Electrical Machines I - Master File PDF

CP23 SEMESTER 3 Electrical Machine 1 SME : Debesh Mandal Prepared by:Debesh Mandal Modified by: Debesh Mandal Verified by:Mr.Ved Prakash Approved by:P...

CP23 SEMESTER 3 Electrical Machine 1 SME : Debesh Mandal Prepared by:Debesh Mandal Modified by: Debesh Mandal Verified by:Mr.Ved Prakash Approved by:Program manager – CP23 Rev No : 1 Released Date : 01/07/2020  ` Table of Content Contents 1. CONCEPTS OF INDUCED EMF AND LAWS.............................................................................................. 2 1.1Types of induced EMF - static and dynamic............................................................................................ 2 1.2 Fleming’s Right Hand and Left Hand Rule, Thumb Rule......................................................................... 3 2.0 D C GENERATORS..................................................................................................................................... 5 2.1 Construction details, types of DC Machine, Armature windings and its types..................................... 5 2.2 Working principle of generator, direction of EMF, Equation of EMF....................................................... 9 2.3 Characteristics of DC generators.......................................................................................................... 12 2.4 Critical Resistance, Methods of excitation............................................................................................ 19 2.5 Armature Reaction & its Compensation............................................................................................. 20 2.6 Commutation, causes and improvement........................................................................................ 23 2.7 Application of DC generators................................................................................................................ 31 3. DC MOTORS............................................................................................................................................. 32 3.1 Working principle, Back EMF, Equation of voltage, Torque and speed- Simple problem.................... 32 3.2 Characteristics of DC Motors................................................................................................................ 37 3.3 Speed control and braking of DC motors............................................................................................ 42 3.4 Testing, Efficiency and losses of DC Machines...................................................................................... 45 3.5 Working of Starters- 3 point/4 points starters...................................................................................... 48 4.0 TRANSFORMER...................................................................................................................................... 54 4.1 Introduction – Working Principle, Construction and types................................................................... 54 4.2 EMF equation, Voltage Transformation ratio-simple problems........................................................... 57 4.3 Equivalent circuit parameters.................................................................................................... 59 4.4 Losses and efficiency, Condition for maximum efficiency, Voltage regulation..................................... 60 4.5 All day efficiency of a transformer........................................................................................................ 65 4.6 OC and SC test, Polarity Test................................................................................................................ 66 4.7 Concept of Auto Transformer, Tertiary windings.................................................................................. 68 4.8 Introduction-Necessity for tap changers – on load and off load......................................................... 74 4.9 Three phase transformers , connection diagram, Scott-connection.................................................... 78 4.10 Parallel operation, Load sharing, Condition for parallel operation............................................... 81 5.0 SPECIAL MACHINES................................................................................................................................ 85 5.1 STEPPER MOTOR.................................................................................................................................... 85 5.2 SERVO MOTORS..................................................................................................................................... 86 5.3 PMDC, BLDC........................................................................................................................................... 95 Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 1  ` 1. CONCEPTS OF INDUCED EMF AND LAWS Whenever a conductor is placed in a varying magnetic field, EMF is induced in the conductor and this EMF is called induced EMF. 1.1Types of induced EMF - static and dynamic – I. Dynamically induced EMF When the conductor is in motion and the field is in stationary so the EMF is induced in the conductor, this type of EMF is called dynamically induced EMF. II. Statically induced EMF When the conductor is in stationary and the field is changing (varying) then in this case EMF is also induced in the conductor, which is called statically induced EMF. Statically induced EMF is of two types Self induced EMF Self-induced EMF is that EMF which is induced in the conductor by changing in its own. When current is changing the magnetic field is also changing around the coil and hence Faraday law is applied here and EMF are induced in the coil to it self which called self induced EMF. Mutually induced EMF When an alternating voltage or current is applied to the coil 'a' alternating current will flow in the coil' a' and is a result of which a varying magnetic field will produced around the coil' a'.if we placed another coil 'b' in the field of coil 'a' then Faraday law is also applied here and EMF are induced in coil `b' this EMF is called mutually induced EMF. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 2  ` 1.2 Fleming’s Right Hand and Left Hand Rule, Thumb Rule If a current carrying conductor placed in a magnetic field, it experiences a force due to the magnetic field. On the other hand, if a conductor moved in a magnetic field, an emf gets induced across the conductor (Faraday's law of electromagnetic induction). John Ambros Fleming originated two rules to determine the direction of motion (in electric motors) or the direction of induced current (in electric generators). The rules are called as, Fleming's left hand rule (for motors) and Fleming's right hand rule (for generators). Fleming's Left Hand Rule Fleming's left hand rule is applicable for electric motors. Whenever a current carrying conductor is placed in a magnetic field, the conductor experiences a force. According to Fleming's left hand rule, if the thumb, fore-finger and middle finger of left hand are stretched perpendicular to each other as shown the figure above, and if fore finger represents the direction of magnetic field, the middle finger represents the direction of current, then the thumb represents the direction of force. As per Faraday's law of electromagnetic induction, whenever a conductor moves inside a magnetic field, there will be an induced current in it. If this conductor gets forcefully moved inside the magnetic field, there will be a relation between the direction of applied force, magnetic field and the current. This relation among Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 3  ` these three directions is determined by Fleming Right Hand rule This rule states "Hold out the right hand with the first finger, second finger and thumb at right angle to each other. If forefinger represents the direction of the line of force, the thumb points in the direction of motion or applied force, then second finger points in the direction of the induced current. Thumb Rule[Right hand grip rule] Grip the wire with right hand ,with the thumb pointing along the direction of current. The other fingers give the direction of the magnetic field around the wire To understand the structure of atom; please click the link below https://www.youtube.com/watch?v=tC6E9J925pY QUESTION BANK 1. In DC Motor, emf induced in armature winding. Which type of emf induced? 2. Is thumb rule equally works with left hand? Explain. 3. Suppose there is one known parameter out of 3 parameters used in Fleming’s rule. Can we apply Fleming’s rule(left/right) in this condition? Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 4  ` 2.0 D C GENERATORS 2.1 Construction details, types of DC Machine, Armature windings and its types. There are two types of generators, one is ac generator and other is dc generator. Whatever may be the types of generators, it always converts mechanical power to electrical power. An ac generator produces alternating power. A DC generator produces direct power. Both of these generators produce electrical power, based on same fundamental principle of Faraday's law of electromagnetic induction. According to these law, when an conductor moves in a magnetic field it cuts magnetic lines force, due to which an emf is induced in the conductor. The magnitude of this induced emf depends upon the rate of change of flux (magnetic line force) linkage with the conductor. This emf will cause an current to flow if the conductor circuit isNow we will go through working principle of dc generator. Single Loop DC Generator In the figure above, a single loop of conductor of rectangular shape is placed between two opposite poles of magnet. Let's us consider, the rectangular loop of conductor is ABCD which rotates inside the magnetic field about its own axis ab. When the loop rotates from its vertical position to its horizontal position, it cuts the flux lines of the field. As during this movement two sides, i.e. AB and CD of the loop cut the flux lines there will be an emf induced in these both of the sides (AB & BC) of the loop. