WINDING Factors & EMF Equation PDF

Winding, Winding Factors and EMF Equation Dr. Mohd Faisal Jalil (B.Tech., M. Tech., Ph.D.) Dept. of Electrical Engineering Aligarh Muslim University, Aligarh 1  CONTE...

Winding, Winding Factors and EMF Equation Dr. Mohd Faisal Jalil (B.Tech., M. Tech., Ph.D.) Dept. of Electrical Engineering Aligarh Muslim University, Aligarh 1  CONTENTS Brief Overview of Basics Coil Pitch Pole Pitch Winding Coefficients : Coil Span Factor(KC) Distribution Factor(Kd) EMF equation  TURN A turn consists of two conductors connected to one end by an end connector. Single Turn is the only turn  COIL A coil is formed by connecting several turns in. the series  WINDING A winding is formed by connecting several coils in series.  TYPES OF WINDING Armature Winding is the windings, in which voltage is induced. The Field Winding is the winding in which the main field flux is produced when the current through the winding is passed. A winding in which current is supplied.  ELECTRICAL & MECHANICAL DEGREES The concept of electrical degree is very important in the study of the machine. For a (P) pole machine, the electrical degree is defined as given below. Where, θmd is the mechanical degrees or an angular measure in space. θ ed is the electrical degrees or an angular measure in cycles.  1 : Number of poles , P=2 mechanical angle θmd= 180° 2 : Number of poles , P=4 3 : Number of poles , P=6 Putting value in equation1, mechanical angle θmd= 90° mechanical angle θmd= 60° We get the value of θed= 180° Putting value in equation1, Putting value in equation1, We get the value of θed= 180° We get the value of θed= 180° So, we come to the conclusion that irrespective of the number of poles or the value of mechanical angle, electrical angle θed would always be equal to 180° i.e θed = 180°  POLE PITCH & COIL PITCH POLE PITCH : The angular distance between the centers of two adjacent poles on a machine is known as pole pitch or pole span. But Pole Pitch is always measured in electrical degrees ,therefore Pole Pitch is always equal to 180° COIL PITCH : The two sides of a coil are placed in two slots on the stator surface. The distance between the two sides of a coil is called the coil-pitch. If the coil pitch is one pole pitch, it is called the Full Pitch Coil. If the coil pitch is less than one pole pitch, the coil is called the Short Pitch or Fractional Pitch coil  WINDING COEFFECIENTS Coil Span Factor (Kc) The Coil Span Factor or Pitch Factor Kc is defined as the ratio of the voltage generated in the short pitch coil to the voltage generated in the full pitch coil. It is also known as Chording Factor Advantages of Short Pitch Coil or Chording : It shortens the ends of the winding and, therefore, there is a saving in the conductor’s material. It Reduces the effects of distorting harmonics and thus the waveform of the generated voltage is improved and making it a sine wave.  In case of a full pitch coil, the distance between the two sides of the coil is exactly equal to the pole pitch of 180⁰ electrical. As a result, the voltage in a full pitch coil is such that the voltage of each side of the coil is in phase. Let EC1 and EC2 be the voltages generated in the coil sides, and EC is the resultant coil voltage. Since EC1 and EC2 are in phase, the resultant coil voltage EC is equal to their arithmetic sum. Therefore,  A stator winding using fractional pitch coil is called a chorded winding. If the span of the coil is reduced by an angle α electrical degrees, the coil span will be (180 – α) electrical degrees. If the coil span of a single coil is less than the pole pitch of 180⁰ electrical, the voltages generated on each coil side are not in phase. The resultant coil voltage EC is equal to the phasor sum of EC1 and EC2  If the coil span is reduced by an angle α electrical degrees, the coil span is (180 – α) electrical degrees. The voltage generated EC1 and EC2 in the two coil sides will be out of phase with respect to each other by an angle α electrical degrees. The phasor sum of EC1 and EC2 is EC, which is equal to AC as shown in the phasor diagram above.  For full pitch coil, the value of α will be 0⁰, cos α/2 = 1 and KC = 1. For a short pitch coil KC < 1.  Distribution Factor The Distribution Factor or the Breadth Factor is defined as the ratio of the actual voltage obtained to the possible voltage if all the coils of a polar group were concentrated in a single slot. It is denoted by Kd and is given by the equation shown below.  Concentrated and Distributed Winding  In a concentrated winding, each phase of a coil is concentrated in a single slot. The individual coil voltages induced are in phase with each other. These voltages must be added arithmetically. In order to determine the induced voltage per phase, a given coil voltage is multiplied by the number of series connected coils per phase. In actual practice, in each phase, coils are not concentrated in a single slot. They are distributed in a number of slots in space to form a polar group under each pole. The voltages induced in coil sides are not in phase, but they differ by an angle β which is known as the angular displacement of the slots.  