secondary terminal voltage. (24.2) The full-load efficiency. 25 A 240/400-V single-phase transformer absorbs 35-W when its LV winding is connected to a 240-V, 50-Hz supply, the secondary being open-circuit. When the LV winding is short-circuited and a 10-V, 50-Hz supply is connected to HV winding, the power absorbed was 48-W and the current in the HV winding is 15-A, which is the full-load current. Calculate the: (25.1) Full-load rating of the transformer (25.2) Efficiency of the transformer when it delivers 40% of rated kVA at a power factor of 0.8 lagging. 26 A single-phase, 200-kVA, 6351/660-V transformer has the following data: [O.C.T: 6351 Vπ»π 1663π΄π»π, 4.8 πππ»π]; [π. πΆ. π: 500 ππ»π , 30 π΄π»π , 8.2 πππ»π ]. Use the approximate equivalent diagram and calculate π πΆ , ππ , π π1 , ππ1 , ππ1 , ΙΈπ . 27 A 20 kVA, 4000/400 V, 50 Hz single-phase transformer has the following parameters: HV: π = 3 Ω, π = 5 Ω, π πΆ = 20 πΩ, ππ = 1 πΩ. LV: π = 0.04 Ω π = 0.05 Ω. Determine: (27.1) The total resistance, leakage reactance and impedance referred to the HV side (27.2) The total resistance, leakage reactance and impedance referred to the LV side. (27.3) The full-load copper loss and iron loss of the transformer (