Electrical Machines -1 Lecture Notes PDF

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY LECTURE NOTES On Electrical Machine 1 Name of the Department- Electrical Engineering SUBJECT CODE-1302 NAME OF THE SUBJECT-...

VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY LECTURE NOTES On Electrical Machine 1 Name of the Department- Electrical Engineering SUBJECT CODE-1302 NAME OF THE SUBJECT- ELECTRICAL MACHINE1 (PART 1) SEMESTER- 3RD BRANCH- EE&EEE PART1- MODULE1+ MODULE2 ELECTRICAL MACHINE 1 (BEE-1302) 1  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY DETAIL SYLLABUS Veer Surendra Sai University of Technology, Orissa, Burla, India Department of Electrical Engineering, Syllabus of Bachelor of Technology in Electrical & Electronics Engineering, 2010 (3RD SEMESTER) ELECTRICAL MACHINES-I (3-1-0) MODULE-I (10 HOURS) Electromechanical Energy conversion, forces and torque in magnetic field systems – energy balance, energy and force in a singly excited magnetic field system, determination of magnetic force , coenergy, multi excited magnetic field systems. DC Generators – Principle of operation, Action of commutator, constructional features, armature windings, lap and wave windings, simplex and multiplex windings, use of laminated armature, E. M.F. Equation, Methods of Excitation: separately excited and self excited generators, build up of E.M.F., critical field resistance and critical speed , causes for failure to self excite and remedial measures, Armature reaction: Cross magnetizing and demagnetizing AT/pole, compensating winding, commutation, reactance voltage, methods of improving commutation Load characteristics of shunt, series and compound generators, parallel operation of DC generators, use of equalizer bar and cross connection of field windings, load sharing. MODULE-II (10 HOURS) Transformers: Single phase transformer, Constructional details, Core, windings, Insulation, principle of operation, emf equation, magnetising current and core losses, no load and on load operation, Phasor diagram, equivalent circuit, losses and efficiency, condition for maximum efficiency, voltage regulation, approximate expression for voltage regulation, open circuit and short circuit tests, Sumpner’s test, Inrush of switching currents, harmonics in single phase transformers, magnetizing current wave form, Parallel operation of transformers. MODULE-III (10 HOURS) DC Motors: Principle of operation, Back E.M.F., Torque equation, characteristics and application of shunt, series and compound motors, Armature reaction and commutation, Starting of DC motor, Principle of operation of 3 point and 4 point starters, drum controller, Constant & Variable losses, calculation of efficiency, condition for maximum efficiency. Speed control of DC Motors: Armature voltage and field flux control methods, Ward Leonard method. ELECTRICAL MACHINE 1 (BEE-1302) 2  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Methods of Testing: direct, indirect and regenerative testing, brake test, Swinburne’s test, Load test, Hopkinson’s test, Field’s test, Retardation test, separation of stray losses in a DC motor test. MODULE-IV (10 HOURS) Three phase Transformer: Constructional features of three phase transformers – three phase connection of transformers (Dd0, Dd6, Yy0, Yy6, Dy1, Dy11, Yd1, Yd11, zigzag), Scott connection, open delta connection, three phase to six phase connection, oscillating neutral, tertiary winding, three winding transformer, equal and unequal turns ratio, parallel operation, load sharing.Distribution transformers, all day efficiency, Autotransformers, saving of copper, applications, tap- changing transformers, cooling of transformers. ELECTRICAL MACHINE 1 (BEE-1302) 3  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Disclaimer This document does not claim any originality and cannot be used as a substitute for prescribed textbooks. The information presented here is merely a collection by the committee members for their respective teaching assignments. Various sources as mentioned at the end of the document as well as freely available material from internet were consulted for preparing this document. The ownership of the information lies with the respective authors or institutions. Further, this document is not intended to be used for commercial purpose and the committee members are not accountable for any issues, legal, or otherwise, arising out of this document. The committee members make no representations or warranties with respect to the accuracy or completeness of the contents of this document and specially disclaim any implied warranties of merchantability or fitness for a particular purpose. The committee members shall not be liable for any loss or profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. ELECTRICAL MACHINE 1 (BEE-1302) 4  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY ELECTRICAL MACHINE 1 (BEE-1302) 5  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY TOPICS Electromechanical Energy conversion, forces and torque in magnetic field systems – energy balance, energy and force in a singly excited magnetic field system, determination of magnetic force, co- energy, multi excited magnetic field systems. DC Generators – Principle of operation, Action of commutator, constructional features, armature windings, lap and wave windings, simplex and multiplex windings, use of laminated armature, E. M.F. Equation, Methods of Excitation: separately excited and self -excited generators, build-up of E.M.F., critical field resistance and critical speed , causes for failure to self-excite and remedial measures, Armature reaction: Cross magnetizing and demagnetizing AT/pole, compensating winding, commutation, reactance voltage, methods of improving commutation MODULE-I Load characteristics of shunt, series and compound generators, parallel operation of DC generators, use of equalizer bar and cross connection of field DC GENERATOR windings, load sharing. [Topics are arranged as per above sequence] ELECTRICAL MACHINE 1 (BEE-1302) 6  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 1.1 Electromechanical-Energy-Conversion Principles The electromechanical-energy-conversion process takes place through the medium of the electric or magnetic field of the conversion device of which the structures depend on their respective functions.  Transducers: microphone, pickup, sensor, loudspeaker  Force producing devices: solenoid, relay, and electromagnet  Continuous energy conversion equipment: motor, generator 1.2 Forces and Torques in Magnetic Field Systems The Lorentz Force Law gives the force F on a particle of charge q in the presence of electric and magnetic fields. F= q(E+v×B) Where, F : newtons, q: coulombs, E: volts/meter, B : telsas, v: meters/second > In a pure electric-field system, F = qE > In pure magnetic-field systems, F= q(v×B) Fig 1.1 Right-hand rule for F = q(v× B) > For situations where large numbers of charged particles are in motion, Fv = ρ(E+v×B) J = ρv ELECTRICAL MACHINE 1 (BEE-1302) 7  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fv =J×B ρ (charge density): coulombs/m , Fv (force density): newtons/m3, J = ρv (current density): amperes/m2. 3 Most electromechanical-energy-conversion devices contain magnetic material.  Forces act directly on the magnetic material of these devices which are constructed of rigid, non- deforming structures.  The performance of these devices is typically determined by the net force, or torque, acting on the moving component. It is rarely necessary to calculate the details of the internal force distribution.  