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Electrical Technology (EET 103/ERT105) Tutorial Module TUTORIAL 5 – TRANSFORMER Question 1 The secondary winding of a transformer has a terminal voltage of vs (t) = 282.8 sin 377t V. The turns ratio of the transformer is 100:200. If the secondary current of the transformer is (t) =7.07 sin (377t - 36.87o) A, the impedances of this transformer referred to the primary side are: Req = 0.20Ω Xeq = 0.750Ω Rc = 300Ω XM = 80Ω Determine: i. ii. the primary current of this transformer. the voltage regulation and efficiency. (Ans: I p 11.1 41o A , VR = 6.2%, η = 93.7%) Question 2 A 20-kVA 8000/480-V distribution transformer has the following resistances and reactances: Rp = 32Ω Rs = 0.05Ω Xp = 45Ω Xs = 0.06Ω RC = 250kΩ XM = 30kΩ The excitation branch impedances are given referred to the primary side of the transformer. a) Find the equivalent circuit of this transformer referred to the primary side. b) Assume that this transformer is supplying rated load at 480V and 0.8 PF lagging. What is this transformer’s input voltage, Vp? What is its voltage regulation, VR? c) What is the transformer’s efficiency, η under the conditions of part (c)? (Ans: a) Rs’ = 13.9Ω, Xs’ = 16.7Ω b) Rp = 0.01, Xp = j0.0141, Rs’ = 0.0043, Xs’ = j0.0052, RC = 78.125, XC = j9.375 c) V p 81850.38o V , VR = 2.31% d) η = 96.6%) UNIVERSITI MALAYSIA PERLIS 1 Electrical Technology (EET 103/ERT105) Tutorial Module Question 3 A 1000-VA 230/115-V transformer has been tested to determine its equivalent circuit. The results of the tests are shown below. Open circuit test VOC = 230V IOC = 0.45A POC = 30W Short circuit test VSC = 19.1V ISC = 8.7A PSC = 42.3W All data given were taken from the primary side of the transformer. a) Find the equivalent circuit of this transformer referred to the low-voltage side of the transformer. b) Find the transformer’s voltage regulation at rated conditions and (1) 0.8 PF lagging, (2) 1.0 PF, (3) 0.8 PF leading. c) Determine the transformer’s efficiency at rated conditions and 0.8 PF lagging. (Ans: a) Req,s =0.140Ω, Xeq,s = j0.532Ω, RC,s =441Ω, XM,s = 134Ω b) VR = 3.3%, 1.1%, -1.5%, η = 94.9%) UNIVERSITI MALAYSIA PERLIS 2 Electrical Technology (EET 103/ERT105) Tutorial Module Question 4 The results of the Open circuit and Short circuit tests are shown in Table 2 for a 20 kVA, 1900/240 V transformer. This test is to determine its excitation branch components, its series impedances and its voltage regulation. Open circuit VOC = 1900V IOC = 0.45A POC = 60W Table 2 Short circuit VSC = 50V ISC = 9A PSC = 250W a) Calculate the approximate equivalent circuit of this transformer referred to its primary voltage side. b) Calculate the approximate equivalent circuit of this transformer referred to its secondary voltage side. c) Calculate the full load voltage regulation at Power Factor 0.8 lagging. d) Calculate the efficiency of the transformer at full load with a Power Factor 0.8 lagging. UNIVERSITI MALAYSIA PERLIS 3 Electrical Technology (EET 103/ERT105) Tutorial Module Question 5 A 15-kVA 8000/230V distribution transformer has impedance referred to the primary of 80 + j300 Ω. The components of the excitation branch referred to the primary side are RC = 350kΩ and XM = 70kΩ. a) If the primary voltage is 7967 V and the load impedance is ZL = 3.0 + j1.5Ω, what is the secondary voltage of the transformer? What is the voltage regulation of the transformer? b) If the load is disconnected and a capacitor of –j4.0Ω is connected in its place, what is the secondary voltage of the transformer? What is its voltage regulation under these conditions? (Ans: (a) Vs 218.8 3.1o V , VR = 4.7% (b) Vs 246.5 1.2 o V , VR = -7.07%) UNIVERSITI MALAYSIA PERLIS 4 Electrical Technology (EET 103/ERT105) Tutorial Module Question 6 UNIVERSITI MALAYSIA PERLIS 5