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- ELECTRICAL MACHINES - III - EM 3
- Note
**Jawaharlal Nehru Technological University Anantapur (JNTU) College of Engineering (CEP), Pulivendula, Pulivendula, Andhra Pradesh, India - JNTUACEP**- 1 Topics
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windings are required, one for each phase connected in star. Fig. 1 shows one stator lamination of a synchronous generator. In case of generators where the diameter is too large stator lamination can not be punched in on circular piece. In such cases the laminations are punched in segments. A number of segments are assembled together to form one circular laminations. All the laminations are insulated from each other by a thin layer of varnish. Figure 1.1. Non Salient pole generator Figure: 1.2. Salient pole generator. 2

Rotor of water wheel generator consists of salient poles. Poles are built with thin silicon steel laminations of 0.5mm to 0.8 mm thickness to reduce eddy current laminations. The laminations are clamped by heavy end plates and secured by studs or rivets. For low speed rotors poles have the bolted on construction for the machines with little higher peripheral speed poles have dove tailed construction as shown in Figs. Generally rectangular or round pole constructions are used for such type of alternators. However the round poles have the advantages over rectangular poles. Generators driven by water wheel turbines are of either horizontal or vertical shaft type. Generators with fairly higher speeds are built with horizontal shaft and the generators with higher power ratings and low speeds are built with vertical shaft design. Vertical shaft generators are of two types of designs (i) Umbrella type where in the bearing is mounted below the rotor. (ii) Suspended type where in the bearing is mounted above the rotor. In case of turbo alternator the rotors are manufactured form solid steel forging. The rotor is slotted to accommodate the field winding. Normally two third of the rotor periphery is slotted to accommodate the winding and the remaining one third unslotted portion acts as the pole. Rectangular slots with tapering teeth are milled in the rotor. Generally rectangular aluminum or copper strips are employed for filed windings. The field windings and the overhangs of the field windings are secured in place by steel retaining rings to protect against high centrifugal forces. Hard composition insulation materials are used in the slots which can with stand high forces, stresses and temperatures. Perfect balancing of the rotor is done for such type of rotors. Damper windings are provided in the pole faces of salient pole alternators. Damper windings are nothing but the copper or aluminium bars housed in the slots of the pole faces. The ends of the damper bars are short circuited at the ends by short circuiting rings similar to end rings as in the case of squirrel cage rotors. These damper windings are serving the function of providing mechanical balance; provide damping effect, reduce the effect of over voltages and damp out hunting in case of alternators. In case of synchronous motors they act as rotor bars and help in self starting of the motor. Relation between Speed and Frequency: In the previous course on induction motors it is established that the relation between speed and frequency and number of poles is given by Frequency f = P x N /120 Hz Windings in Alternators: In case of three phase alternators the following types of windings are employed. (i) Lap winding, (ii) wave winding and (iii) Mush winding. Based on pitch of the coil (i) full pitched (ii) short pitched windings Based on number of layers (i) Single layer (ii) Double layer Figure: 1.3. Single layer winding 3

Figure: 1.4. Double layer winding EMF Equation of an alternator: Consider the following Φ = flux per pole in wb P = Number of poles Ns = Synchronous speed in rpm f = frequency of induced emf in Hz Z = total number of stator conductors Zph = conductors per phase connected in series Tph = Number of turns per phase Assuming concentrated winding, considering one conductor placed in a slot According to Faradays Law electromagnetic induction, The average value of emf induced per conductor in one revolution eavg = d /dt eavg = Change of Flux in one revolution/ Time taken for one revolution Change of Flux in one revolution = p x Time taken for one revolution = 60/Ns seconds Hence eavg = (p x ) / ( 60/Ns) = p x x Ns / 60 We know f = PNs /120 hence PNs /60 = 2f Hence eavg = 2 f volts Hence average emf per turn = 2 x 2 f volts = 4 f volts If there are Tph, number of turns per phase connected in series, then average emf induced in T ph turns is Eph, avg = Tph x eavg = 4 f ø Tph volts Hence RMS value of emf induced E = 1.11 x Eph, avg = 1.11 x 4 f ø Tph volts = 4.44 f ø Tph volts This is the general emf equation for the machine having concentrated and full pitched winding. In practice, alternators will have short pitched winding and hence coil span will not be 180 0, but on or two slots short than the full pitch. Pitch Factor: Pitch factor Kp= emf induced in a short pitched coil/ emf induced in a full pitched coil = (2E cos α/2 )/ 2E Kp = cos α/2 where α is called chording angle. Distribution Factor: Even though we assumed concentrated winding in deriving emf equation, in practice an attempt is made to distribute the winding in all the slots coming under a pole. Such a winding is called distributed winding. In concentrated winding the emf induced in all the coil sides will be same in magnitude and in phase with each other. In case of distributed winding the magnitude of emf will be same but the emfs induced in each coil side will not be in phase with each other as they are distributed in the slots under a pole. Hence the total emf will not be same as that in concentrated winding but will be equal to the vector sum of the emfs induced. Hence it will be 4

less than that in the concentrated winding. Now the factor by which the emf induced in a distributed winding gets reduced is called distribution factor and defined as the ratio of emf induced in a distributed winding to emf induced in a concentrated winding. Distribution factor Kd = emf induced in a distributed winding/ emf induced in a concentrated winding = vector sum of the emf/ arithmetic sum of the emf Let E = emf induced per coil side m = number of slots per pole per phase, n = number of slots per pole β = slot angle = 180/n The emf induced in concentrated winding with m slots per pole per phase = mE volts. Fig below shows the method of calculating the vector sum of the voltages in a distributed winding having a mutual phase difference of β. When m is large curve ACEN will form the arc of a circle of radius r. From the figure below AC = 2 x r x sin β/2 Hence arithmetic sum = m x 2r sinβ/2 Now the vector sum of the emfs is AN as shown in figure below = 2 x r x sin mβ/2 Hence the distribution factor Kd = vector sum of the emf / arithmetic sum of the emf = (2r sin mβ/2) / (m x 2r sin β/2) Kd = ( sin mβ/2) / (m sin β/2) Figure: 1.5. Calculation of vector sum In practical machines the windings will be generally short pitched and distributed over the periphery of the machine. Hence in deducing the emf equation both pitch factor and distribution factor has to be considered. Hence the general emf equation including pitch factor and distribution factor can be given as EMF induced per phase = 4.44 f Tph x KpKd volts Eph = 4.44 KpKd f Tph vlolts Hence the line Voltage EL = √3 x phase voltage = √3 Eph Harmonics: When the uniformly sinusoidal distributed air gap flux is cut by either the stationary or rotating armature sinusoidal emf is induced in the alternator. Hence the nature of the waveform of induced emf and current is sinusoidal. But when the alternator is loaded waveform will not continue to be sinusoidal or becomes non sinusoidal. Such non sinusoidal wave form is called complex wave form. By using Fourier series representation it is possible to represent complex non sinusoidal waveform in terms of series of sinusoidal components called harmonics, whose frequencies are integral multiples of fundamental wave. The fundamental wave form is one which is having the frequency same as that of complex wave. 5

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