Just as a compass needle tries to align with the earth’s magnetic field, the two sets of fields associated with the rotor and the stator of rotating machinery attempt to align, and torque is associated with their displacement from alignment. o In a motor, the stator magnetic field rotates ahead of that of the rotor, pulling on it and performing work. o For a generator, the rotor does the work on the stator. The Energy Method > Based on the principle of conservation of energy: energy is neither created nor destroyed; it is merely changed in form. > Fig. 1.2 shows a magnetic-field-based electromechanical-energy-conversion device. - A lossless magnetic-energy-storage system with two terminals - The electric terminal has two terminal variables: e (voltage), i (current). - The mechanical terminal has two terminal variables: ffld (force), x (position) - The loss mechanism is separated from the energy-storage mechanism. – Electrical losses: ohmic losses... – Mechanical losses: friction, windage... ELECTRICAL MACHINE 1 (BEE-1302) 8  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY > Fig. 1.3: a simple force-producing device with a single coil forming the electric terminal, and a movable plunger serving as the mechanical terminal. - The interaction between the electric and mechanical terminals, i.e. the electromechanical energy conversion, occurs through the medium of the magnetic stored energy. Fig 1.2 Schematic diagram of magnetic- field electromechanical-energy-conversion device Fig. 1.3 Schematic diagram of simple force-producing device - Wfld : the stored energy in the magnetic field dWfld dx  ei  f fld dt dt d e dt dWfld  id   f fld dx - From the above equation force can be solved as a function of the flux λ and the mechanical terminal position x. - The above equations form the basis for the energy method 1.3 Energy Balance Consider the electromechanical systems whose predominant energy-storage mechanism is in magnetic fields. For motor action, the energy transfer can be accounted as ELECTRICAL MACHINE 1 (BEE-1302) 9  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY The ability to identify a lossless-energy-storage system is the essence of the energy method. > This is done mathematically as part of the modeling process. > For the lossless magnetic-energy-storage system of Fig. 1.2 can be rearranged and gives dWelec  dWmech  dWfld where dWelec  id = differential electric energy input dWmech  fflddx = differential mechanical energy output dWfld = differential change in magnetic stored energy >Here e is the voltage induced in the electric terminals by the changing magnetic stored energy. It is through this reaction voltage that the external electric circuit supplies power to the coupling magnetic field and hence to the mechanical output terminals. dWelec ei dt > The basic energy-conversion process is one involving the coupling field and its action and reaction on the electric and mechanical systems. > Combining above two equation – dWelec  ei dt  dWmech  dWfld 1.4 Energy in Singly-Excited Magnetic Field Systems In energy-conversion systems the magnetic circuits have air gaps between the stationary and moving members in which considerable energy is stored in the magnetic field. > This field acts as the energy-conversion medium, and its energy is the reservoir between the ELECTRICAL MACHINE 1 (BEE-1302) 10  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY electric and mechanical system. Fig. 1.4 shows an electromagnetic relay schematically. The predominant energy storage occurs in the air gap, and the properties of the magnetic circuit are determined by the dimensions of the air gap. Fig.1.4 Schematic of an electromagnetic relay   L( x)i dWmech  f fld dx dWfld  id   f fld dx Wfld is uniquely specified by the values of  and x. Therefore,  and x are referred to as state variables. Since the magnetic energy storage is lossless, it is conservative system. Wfld is the same regardless of how  and x are brought to their final values. Fig 1.5 shows where tow separate the paths. Fig. 1.5 Integration paths for Wfld On path 2a, dand ffld =0. Thus dffld =0 on path 2a. On path 2b, dx= 0. Therefore the following equation can be written ELECTRICAL MACHINE 1 (BEE-1302) 11  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 0 Wfld (0 , x0 )   i( , x0 )d  0 For a linear system in which is proportional to i the equation will change and can be written as-   ' 1 2 Wfld ( , x)   i( ' , x)d  '   d'  0 0 L( x ) 2 L( x ) V: the volume of the magnetic field B  Wfld     H.dB ' dV V0  If B   H , then  B2  Wfld    dV V 2  1.5 Determination of Magnetic Force and Torque form Energy The magnetic stored energy is a state function, determined uniquely by the values of the Wfld independent state variables  and x. 1.6 Energy and Co-energy: It is that energy from which the force can be obtained directly as a function of the current. The selection of energy or co-energy as the state function is purely a matter of convenience. The co-energy Wfld' (i, x) is defined as a function of I and x such that ELECTRICAL MACHINE 1 (BEE-1302) 12  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY From the above equation co-energy Wfld' (i, x) can be seen to be a state function of the two independent variables i and x. For a system with a rotating mechanical displacement, If the system is magnetically linear, In field-theory terms, for soft magnetic materials For permanent-magnet (hard) materials ELECTRICAL MACHINE 1 (BEE-1302) 13  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY For a magnetically-linear system, the energy and co-energy (densities) are numerically equal: For a nonlinear system in which  and i or B and H are not linearly proportional, the two functions are not even numerically equal. Fig.1.6 Graphical interpretation of energy and co-energy in a singly-excited system 1.7 Multiply-Excited Magnetic Field Systems Many electromechanical devices have multiple electrical terminals. > Measurement systems: torque proportional to two electric signals; power as the product of voltage and current. > Energy conversion devices: multiply-excited magnetic field system. > A simple system with two electrical terminals and one mechanical terminal: ELECTRICAL MACHINE 1 (BEE-1302) 14  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.7 Multiply-excited magnetic energy storage system To find Wfld, use the path of integration as shown in Fig 1.8. Fig. 1.8 Integration path to obtain Wfld 10 , 20 ,0  > In a magnetically-linear system, Note that Lij Lij ( ) ELECTRICAL MACHINE 1 (BEE-1302) 15  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY The energy for this linear system is Co-energy function for a system with two windings can be defined as For a linear system  Note that the co-energy function is a relatively simple function of displacement.  