Machine Transformer Lecture Notes PDF

Machine MITE Department Al Maarif University Machine MIET Department Al-Mareef University Lect # 1 Transformer...

Machine MITE Department Al Maarif University Machine MIET Department Al-Mareef University Lect # 1 Transformer Assistant Lecturer Saad Rajab Al_Dulaimy E-mail: [email protected] Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Outline What is the machine? Type of machines What is the electrical machine? Electrical Transformers and its types Activities Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Machine Man has invented machines, equipment and devices, and worked on developing and using them in a way that benefits his life, and the lives of people in general, benefits from them, and helps him in life, progress and production, and solves problems and difficulties, and his tasks in them, and no person can ignore the importance and role of machines in people's lives, their tasks, and functions, which affect many aspects of life. The concepts of machines have developed and become diverse in various shapes and sizes to serve man, overcome difficulties and speed up the time process in terms of production speed, for example Machines in general are any device that converts energy from one form to another or a specific task, There are two types of machines, including mechanical machines that convert any type of energy into movement, such as internal combustion cars and electric cars, etc., As for the second type, the electrical machine that converts any type of energy into electrical energy, such as generators for generating electrical energy, turbines for generating energy, solar panels system, etc.... Machine Electrical Mechanical Machine Machine Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Electrical Machine Electricity does not exist naturally in any useful form. It has to be generated from any other sources of energy such as solar, wind, hydro, thermal, atom, etc. Photovoltaic cells help us trap energy from the sunlight and generators are used to convert mechanical power available in other forms to electricity. The mechanical power can be obtained from wind, flowing water, and steam using turbines. Motors are used to convert back the electricity to mechanical power. So, collectively, electric machines are devices that convert mechanical energy to electrical energy and vice versa. Let’s start with transformers so that you can understand the basic concept of electromagnetic induction that happens in every electric machine. Classification of Electric machines Static Electric machines – Transformers Rotating Electric machines – Motors (convert electrical energy to mechanical energy) and Generators (convert mechanical energy to electrical energy) Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University TRANSFORMER Introduction The main advantage of alternating currents over direct currents is that the alternating currents can be easily transferable from low voltage to high or from high voltage to low. Alternating voltages can be raised or lowered in the different stages of electrical network as generation, transmission, distribution and utilization. This is possible with a static device is called transformer. The transformer works on the principle of mutual induction. It transfers an electric energy from one circuit to another (with the desired change in voltage and current, without any change in the frequency) when there is no electrical connection between the two circuits. So, The static electrical device which transfers the voltage from one level to another level by the principle of self and mutual induction without change in frequency. A basic transformer consists of two coils that are coupled using a magnetic core. In the case of three-phase transformers, two sets of coil per phase will be present. One set of coils is known as the primary winding and the other is known as the secondary winding. These two windings are insulated from each other and are magnetically coupled through the iron core. Michael Faraday propounded the principle of electro-magnetic induction in 1831It states that a voltage appears across the terminals of an electric coil when the flux linked with the same changes. The magnitude of the induced voltage is proportional to the rate of change of the flux linkages. This finding forms the basis for many magnetos electric machines Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University There are two types from Transformer Step up Transformer Set Down Transformer When a transformer is used to “increase” the voltage on its secondary winding with respect to the primary, it is called a Step-up transformer. When it is used to “decrease” the voltage on the secondary winding with respect to the primary it is called a Step-down transformer. However, a third condition exists in which a transformer produces the same voltage on its secondary as is applied to its primary winding. In other words, its output is identical with respect to voltage, current and power transferred. This type of transformer is called an “Impedance Transformer” and is mainly used for impedance matching or the isolation of adjoining electrical circuits. The difference in voltage between the primary and the secondary windings is achieved by changing the number of coils turns in the primary winding (NP) compared to the number of coil turns on the secondary winding (NS). As the transformer is basically a linear device, a ratio now exists between the number of turns of the primary coil divided by the number of turns of the secondary coil. This ratio, called the ratio of transformation, more commonly known as a transformer “turns ratio”, (TR). This turns ratio value dictates the operation of the transformer and the corresponding voltage available on the secondary winding. It is necessary to know the ratio of the number of turns of wire on the primary winding compared to the secondary winding. The turns ratio, which has no units, compares the two windings in order and is written with a colon, such as 3:1 (3-to-1). This means in this example, that if there are 3 volts on the primary winding there will be 1 volt on the secondary winding, 3 volts-to-1 volt. Then we can see that if the ratio between the number of turns changes the resulting voltages must also change by the same ratio, and this is true. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Principle of Working Basically, a transformer consists of a core and two separate coils that work through electrical induction. The principle of mutual induction states that when two coils are inductively connected and if the current in one coil changes uniformly, an electromotive force is induced in the other coil. This electromotive force can drive a current, when a closed path is provided for it. A transformer works on the same principle. In its basic form, it consists of two inductive coils (having high mutual inductance) that are electrically separated but connected through a common magnetic circuit. The basic of the transformer is seen in that one of the coils is connected to an AC voltage source. This coil is called the primary coil (P). The other coil is connected to the load. This coil is called the secondary coil (S). The primary coil has N1 number of turns while the secondary coil has N2 number of turns. If primary winding is connected to a source of alternating voltage, an alternating flux is set up in the laminated core, most of which is linked with the secondary winding in which it produces mutually induced e.m.f. (according to Faraday’s Laws of Electromagnetic Induction e= MdI/dt). If the secondary winding is closed, a current flows in it and so electric energy is transferred (entirely magnetically) from the primary winding to secondary winding. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Transformer Construction A simple two-winding transformer construction consists of each winding being wound on a separate soft iron limb or core which provides the necessary magnetic circuit A transformer construction provides a magnetic circuit, known more commonly as the “transformer core”, which is designed to provide a path for the magnetic field to flow around. This magnetic path is necessary for the induction of voltage between the two input and output windings. There are two basic parts of a transformer: Magnetic core Winding or coils. Magnetic core Magnetic core of the transformer is either square or rectangular in size. It is further divided into two parts. The vertical portion on which coils are wound is called limb while the top and bottom horizontal portion is called yoke of the core. Core is made up of laminations to reduce eddy current losses. Generally high-grade silicon steel laminations [0.3 to 0.5 mm thick] are used to reduce hysteresis loss. These laminations are insulated from each other by using insulation like varnish. Laminations are overlapped so that to avoid the air gap at the joints. For this generally L shaped or I shaped laminations are used. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University I type Lamentation T type Lamentation WINDING: There are two windings, which are wound on the two limbs of the core, which are insulated from each other and from the limbs as shown in fig. 4. The windings are made up of copper, so that, they possess a very small resistance. The winding which is connected to the load is called secondary winding and the winding which is connected to the supply is called primary winding. The primary winding has N1 number of turns and the secondary windings have N2 number of turns Primary Winding Secondary Winding (N1) (N2) The cross-section of the limb depends on the type of coil to be used either circular or rectangular. The different cross-sections of limbs, The shape (a) for small transformer and shapes (b, c, d) for large transformer Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University The coils used are wound on the limbs and are insulated from each other. In the basic transformer, the two windings wound are shown on two different limbs i.e. primary on one limb while secondary on another limb. But due to this leakage flux increases which affects the transformer performance badly. Similarly, it is necessary that the windings should be very closes to each other to have high mutual inductance. To achieve this, the two windings are split into number of coils and are wound adjacent to each other on the same limb. A very common arrangement is cylindrical concentric coils Such cylindrical coils are used in the core type transformer. These coils are mechanically strong. These are wound in the helical layers. The different layers are insulated from each other by paper, cloth or mica. The low voltage winding is placed near the core from ease of insulating it from the core. The high voltage is placed after it. The other type of coils which is very commonly used for the shell type of transformer is sandwich coils. Each high voltage portion lies between the two low voltage portion sandwiching the high voltage portion. Such subdivision of windings into small portions reduces the leakage flux. Higher the degree of subdivision, smaller is the reactance. The top and bottom coils are low voltage coils. All the portions are insulated from each other by paper. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Types of Transformers The classification of the transformers is based on the relative arrangement or disposition of the core and the windings. There are three main types of the transformers which are: Core Type Shell Type Berry Type 1. Core Type It has a single magnetic circuit. The core is rectangular having two limbs. The winding encircles the core. The coils used are of cylindrical type. Core is made up of large number of thin laminations. The coils can be easily removed by removing the laminations of the top yoke, for maintenance. 2. Shell Type It has a double magnetic circuit. The core has three limbs. Both the windings are placed on the central limb. The core encircles most part of the windings. The coils used are generally multilayer disc type or sandwich coils. Generally, for very high voltage transformers, the shell type construction is preferred. For removing any winding for maintenance, large number of laminations are required to be removed. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University 1. Berry Type Transformer This has distributed magnetic circuit The number of independent magnetic circuits are more than 2. Its core construction is like spokes of a wheel. Otherwise, it is symmetrical to that of shell type. the transformers are generally kept in tightly fitted sheet metal tanks. The tanks are constructed of specified high quality steel plate. The tanks are filled with the special insulating oil. The entire transformer assembly is immersed in the oil. The oil serves two functions: Keeps the coils cool and Provides the transformers an additional insulation. The oil should be absolutely free from alkalis, Sulphur and specially from moisture. Presence of very small moisture lowers the dielectric strength of oil, affecting its performance badly. L.V: Low Voltage H.V: High Voltage Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Table: Comparison between core and shell type transformers 0 Core Type Shell Type The winding encircles the core. The core encircles most part of the 1 windings. 2 It has single magnetic circuit. It has double magnetic circuits. The cylindrical coils are used. The multilayer disc or sandwich type coils 3 are used. The coils can be easily removed from The coils cannot be removed easily. 4 maintenance point of view. 5 Preferred for low voltage transformers. Preferred for high voltage transformers. 6 The core has two limbs. The core has three limbs. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Principle of Operation of a Single-Phase Transformer A single-phase transformer works on the principle of mutual induction between two magnetically coupled coils. When the primary winding is connected to an alternating voltage of r.m.s value, V1 volts, an alternating current flows through the primary winding and setup an alternating flux ϕ in the material of the core. This alternating flux ϕ, links not only the primary windings but also the secondary windings. Therefore, an e.m.f. e1 is induced in the primary winding and an e.m.f e2 is induced in the secondary winding, Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University E.M.F Equation of a transformer: When the primary winding is excited by an alternating voltage Vt, it circulates alternating current, producing an alternating flux Φ. The primary winding has N1 number of turns. The alternating flux Φ linking with the primary winding itself induces an e.m.f. in it denoted as E1. The flux links with secondary winding through the common magnetic core. It produces induced e.m.f. E2 in the secondary winding. This is mutually induced e.m.f. Let us derive the equations for E1 and E2. The primary winding is excited by purely sinusoidal alternating voltage. Hence the flux produced is also sinusoidal in nature having maximum value of Φm. Consider a transformer having, Φ = Flux Φm = Maximum value of flux N1 = Number of primary winding turns N 2 = Number of secondary winding turns f = Frequency of the supply voltage E 1 = R.M.S. value of the primary induced e.m.f. E2 = R.M.S. value of the secondary induced e.m.f. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University From Faraday's law of electromagnetic induction, the average e.m.f. induced in each turn is proportional to the average rate of change of flux. 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑒. 𝑚. 𝑓. 𝑝𝑒𝑟 𝑡𝑢𝑟𝑛 = 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒 𝑜𝑓 𝑓𝑙𝑢𝑥 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑒. 𝑚. 𝑓. 𝑝𝑒𝑟 𝑡𝑢𝑟𝑛 = 𝑑𝛷/ 𝑑𝑡 𝑑𝛷 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑓𝑙𝑢𝑥 = 𝑑𝑡 𝑇𝑖𝑚𝑒 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑓𝑜𝑟 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑓𝑙𝑢𝑥 The flux in the core will vary sinusoidally as shown in figure, so that it increases from zero to maximum "ϕm" in one quarter of the cycle (1/4) i.e., 𝑑𝛷 ϕm−0 = 1 as (dt) for (1/4) time period is (l/4f) seconds 𝑑𝑡 4𝑓 𝑑𝛷 = 4𝑓 𝛷𝑚 𝑊𝑏/𝑠𝑒𝑐 𝑑𝑡 Average e.m.f. / turn = 4f ϕm volts 𝑅. 𝑀. 𝑆 𝑉𝑎𝑙𝑢𝑒 𝐹𝑟𝑜𝑚 𝐹𝑎𝑐𝑡𝑜𝑟 (𝑓. 𝑓) = = 1.11 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑉𝑎𝑙𝑢𝑒 R.M.S. value = 1.11 × Average value R.M.S. value of induced e.m.f. /turn= 1.11 × 4f Φm = 4.44f Φm R.M.S. value of induced e.m.f. for whole primary windings (E1)= N1× 4.44f Φm volts R.M.S. value of induced e.m.f. for whole secondary windings (E2)= N2× 4.44f Φm volts The expressions of E1 & E2 are called e.m.f. equations of transformer: E1 = 4.44f Φm N1 volts E2 = 4.44f Φm N2 volts from above equation, we notice e.m.f./turn is the same in both the primary and secondary windings. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Ratio of Transformer 1. Voltage Ration From the e.m.f. equation of transformer, E1 = 4.44f Φm N1 & E2 = 4.44f Φm N2. Taking the ratio of the two equations we get, 𝐸2 N2 = =𝐾 𝐸1 N1 This ratio secondary induced e.m.f. to primary induced e.m.f. is known as voltage transformation ratio denoted as K, while (N1 / N2) known as turn ration. N2 𝑤ℎ𝑒𝑟𝑒 𝐾 = the equation will be E2 = K*E1 N1 You can notice: If N2 > N1 (i.e. K > 1), we get E2 > E1 then the transformer is called step-up transformer. If N2 < N1 (i.e. K < 1), we get E2 < E1 then the transformer is called step-down transformer. If N2 = N1 (i.e. K = 1), we get E2 = E1 then the transformer is called isolation transformer' or 1:1 transformer. 2. Current Ratio Consider an ideal transformer and we have the input voltampere is equal to output voltampere. Mathematically, Input Voltampere = Output Voltampere 𝑉1 𝐼1 = 𝑉2 𝐼2 𝑉2 I1 = =𝐾 𝑉1 I2 𝑁1 I2 = 𝑁2 I1 Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Ideal Transformer A transformer is said to be ideal if it satisfies following properties: It has no losses. Its windings have zero resistance. Leakage flux is zero i.e. 100 % flux produced by primary links with the secondary. Permeability of core is so high that negligible current is required to establish the flux in it. For an ideal transformer, the primary applied voltage Vt is same as the primary induced e.m.f. E1 as there are no voltage drops. Similarly, the secondary induced e.m.f. E2 is also same as the terminal voltage V2 across the load. Hence for an ideal transformer we can write, 𝐸2 V2 = =𝐾 𝐸1 V1 No transformer is ideal in practice but the value of E1 is almost equal to V1for properly designed transformer. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Exercises Q1) Why can't DC power supply be used for transformers? The transformer works on the principle of mutual induction, for which current in one coil must change uniformly. If D.C. supply is given, the current will not change due to constant supply and transformer will not work. This is why DC currents cannot provide frequency and therefore cannot be used in transformers. Q2) The number of primary and secondary windings is 100 and 350 respectively. The primary voltage is given by 200V, determine the secondary voltage! 𝐸2 N2 Solution: = 𝐸1 N1 𝐸2 350 = 𝐸2 = 700 𝑣 200 100 We notice E1= 200 v, when we solved the problem to extract the value of the second voltage we got E2= 700 v, that mean the transformer is step up Q3) The number of primary and secondary windings is 60 and 100 respectively. The secondary voltage is given by 250V, determine the primary voltage. 𝐸2 N2 60 = E1 = (250) = 150 v 𝐸1 N1 100 We notice E2= 250 v, when we solved the problem to extract the value of the second voltage we got E2=1= 150 v, that mean the transformer is step down Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Q4) A portable x-ray unit has a step-up transformer, the 120 V input of which is transformed to the 100 kV output needed by the x-ray tube. The primary has 50 loops and draws a current of 10.00 A when in use. a. What is the number of loops in the secondary? b. Find the current output of the secondary? Solution a) 𝑉2 N2 V2 100,000 𝑣 = 𝑁2 = 𝑁1 = (50) = 41666 𝑉1 N1 V1 120 v A large number of loops in the secondary (compared with the primary) is required to produce such a large voltage. This would be true for neon sign transformers and those supplying high voltage inside TVs and CRTs. b) 𝑁1 I2 N1 50 = 𝐼2 = 𝐼1 = (10) = 12 𝑚𝐴 𝑁2 I1 N2 41666 As expected, the current output is significantly less than the input. In certain spectacular demonstrations, very large voltages are used to produce long arcs, but they are relatively safe because the transformer output does not supply a large current. Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Q5) A single-phase transformer has 400 primary and 1000 secondary turns. The net cross-sectional area of the core is 60 cm2. If the primary winding be connected to a 50 Hz supply at 520 V, calculate a. The peak value of flux density in the core b. The voltage induced in the secondary winding. Solution: 𝐸2 N2 𝐸2 1000 a. = = 𝐸1 N1 520 400 400 * E2 = 520 * 1000 E2 = (520 * 1000) / 400 = 1300 V Set up Transformer b. E1= 4.44 f N1 Bm A 520 = 4.44 * 50 * 400 * Bm * (60*10-4) Bm = 520 / (4.44 * 50 * 400 * Bm * (60*10-4)) =0.976 Wb/m2 Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Activates 1. What is the primary function of a transformer? a. To convert AC to DC b. To generate electricity c. To increase or decrease voltage levels d. To store energy Answer) ???? 2. In a step-up transformer, the number of turns in the primary coil is: a. Greater than the secondary coil b. Less than the secondary coil c. Equal to the secondary coil d. Irrelevant to the transformation Answer) ???? 3. What type of current do transformers typically operate with? a. Direct Current (DC) b. Alternating Current (AC) c. Both AC and DC d. None of the above Answer) ???? 4. What is the main component that enables a transformer to operate? a. Insulator b. Capacitor c. Resistor d. Magnetic core Answer) ???? Saad Rajab Al_Dulaimy [email protected] Machine MITE Department Al Maarif University Question: How does the principle of electromagnetic induction allow a transformer to transfer energy between its coils without direct electrical connection? ??? Think then answer Question: Why is it important to use transformers in power distribution systems, and how do they contribute to energy efficiency? ??? Think then answer Saad Rajab Al_Dulaimy [email protected]