Page 1 Module 7 Transformer Version 2 EE IIT, Kharagpur Page 2 Module 7 Transformer Version 2 EE IIT, Kharagpur Lesson 24 Practical Transformer Version 2 EE IIT, Kharagpur Page 3 Module 7 Transformer Version 2 EE IIT, Kharagpur Lesson 24 Practical Transformer Version 2 EE IIT, Kharagpur Contents 24 Practical Transformer 4 24.1 Goals of the lesson …………………………………………………………………. 4 24.2 Practical transformer ………………………………………………………………. 4 24.2.1 Core loss………………………………………………………………….. 7 24.3 Taking core loss into account ……………………………………………………… 7 24.4 Taking winding resistances and leakage flux into account ……………………….. 8 24.5 A few words about equivalent circuit ……………………………………………... 10 24.6 Tick the correct answer ……………………………………………………………. 11 24.7 Solve the problems ………………………………………………………………… 12 Version 2 EE IIT, Kharagpur Page 4 Module 7 Transformer Version 2 EE IIT, Kharagpur Lesson 24 Practical Transformer Version 2 EE IIT, Kharagpur Contents 24 Practical Transformer 4 24.1 Goals of the lesson …………………………………………………………………. 4 24.2 Practical transformer ………………………………………………………………. 4 24.2.1 Core loss………………………………………………………………….. 7 24.3 Taking core loss into account ……………………………………………………… 7 24.4 Taking winding resistances and leakage flux into account ……………………….. 8 24.5 A few words about equivalent circuit ……………………………………………... 10 24.6 Tick the correct answer ……………………………………………………………. 11 24.7 Solve the problems ………………………………………………………………… 12 Version 2 EE IIT, Kharagpur 24.1 Goals of the lesson In practice no transformer is ideal. In this lesson we shall add realities into an ideal transformer for correct representation of a practical transformer. In a practical transformer, core material will have (i) finite value of µ r , (ii) winding resistances, (iii) leakage fluxes and (iv) core loss. One of the major goals of this lesson is to explain how the effects of these can be taken into account to represent a practical transformer. It will be shown that a practical transformer can be considered to be an ideal transformer plus some appropriate resistances and reactances connected to it to take into account the effects of items (i) to (iv) listed above. Next goal of course will be to obtain exact and approximate equivalent circuit along with phasor diagram. Key words : leakage reactances, magnetizing reactance, no load current. After going through this section students will be able to answer the following questions. • How does the effect of magnetizing current is taken into account? • How does the effect of core loss is taken into account? • How does the effect of leakage fluxes are taken into account? • How does the effect of winding resistances are taken into account? • Comment the variation of core loss from no load to full load condition. • Draw the exact and approximate equivalent circuits referred to primary side. • Draw the exact and approximate equivalent circuits referred to secondary side. • Draw the complete phasor diagram of the transformer showing flux, primary & secondary induced voltages, primary & secondary terminal voltages and primary & secondary currents. 24.2 Practical transformer A practical transformer will differ from an ideal transformer in many ways. For example the core material will have finite permeability, there will be eddy current and hysteresis losses taking place in the core, there will be leakage fluxes, and finite winding resistances. We shall gradually bring the realities one by one and modify the ideal transformer to represent those factors. Consider a transformer which requires a finite magnetizing current for establishing flux in the core. In that case, the transformer will draw this current I m even under no load condition. The level of flux in the core is decided by the voltage, frequency and number of turns of the primary and does not depend upon the nature of the core material used which is apparent from the following equation: max f = 1 1 2 V fN p Version 2 EE IIT, Kharagpur Page 5 Module 7 Transformer Version 2 EE IIT, Kharagpur Lesson 24 Practical Transformer Version 2 EE IIT, Kharagpur Contents 24 Practical Transformer 4 24.1 Goals of the lesson …………………………………………………………………. 4 24.2 Practical transformer ………………………………………………………………. 4 24.2.1 Core loss………………………………………………………………….. 7 24.3 Taking core loss into account ……………………………………………………… 7 24.4 Taking winding resistances and leakage flux into account ……………………….. 8 24.5 A few words about equivalent circuit ……………………………………………... 10 24.6 Tick the correct answer ……………………………………………………………. 