The use of a co-energy function of the terminal currents simplifies the determination of torque or force. ELECTRICAL MACHINE 1 (BEE-1302) 16  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY  Systems with more than two electrical terminals are handled in analogous fashion. DC Generators 1.8 Principle of operation of DC Generator A D.C generator as shown in figure below the armature be driven by a prime mover in the clock wise direction and the stator field is excited to produce the field poles as shown. There will be induced voltage in each armature conductor. The direction of the induced voltage can be determined by applying Fleming's right hand rule. All the conductors under the influence of North Pole will have directed induced voltage, while the conductors under the influence of South Pole will have induced voltage in them. For a loaded generator the direction of the armature current will be same as that of the induced voltages. Thus and also represent the direction of the currents in the conductors. We know, a current carrying conductor placed in a magnetic field experiences force, the direction of which can be obtained by applying Fleming's left hand rule. Applying this rule to the armature conductors in fig 1.9, the rotor experiences a torque (Te) in the counter clockwise direction (i.e., opposite to the direction of rotation) known as back torque. For steady speed operation back torque is equal to the machines input torque (Tpm) i.e. the torque supplied by prime mover. Fig. 1.9 Action of DC generator 1.9 Action of Commutator In DC machines the current in each wire of the armature is actually alternating, and hence a device is required to convert the alternating current generated in the DC generator by electromagnetic induction into direct current, or at the armature of a DC motor to convert the input direct current into alternating ELECTRICAL MACHINE 1 (BEE-1302) 17  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY current at appropriate times, as illustrated in Fig. 1.10. DC generator: induced AC emf is converted to DC voltage; DC motor: input direct current is converted to alternating current in the armature at appropriate times to produce a unidirectional torque. The commutator consists of insulated copper segments mounted on an insulated tube. Armature coils are connected in series through the commutator segments. Two brushes are pressed to the commutator to permit current flow. The brushes are placed in the neutral zone, where the magnetic field is close to zero, to reduce arcing. The commutator switches the current from one rotor coil to the adjacent coil. The switching requires the interruption of the coil current. The sudden interruption of an inductive current generates high voltages. The high voltage produces flashover and arcing between the commutator segment and the brush. Fig. 1.10Action of Commutator Fig. 1.11 Mechanical view of commutator ELECTRICAL MACHINE 1 (BEE-1302) 18  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 1.10 Constructional Features The stator of the dc machine has poles, which are excited by dc current to produce magnetic fields. In the neutral zone, in the middle between the poles, commutating poles or interpoles are placed to reduce sparking of the commutator due to armature reaction. The commutating poles are supplied by dc current. Compensating windings are mounted on the main poles. Field poles are mounted on an iron core that provides a closed magnetic circuit. The motor housing supports the iron core, the brushes and the bearings. The rotor has a ring-shaped laminated iron core with slots. Coils with several turns are placed in the slots. The distance between the two legs of the coil is about 180 electric degrees for full pitch. The coils are connected in series through the commutator segments. The ends of each coil are connected to a commutator segment. Fig. 1.12 Cross sectional view of DC Machine ELECTRICAL MACHINE 1 (BEE-1302) 19  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.13 Armature of DC Machine 1.11 Armature Winding DC machines armature consists of armature conductors. The conductors distributed in slots provided on the periphery of the armature is called armature winding. Depending on the way in which the coils are interconnected at the commutator end of the armature, the windings can be classified as lap and wave windings. Further they can be classified as simplex and multiplex. 1.11.1 Coil Span/Coil Pitch: It represents the span of the coil. For full pitched winding, the span is 1800 electrical or number of slots per pole. Coil pitch can be represented in terms of electrical degrees, slots or conductor. A full pitched coil leads to maximum voltage per coil. 1.11.2 Back Pitch (Yb): It is the distance measured in between the two coil sides of the same coil at the back end of the armature, the commutator end being the front end of armature. It can be represented in terms of number of slots or coil sides. Back pitch also represents the span of coil. 1.11.3 Front Pitch (Yf): The distance between the two coil sides of two different coils connected in series at the front end of the armature is called front pitch. 1.12 Lap Winding Lap winding is suitable for low voltage high current machines because of more number of parallel paths. The number of parallel path in lap winding is equal to number of poles. A=P Equalizing rings are connected in lap winding. ELECTRICAL MACHINE 1 (BEE-1302) 20  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.14 Winding diagram of lap winding 1.13Wave Winding Wave winding is used for high voltage low current machines. In case of wave winding, the number of parallel path (A) = 2 irrespective of number of poles. Each path will have conductors connected in series. Equalizing rings are not required in wave winding. Fig. 1.15 Winding diagram of wave winding 1.14 Simplex and Multiplex Winding Fig 1.14 and Fig. 1.15 shows simplex lap and simplex wave winding. The degree of multiplicity of a multiplex winding indicates the relative number of parallel paths with respect to the number of parallel paths in the corresponding simplex winding. For example a duplex lap or wave winding is a lap or wave winding having twice as many as parallel paths as a simplex lap or wave winding respectively. The winding can be triplex or quadruplex winding in similar manner. 1.15 Use of Laminated Armature The armature winding of DC machine should be laminated to reduce eddy current losses. The armature body (rotor) rotates in the field magnetic field. Thus in the core of the armature voltage induced which in ELECTRICAL MACHINE 1 (BEE-1302) 21  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY turn causes current to flow in the body. This current is known as eddy current. This current causes loss and thus heat will be generated. This loss depends on the amount of current flow. To reduce the amount of current flow the resistance of the body should be increased. Thus using lamination the resistance of the path through which current flows will be increased. The amount of eddy current will be reduced and thus eddy current loss can be minimized. 1.16 EMF Equation Let  = flux per pole in weber Z = number of armature conductors = Number of slots X conductors per slot. P = Number of poles; A= Number of parallel paths in armature. A= P for lap wound armature; A=2 for wave wound armature N = speed of armature in rpm; E = induced emf in each parallel path. d Average emf generated/conductor in one revolution = dt Flux cut by a conductor in one revolution = d = P weber. N Since Number of revolutions/second= 60 60 Time taken for one revolution = dt = seconds N d P P  N EMF generated/conductor =   dt 60 60 N Z Since each path has conductors in series, A P N Z EMF generated in each path is E   60 A P ZN E 60A 1.17 Methods of excitation DC machines are excited in two ways- 1.17.1Separate excitation: ELECTRICAL MACHINE 1 (BEE-1302) 22  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY When the field winding is connected to an external source to produce field flux. According to the type of excitation this machines are called separately excited dc machine. Fig. 1.16 Schematic diagram of separately excited dc machine 1.17.2 Self-excitation: When the field winding is connected with the armature to produce field flux. A self-excited machine requires residual magnetism for operation. According to the type of excitation this machines are called self-excited dc machine. Depending