Let, m = slots per pole per phase β = angular displacement between adjacent slots in electrical degrees Thus, one phase of the winding consists of coils arranged in m consecutive slots. Voltages EC1, EC2, EC3….. are the individual coil voltages. Each coil voltage EC will be out of phase with the next coil voltages by the slot pitch β.  The figure below shows the voltage polygon of the induced voltages in the four coils of a group (m = 4) The voltages EC1, EC2, EC3 and EC4 are represented by the phasors AB, BC, CD and DF respectively. Each of these phasors is a chord of a circle with the center O and subtends an angle β at the point O. The phasor sum AF, represents the resultant winding voltage, subtends at an angle mβ at the center.  The arithmetic sum of the individual coil voltage is given as The phasor sum of the individual coil voltages is given as Therefore, from the equation (1) shown above, we know that, The distribution factor Kd for a given number of phases is dependent only on the number of distributed slots under a given pole. It is independent of the type of the winding, lap or wave or the number of turns per coil, etc. the distribution factor decreases as the number of slots per pole increases.  Winding Factor Winding Factor is defined as the product of Distribution factor (Kd) and the coil span factor (Kc). It is denoted by Kw. The winding factor is the method of improving the rms generated voltage in a three phase AC machines so that the torque and the output voltage does not consists any harmonics which reduces the efficiency of the machine.  Speed & Frequency Relation The frequency of the generated voltage depends upon the number of field poles and on the speed at which the field poles are rotated. one complete cycle of voltage is generated in an armature coil when a pair of field poles passes over the coil. P = total number of field poles. p = pair of field poles N = speed of the field in r.p.m. n = speed of field poles in r.p.s. f = frequency of the generated voltage in Hz. Since one cycle is generated in an armature coil when the pair of field poles passes over the coil, the number of cycles generated in one revolution of the rotor will be equal to the number of pars of the poles. that is, Number of cycles per revolution = p Also number of revolution per second = n Equation give the relationship between the number of poles, speed and frequency.  EMF Equation of Rotating Machine The equation of voltage that we get as output from armature winding is the e.m.f equation. Let, P is the number of poles ϕ is Flux per pole in Webers n = speed of rotation of rotor in revolution per second (r.p.s.) N is the speed in revolution per minute (r.p.m) f is the frequency in Hertz Zph is the number of conductors connected in series per phase Tph is the number of turns connected in series per phase Kc is the coil span factor Kd is the distribution factor Flux cut by each conductor during one revolution is given as Pϕ Weber. Time taken to complete one revolution is given by 60/N sec Since the flux per pole is Φ , each stator conductor cuts flux PΦ. The average value of generated voltage per conductor = flux cut per revolution in Wb time taken for one revolution in seconds Since n revolution are made in one second, one revolution will be made in 1/n second. therefore the time for one revolution of the armature is 1/n second. Eav/ conductor = PΦ = nPΦ................(1). 1/n We know that f = PN/120 = Pn/2 Therefore, Pn = 2f these value put in equation 1 we get , Eav/ conductor = 2fΦ...................(2). since there are Zph conductor in series per phase , the average voltage generated per phase is given by Eav/ phase = 2fΦ Zph since one turn or coil has two sides Zph = 2Tph , the expression for the average generated voltage per phase can be written as Eav/ phase = 4fΦTph ………(2) for voltage wave , the form factor is given by Kf = r.m.s. value/ average value For a sinusoidal voltage , Kf =1.11. therefore. the r.m.s. value of generated voltage per phase can be written as Er.m.s. / phase = Kf x Eav / phase = 1.11 x 4fΦTph = 4.44fΦTp the r.m.s. value of generated voltage per phase is given by Ep = 4.44fΦTph  If the coil span factor Kc and the distribution factor Kd , are taken into consideration than the Actual EMF induced per phase is given as Equation (1) shown above is the EMF equation of the Synchronous Generator As we know, Winding Factor is defined as the product of Distribution factor (Kd) and the coil span factor (Kc). Thank You