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 5  ` As the loop is closed there will be a current circulating through the loop. The direction of the current can be determined by Fleming's right hand Rule. This rule says that is you stretch thumb, index finger and middle finger of your right hand perpendicular to each other, then thumbs indicates the direction of motion of the conductor, index finger indicates the direction of magnetic field i.e. N - pole to S - pole, and middle finger indicates the direction of flow of current through the conductor. Now if we apply this right hand rule, we will see at this horizontal position of the loop, current will flow from point A to B and on the other side of the loop current will flow from point C to D. Now if we allow the loop to move further, it will come again to its vertical position, but now upper side of the loop will be CD and lower side will be AB (just opposite of the previous vertical position). At this position the tangential motion of the sides of the loop is parallel to the flux lines of the field. Hence there will be no question of flux cutting and consequently there will be no current in the loop. If the loop rotates further, it comes to again in horizontal position. But now, said AB side of the loop comes in front of N pole and CD comes in front of S pole, i.e. just opposite to the previous horizontal position as shown in the figure beside. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 6  ` Here the tangential motion of the side of the loop is perpendicular to the flux lines, hence rate of flux cutting is maximum here and according to Flemming's right hand rule, at this position current flows from B to A and on other side from D to C. Now if the loop is continued to rotate about its axis, every time the side AB comes in front of S pole, the current flows from A to B and when it comes in front of N pole, the current flows from B to A. Similarly, every time the side CD comes in front of S pole the current flows from C to D and when it comes in front of N pole the current flows from D to C. If we observe this phenomena in different way, it can be concluded, that each side of the loop comes in front of N pole, the current will flow through that side in same direction i.e. downward to the reference plane and similarly each side of the loop comes in front of S pole, current through it flows in same direction i.e. upwards from reference plane. From this, we will come to the topic of principle of dc generator. Now the loop is opened and connect it with a split ring as shown in the figure below. Split ring are made out of a conducting cylinder which cuts into two halves or segments insulated from each other. The external load terminals are connected with two carbon brushes which are rest on these split slip ring segments. Direction of EMF Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 7  ` It is seen that in the first half of the revolution current flows always along ABLMCD i.e. brush no 1 in contact with segment a. In the next half revolution, in the figure the direction of the induced current in the coil is reversed. But at the same time the position of the segments a and b are also reversed which results that brush no 1 comes in touch with that segment b. Hence, the current in the load resistance again flows from L to M. The wave from of the current through the load circuit is as shown in the figure. This current is unidirectional Position of the brushes of DC generator is so arranged that the change over of the segments a and b from one brush to other takes place when the plane of rotating coil is at right angle to the plane of the lines of force. This is basic working principle of DC generator, explained by single loop generator model. E.M.F generated/conductor is dΦ/dt=ΦPN/60 volt For a simplex wave-wound generator No. of parallel paths = 2 No. of conductors (in series) in one path = Z/2 E.M.F. generated/path is ΦPN/60*Z/2= ΦZPN/120 volt For a simplex lap-wound generator No. of parallel paths = P No. of conductors (in series) in one path = Z/P E.M.F. Generated/path ΦPN/60*Z/P=ΦZN/60 Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 8  ` In general generated e.m.f Eg= ΦZN/60*(P/A)volt where A = 2 - for simplex wave-winding = P - for simplex lap-winding 2.2 Working principle of generator, direction of EMF, Equation of EMF 1. Magnetic frame or yoke 2. Pole –Cores and Pole shoes. 3. Pole coils or field coils. 4. Armature Core 5. Armature windings or Conductors 6. Commutator 7. Brushes and Bearings TYPES OF DC GENERATORS BASED ON EXCITATION Generators are usually classified according to the way in which their fields are excited. The field windings provide the excitation necessary to set up the magnetic fields in the machine. Generators may be divided in to (a) Separately-excited generators and (b) Self-excited generators. (a) Separately-excited generators are those whose field magnets are energized from an independent external source of DC current. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 9  ` (b) Self-excited generators are those whose field magnets are energized by the current produced by the generators themselves. Due to residual magnetism, there is always present some flux in the poles. When the armature is rotated, some e.m.f and hence some induced current is produced which is partly or fully passed through the field coils thereby strengthening the residual pole flux. Self-excited generators are classified according to the type of field connection they use. There are three types of field connections:- a. SERIES-WOUND, b. SHUNT-WOUND (parallel) c. COMPOUND-WOUND. Generators are further classified as cumulative-compound and differential- compound. a. SERIES-WOUND GENERATOR In the series-wound generator, shown in figure, the field windings are connected in series with the armature. Current that flows in the armature flows through the external circuit and through the field windings. b. SHUNT WOUND GENERATOR The field windings are connected across or in parallel with the armature conductors and have the full voltage of the generator applied across them. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 10  ` c. COMPOUND-WOUND GENERATOR Compound-wound generators have a series-field winding in addition to a shunt- field winding, as shown in figure. The shunt and series windings are wound on the same pole pieces. They can be either short-shunt or long-shunt as shown in figures. In a compound generator, the shunt field is stronger than the series field. When series field aids the shunt field, generator is said to be commutatively- compounded. On the other hand if series field opposes the shunt field, the generator is said to be differentially compounded. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 11  ` 2.3 Characteristics of DC generators Separately Excited Generator In a separately excited DC generator, the field winding is excited by an external independent source. There are generally three most important characteristic of DC generator: Magnetic or Open Circuit Characteristic of Separately Excited DC Generator (E0) in the armature The curve which gives the relation between field current (If) and the generated voltage on no load is called magnetic or open circuit characteristic of a DC generator. The plot of this curve is practically same for all types of generators, whether they are separately excited or self-excited. This curve is also known as no load saturation characteristic curve of DC generator. Here in this figure below we can see the variation of generated emf on no load with field current for different fixed speeds of the armature. For higher value of constant speed, the steepness of the curve is more. When the field current is zero, for the effect residual magnetism in the poles, there will be a small initial emf (OA) as show in figure.E0 for a constant field current. If there is no armature reaction and Let us consider a separately excited DC generator giving its no load voltage armature voltage drop in the machine then the voltage will remain constant. Therefore, if we plot the rated voltage on the Y axis and load current on the X axis then the curve will be a straight line and parallel to X-axis as shown in figure below. Here, AB line indicating the no load voltage (E0). When the generator is loaded then the voltage drops due to two main reasons- 1) Due to armature reaction, 2) Due to ohmic drop ( IaRa ). Internal or Total Characteristic of Separately Excited DC Generator The internal characteristic of the separately excited DC generator is obtained by subtracting the drops due to armature reaction from no load voltage. This curve of actually generated voltage ( Eg ) will be slightly dropping. Here, AC line in the diagram indicating the actually generated voltage (E_g ) with respect to load current. This curve is also called total characteristic of separately excited DC generator. External Characteristic of Separately Excited DC Generator The external characteristic of the separately excited DC generator is obtained by subtracting the drops due to ohmic loss ( Ia Ra ) in the armature from generated voltage ( Eg ). Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 12  ` Terminal voltage(V) = Eg - Ia Ra. This curve gives the relation between the terminal voltage (V) and load current. The external characteristic curve lies below the internal characteristic curve. Here, AD line in the diagram below is indicating the change in terminal voltage(V) with increasing load current. It can be seen from figure that when load current increases then the terminal voltage decreases slightly. This decrease in terminal voltage can be maintained easily by increasing the field current and thus increasing the generated voltage. Therefore, we can get constant terminal voltage. It can operate in stable condition with any field excitation and gives wide range of output voltage. The main disadvantage of these Separately excited DC generators have many advantages over generators kinds of generators is that it is very expensive of providing a separate excitation source. Characteristic of self excited DC Generator Shunt Wound DC Generator In shunt wound DC generators the field windings are connected in parallel with armature conductors as shown in figure below. In these type of generators the armature current Ia divides in two parts. One part is the shunt field current Ish flows through shunt field winding and the other part is the load current IL goes through the external load. Three most important characteristic of shunt wound dc generators are discussed below: Magnetic or Open Circuit Characteristic of Shunt Wound DC Generator (E0). For a given excitation current or field current, the emf generated at no load E0 varies in proportionally with the rotational speed of the armature. This curve is drawn between shunt field current(Ish) and the no load voltage Here in the diagram the magnetic characteristic curve for various speeds are drawn. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 13  ` Due to residual magnetism the curves start from a point A slightly up from the origin O. The upper portions of the curves are bend due to saturation. The external load resistance of the machine needs to be maintained greater than its critical value otherwise the machine will not excite or will stop running if it is already in motion. AB, AC and AD are the slops which give critical resistances at speeds N1, N2 and N3. Here, N1 > N2 > N3. Critical Load Resistance of Shunt Wound DC Generator This is the minimum external load resistance which is required to excite the shunt wound generator. Characteristic of Shunt Wound DC Generator Internal The internal characteristic curve represents the relation between the generated voltage Eg and the load current IL. When the generator is loaded then the generated voltage is decreased due to armature reaction. So, generated voltage will be lower than the emf generated at no load. Here in the figure below AD curve is showing the no load voltage curve and AB is the internal characteristic curve. External Characteristic of Shunt Wound DC Generator AC curve is showing the external characteristic of the shunt wound DC generator. It is showing the variation of terminal voltage with the load current. Ohmic drop due to armature resistance gives lesser terminal voltage the generated voltage. That is why the curve lies below the internal characteristic curve. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 14  ` The terminal voltage can always be maintained constant by adjusting the of the load terminal. When the load resistance of a shunt wound DC generator is decreased, then load current of the generator increased as shown in above figure. But the load current can be increased to a certain limit with (upto point C) the decrease of load resistance. Beyond this point, it shows a reversal in the characteristic. Any decrease of load resistance, results in current reduction and consequently, the external characteristic curve turns back as shown in the dotted line and ultimately the terminal voltage becomes zero. Though there is some voltage due to residual magnetism. We know, Terminal voltage Now, when IL increased, then terminal voltage decreased. After a certain limit, due to heavy load current and increased ohmic drop, the terminal voltage is reduced drastically. This drastic reduction of terminal voltage across the load, results the drop in the load current although at that time load is high or load resistance is low. That is why the load resistance of the machine must be maintained properly. The point in which the machine gives maximum current output is called breakdown point (point C in the picture). Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 15  ` Characteristics of Series Wound DC Generator In these types of generators the field windings, armature windings and external load circuit all are connected in series as shown in fig below Therefore, the same current flows through armature winding, field winding and the load. Let, I = Ia = Isc = IL Here, Ia = armature current Isc = series field current IL = load current There are generally three most important characteristics of series wound DC generator which show the relation between various quantities such as series field current or excitation current, generated voltage, terminal voltage and load current. Magnetic or Open Circuit Characteristic of Series Wound DC Generator The curve which shows the relation between no load voltage and the field excitation current is called magnetic or open circuit characteristic curve. As during no load, the load terminals are open circuited, there will be no field current in the field since, the armature, field and load are series connected and these three make a closed loop of circuit. So, this curve can be obtained practically be separating the field winding and exciting the DC generator by an external source. Here in the diagram below AB curve is showing the magnetic characteristic of series wound DC generator. The linearity of the curve will continue till the saturation of the poles. After that there will be no further significant change of terminal voltage of DC generator for increasing field current. Due to residual magnetism there will be a small initial voltage across the armature that is why the Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 16  ` curve started from a point A which is a little way up to the origin O. Internal Characteristic of Series Wound DC Generator The internal characteristic curve gives the relation between voltage generated in the armature and the load current. This curve is obtained by subtracting the drop due to the demagnetizing effect of armature reaction from the no load voltage. So, the actual generated voltage ( Eg) will be less than the no load voltage (E0). That is why the curve is slightly dropping from the open circuit characteristic curve. Here in the diagram below OC curve is showing the internal characteristic or total characteristic of the series wound DC generator. External Characteristic of Series Wound DC Generator The external characteristic curve shows the variation of terminal voltage (V) with the load current ( IL). Terminal voltage of this type of generator is obtained by subtracting the ohomic drop due to armature resistance (Ra) and series field resistance ( Rsc) from the actually generated voltage ( Eg). Terminal voltage V = Eg - I(Ra + Rsc) The external characteristic curve lies below the internal characteristic curve because the value of terminal voltage is less than the generated voltage. Here in the figure OD curve is showing the external characteristic of the series wound DC generator. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 17  ` It can be observed from the characteristics of series wound DC generator, that with the increase in load (load is increased when load current increases) the terminal voltage of the machine increases. But after reaching its maximum value it starts to decrease due to excessive demagnetizing effect of armature reaction. This phenomenon is shown in the figure by the dotted line. Dotted portion of the characteristic gives approximately constant current irrespective of the external load resistance. This is because if load is increased, the field current is increased as field is series connected with load. Similarly if load is increased, armature current is increased as the armature is also series connected with load. But due to saturation, there will be no further significance raise of magnetic field strength hence any further increase in induced voltage. But due to increased armature current, the affect of armature reaction increases significantly which causes significant fall in load voltage. If load voltage falls, the load current is also decreased proportionally since current is proportional to voltage as per Ohm’s law. So, increasing load, tends to increase the load current, but decreasing load voltage, tends to decrease load current. Due these two simultaneous effects, there will be no significant change in load current in dotted portion of external characteristics of series wound DC generator. That is why series DC generator is called constant current DC generator. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 18  ` Characteristics Of DC Compound Generator The above figure shows the external characteristic of DC compound generators. If series winding is adjusted so that, increase in load current causes increase in terminal voltage then the generator is called to be over compounded. The external characteristic for over compounded generator is shown by the curve AB in above figure. If series winding is adjusted so that, terminal voltage remains constant even the load current is increased, then the generator is called to be flat compounded. The external characteristic for a flat compounded generator is shown by the curve AC. If the series winding has lesser number of turns than that would be required to be flat compounded, then the generator is called to be under compounded. The external characteristics for an under compounded generator is shown by the curve AD. 2.4 Critical Resistance, Methods of excitation Critical resistance Critical resistance is that resistance which is higher then the shunt field resistance. If the critical resistance is not higher then the shunt field resistance the generator is not possible to build up voltage. After drawing OCC curve, Then tangent is drawn to its initial portion. The slope of the curve give the critical resistance. The value of the resistance represented by the tangent to the curve is known as critical resistance for a given speed. Conditions for Self excitation of Generators There must be some residual magnetism in the generator poles. For the given direction of rotation, the shunt field coils must be correctly Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 19  ` connected to the armature i,e they should be so connected that induced current reinforces the emf produced initially due to residual magnetism. If excited on open circuit, its shunt field resistance should be less than the critical resistance. 2.5 Armature Reaction & its Compensation In a DC machine, the carbon brushes are always placed at the magnetic neutral axis. In no load condition, the magnetic neutral axis coincides with the geometrical neutral axis. Now, when the machine is loaded, the armature flux is directed along the inter polar axis (the axis in between the magnetic poles)and is triangular in wave shape. This results an armature current flux directed along the brush axis and causes cross magnetization of the main field. This cross magnetization effect results in the concentration of flux at the trailing pole tip in generator action and at the leading pole tip in motor action. What is leading and trailing pole tip? The tip of the pole from where the armature conductors come into influence is called leading tip and the other tip opposite in direction to it will be the trailing tip. For example, in the above figure if the motor rotates clockwise, then for North Pole, the lower tip is leading tip and for South Pole upper tip is leading tip. If the motion is reversed (in case of generator), the tips is interchanged. Due to cross magnetization, the magnetic neutral axis on load, shifts along the direction of rotation in DC generator and opposite to the direction of rotation in DC motor. If the brushes remain at their previous positions, then back e.m.f in case of motor or generated e.m.f in case of generator would reduce and commutation would be accompanied by heavy sparking. This is because commutation occurs at the coils located on the brushes only, and the coil undergoing commutation comes under the influence of the alternate pole(changes its location from north to south pole or vice versa). Hence, the direction of current flowing in the coil also reverses in a very short duration of time i.e., current changes from + i to – i or vice versa in a small span of time. This induces a very high magnitude of reactance voltage (L*di/dt) in the coil which emerges out in the form of heat energy along with sparking, thus damaging the brushes and commutator segment. To reduce the adverse effects mentioned above and to improve the machine’s performance, following methods are used: Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 