on the type of field winding connection DC machines can be classified as: 1.17.2.1 Shunt machine: The field winding consisting of large number of turns of thin wire is usually excited in parallel with armature circuit and hence the name shunt field winding. This winding will be having more resistance and hence carries less current. Fig. 1.17 Schematic diagram of dc shunt machine 1.17.2.2 Series machine: The field winding has a few turns of thick wire and is connected in series with armature. ELECTRICAL MACHINE 1 (BEE-1302) 23  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig.1.18 Schematic diagram of dc series machine 1.17.2.3 Compound machine: Compound wound machine comprises of both series and shunt windings and can be either short shunt or long shunt, cumulative, differential or flat compounded. A B Fig. 1.19 A A Schematic diagram of short -shunt compound machine Fig.1.19 B Schematic diagram of long-shunt compound machine 1.18 Build-up of E.M.F When the armature is rotating with armature open circuited, an emf is induced in the armature because of the residual flux. When the field winding is connected with the armature, a current flows through the field winding ( in case of shunt field winding, field current flows even on No-load and in case of series field winding only with load) and produces additional flux. This additional flux along with the residual flux generates higher voltage. This higher voltage circulates more current to generate further higher voltage. This is a cumulative process till the saturation is attained. ELECTRICAL MACHINE 1 (BEE-1302) 24  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.20 Process of voltage build-up in DC generator Here OM is the field resistance curve in Fig. 1.20. Initially there will be residual voltage which will create OA field current. This field current will increase the existing magnetic field and the induced voltage will increase up-to OB. This OB voltage will further applied to the field winding and increase the field current to OC. This process will continue upto the point L where the emf curve intersect with field resistance and finally the induced voltage will be OJ. This way voltage builds-up in dc generator. 1.19 Critical Resistance:- The voltage to which it builds is decided by the resistance of the field winding as shown in the figure 1.21. If field circuit resistance is increased such that the resistance line does not cut OCC like ‘OP’ in the figure1.21, then the machine will fail to build up voltage to the rated value. The slope of the air gap line drawn as a tangent (OQ) to the initial linear portion of the curve represents the maximum resistance that the field circuit can have beyond which the machine fails to build up voltage. This value of field circuit resistance is called critical field resistance. The field circuit is generally designed to have a resistance value less than this so that the machine builds up the voltage to the rated value. ELECTRICAL MACHINE 1 (BEE-1302) 25  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.21 Field current vs No-load voltage for different field resistances Critical field resistance is defined as the maximum field circuit resistance for a given speed with which the shunt generator would excite. The shunt generator will build up voltage only if field circuit resistance is less than critical field resistance. 1.20 Critical Speed: Voltage of a dc generator is proportional to its speed. Thus when speed will be reduced then the induced voltage will reduced. There can be such situation occur when the speed will be so low that the existing field winding resistance voltage bulid up will not occur. The speed of the generator can be lowered upto a certain level. This minimum value of the speed of the generator for which the generator can excite is called critical speed. It can also define as that speed of a generator for which the existing field resistance of generator becomes its critical field resistance. ELECTRICAL MACHINE 1 (BEE-1302) 26  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY connected to the dual flux. Fig. 1.22 Field current vs No-load voltage for different speed In the above figure it is showing that when speed of the generator changes from n1 to n2 and then n3 emf production changes accordingly. Here n1>n2>n3. For speed n3 voltage build-up is not possible. The speed n2 is the critical speed. As shown in the figure at speed n2 generator field resistance become its critical field resistance. 1.21 Causes for failure to self-excite and its remedial i. The field poles may not have residual magnetism. Then the generator will fail to excite. Then to restore residual magnetism field winding should be connected to an external dc voltage source. This is called flashing of field. ii. When the direction of rotation is not proper such that flux produced by the field current reinforces the residual magnetism. The rotation of the machine has to be reversed. iii. The field winding resistance is more than critical resistance then the machine will fail to excite. The field winding resistance should be less than critical field resistance. iv. When the speed of the machine is less than critical speed. The machine’s speed should be more than critical speed. ELECTRICAL MACHINE 1 (BEE-1302) 27  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY v. If the field winding connections are such that newly generated field flux is working in opposite to the existing residual magnetism. Then the generator will fail to excite. Then the field winding connection should be reversed. 1.22Armature Reaction The action of magnetic field set up by armature current on the distribution of flux under main poles of a DC machine is called armature reaction. When the armature of a DC machines carries current, the distributed armature winding produces its own mmf. The machine air gap is now acted upon by the resultant mmf distribution caused by the interaction of field ampere turns (ATf) and armature ampere turns (ATa). As a result the air gap flux density gets distorted. Fig. a Fig. b Fig. c Fig. d Figure a shows a two pole machine with single equivalent conductor in each slot and the main field mmf (Ff) acting alone. The axis of the main poles is called the direct axis (d-axis) and the interpolar axis is called quadrature axis (q-axis). It can be seen from the Figure b that armature mmf (Fa) is along the ELECTRICAL MACHINE 1 (BEE-1302) 28  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY interpolar axis. Fa which is at 900 to the main field axis is known as cross magnetizing mmf. Figure c shows the practical condition in which a DC machine operates when both the Field flux and armature flux are existing. Because of both fluxes are acting simultaneously, there is a shift in brush axis and crowding of flux lines at the trailing pole tip and flux lines are weakened or thinned at the leading pole tip. (The pole tip which is first met in the direction of rotation by the armature conductor is leading pole tip and the other is trailing pole tip). If the iron in the magnetic circuit is assumed unsaturated, the net flux/pole remains unaffected by the armature reaction though the air gap flux density distribution gets distorted. If the main pole excitation is such that the iron is in the saturated region of magnetization (practical case) the increase in flux density at one end of the poles caused by armature reaction is less than the decrease at the other end, so that there is a net reduction in the flux/pole. This is called the demagnetizing effect. Thus it can be summarized that the nature of armature reaction in a DC machine