1 Electrical Machines EELE 4350 Dr Assad AbuJasser
1 Electrical Machines (EELE 4350) Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
2 Assad Abu-Jasser, Ph. D Electric Power Engineering site. iugaza. edu. ps/ajasser@iugaza. edu. ps Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
3 Chapter Four Transformers Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
4 Introduction A Transformer is a device that involves two electrically isolated but magnetically strong coupled coils These are primary winding connected to the source and secondary winding connected to the load Induced emf is proportional to the number of turns in the coil. If the secondary voltage is higher than the source, the transformer is called step-up transformer. On the other hand, a step-down transformer has higher source voltage than the load voltage. One-to-One ratio transformer is called isolation transformer. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
5 Construction of a Transformer core is built up of thin lamination of highly permeable ferromagnetic material such as silicon sheet steel The lamination’s thickness varies from 0. 014 to 0. 024 inch to keep core losses to a minimum. A thin coating varnish is applied to provide electrical insulation. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
6 An Ideal Transformer has the following properties: The core is highly permeable i. e. it requires a very small mmf to set up flux Φ The core does not have any eddy-current or hysteresis loss The core exhibits no flux leakage i. e. the flux is confined within the core The resistance of winding is negligible Dr. Assad Abu-Jasser, EE- Department -IUGaza each Electrical Machines (EELE 4350)
7 Transformer Polarity and Ratings Transformer Polarity The nameplate of a transformer provides information on power and voltage-handling capacity of each winding A 5 -k. VA, 500/250 -V, step-down transformer has the following Full-load power rating is 5 k. VA or the transformer can deliver 5 k. VA on a continuous basis Nominal Primary voltage V 1=500 V and nominal secondary voltage V 2=250 V Full-load primary current I 1=5000/500=10 A and full-load secondary current I 2=5000/250=20 A The transformation ratio is usually not given by manufacturer but it can be calculated a=V 1/V 2=500/250=2 Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
8 Example 4. 1 The core of the two-winding transformer shown is subjected to the magnetic flux variation as indicated. What is the induced emf in each winding? Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
9 Example 4. 2 An ideal transformer has a 150 -turn primary and 750 -turn secondary. The primary is connected to a 240 -V, 50 -Hz source. The secondary winding supplies a load of 4 A at a lagging power factor of 0. 8, Determine (a) the a-ratio, (b) the current in the primary, (c) the power supplied to the load, and (d) the flux in the core. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
10 A Nonideal Transformer has the following parameters Winding Resistances Leakage Fluxes Finite Core Permeability Core losses (Eddy-Current & Hysteresis) Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
11 Example 4. 3 A 23 -k. VA, 2300/230 -V, 60 -Hz, step-down transformer has the following resistance and leakage-reactance values: R 1=4Ω, R 2=0. 04Ω, X 1=12Ω, and X 2=0. 12Ω. The transformer is operating at 75% of its rated load. If the power factor of the load is 0. 866 leading, determine the efficiency of the transformer. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
12 Finite Permeability When the load on the transformer increases The secondary winding current increases The current supplied by the source increases The voltage drop across primary impedance increases The induced emf E 1 drops The mutual flux decreases because magnetizing current drops Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
13 Example 4. 4 The equivalent core-loss resistance and the magnetizing reactance on the primary side of the transformer of example 4. 3 are 20 kΩ and 15 kΩ, respectively. If the transformer delivers the same load, what is its efficiency? Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
14 Phasor Diagram Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
15 Approximate Equivalent Circuit The low core loss implies high core loss resistance The high permeability of the core ensures high magnetizing reactance The impedance of the parallel branch across the primary is very high compared with Z 1 and Z 2 The high impedance of the parallel branch assures low excitation current and thus it can be moved as shown Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