20  ` Brush Shift A natural solution to the problem appears to shift the brushes along the direction of rotation in generator action and against the direction of rotation in motor action, this would result into a reduction in air gap flux. This will reduce the induced voltage in generator and would increase the speed in motor. The demagnetizing m.m.f (magneto motive force) thus produced is given by: Where, Ia = armature current, Z = total number of conductors, P = total number of poles, β = angular shift of carbon brushes (in electrical Degrees). Brush shift has serious limitations, so the brushes have to be shifted to a new position every time the load changes or the direction of rotation changes or the mode of operation changes. In view of this, brush shift is limited only to very small machines. Here also, the brushes are fixed at a position corresponding to its normal load and the mode of operation. Due to these limitations, this method is generally not preferred. Inter Pole The limitation of brush shift has led to the use of inter poles in almost all the medium and large sized DC machines. Inter poles are long but narrow poles placed in the inter polar axis. They have the polarity of succeeding pole(coming next in sequence of rotation) in generator action and proceeding (which has passed behind in rotation sequence) pole in motor action. The inter pole is designed to neutralize the armature reaction mmf in the inter polar axis. This is because the direction of armature reaction m.m.f is in the inter polar axis. It also provides commutation voltage for the coil undergoing commutation such that the commutation voltage completely neutralizes the reactance voltage (L di/dt). Thus, no sparking takes place. Inter polar windings are always kept in series with armature, So inter polar winding carries the armature current ; therefore works satisfactorily irrespective of load, the direction of rotation or the mode of operation. Inter poles are made narrower to ensure that they influence only the coil undergoing commutation and its effect does not spread to the other coils. The base of the inter poles is made Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 21  ` wider to avoid saturation and to improve response. Compensating Winding Commutation problem is not the only problem in D.C machines. At heavy loads, the cross magnetizing armature reaction may cause very high flux density in the trailing pole tip in generator action and leading pole tip in the motor action. Consequently, the coil under this tip may develop induced voltage high enough to cause a flashover between the associated adjacent commutator segments particularly, because this coil is physically close to the commutation zone (at the brushes) where the air temperature might be already high due to commutation process. This flashover may spread to the neighboring commutator segments, leading ultimately to a complete fire over the commutator surface from brush to brush. Also, when the machine is subjected to rapidly fluctuating loads, then the voltage L* di/dt, that appears across the adjacent commutator segments may reach a value high enough to cause flashover between the adjacent commutator segments. This would start from the centre of pole as the coil below it possesses the maximum inductance. This may again cause a similar fire as described above. This problem is more acute while the load is decreasing in generating action and increasing in motor action as then, the induced e.m.f and voltage L* di/dt will support each other. The above problems are solved by use of compensating winding. Compensating winding consists of conductors embedded in the pole face that run parallel to the shaft and carry an armature current in a direction opposite to the direction of current in the armature conductors under that pole arc. With complete compensation the main field is restored. This also reduces armature circuit’s inductor and improves system response.Compensating winding functions satisfactorily irrespective of the load, direction of rotation and mode of operation. Obviously it is help in commutation as the inter polar winding gets relieved from its duty to compensate for the armature m.m.f under the pole arc. NOTE: The phenomenon is thus known as the demagnetizing effect of cross magnetizing armature reaction, which is further compensated by the use of 1. The cross magnetizing armature reaction effect is mainly caused by armature conductors which are located under the pole arc. At high loads, this Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 22  ` effect of armature reaction may cause excessive flux density in the trailing pole tip (in generator) and leading pole tip (in motor). Due to saturation in the pole shoe, the increase in flux density may be less than the reduction in the flux density in remaining section of the pole shoe. This would ultimately result into a net reduction in flux per pole. This compensating windings. 2. Inter polar winding and compensating windings are connected in series with the armature winding but on the opposite sides with respect to armature. 3. The primary duty of inter polar winding is to improve the commutation process, and that of the compensating winding is to compensate for the increase or decrease in the net air gap flux i.e., to maintain its constant value. To understand the history of electronics; please click the link below https://www.youtube.com/watch?v=zOOk6-h6tXY 2.6 Commutation, causes and improvement The voltage generated in the armature, placed in a rotating magnetic field, of a DC generator is alternating in nature. The commutation in DC machine or more specifically commutation in DC generator is the process in which generated alternating current in the armature winding of a dc machine is converted into direct current after going through the commutator and the stationary brushes. Again in DC Motor, the input DC is to be converted in alternating form in armature and that is also done through commutation in DC motor. This transformation of current from the rotating armature of a dc machine to the stationary brushes needs to maintain continuously moving contact between the commutator segments and the brushes. When the armature starts to rotate, then the coils situated under one pole (let it be N pole) rotates between a positive brush and its consecutive negative brush and the current flows through this coil is in a direction inward to the commutator segments. Then the coil is short circuited with the help of a brush for a very short fraction of time(1⁄500 sec). It is called commutation period. After this short-circuit time the armature coils rotates under S pole and rotates between a negative brush and its succeeding positive brush. Then the direction of become is reversed which is in the away from the commutator segments. This phenomena of the reversal of current is termed as commutation process. We get direct current from the brush terminal. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 23  ` The commutation is called ideal if the commutation process or the reversal of current is completed by the end of the short circuit time or the commutation period. If the reversal of current is completed during the short circuit time then there is sparking occurs at the brush contacts and the commutator surface is damaged due to overheating and the machine is called Poorly commuted. Physical Concept of Commutation in DC Machine For the explanation of commutation process, let us consider a dc machine having an armature wound with ring winding. Let us also consider that the width of the commutator bar is equal to the width of the brush and current flowing through the conductor is IC. Let the commutator is moving from left to right. Then the brush will move from right to left. At the first position, the brush is connected the commutator bar b (as shown in fig 1). Then the total current conducted by the commutator bar b into the brush is 2IC. When the armature starts to move right, then the brush comes to contact of bar a. Then the armature current flows through two paths and through the bars a and b (as shown in fig 2). The total current (2IC) collected by the brush remain same. As the contact area of the bar a with the brush increases and the contact area of the bar b decreases, the current flow through the bars increases and decreases simultaneously. When the contact area become same for both the commutator bar then same current flows through both the bars (as shown in fig 3). When the brush contact area with the bar b decreases further, then the current flowing through the coil B changes its direction and starts to flow counter- Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 24  ` clockwise (as shown in fig 4). When the brush totally comes under the bar a (as shown in fig 5) and disconnected with the bar b then current IC flows through the coil B in the counter-clockwise direction and the short circuit is removed. In this process the reversal of current or the process of commutation is done. To understand the history of electronics; please click the link below https://www.youtube.com/watch?v=gZd47uumWis Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 25  ` Losses and Efficiency of DC Generator Every armature winding has its own resistance. Generally the armature resistance is measured by applying the known d.c. voltage and measuring the d.c. current through it. The ratio of applied voltage and measured current is the armature resistance. Understanding Voltage Drop A voltage drop is the reduction in voltage in an electrical circuit that occurs when the current is passed through the wire. Essentially, when a current flows about a circuit, there is a drop in energy potential across the circuit. Wires carrying current always have an inherent degree of resistance, or impedance, to that current’s flow. The greater resistance of the circuit, the higher the voltage drop that occurs. How do you know when a voltage drop becomes inefficient or even unsafe? Here’s a summary of what’s considered a normal voltage drop and when it’s considered in excess and therefore problematic. Voltage Drop Parameters When a certain amount of energy is lost to the wire that’s carrying it, or voltage drop, is a normal electric function within certain parameters. Depending on the type of circuit, its amperage, its length, the type of conductor, and its load, national and local electrical codes set guidelines for the maximum voltage drop allowed in a circuit. This not only ensures efficient distribution of energy and proper operation of the equipment being powered, but it also speaks to electrical safety issues. Generally, for power efficiency, the National Electric Code (NEC) holds a recommended standard of 5% maximum voltage drop. Causes of Excess Voltage Drop When excess voltage drop occurs, it’s caused by too much resistance in the wire, which lowers the amount of power that reaches the “load,” or what’s drawing the electricity from its source. This is typically caused by a wire that doesn’t meet code standards, meaning it isn’t appropriate for that particular circuit. A high-resistance connection can also be caused by poor splicing, loose or intermittent connections, or corroded connections within the circuit. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 26  ` Consequences of Excess Voltage Drop When the voltage drop is too steep, it can cause the load to work harder with less voltage pushing the current. Overall, this leads to poor efficiency and wasted energy. A low voltage to the equipment being powered can also cause improper, erratic, or ceased operation, which can ultimately result in damage to the equipment. Even more alarming, heating a high-resistance voltage connection can result in a fire if it’s in contact with a combustible material or there isn’t enough air flow to dissipate the heat. In electric design and power transmission, voltage drop needs to be taken into consideration. Electricians can always use various techniques to compensate for the effect of voltage drop, the most simple being to increase the diameter of the conductor between the source and the load, thereby lowering the overall resistance. Losses and Efficiencies in D.C.Generator Generator Losses – a. Copper b. Hysteresis c. Eddy Current d. Mechanical losses In dc generators, as in most electrical devices, certain forces act to decrease the efficiency. These forces, as they affect the armature, are considered as losses and may be defined as follows 1. Copper loss in the winding 2. Magnetic Losses 3. Mechanical Losses Copper loss The power lost in the form of heat in the armature winding of a generator is known as Copper loss. Heat is generated any time current flows in a conductor. It is.It increases as current increases. The amount of heat generated is also proportional to the resistance of the conductor. The resistance of the conductor Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 27  ` varies directly with its length and inversely with its cross- sectional area. Copper loss is minimized in armature windings by using large diameter wire. Copper loss is again divided as (i) Armature copper loss = Armature copper loss. Where Ra =resistance of armature and inter poles and series field winding etc. This loss is about 30 to 40% of full -load losses. (ii) Field copper loss: It is the loss in series or shunt field of generator. is the field copper loss in case of series generators, where Rse is the resistance of the series field winding. is the field copper loss in case of shunt generators This loss is about 20 to 30% of F.L losses. (iii) The loss due to brush contact resistance. It is usually included in the armature copper loss. Magnetic Losses (also known as iron or core losses) (i) Hysteresis loss (Wh) Hysteresis loss is a heat loss caused by the magnetic properties of the armature. When an armature core is in a magnetic field, the magnetic particles of the core tend to line up with the magnetic field. When the armature core is rotating, its magnetic field keeps changing direction. The continuous movement of the magnetic particles, as they try to align themselves with the magnetic field, produces molecular friction. This, in turn, produces heat. This heat is transmitted to the armature windings. The heat causes armature resistances to increase. To compensate for hysteresis losses, heat-treated silicon steel laminations are used in most dc generator armatures. After the steel has been formed to the proper shape, the laminations are heated and allowed to cool. This annealing process reduces the hysteresis loss to a low value. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 28  ` Eddy currents, just like any other electrical currents, are affected by the resistance of the material in which the currents flow. The resistance of any material is inversely proportional to its cross-sectional area. Figure, view A, shows the eddy currents induced in an armature core that is a solid piece of soft iron. Figure, view B, shows a soft iron core of the same size, but made up of several small pieces insulated from each other. This process is called lamination. The currents in each piece of the laminated core are considerably less than in the solid core because the resistance of the pieces is much higher. (Resistance is inversely proportional to cross-sectional area.) The currents in the individual pieces of the laminated core are so small that the sum of the individual currents is much less than the total of eddy currents in the solid iron core. Most generators use armatures with laminated cores to reduce eddy current losses. Mechanical or Rotational Losses These consist of (i) friction loss at bearings and commutator. (ii) air-friction or windage loss of rotating armature These are about 10 to 20% of F.L losses. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 29  ` Magnetic and mechanical losses are collectively known as Stray Losses. These are also known as rotational losses for obvious reasons. As said above, field Cu loss is constant for shunt and compound generators. Hence, stray losses and shunt Cu loss are constant in their case. These losses are together known as standing or constant losses Wc Hence for shunt and compound generators Total Loss = armature copper loss +Wc Armature Cu loss is known as variable loss because it varies with the load current. Total Loss=Armature copper loss+Wc=Ia².Ra+Wc=(I+Ish)² Ra+ Wc Total loss = Variable loss + constant losses Wc Generator Efficiency Various power stages in the case of a d.c generator are shown below Following are the three generator efficiencies 1. Mechanical Efficiency 2. Electrical Efficiency 3.Overall or Commercial Efficiency Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 30  ` It is obvious that overall efficiency is the product of mechanical and electrical efficiencies. For good generators, its value may be as high as 95%. Condition for Maximum Efficiency In general generator efficiency = Output / (Output + losses) The condition for maximum efficiency of generator is given by 2.7 Application of DC generators 1. Shunt generator with field regulator are used for ordinary lightening and power supply. 2. Series generators are not used for power supply because of the rising characteristics. Used in distribution system particularly in Railway services. 3. Compound wound generator is the most widely used DC generator. Because its external characteristics used in motor driven widely. QUESTION BANK 1. What are the effects on flux per pole and generated voltage due to the armature reaction in DC machine? 2. There is a delay in Commutation. Explain all reasons. 3. Adverse affect of armature reaction of an unsaturated DC machine is (in terms of magnetization) different. Explain. 4. Increase in flux density at one end of the pole is less than the decrease at the other end. What is this phenomenon called as? 5. Justify your logic a series generator is not widely used in power supply. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 31  ` 3. DC MOTORS An electric motor is a machine which converts electric energy into mechanical energy. In this respect it is the reverse of a generator although it is based fundamentally upon the same general principles. 3.1 Working principle, Back EMF, Equation of voltage, Torque and speed- Simple problem This DC or direct current motor works on the principal, when a current carrying conductor is placed in a magnetic field, it experiences a torque and has a tendency to move. This is known as motoring action. If the direction of current in the wire is reversed, the direction of rotation also reverses. When magnetic field and electric field interact they produce a mechanical force, and based on that the working principle of dc motor established. The direction of rotation of a this motor is given by Fleming’s left hand rule, which states that if the index finger, middle finger and thumb of your left hand are extended mutually perpendicular to each other and if the index finger represents the direction of magnetic field, middle finger indicates the direction of current, then the thumb represents the direction in which force is experienced by the shaft of the dc motor. Structurally and construction wise a direct current motor is exactly similar to a DC generator, but electrically it is just the opposite. Here we unlike a generator we supply electrical energy to the input port and derive mechanical energy from the output port. We can represent it by the block diagram shown below. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 32  ` Here in a DC motor, the supply voltage E and current I is given to the electrical port or the input port and we derive the mechanical output i.e. torque T and speed ω from the mechanical port or output port. The input and output port variables of the direct current motor are related by the parameter K. So from the picture above we can well understand that motor is just the opposite phenomena of a DC generator, and we can derive both motoring and generating operation from the same machine by simply reversing the ports. An electric motor is a machine which converts electric energy into mechanical energy. Its action is based on the principle that when a current- carrying conductor is placed in a magnetic field. It experiences a mechanical force whose direction is given by Fleming’s Left-hand Rule and whose magnitude is given by F = BIL Newton. Constructionally there is no basic difference between a D.C generator and a D.C. motor. In fact, the same D.C. machine can be used interchangeably as a generator or as a motor. D.C. motors are also like generators. Shunt- wound or series-wound or compound-wound. In fig a pan of multi polar D.C motor is shown. When its field magnets are excited and its armature conductors are supplied with current from the supply mains, they experience a force tending to rotate the armature. Armature conductors under N-pole are assumed to carry current down wards (crosses) and those under S-poles. to carry current upwards (dots). By applying Fleming’s Left. Hand Rule, the direction of the force on each conductor can be found conductor. It will be seen that each conductor can be found. Ii will be seen that each conductor experiences a force F which tends to rotate the armature in anticlockwise direction. These forces collectively produce a driving torque which sets the armature rotating, it should be noted that the function of a commutator in the motor is the same as in a generator. By reversing current in each conductor as it passes from one pole to another, it helps to develop a continuous and unidirectional torque Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 33  ` Fig 2.1 Comparison of Generator and Motor Action. The same D.C. machine can be used, as generator or as a motor. When operating as a generator, it is driven by a mechanical machine and it develops voltage which in turn produces a current flow in an electric circuit. When operating as a motor it is supplied by electric current and it develops torque which in turn produces mechanical rotation If a current is sent through the armature conductors to the D.C. machine and it is uncoupled from its prime mover, the conductors will experience a force in the anti-clock wise direction (Fleming’s left hand rule). Hence the machine will start rotating anti-clock wise, there by developing a torque which can produce mechanical rotation. The machine is then said to be rotating. In the case of a generator the magnetic drag will provide the necessary opposition. When the motor armature rotates, the conductors also rotate and hence cut the flux. In accordance with the laws of electromagnetic induction, e.m.f. is induced in them whose direction, as found by Fleming’s Right hand Rule, is in opposition to the applied voltage. Because of its opposing direction, it is referred to as counter e.m.f. or back e.m.f, Eb. The equivalent circuit of a motor is shown in Figure. The rotating armature generating the back e.m.f. Eb is like a battery of e.m.f. Eb, put across a supply mains of V volts. Obviously, V has to drive Ia, against the opposition of Eb. The power required to overcome this opposition is EbIa. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 34  ` In the case of a cell, this power over an interval of time is converted into chemical energy, but in the present case, it is converted into mechanical energy. Back e.m.f. depends, among other factors, upon the armature speed. If speed is high, Eb is large, hence armature current Ia, seen from the above equation, is small. If the speed is less, then Eb is less, hence more current flows which develops motor torque. So, we find that Eb acts like a governor i.e. it makes a motor self-regulating so that it draws as much current as is just necessary. Voltage Equation of a Motor The voltage V applied across the motor armature has to (1) overcome the back e.m.f. Eb and (2) supply the armature ohmic drop IaRa. V = E+IaRa This is known as voltage equation of a motor. Now, multiplying both sides by Ia, we get VIa = EbIa + Ia Ra As shown in Fig Fig 2. V Ia = Electrical input to the armature EbIa = Electrical equivalent of mechanical power developed in the armature Ia2Ra=Cu loss in the armature Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 35  ` Hence, out of the armature input, some is wasted in I2R loss and the rest is converted into mechanical power within the armature. It may also be noted that motor efficiency is given by the ratio of power developed by the armature to its input i.e. EbIa /VIa= Eb/V. So when the value of Eb is high compared to V the motor efficiency is high. Torque And Speed By the term torque is meant the turning or twisting moment of a force about an axis. It is measured by the product of the force and the radius at which this force acts. Consider a pulley of radius r meter acted upon by a circumferential force of F Newton which is to rotate at N r.p.m. Then torque T = F x r Newton-meter (N - m) Work done by this force in one revolution = Force x distance = F x 2πr Joule Power developed = F x 2πr x N joule/second or Watt = (Fxr) x 2πN Watt. Now 2πN = Angular velocity ω in radian/second and Fxr=Torque Power developed = Txω watt or P = Txω watt Moreover, if N is in r.p.m., then ω= 2πN/60rad/s P= (2πN/60)*T P=NT/9.55 Armature Torque of a motor If Ta is the armature torque and N is the speed in r.p.s, then Power developed =Ta*2πN watt We also know that electrical power converted into mechanical power in the armature = Eb.Ia watt So Ta*2πN = Eb.Ia Since, Eb =ΦZN*(P/A) volts Ta=0.159ΦZIa*(P/A) N-m In case of series motor, Ta αI a For shunt motor, Ta α Ia2 If N is in r.p.m then Ta=9.55(Eb.Ia)/N N-m Shaft Torque (Ts h) The torque which is available for doing useful work known as shaft torque Tsh. It is so called because it is available at the shaft. The motor output is given by Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 36  ` Output = Tsh x 2πN Watt Tsh=Output/2πN N-m Tsh=9.55(Output/N) N-m Rated Speed of a D.C. Motor ΦZN/60(P/A) =V- Ia. Ra N= (V-Ia.Ra)/Φ*(60A/ZP) r.p.m N=K.Eb/Φ, (V-Ia.Ra) = Eb For series motor, N2/N1= (Eb2/Eb1). (Ia1/Ia2), ΦαIa For shunt motor, N2/N1= (Eb2/Eb1).(Φ1/Φ2) Φ1=Φ2 N2/N1=Eb2/Eb1 Rated Speed And Speed regulation It is the change in speed with change in applied load torque, other conditions remaining constant. In other words speed regulation means change in speed when the load on the motor is reduced from the rated value to zero, expressed as percent of the rated load speed. % speed regulation = [(N.L.SPEED-F.L.SPEED)/F.L.SPEED].100 = (dN/N)*100 3.2 Characteristics of DC Motors The characteristic curves of a motor are those curves which show relationships between the following quantities. (i) Torque and armature current i.e. Ta/Ia characteristic. It is known as electrical characteristic. (ii) Speed and armature current i.e. N/Ia characteristic. CHARACTERISTICS OF DC SHUNT MOTOR (i)T/Ia Characteristic We know that T α ΦIa, but in case of shunt motor Φ is constant. Therefore T α Ia so the characteristic is a straight line and passes through the origin. and shaft torque is less than the armature torque due to stray losses Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 37  ` (ii) N/Ia Characteristic We know that N α Eb/Φ, if in case of shunt motor Φ is constant. Also Eb is practically constant. Therefore the characteristic curve is a straight line because N α Eb. So speed is constant. But both Eb and Φ decreases with increasing load. However, Eb decreases slightly more than Φ so that on the whole, there is some decrease in speed. CHARACTERISTICS OF DC SERIES MOTOR (i) Torque Vs Armature Current (T/Ia) Characteristic We know that T α ΦIa, but in series motor Φ α Ia up to the point of magnetic saturation. Hence, before saturation, T α ΦIa and T α Ia2. At light load Ia and Φ is small but as Ia increases T increases as the square of the Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 38  ` armature current. So that T Vs Ia curve is parabolic. After saturation Φ is almost independent of Ia hence T α Ia only. So the characteristic becomes a straight line which is shown by dotted line. Then the shaft torque Tsh < Ta due to the stray losses. Finally we conclude that on heavy load a series motor torque proportional to the square of armature current. T α Ia2 Speed Vs Armature current( N/Ia) Characteristic We know that N α Eb/Φ. Change in Eb, for various load currents is small and hence may be neglected for the time being. With increased Ia, Φ also increases. Hence speed varies inversely as armature current. When load is heavy, Ia is large. Hence, speed is low (this decreases Eb and allows more armature current to flow). But when load current and hence Ia falls to a small value, speed becomes dangerously high. Hence, a series motor should never be started without some mechanical load on it otherwise it may Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 39  ` develop excessive speed and get damaged due to heavy centrifugal forces so produced. It should be noted that series motor is a variable speed motor. Speed Vs Armature Torque (N/T) Characteristics This characteristic is also called as mechanical characteristic. From the above two characteristics of DC series motor, it can be found that when speed is high, torque is low and vice versa. CHARACTERISTICS OF DC COMPOUND MOTORS These motors have both series and shunt windings. If series excitation helps the shunt excitation i.e. series flux is in the same direction: then the motor is said to be cumulatively compounded. If series field opposes the shunt field, then the motor is said to be differentially compounded. The characteristics of such motors lie in between those of shunt and series motors as shown below (i) T/Ia Characteristic Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 40  ` (ii) N/Ia Characteristic (a) Cumulative-compound Motors Such machines are used where series characteristics are required and where, in addition, the load is likely to be removed totally such as in some types of coal cutting machines or for driving heavy machine tools which have to take sudden cuts quite often. Due to shunt windings, speed will not become excessively high but due to series windings, it will be able to take heavy loads. Compound-wound motors have greatest application with loads that require high starting torques or pulsating loads. They are used to drive electric shovels, metal- stamping machines, reciprocating pumps, hoists and compressors etc. (b)Differential-compound Motors Since series field opposes the shunt field, the flux is decreased as load is applied to the motor. This result in the motor speed remaining almost constant or even increasing with increase in load (because, N α Eb/Φ). Due to this reason, there is a decrease in the rate at which the motor torque increases with the load. Such motors are not in common use. But because they can be designed to give an accurately constant speed under all conditions, they find limited application for experimental and research work. one of the biggest drawback of such a motor is that due to weakening of flux with increases in load, there is a tendency towards speed instability and motor running away unless designed properly. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 41  ` 3.3 Speed control and braking of DC motors Factors Controlling Motor Speed- It has be shown earlier that speed of a motor is given by the relation N= (V-Ia.Ra)/Φ*(60A/ZP) N=K. (V-Ia.Ra)/Φ r.p.s Where Ra=Armature Circuit resistance. It is obvious that the speed can be controlled by varying a) flux/pole b) resistance Ra of armature circuit ( Rheostatic Control) and c) applied voltage. Speed Control of Shunt motors- a) Variation of flux or flux control method Nα1/Φ The speed can be decreased by increasing the flux and vice-versa.so we call this method as field control or flux control. b) Armature or Rheostatic Control Method Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 42  ` This method is used when the speeds below the no load speed is required. As controller resistance is increased, p.d across the armature is decreased, thereby decreasing the armature speed. c) Voltage control method i ) Multiple voltage control method In this method the shunt field of the motor is connected permanently to a fixed exciting voltage but the armature is supplied with different voltages by connecting it across the one of several different voltages by means of switch gear. The armature speed will be approximately proportional to these different voltages. The intermediate speed can be obtained by adjusting the shunt field regulator. ii) Ward-Leonard system This method is used where usually a wide (up to 10:1) and very sensitive speed control is required. The field of the main motor is permanently connected across the D.C. supply lines. By applying variable voltage across its armature, any speed can be obtained. The variable voltage is motor, directly coupled to generator. Speed control of DC Series motors- 1. Flux control method a) Field Diverters Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 43  ` The series winding are shunted by a variable resistance known as field diverter. Any desired amount of current can be passed through the diverter by adjusting its resistance. Hence the flux can be decreased and speed of the motor can be increased. b) Armature Diverter. A diverter across the armature can be used for giving speeds lower than the normal speed. For a given constant load torque ,if Ia is reduced due to armature diverter , the Φ must increase.This result in increase in current taken from the supply(which increases the flux and a fall in speed).The variation in speed can be controlled by varying the resistance in armature diverter. c) Trapped field control This method is often used in electric traction. The number of series field turns in the circuit can be changed. With full field, the motor runs at its minimum speed which can be raised in steps by cutting out some of series turns. d) Paralleling field coils It is used for fan motors. Several speed can be obtained by regrouping the field coils. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 44  ` 2. Variable resistance in series with motor 3.4 Testing, Efficiency and losses of DC Machines Testing of DC motors Swinburne Test of DC Machine This method is an indirect method of testing a dc machine. It is named after Sir James Swinburne. Swinburne's test is the most commonly used and simplest method of testing of shunt and compound wound dc machines which have constant flux. In this test the efficiency of the machine at any load is pre- determined. We can run the machine as a motor or as a generator. In this method of testing no load losses are measured separately and eventually we can determine the efficiency. The circuit connection for Swinburne's test is shown in figure below. The speed of the machine is adjusted to the rated speed with the help of the shunt regulator R as shown in figure. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 45  ` Advantages of Swinburne's Test The main advantages of this test are : This test is very convenient and economical as it is required very less power from supply to perform the test. Since constant losses are known, efficiency of Swinburne's test can be pre- determined at any load. Disadvantages of Swinburne's Test The main disadvantages of this test are : Iron loss is neglected though there is change in iron loss from no load to full load due to armature reaction. We cannot be sure about the satisfactory commutation on loaded condition because the test is done on no-load. We can’t measure the temperature rise when the machine is loaded. Power losses can vary with the temperature. In dc series motors, the Swinburne’s test cannot be done to find its efficiency as it is a no load test. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 46  ` Losses In A DC Machine Copper Losses These losses are the losses due to armature and field copper windings. Thus copper losses consists of Armature copper loss, Field copper loss and loss due to brush contact resistance Armature copper loss = Ia2Ra (Where Ia is Armature current and Ra is Armature resistance) This loss is about 30 to 40% of full load losses. Field copper loss = If2Rf (where If is field current and Rf is field resistance) In case of shunt wounded field, this loss is practically constant. Field copper loss is about 20 to 30% of full load losses. Brush contact resistance also contributes to this type of loss. Generally this loss is included into armature copper loss. Iron Losses (Magnetic Losses) As iron core of the armature is continuously rotating in a magnetic field, there are some losses taking place in the core. Therefore iron losses are also known as Core losses. This loss consists of Hysteresis loss and Eddy current loss Hysteresis loss is due to reversal of magnetization of the armature core. When the core passes under one pair of poles, it undergoes one complete cycle of magnetic reversal. The frequency of magnetic reversal if given by, f=PN/120 (where, P = no. of poles and N = Speed in rpm) The loss depends upon the volume and grade of the iron, frequency of magnetic reversals and value of flux density. Hysteresis loss is given by, Steinmetz formula: Wh=ηBmax1.6fV (watts) where, η = Steinmetz hysteresis constant V = volume of the core in m3 Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 47  ` Eddy current loss: When the armature core rotates in the magnetic field, an emf is also induced in the core (just like it induces in armature conductors), according to the Faraday's law of electromagnetic induction. Though this induced emf is small, it causes a large current to flow in the body due to low resistance of the core. This current is known as eddy current. The power loss due to this current is known as eddy current loss. Mechanical Losses Mechanical losses consists of the losses due to friction in bearings and commutator. Air friction loss of rotating armature also contributes. T hese losses are about 10 to 20% of full load losses The losses taking place in the motor are the same as in generators. These are (i) copper losses (ii) magnetic losses and (iii) mechanical losses. The condition for maximum power developed by the motor is IaRa=V/2=Eb The condition for maximum efficiency is that armature cu losses are equal to constant losses. 3.5 Working of Starters- 3 point/4 points starters Working Principle and Construction of Three Point Starter A 3 point starter in simple words is a device that helps in the starting and running of a shunt wound DC motor or compound wound DC motor. Now the question is why these types of DC motors require the assistance of the starter in the first case. The only explanation to that is given by the presence of back emf Eb, which plays a critical role in governing the operation of the motor. The back emf, develops as the motor armature starts to rotate in presence of the magnetic field, by generating action and counters the supply voltage. This also essentially means, that the back emf at the starting is zero, and develops gradually as the motor gathers speed. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 48  ` The general motor emf equation E = Eb + Ia.Ra, at starting is modified to E = Ia.Ra as at starting Eb = 0. Thus we can well understand from the above equation that the current will be dangerously high at starting (as armature resistance Ra is small) and hence its important that we make use of a device like the 3 point starter to limit the starting current to an allowable lower value. Let us now look into the construction and working of three point starter to understand how the starting current is restricted to the desired value. For that let’s consider the diagram given below showing all essential parts of the three point starter. Construction of 3 Point Starter Construction wise a starter is a variable resistance, integrated into number of sections as shown in the figure beside. The contact points of these sections are called studs and are shown separately as OFF, 1, 2,3,4,5, RUN. Other than that there are 3 main points, referred to as 1. 'L' Line terminal. (Connected to positive of supply.) 2. 'A' Armature terminal. (Connected to the armature winding.) 3. 'F' Field terminal. (Connected to the field winding.) And from there it gets the name 3 point starter. Now studying the construction of 3 point starter in further details reveals that, the point 'L' is connected to an electromagnet called overload release (OLR) as shown in the figure. The other end of 'OLR' is connected to the lower end of conducting lever of starter handle where a spring is also attached with it and the starter handle contains also a soft iron piece housed on it. This handle is free to move to the other side RUN against the force of the spring. This spring brings back the handle to its original OFF position under the influence of its own force. Another Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 49  ` parallel path is derived from the stud '1', given to the another electromagnet called No Volt Coil (NVC) which is further connected to terminal 'F'. The starting resistance at starting is entirely in series with the armature. The OLR and NVC acts as the two protecting devices of the starter. Working of Three Point Starter Having studied its construction, let us now go into the working of the 3 point starter. To start with the handle is in the OFF position when the supply to the DC motor is switched on. Then handle is slowly moved against the spring force to make a contact with stud No. 1. At this point, field winding of the shunt or the compound motor gets supply through the parallel path provided to starting resistance, through No Voltage Coil. While entire starting resistance comes in series with the armature. The high starting armature current thus gets limited as the current equation at this stage becomes Ia = E/(Ra+Rst). As the handle is moved further, it goes on making contact with studs 2, 3, 4 etc., thus gradually cutting off the series resistance from the armature circuit as the motor gathers speed. Finally when the starter handle is in 'RUN' position, the entire starting resistance is eliminated and the motor runs with normal speed. This is because back emf is developed consequently with speed to counter the supply voltage and reduce the armature current. So the external electrical resistance is not required anymore, and is removed for optimum operation. The handle is moved manually from OFF to the RUN position with development of speed. Now the obvious question is once the handle is taken to the RUN position how is it supposed to stay there, as long as motor is running ? To find the answer to this question let us look into the working of No Voltage Coil. Working of No Voltage Coil of 3 Point Starter The supply to the field winding is derived through no voltage coil. So when field current flows, the NVC is magnetized. Now when the handle is in the 'RUN' position, soft iron piece connected to the handle and gets attracted by the magnetic force produced by NVC, because of flow of current through it. The NVC is designed in such a way that it holds the handle in 'RUN' position against the force of the spring as long as supply is given to the motor. Thus NVC holds the handle in the 'RUN' position and hence also called hold on coil. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 50  ` Now when there is any kind of supply failure, the current flow through NVC is affected and it immediately looses its magnetic property and is unable to keep the soft iron piece on the handle, attracted. At this point under the action of the spring force, the handle comes back to OFF position, opening the circuit and thus switching off the motor. So due to the combination of NVC and the spring, the starter handle always comes back to OFF position whenever there is any supply problems. Thus it also acts as a protective device safeguarding the motor from any kind of abnormality. Working Principle and Construction of Four Point Starter The 4 point starter has a lot of constructional and functional similarity to a three point starter, but this special device has an additional point and a coil in its construction, which naturally brings about some difference in its functionality, though the basic operational characteristic remains the same. Now to go into the details of operation of 4 point starter, lets have a look at its constructional diagram, and figure out its point of difference with a 3 point starter. Construction and Operation of Four Point Starter A 4 point starter as the name suggests has 4 main operational points, namely 1. 'L' Line terminal. (Connected to positive of supply.) 2. 'A' Armature terminal. (Connected to the armature winding.) 3. 'F' Field terminal. (Connected to the field winding.) Like in the case of the 3 point starter, and in addition to it there is, 4. A 4th point N. (Connected to the No Voltage Coil) The remarkable difference in case of a 4 point starter is that the No Voltage Coil is connected independently across the supply through the fourth terminal called 'N' in addition to the 'L', 'F' and 'A'. As a direct consequence of that, any change in the field supply current does not bring about any difference in the performance of the NVC. Thus it must be ensured that no voltage coil always produce a force which is strong enough to hold the handle in its 'RUN' position, against force of the spring, under all the operational conditions. Such a current is adjusted through No Voltage Coil with the help of fixed resistance R connected in series with the NVC using fourth point 'N' as shown in the figure above. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 51  ` Apart from this above mentioned fact, the 4 point and 3 point starters are similar in all other ways like possessing is a variable resistance, integrated into number of sections as shown in the figure above. The contact points of these sections are called studs and are shown separately as OFF, 1, 2, 3, 4, 5, RUN, over which the handle is free to be maneuvered manually to regulate the starting current with gathering speed. Now to understand its way of operating lets have a closer look at the diagram given above. Considering that supply is given and the handle is taken stud No.1, then the circuit is complete and line current that starts flowing through the starter. In this situation we can see that the current will be divided into 3 parts, flowing through 3 different points. i) 1 part flows through the starting resistance (R1+ R2+ R3…..) and then to the armature. ii) A 2nd part flowing through the field winding F. iii) And a 3rd part flowing through the no voltage coil in series with the protective resistance R. So the point to be noted here is that with this particular arrangement any change in the shunt field circuit does not bring about any change in the no voltage coil as the two circuits are independent of each other. This essentially means that the electromagnet pull subjected upon the soft iron bar of the handle by the no voltage coil at all points of time should be high enough to keep the handle at its RUN position, or rather prevent the spring force from restoring the handle at its original OFF position, irrespective of how the field rheostat is adjusted. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 52  ` This marks the operational difference between a 4 point starter and a 3 point starter. As otherwise both are almost similar and are used for limiting the starting current to a shunt wound DC motor or compound wound DC motor, and thus act as a protective device. APPLICATION OF DC MOTOR 1. Series Motors The series DC motors are used where high starting torque is required, and variations in speed are possible. For example – the series motors are used in Traction system, Cranes, air compressors. 2. Shunt Motors The shunt motors are used where constant speed is required and starting conditions are not severe. The various applications of DC shunt motor are in Lathe Machines, Centrifugal Pumps, Fans, Blowers, Conveyors, Lifts, Weaving Machine, Spinning machines, etc. 3. Compound Motors The compound motors are used where higher starting torque and fairly constant speed is required. The examples of usage of compound motors are in Presses, Shears, Conveyors, Elevators, Rolling Mills, Heavy Planners, etc. QUESTION BANK 1. What will happen if DC shunt motor is connected across AC supply? 2. What will happen if the back emf of a DC motor vanishes suddenly? 3. Where speed-current characteristic of DC shunt motor lies with respect to DC cumulative compound motor (assume current smaller than full load current)? 4. The hysteresis loss in a DC machine depends on many factor.List out the factors in which the loss least depends on? Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 53  ` 4.0 TRANSFORMER 4.1 Introduction – Working Principle, Construction and types Transformer is a static device which transforms electrical energy from one electrical circuit to another electric circuit through a medium of magnetic field without any change in frequency. PRINCIPLE OF OPERATION The basic operation of a transformer is mutual induction between two circuits linked by a common magnetic flux. In its simplest form, it consists of two inductive coils which are electrically separated but magnetically linked through a path of low reluctance as shown in figure below. The two coils possess high mutual inductance. If one coil 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 other coil in which it produces mutually induced e.m.f. (according to Faraday’sLaws of Electromagnetic Induction e= MdI/dt). If the second coil circuit is closed,a current flows in it and so electric energy is transferred (entirely magnetically) from the first coil to the second coil. The first coil, in which electric energy is fed from the a.c. supply mains, is called primary winding and the other from which energy is drawn out is called secondary winding. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 54  ` CONSTRUCTION The simple elements of a transformer consist of two coils having mutual inductance and a laminated steel core. The two coils are insulated from each other and the steel core. Other necessary parts are: some suitable container for assembled core and windings; a suitable medium for insulating the core and its windings from its container; suitable bushings (either of porcelain, oil-filled or capacitor-type) for insulating and bringing out the terminals of windings from the tank. The core is made of transformer sheet steel laminations assembled to provide a continuous magnetic path with a minimum of air-gap included. The steel used is of high silicon content, sometimes heat treated to produce a high permeability and a low hysteresis loss at the usual operating flux densities. The core is insulated by each other by a small coat of varnish to reduce eddy current. To understand the history of electronics; please click the link below https://www.youtube.com/watch?v=VucsoEhB0NA Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 55  ` Types of Transformers Constructionally, the transformers are of two general types, distinguished from each other merely by the manner in which the primary and the secondary coils are placed around the laminated core. The two types are (i) core type and (ii) shell type. CORE-TYPE TRANSFORMERS In the core type transformers, the windings surround a considerable part of the core. It has a single magnetic flux path. It is in general shape of rectangle, square, and circular. The circular cylindrical coils are used in most of the core-type transformers because of their mechanical strength. In core type transformer the concentric windings are used. In core type transformer minimum length of core is large whereas minimum length of coil turn is short so that the voltage transformation is higher. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 56  ` SHELL TYPE TRANSFORMERS In shell-type transformer the core is surrounded by a considerable part of winding. It has double magnetic circuit and three limbs. Both windings are placed in the central limb. The coils occupy the entire space of the winding. The coils are sandwich type or multi layer disc type. The low voltage coils are placed and the core is laminated. The shell type construction is preferred for a few high voltage transformers. To remove any winding during maintenance removal of large laminations are required. High mechanical forces are required for high current during short circuit. 4.2 EMF equation, Voltage Transformation ratio-simple problems Let N1= No. of turns in primary N2= No. of turns in secondary øm= Maximum flux in core in webers = Bm * A f= Frequency of a.c. input in Hz As shown in figure flux increases from its zero value to maximum value øm in one quarter of the cycle i.e. in 1/4f second. Therefore average rate of change of flux = 4føm Wb/s or volt Now, rate of change of flux per turn means induced e.m.f. in volts. Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 57  ` Therefore, average e.m.f./turn = 4føm volt If flux ø varies sinusoidally, then r.m.s. value of induced e.m.f. is obtained by multiplying the average value with form factor. Form factor = = 1.11 Therefore r.m.s. value of e.m.f./turn = 1.11*4føm =4.44føm volt Now, r.m.s. value of the induced e.m.f. in the whole of primary winding = (induced e.m.f./turn) * No. of primary turns E1 = 4.44 f N1 øm= 4.44 f N1 BmA …. (i) Similarly, r.m.s. value of the e.m.f. induced in secondary is, E2= 4.44 f N2 øm= 4.44 f N2 BmA …. (ii) It is seen from (i) and (ii) that E1/N1 = E2/N2 = 4.44føm. It means that e.m.f./turn is the same in both the primary and secondary windings. In an ideal transformer on no-load, V1 = E1 and E2 = V2 where V2 is the terminal voltage. VOLTAGE TRANSFORMATION RATIO (K) From equations (i) and (ii), we get E2/E1 = N2/N1 = K Go to Table of Content NTTF_DIPLOMA IN ELECTRICAL AND ELECTRONICS ENGINEERING_SEMESTER 3_ELECTRICAL MACHINES 1 58  ` This constant K is known as voltage transformation ratio. (i) If N2 > N1 i.e. K>1, then transformer is called step-up transformer. (ii) If N2 < N1 i.e. K