is 1. Cross magnetizing with its axis along the q-axis. 2. It causes no change in flux/pole if the iron is unsaturated but causes reduction in flux/pole in the presence of iron saturation. This is termed as demagnetizing effect. The resultant mmf ‘F’ is shown in figure d. 1.22.1Cross Magnetizing Ampere Turns/pole(ATc) If the brush is shifted by an angle θ as shown in figure 1.23 then the conductors lying in between the angles BOC and DOA are carrying the current in such a way that the direction of the flux is downwards i.e., at right angles to the main flux. This results is the distortion in the main flux. Hence, these conductors are called cross magnetizing or distorting ampere conductors. Z Total armature conductors/pole= P 2 Demagnetizing conductors / pole = Z 360 ELECTRICAL MACHINE 1 (BEE-1302) 29  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Z 2 Therefore cross magnetizing conductors/pole= Z P 360 ZI a  1   Cross magnetizing ampere turns/pole ATc=    a  2 P 360  Fig. 1.23 Cross-magnetizing ampere conductors 1.22.2 Demagnetizing Ampere Turns /pole (ATd) The exact conductors which produce demagnetizing effect are shown in Fig 1.24, Where the brush axis is given a forward lead of θ so as to lie along the new axis of M.N.A. The flux produced by the current carrying conductors lying in between the angles AOC and BOD is such that, it opposes the main flux and hence they are called as demagnetizing armature conductors. Fig. 1.24 Demagnetizing ampere conductors Z= total no of armature conductors Ia Current in each armature conductors= a θ =Forward lead in mechanical or angular deg. 4 Total no of armature conductors in between angles AOC & BOD = Z 360 Z I a Demagnetizing amp turns/poles AT d = 360a ELECTRICAL MACHINE 1 (BEE-1302) 30  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 1.23 Compensating Winding Due to armature reaction flux density wave get distorted and reduced. Due to distortion of flux wave the peak flux density increases to such a high value that it creates high induced emf. If this emf is higher than the breakdown voltage across adjacent segments, a spark over could result which can easily spread over the whole commutator, and there will be a ring of fire, resulting in the complete short circuit of the armature. To protect armature from such adverse condition armature reaction must be neutralized. To neutralize the armature reaction ampere-turns by compensating winding placed in the slots cut out in pole face such that the axis of the winding coincides with the brush axis as shown figure 1.25. Fig. 1.25 Compensating conductors in field poles and the connection of compensating conductors with armature The compensating windings neutralize the armature mmf directly under the pole which is the major portion because in the interpole region the air gap will be large. Compensating windings are connected in series with armature so that it will create mmf proportional to armature mmf. The number of ampere-turns required in the compensating windings is given by Pole Arc ATc = Total Armature Ampere Turns  Pole Pitch 1.24 Commutation The process of reversal of current in the short circuited armature coil is called ‘Commutation’. This process of reversal takes place when coil is passing through the interpolar axis (q-axis), the coil is short circuited through commutator segments and brush. ELECTRICAL MACHINE 1 (BEE-1302) 31  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY The process of commutation of coil ‘CD’ is shown Fig. 1.26. In sub figure ‘c’ coil ‘CD’ carries 20A current from left to right and is about to be short circuited in figure ‘d’ brush has moved by a small width and the brush current supplied by the coil are as shown. In figure ‘e’ coil ‘CD’ carries no current as the brush is at the middle of the short circuit period and the brush current in supplied by coil ‘AB’ and coil ‘EF’. In sub figure ‘f’ the coil ‘CD’ which was carrying current from left to right carries current from right to left. In sub fig ‘g’ spark is shown which is due to the reactance voltage. As the coil is embedded in the armature slots, which has high permeability, the coil possess appreciable amount of self inductance. The current is changed from +20 to –20. So due to self inductance and variation in the current from +20 to –20, a voltage is induced in the coil which is given by L dI/dt. This emf opposes the change in current in coil ‘CD’ thus sparking occurs. Fig a Fig b ELECTRICAL MACHINE 1 (BEE-1302) 32  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig.c Fig.d Fig.e Fig.f Fig.g Fig.1.26 a-g shows the process of commutation ELECTRICAL MACHINE 1 (BEE-1302) 33  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 1.25 Reactance Voltage During commutation sparking occurs in the commutator segment and brush due to presence of reactance voltage. This voltage is generated due to change of current in the commutating coil for its self- inductance and also due to mutual inductance of the adjacent coils. This voltage is called reactance voltage and according to Lenz’s law this induced voltage oppose its cause of production. Here the cause of production is the change in current in the coil under commutation. Thus the commutation becomes poorer. di Reactance voltage = co-efficient of self-inductance X rate of change of current= L dt Time of short circuit = Tc = (time required by commutator to move a distance equal to the circumferential thickness of brush)–(one mica insulating strip) = Time of commutation Let Wb= brush width in cm Wi = width of mica insulation in cm Vc = peripheral velocity of commutator segments in cm/sec. Wb -Wi Then Tc = sec Vc Total change in current = I - (-I) = 2I 2I Therefore self-induced or reactance voltage = L for linear commutation Tc 2I = 1.11L for sinusoidal commutation Tc If brush width is given in terms of commutator segments, then commutator velocity should be converted in terms of commutator segments/seconds. 1.26 Method of Improving Commutation Commutation can be improved in two ways by (i) Resistance commutation ELECTRICAL MACHINE 1 (BEE-1302) 34  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY (ii) E.M.F commutation. 1.26.1Resistance Commutation Fig. 1.27 In this method the resistance of the brushes are increased by changing then from copper brush to carbon brush. From the above figure 1.27 it is seen that when current ‘20A’ from coil ‘EF’ reaches the commutator segment ‘5’, it has two parallel paths opened to it. The first path is straight from bar ‘5’ to the brush and the other is via short circuited coil ‘CD’ to bar ‘4’ and then to brush. If copper brushes are used the current will follow the first path because of its low contact resistance. But when carbon brushes having high resistance are used, then current ‘20A’ will prefer the second path because the resistance r1 of first path will increase due to reducing area of contact with bar ‘5’ and the resistance r2 of second path decreases due to increasing area of contact with bar ‘4’. Hence carbon brushes help in obtaining sparkles commutation. Also, carbon brushes lubricate and polish commutator. But, because of high resistance the brush contact drop increases and the commutator has to be made larger to dissipate the heat due to loss. Carbon brushes require larger brush holders because of lower current density. 1.26.2 E.M.F commutation: To neutralize sparking caused by reactance voltage in this method an emf is producied whichacts in opposite direction to that of reactance voltage, so that the reactance voltage is completely eliminated. The neutralization of emf may be done in two ways (i) by giving brush a forward lead sufficient enough to bring the short circuited coil under the influence of next pole of opposite polarity or (ii) by using ELECTRICAL MACHINE 1 (BEE-1302) 35  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY interpoles or compoles. The second method is commonly employed. 