16 Example 4. 5 Analyze the transformer discussed in examples 4. 3 and 4. 4 using the approximate equivalent circuit as viewed from the primary side. Also sketch its phasor diagram. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
17 Voltage Regulation Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
18 Example 4. 6 A 2. 2 -k. VA, 440/220 -V, 50 -Hz, step-down transformer has the following parameters referred to the primary side: Re 1=3 Ω, Xe 1=4 Ω, Rc 1=2. 5 kΩ, and Xm 1=2 kΩ. The transformer is delivering full load at rated voltage with a power factor of 0. 707 lagging. Determine the efficiency and the voltage regulation of the transformer. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
19 Maximum Efficiency Criterion Core Losses (eddy-current and hysteresis) are constant and called fixed losses Copper losses are varying as the square of the current and called Variable losses Efficiency is zero at no load & it increases to reach its maximum at certain load Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
20 Example 4. 7 A 120 -k. VA, 2400/240 -V, step-down transformer has the following parameters: R 1=0. 75 Ω, X 1=0. 8 Ω, R 2=0. 01 Ω, X 2=0. 02 Ω. The transformer is designed to operate at maximum efficiency at 70% of its rated load with 0. 8 power factor lagging. Determine (a) the k. VA rating of the transformer at maximum efficiency, (b) the maximum efficiency, (c) the efficiency at full load and 0. 8 power factor lagging, and (d) the equivalent core-loss resistance. Use the approximate equivalent circuit. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
21 Determination of Transformer Parameters The Open-Circuit Test One winding of the transformer is left open while the other is excited by rated voltage and rated frequency It does not matter which side is excited, however it is safer to perform this test in the low-voltage side Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
22 Determination of Transformer Parameters The Short-Circuit Test The test is designed to determine the winding resistances and leakage reactances The test is conducted by placing a short circuit across one winding and exciting the other with rated frequency The applied voltage is carefully adjusted until rated current flows in the windings It does not matter on which side the test is conducted. But for safety it is conducted on the high-voltage side Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
Voltage (V) Current (A) Power (W) 23 Example 4. 8 --------------------Open-circuit test: 240 2 120 Short-circuit test: 150 10 600 OC-Test SC-Test The following data were obtained from testing a 48 -k. VA, 4800/240 -V. step-down transformer; Voltage (V) Current (A) Power (W) --------------------------------------Open-circuit test: 240 2 120 Short-circuit test: 150 10 600 Determine the equivalent circuit of the transformer as viewed from (a) the high-voltage side and (b) the low-voltage side Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
24 Per-Unit Computations When an electric machine is designed or analyzed using actual values of its parameters, it is not immediately obvious how its performance compare with similar-type machine Expressing machine parameters in per-unit shows immediately how the machine operates around its ratings Per-unit values of machines of the same type with widely different ratings lie within a narrow range An electric system has four quantities of interest: voltage, current, apparent power, and impedance If base (reference) values of any two of them are selected, the remaining two can be calculated Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
25 Example 4. 9 A single-phase generator with an internal impedance of 23+j 92 mΩ is connected to a load via a 46 -k. VA, 230/2300 -V, step-up transformer, a short transmission line, and a 46 -k. VA, 2300/115 V, step down transformer. The impedance of the transmission line is 2. 07+j 4. 14 Ω. The parameters of step-up and step-down transformers are: RH XH RL XL Rc. H Xm. H ------------------------------------------------Step-up: 2. 3Ω 6. 9Ω 23 mΩ 69 mΩ 13. 8 kΩ 6. 9 kΩ Step-down 2. 3Ω 6. 9Ω 5. 75 mΩ 17. 25 mΩ 11. 5 kΩ 9. 2 kΩ Determine (a) the generator voltage, (b) the generator current, (c) the overall efficiency of the system at full load and 0. 866 power factor lagging. Use per-unit quantities in the calculations. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
26 The Autotransformer When the two windings of a transformer are interconnected electrically, it is called an autotransformer The direct electrical connection between the windings ensures that a part of the energy is transferred by conduction in addition to the part transferred by the magnetic induction Autotransformer is cheaper in first cost than a conventional twowinding transformer of a similar rating Autotransformer delivers more power than a two-winding transformer of similar physical dimensions For a similar power rating, an autotransformer is more efficient than a two-winding transformer An autotransformer requires lower excitation current than a twowinding transformer to establish the same flux Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