11 24.7 Solve the problems ………………………………………………………………… 12 Version 2 EE IIT, Kharagpur 24.1 Goals of the lesson In practice no transformer is ideal. In this lesson we shall add realities into an ideal transformer for correct representation of a practical transformer. In a practical transformer, core material will have (i) finite value of µ r , (ii) winding resistances, (iii) leakage fluxes and (iv) core loss. One of the major goals of this lesson is to explain how the effects of these can be taken into account to represent a practical transformer. It will be shown that a practical transformer can be considered to be an ideal transformer plus some appropriate resistances and reactances connected to it to take into account the effects of items (i) to (iv) listed above. Next goal of course will be to obtain exact and approximate equivalent circuit along with phasor diagram. Key words : leakage reactances, magnetizing reactance, no load current. After going through this section students will be able to answer the following questions. • How does the effect of magnetizing current is taken into account? • How does the effect of core loss is taken into account? • How does the effect of leakage fluxes are taken into account? • How does the effect of winding resistances are taken into account? • Comment the variation of core loss from no load to full load condition. • Draw the exact and approximate equivalent circuits referred to primary side. • Draw the exact and approximate equivalent circuits referred to secondary side. • Draw the complete phasor diagram of the transformer showing flux, primary & secondary induced voltages, primary & secondary terminal voltages and primary & secondary currents. 24.2 Practical transformer A practical transformer will differ from an ideal transformer in many ways. For example the core material will have finite permeability, there will be eddy current and hysteresis losses taking place in the core, there will be leakage fluxes, and finite winding resistances. We shall gradually bring the realities one by one and modify the ideal transformer to represent those factors. Consider a transformer which requires a finite magnetizing current for establishing flux in the core. In that case, the transformer will draw this current I m even under no load condition. The level of flux in the core is decided by the voltage, frequency and number of turns of the primary and does not depend upon the nature of the core material used which is apparent from the following equation: max f = 1 1 2 V fN p Version 2 EE IIT, Kharagpur Hence maximum value of flux density BB max is known from B max B = max , i A f where A i is the net cross sectional area of the core. Now H max is obtained from the B – H curve of the material. But we know H max = 1max , m i NI l where I mmax is the maximum value of the magnetizing current. So rms value of the magnetizing current will be I m = max . 2 m I Thus we find that the amount of magnetizing current drawn will be different for different core material although applied voltage, frequency and number of turns are same. Under no load condition the required amount of flux will be produced by the mmf N 1 I m . In fact this amount of mmf must exist in the core of the transformer all the time, independent of the degree of loading. Whenever secondary delivers a current I 2 , The primary has to reacts by drawing extra current I’ 2 (called reflected current) such that I’ 2 N 1 = I 2 N 2 and is to be satisfied at every instant. Which means that if at any instant i 2 is leaving the dot terminal of secondary, 2 i ' will be drawn from the dot terminal of the primary. It can be easily shown that under this condition, these two mmfs (i.e, N 2 i 2 and 21 iN ' ) will act in opposition as shown in figure 24.1. If these two mmfs also happen to be numerically equal, there can not be any flux produced in the core, due to the effect of actual secondary current I 2 and the corresponding reflected current 2 I ' Figure 24.1: MMf directions by I 2 and ' 2 I N 1 ' 12 Ni N 2 N 2 i 2 i 2 ' 2 i The net mmf therefore, acting in the magnetic circuit is once again I m N 1 as mmfs 21 IN ' and I 2 N 2 cancel each other. All these happens, because KVL is to be satisfied in the primary demanding f max to remain same, no matter what is the status (i., open circuited or loaded) of the secondary. To create f max , mmf necessary is N 1 I m . Thus, net mmf provided by the two coils together must always be N 1 I m – under no load as under load condition. Better core material is used to make I m smaller in a well designed transformer. Keeping the above facts in mind, we are now in a position to draw phasor diagram of the transformer and also to suggest modification necessary to an ideal transformer to take magnetizing current m I into account. Consider first, the no load operation. We first draw the max f phasor. Since the core is not ideal, a finite magnetizing current m I will be drawn from supply and it will be in phase with the flux phasor as shown in figure 24.2(a). The induced voltages in primary 1 E and secondary 2 E are drawn 90º ahead (as explained earlier following convention 2). Since winding resistances and the leakage flux are still neglected, terminal voltages 1 V and 2 V will be same as 1 E and 2 E respectively. Version 2 EE IIT, KharagpurRead More

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