1.26.3 Interpoles or Compoles These are small poles fixed to the yoke and placed in between the main poles as shown in figure 1.28. They are wound with few turns of heavy gauge copper wire and are connected in series with the armature so that they carry full armature current. Their polarity in case of generator is that of the main pole ahead in the direction of rotation. Their polarity in case of motor is that of the main pole behind in the direction of rotation. Fig. 1.28 Inter-poles of DC machines The function of interpoles is (i) to induce an emf which is equal and opposite to that of the reactance voltage. Interpoles neutralize the cross magnetizing effect of armature reaction. 1.27 DC Machines Characteristics There main characteristics of dc machines are i. No-load characteristics or Open Circuit Characteristics ii. Load characteristics ELECTRICAL MACHINE 1 (BEE-1302) 36  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 1.27.1No-load characteristics or Open Circuit Characteristics of separately excited generator In this type of generator field winding is excited from a separate source, hence field current is independent of armature terminal voltage as shown on figure 1.29. The generator is driven by a prime mover at rated speed, say N rpm. With switch S in opened condition, field is excited via a potential divider connection from a separate d.c source and field current is gradually increased. The field current will establish the flux per pole . The voltmeter V connected across the armature terminals of the P ZN machine will record the generated emf ( E g   k N ). As field current is increased, E g will 60A increase. E g versus If plot at speed N1,N2,N3 is shown in figure below. Where N1>N2>N3. ELECTRICAL MACHINE 1 (BEE-1302) 37  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.29 Open circuit characteristics of DC separately excited generator 1.27.2Load characteristic of separately excited generator Load characteristic is the characteristics in between terminal voltage VT with load current IL of a generator with constant speed and constant field current. For IL = 0, VT = Eg should be the first point on the load characteristic. With increase of load current the terminal voltage will drop due to armature resistance and reaction drop. In the figure below the rated load current shown by point A. Hence the load characteristic will be drooping in nature as shown in figure 1.30. Fig 1.30 Load characteristics of DC separately excited generator 1.27.3 Characteristics of a shunt generator ELECTRICAL MACHINE 1 (BEE-1302) 38  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig 1.31 Connection diagram to obtain no-load and load characteristic To obtain OCC of DC shunt generator the above circuit will be used with switch S kept open in fig. 1.31. As this machine is self-excited thus there is no need to use separate dc source for producing field current. The voltage build up process is described earlier. The open nature of the OCC will be similar to separately excited machine. Fig. 1.32 Open circuit characteristics of DC shunt generator 1.27.4 Load characteristic of shunt generator With switch S in open condition in fig. 1.31, the generator is practically under no load condition as field current is pretty small. The voltmeter reading will be Eg as shown in figures below. In other words, VT = Eg, IL = 0 is the first point in the load characteristic. To load the machine S is closed and the load resistances decreased so that it delivers load current IL. Unlike separately excited motor, here IL ≠ Ia. In ELECTRICAL MACHINE 1 (BEE-1302) 39  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY fact, for shunt generator, Ia = IL - If. So increase of IL will mean increase of Ia as well. The drop in the terminal voltage will be caused by the usual Iara drop, brush voltage drop and armature reaction effect. Apart from these, in shunt generator, as terminal voltage decreases, field current hence  also decreases causing additional drop in terminal voltage. Remember in shunt generator, field current is decided by the terminal voltage by virtue of its parallel connection with the armature. Figure 1.33 gives the plot of terminal voltage versus load current which is called the load characteristic. As the load resistance is decreased (load current increased), the terminal voltage drops until point B is reached. If load resistance is further decreased, the load current increases momentarily. This momentary increase in load current produces more armature reaction thus causing a reduction in the terminal voltage and field current. The net reduction in terminal voltage is so large that the load current decreases and the characteristic turns back. In case the machine is short circuited, the curve terminates at point H. Here OH is the load current due to the voltage generated by residual flux. Fig. 1.33 Load characteristics of DC shunt generator 1.27.5 Compound generator As introduced earlier, compound machines have both series and shunt field coils. Series field coil may be connected in such a way that the mmf produced by it aids the shunt field mmf-then the machine is said to be cumulative compound machine, otherwise if the series field mmf acts in opposition with the shunt field mmf – then the machine is said to be differential compound machine. ELECTRICAL MACHINE 1 (BEE-1302) 40  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 1.34 Load characteristics of DC compound generator In a compound generator, series field coil current is load dependent. Therefore, for a cumulatively compound generator, with the increase of load, flux per pole increases. This in turn increases the generated emf and terminal voltage. Unlike a shunt motor, depending on the strength of the series field mmf, terminal voltage at full load current may be same or more than the no load voltage. When the terminal voltage at rated current is same that at no load condition, then it is called a level compound generator. If however, terminal voltage at rated current is more than the voltage at no load, it is called a over compound generator. The load characteristic of a cumulative compound generator will naturally be above the load characteristic of a shunt generator as depicted in figure 1.34. At load current higher than the rated current, terminal voltage starts decreasing due to saturation, armature reaction effect and more drop in armature and series field resistances. 1.28 Parallel Operation of DC Generator 1.28.1 Advantages of DC generator operating in parallel In a dc power plant, power is usually supplied from several generators of small ratings connected in parallel instead of from one large generator. This is due to the following reasons: a. Continuity of service: If a single large generator is used in the power plant, then in case of its breakdown, the whole plant will be shut down. However, if power is supplied from a number of small units operating in parallel, then in case of failure of one unit, the continuity of supply can be maintained by other healthy units. ELECTRICAL MACHINE 1 (BEE-1302) 41  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY b. Efficiency: Generators run most efficiently when loaded to their rated capacity. Therefore, when load demand on power plant decreases, one or more generators can be shut down and the remaining units can be efficiently loaded. c. Maintenance and repair: Generators generally require routine-maintenance and repair. Therefore, if generators are operated in parallel, the routine or emergency operations can be performed by isolating the affected generator while load is being supplied by other units. This leads to both safety and economy. d. Increasing plant capacity: In the modern world of increasing population, the use of electricity is continuously increasing. When added capacity is required, the new unit can be simply paralleled with the old units. e. Non-availability of single large unit: In many situations, a single unit of desired large capacity may not be available. In that case a number of smaller units can be operated in parallel to meet the load requirement. Generally a single large unit is more expensive. 