27 The Autotransformer Connections Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
28 The Autotransformer a-ratio of Autotransformer Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
29 Example 4. 10 A 24 -k. VA, 2400/240 -V distribution transformer is to be connected as an autotransformer. For each possible combination, determine (a) the primary winding voltage, (b) the secondary winding voltage, (c) the ratio of transformation, and (d) the nominal rating of the autotransformer. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
30 A Nonideal Autotransformer An equivalent circuit of a nonideal autotransformer can be obtained by including the winding resistances, the leakage reactances, the core-loss resistance, and the magnetizing reactance. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
31 Example 4. 11 A 720 -VA, 360/120 -V, two-winding transformer has the following constants: RH=18. 9 Ω, XH=21. 6 Ω, RL=2. 1 Ω, and XL=2. 4 Ω, Rc. H=8. 64 kΩ, and Xm. H=6. 84 kΩ. The transformer is connected as a 120/480 -V, step-up autotransformer. If the autotransformer delivers the full load at 0. 707 power factor leading, determine its efficiency and the voltage regulation. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
32 Three-Phase Transformers Power is generated, transmitted, and consumed in three-phase form. 3 -phase transformers are used in such systems Three exactly alike single-phase transformers are used to form a single three-phase transformer For economic reasons, a three-phase transformer is designed to have all six windings on a common magnetic core A common magnetic core of a three-phase transformer can be either a core type or a shell type Shell-type transformer exhibits less waveform distortion than core -type and this makes it preferable over the core-type A three-phase winding on either side can be connected either in wye (Y) or in delta (∆) Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
33 Three-Phase Transformers Construction and Windings Connection ∆-∆ Y-∆ ∆-Y Y-Y Connection Core Type Shell-Type Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
34 Analysis of a 3 -Phase Transformer Under steady-state conditions, a single 3 -phase transformer operates exactly the same as 3 single-phase transformers In our analysis we assume that we have 3 identical 1 -phase transformers connected to form a single 3 -phase transformer Such an understanding allows the development of the per-phase equivalent circuit of a three-phase transformer It is also assumed that the 3 -phase transformers delivers a balanced load and the waveforms are pure sinusoidal This enables us employ the per-phase equivalent circuit of a transformer. A ∆-connected winding can be replaced by its equivalent Y-connected winding using ∆-to-Y transformation ZY=Z∆/3 and Vn=VL/√ 3 with ± 30 o phase difference Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
35 Example 4. 12 A three-phase transformer is assembled by connecting three 720 -VA, 360/120 -V, single-phase transformers. The constants for each transformer are RH=18. 9 Ω, XH=21. 6 Ω, RL=2. 1 Ω, and XL=2. 4 Ω, Rc. H=8. 64 kΩ, and Xm. H=6. 84 kΩ. For each of the four configurations, determine the nominal voltage and power ratings of the three-phase transformer. Draw the winding arrangements and the per-phase equivalent circuit for each configuration. Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
36 Example 4. 13 Three single-phase transformers, each rated at 12 -k. VA, 120/240 -V, 60 -Hz, are Y/∆ Connection Primary Secondary connected to form a three-phase, step-up, Y-∆ connection. The parameters of each transformer are RHVoltage =133. 5 mΩ, XH=201 120 mΩ, RL=39. 5 mΩ, 240 and XL=61. 5 mΩ, Phase Rc. L=240 Ω, and Xm. L=290Ω. What are the nominal voltage, current, and power ratings of the three-phase transformer. When it delivers the rated load at the rated Line Voltage 208 240 voltage and 0. 8 pf lagging, determine the line voltages, the line currents, and the efficiency. Phase of the transformer. Current 100 50 Line Current Y/Y Connection Phase Voltage Line Voltage Phase Current Line Current Dr. Assad Abu-Jasser, EE- Department -IUGaza 100 86. 6 Primary 120 208 100 Secondary 138. 564 240 86. 6 Electrical Machines (EELE 4350)
37 End of Chapter Four Dr. Assad Abu-Jasser, EE- Department -IUGaza Electrical Machines (EELE 4350)
- Slides: 37