1.28.2 Connecting Shunt Generators in Parallel: The generators in a power plant are connected in parallel through bus-bars. The bus-bars are heavy thick copper bars and they act as +ve and -ve terminals. The positive terminals of the generators are connected to the +ve side of bus-bars and negative terminals to the negative side of bus-bars. Fig. 1.35 shown shunt generator 1 connected to the bus-bars and supplying load. When the load on the power plant increases beyond the capacity of this generator, the second shunt generator 2 is connected in parallel with the first to meet the increased load demand. The procedure for paralleling generator 2 with generator 1 is as under: i. The prime mover of generator 2 is brought up to the rated speed. Now switch S2 in the field circuit of the generator 2 is closed. ii. Next circuit breaker CB-2 is closed and the excitation of generator 2 is adjusted till it generates voltage equal to the bus-bars voltage. This is indicated by voltmeter V2. ELECTRICAL MACHINE 1 (BEE-1302) 42  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY iii. Now the generator 2 is ready to be paralleled with generator 1. The main switch DPST2 is closed, thus putting generator 2 in parallel with generator 1. Note that generator 2 is not supplying any load because its generated emf is equal to bus-bars voltage. The generator is said to be “floating” (i.e. not supplying any load) on the bus-bars. Fig. 1.35 Schematic diagram of DC generator connected in parallel iv. If generator 2 is to deliver any current, then its generated voltage Eg should be greater than the bus-bars voltage VT. In that case, current supplied by it is I = (Eg - VT)/Ra where Ra is the resistance of the armature circuit. By increasing the field current (and hence induced emf E g), the generator 2 can be made to supply proper amount of load. v. The load may be shifted from one shunt generator to another merely by adjusting the field excitation. Thus if generator 1 is to be shut down, the whole load can be shifted onto generator 2 provided it has the capacity to supply that load. In that case, reduce the current supplied by generator 1 to zero (This will be indicated by ammeter A1) open C.B.-1 and then open the main switch DPST1. 1.29 Equalizer Bar: Compound Generators in Parallel: Under-compounded generators also operate satisfactorily in ELECTRICAL MACHINE 1 (BEE-1302) 43  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY parallel but over compounded generators will not operate satisfactorily unless their series fields are paralleled. This is achieved by connecting two negative brushes together as shown in Fig. 1.36. The conductor used to connect these brushes is generally called equalizer bar. Suppose that an attempt is made to operate the two generators in parallel without an equalizer bar. If, for any reason, the current supplied by generator 1 increases slightly, the current in its series field will increase and raise the generated voltage. This will cause generator 1 to take more load. Since total load supplied to the system is constant, the current in generator 2 must decrease and as a result its series field is weakened. Since this effect is cumulative, the generator 1 will take the entire load and drive generator 2 as a motor. After machine 2 changes from a generator to a motor, the current in the shunt field will remain in the same direction, but the current in the armature and series field will reverse. Thus the magnetizing action, of the series field opposes that of the shunt field. As the current taken by the machine 2 increases, the demagnetizing action of series field becomes greater and the resultant field becomes weaker. The resultant field will finally become zero and at that time machine 2 will be short circuited machine 1, opening the breaker of either or both machines. Fig. 1.36 Connection of equalizer bar in parallel connection of DC compound generator When the equalizer bar is used, a stabilizing action exists and neither machine tends to take all the load. To consider this, suppose that current delivered by generator 1 increases. The increased current will not only pass through the series field of generator 1 but also through the equalizer bar and series field of generator 2. Therefore, the voltage of both the machines increases and the generator 2 will take a part ELECTRICAL MACHINE 1 (BEE-1302) 44  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY of the load. 1.30 Load Sharing: The load sharing between shunt generators in parallel can be easily regulated because of their drooping characteristics. The load may be shifted from one generator to another merely by adjusting the field excitation. Let us discuss the load sharing of two generators which have unequal no-load voltages. Let E1, E2 = no-load voltages of the two generators R1, R2 = their armature resistances VT = common terminal voltage (Bus-bars voltage). Then E -V E -V I1 = 1 T and I 2 = 2 T R1 R2 Thus current output of the generators depends upon the values of E1 and E2. These values may be changed by field rheostats. The common terminal voltage (or bus-bars voltage) will depend upon (i) the emfs of individual generators and (ii) the total load current supplied. It is generally desired to keep the busbars voltage constant. This can be achieved by adjusting the field excitations of the generators operating in parallel. ELECTRICAL MACHINE 1 (BEE-1302) 45  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY TOPICS Transformers: Single phase transformer, Constructional details, Core, windings, Insulation, principle of operation, emf equation, magnetising current and core losses, no load and on load operation, Phasor diagram, equivalent circuit, losses and efficiency, condition for maximum efficiency, voltage regulation, approximate expression for voltage regulation, open circuit and Module II short circuit tests, Sumpner’s test, Inrush of switching currents, harmonics in single phase [TRANSFORMER] transformers, magnetizing current wave form, Parallel operation of transformers. [Topics are arranged as per above sequence] ELECTRICAL MACHINE 1 (BEE-1302) 46  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Transformers 2.1 Introduction The transformer is a device that transfers electrical energy from one electrical circuit to another electrical circuit. The two circuits may be operating at different voltage levels but always work at the same frequency. Basically transformer is an electro-magnetic energy conversion device. It is commonly used in electrical power system and distribution systems. It can change the magnitude of alternating voltage or current from one value to another. This useful property of transformer is mainly responsible for the widespread use of alternating currents rather than direct currents i.e., electric power is generated, transmitted and distributed in the form of alternating current. Transformers have no moving parts, rugged and durable in construction, thus requiring very little attention. They also have a very high efficiency as high as 99%. 2.2. Single Phase Transformer A transformer is a static device of equipment used either for raising or lowering the voltage of an a.c. supply with a corresponding decrease or increase in current. It essentially consists of two windings, the primary and secondary, wound on a common laminated magnetic core as shown in Fig 1. The winding connected to the a.c. source is called primary winding (or primary) and the one connected to load is called secondary winding (or secondary). The alternating voltage V1 whose magnitude is to be changed is applied to the primary. Depending upon the number of turns of the primary (N1) and secondary (N2), an alternating e.m.f. E2 is induced in the secondary. This induced e.m.f. E2 in the secondary causes a secondary current I2. Consequently, terminal voltage V2 will appear across the load. If V2 > V1, it is called a step up-transformer. If V2 < V1, it is called a step-down transformer. ELECTRICAL MACHINE 1 (BEE-1302) 47  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig. 2.1 Schematic diagram of single phase transformer 2.3 Constructional Details Depending upon the manner in which the primary and secondary windings are placed on the core, and the shape of the core, there are two types of transformers, called (a) core type, and (b) shell type. 2.3.1 Core-type and Shell-type Construction In core type transformers, the windings are placed in the form of concentric cylindrical coils placed around the vertical limbs of the core. The low-voltage (LV) as well as the high-voltage (HV) winding are made in two halves, and placed on the two limbs of core. The LV winding is placed next to the core for economy in insulation cost. Figure 2.1(a) shows the cross-section of the arrangement. In the shell type transformer, the primary and secondary windings are wound over the central limb of a three-limb core as shown in Figure 2.1(b). The HV and LV windings are split into a number of sections, and the sections are interleaved or sandwiched i.e. the sections of the HV and LV windings are placed alternately. ELECTRICAL MACHINE 1 (BEE-1302) 48  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY Fig: 2.1 Core type & shell type transformer Core The core is built-up of thin steel laminations insulated from each other. This helps in reducing the eddy current losses in the core, and also helps in construction of the transformer. The steel used for core is of high silicon content, sometimes heat treated to produce a high permeability and low hysteresis loss. The material commonly used for core is CRGO (Cold Rolled Grain Oriented) steel. Conductor material used for windings is mostly copper. However, for small distribution transformer aluminium is also sometimes used. The conductors, core and whole windings are insulated using various insulating materials depending upon the voltage. Insulating Oil In oil-immersed transformer, the iron core together with windings is immersed in insulating oil. The insulating oil provides better insulation, protects insulation from moisture and transfers the heat produced in core and windings to the atmosphere. The transformer oil should possess the following qualities: (a) High dielectric strength, (b) Low viscosity and high purity, (c) High flash point, and ELECTRICAL MACHINE 1 (BEE-1302) 49  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY (d) Free from sludge. Transformer oil is generally a mineral oil obtained by fractional distillation of crude oil. Tank and Conservator The transformer tank contains core wound with windings and the insulating oil. In large transformers small expansion tank is also connected with main tank is known as conservator. Conservator provides space when insulating oil expands due to heating. The transformer tank is provided with tubes on the outside, to permits circulation of oil, which aides in cooling. Some additional devices like breather and Buchholz relay are connected with main tank. Buchholz relay is placed between main tank and conservator. It protect the transformer under extreme heating of transformer winding. Breather protects the insulating oil from moisture when the cool transformer sucks air inside. The silica gel filled breather absorbs moisture when air enters the tank. Some other necessary parts are connected with main tank like, Bushings, Cable Boxes, Temperature gauge, Oil gauge, Tappings, etc. 2.4 Principle of Operation When an alternating voltage V1 is applied to the primary, an alternating flux ϕ is set up in the core. This alternating flux links both the windings and induces e.m.f.s E1 and E2 in them according to Faraday’s laws of electromagnetic induction. The e.m.f. E1 is termed as primary e.m.f. and e.m.f. E2 is termed as secondary e.m.f. Note that magnitudes of E2 and E1 depend upon the number of turns on the secondary and primary respectively. If N2 > N1, then E2 > E1 (or V2 > V1) and we get a step-up transformer. If N2 < N1, then E2 < E1 (or V2< V1) and we get a step-down transformer. ELECTRICAL MACHINE 1 (BEE-1302) 50  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY If load is connected across the secondary winding, the secondary e.m.f. E2 will cause a current I2 to flow through the load. Thus, a transformer enables us to transfer a.c. power from one circuit to another with a change in voltage level. The following points may be noted carefully: (a) The transformer action is based on the laws of electromagnetic induction. (b) There is no electrical connection between the primary and secondary. (c) The a.c. power is transferred from primary to secondary through magnetic flux. (d) There is no change in frequency i.e., output power has the same frequency as the input power. (e) The losses that occur in a transformer are: (a) core losses—eddy current and hysteresis losses (b) copper losses—in the resistance of the windings In practice, these losses are very small so that output power is nearly equal to the input primary power. In other words, a transformer has very high efficiency. 2.4.1 E.M.F. Equation of a Transformer Consider that an alternating voltage V1 of frequency f is applied to the primary as shown in Fig.2.3. The sinusoidal flux ϕ produced by the primary can be represented as: ϕ=ϕm sinωt When the primary winding is excited by an alternating voltage V1, it is circulating alternating current, producing an alternating flux ϕ. ϕ - Flux ϕm - maximum value of flux N1 - Number of primary turns ELECTRICAL MACHINE 1 (BEE-1302) 51  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY N2 - Number of secondary turns f - Frequency of the supply voltage E1 - R.M.S. value of the primary induced e.m.f E2 - R.M.S. value of the secondary induced e.m.f The instantaneous e.m.f. e1 induced in the primary is - Fig. 2.3 From Faraday’s law of electromagnetic induction - The flux increases from zero value to maximum value ϕm in 1/4f of the time period that is in 1/4f seconds. The change of flux that takes place in 1/4f seconds = ϕm - 0 = ϕm webers ELECTRICAL MACHINE 1 (BEE-1302) 52  VEER SURENDRA SAI UNIVERSITY OF TECHNOLOGY 2.4.2 Voltage Ratio Voltage transformation ratio is the ratio of e.m.f induced in the secondary winding to the e.m.f induced in the primary winding. This ratio of secondary induced e.m.f to primary induced e.m.f is known as voltage transformation ratio 1. If N2>N1 i.e. K>1 we get E2>E1 then the transformer is called step up transformer. 2. If N2< N1 i.e. K