Lecture notes AC Machines

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Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl ELECTRICAL MACHINES II Lecturer: Dr. Suad Ibrahim Shahl Suad Ibrahim Shahl Syllabus I. Introduction to AC Machine II. Synchronous Generators III. Synchronous Motors IV. Three-Phase Induction Machines V. Three-Phase Induction Motors VI. Induction Generators VII. Induction Regulators Recommended Textbook : 1) M.G.Say Alternating Current Machines Pitman Pub. 2) A.S. Langsdorf Theory of AC Machinery McGRAW-HILL Pub. 1 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl I. Introduction to AC Machines Classification of AC Rotating Machines •Synchronous Machines: •Synchronous Generators: A primary source of electrical energy. •Synchronous Motors: Used as motors as well as power factor compensators (synchronous condensers). •Asynchronous (Induction) Machines: •Induction Motors: Most widely used electrical motors in both domestic and industrial applications. •Induction Generators: Due to lack of a separate field excitation, these machines are rarely used as generators. Energy Conversion • Generators convert mechanical energy to electric energy. • Motors convert electric energy to mechanical energy. • The construction of motors and generators are similar. • Every generator can operate as a motor and vice versa. • The energy or power balance is : – Generator: Mechanical power = electric power + losses – Motor: Electric Power = Mechanical Power + losses. 2 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl AC winding design The windings used in rotating electrical machines can be classified as  Concentrated Windings • All the winding turns are wound together in series to form one multi-turn coil • All the turns have the same magnetic axis • Examples of concentrated winding are – field windings for salient-pole synchronous machines – D.C. machines – Primary and secondary windings of a transformer  Distributed Windings • All the winding turns are arranged in several full-pitch or fractional-pitch coils • These coils are then housed in the slots spread around the air-gap periphery to form phase or commutator winding • Examples of distributed winding are – Stator and rotor of induction machines – The armatures of both synchronous and D.C. machines Armature windings, in general, are classified under two main heads, namely,  Closed Windings • There is a closed path in the sense that if one starts from any point on the winding and traverses it, one again reaches the starting point from where one had started • Used only for D.C. machines and A.C. commutator machines  Open Windings • Open windings terminate at suitable number of slip-rings or terminals • Used only for A.C. machines, like synchronous machines, induction machines, etc Some of the terms common to armature windings are described below: 1. Conductor. A length of wire which takes active part in the energy- conversion process is a called a conductor. 2. Turn. One turn consists of two conductors. 3. Coil. One coil may consist of any number of turns. 4. Coil –side. One coil with any number of turns has two coil-sides. 3 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl The number of conductors (C) in any coil-side is equal to the number of turns (N) in that coil. Overhang Coil- Coil - Coil- sides sides sides One-turn coil two-turn coil multi-turn coil 5. Single- layer and double layer windings.  Single- layer winding • One coil-side occupies the total slot area • Used only in small ac machines one coil-side per slot  Double- layer winding • Slot contains even number (may be 2,4,6 etc.) of coil-sides in two layers • Double-layer winding is more common above about 5kW machines Top layer Bottom layer Two coil –sides per slot 4-coil-sides per slot 4 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl The advantages of double-layer winding over single layer winding are as follows: a. Easier to manufacture and lower cost of the coils b. Fractional-slot winding can be used c. Chorded-winding is possible d. Lower-leakage reactance and therefore , better performance of the machine e. Better emf waveform in case of generators 6. Pole – pitch. A pole pitch is defined as the peripheral distance between o identical points on two adjacent poles. Pole pitch is always equal to 180 electrical. 7. Coil–span or coil-pitch. The distance between the two coil-sides of a coil is called coil-span or coil-pitch. It is usually measured in terms of teeth, slots or electrical degrees. 8. Chorded-coil.  If the coil-span (or coil-pitch) is equal to the pole-pitch, then the coil is termed a full-pitch coil.  in case the coil-pitch is less than pole-pitch, then it is called chorded, short-pitch or fractional-pitch coil 𝑺𝑺  if there are S slots and P poles, then pole pitch 𝑸𝑸 = slots per pole 𝑷𝑷 𝑺𝑺  if coil-pitch 𝒚𝒚 = , it results in full-pitch winding 𝑷𝑷 𝑺𝑺  in case coil-pitch 𝒚𝒚 , it results in chorded, short-pitched or 𝑷𝑷 fractional-pitch N S N S Pole Pole pitch pitch Coil Coil span span Full-pitch coil Short-pitched or chorded coil 5 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl In AC armature windings, the separate coils may be connected in several different manners, but the two most common methods are lap and wave In polyphase windings it is essential that  The generated emfs of all the phases are of equal magnitude  The waveforms of the phase emfs are identical  The frequency of the phase emfs are equal 𝟐𝟐𝟐𝟐  The phase emfs have mutual time-phase displacement of 𝜷𝜷 = electrical 𝒎𝒎 radians. Here m is the number of phases of the a.c. machine. Phase spread Where field winding on the rotor to produce 2 poles and the stator carries 12 conductors housed in 12 slots. 1 12 2 A N 11 E 3 12 E 1 C E 2 E 11 E 3 E 10 10 E 4 4 E 9 E 5 E 6 E E 7 8 S 9 5 6 8 7 B o 3-phase winding - phase spread is 120 6 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl E 4 E 3 E A E 2 E C E 12 E 1 E 5 E 11 E 6 E 10 E 9 E 7 E 8 E B o Time phase angle is 120 between E , E and E A B C 𝐸𝐸 𝑚𝑚  Maximum emf E induced in conductor 1𝐸𝐸 = R �� m 1 √2  Zero emf induced in conductor 4 (conductor 4 is cutting zero lines of flux)  the emf generated in conductor 7 is maximum (conductor 7 is cutting maximum lines of flux from S pole)  the polarity of emf in conductor 7 will be opposite to that in conductor 1, 𝑬𝑬 𝒎𝒎 𝑬𝑬 = , opposite to E 1 𝟕𝟕 √𝟐𝟐  similarly the emfs generated in conductors 2, 3, 5, 6 and in conductor 8 to 12 can be represented by phasors E , E , E , E and E to E 2 3 5 6 8 12 𝑜𝑜𝑜𝑜 180 180 𝑜𝑜  the slot angle pitch is given by 𝛾𝛾 = = = 30 𝑜𝑜𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑜𝑜𝑆𝑆 6  if 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑐𝑐𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝 𝟏𝟏 𝑆𝑆𝑖𝑖 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑝𝑝𝑏𝑏𝑆𝑆𝑝𝑝𝑒𝑒 𝑆𝑆𝑜𝑜 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑐𝑐𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝 𝟐𝟐 𝑜𝑜𝑝𝑝𝑜𝑜𝑒𝑒𝑆𝑆 𝑒𝑒𝑒𝑒𝑝𝑝 𝑜𝑜𝑜𝑜 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝𝑐𝑐 𝟐𝟐 𝑖𝑖𝑆𝑆 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑝𝑝𝑏𝑏𝑆𝑆𝑝𝑝𝑒𝑒 𝑆𝑆𝑜𝑜 𝑜𝑜𝑝𝑝𝑜𝑜𝑒𝑒𝑆𝑆 𝑝𝑝𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑐𝑐𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒 𝟑𝟑� 𝐸𝐸 =𝐸𝐸 +𝐸𝐸 +𝐸𝐸 +𝐸𝐸 𝐴𝐴 1 2 3 4 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝𝑐𝑐 𝟑𝟑𝑆𝑆𝑖𝑖 𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑝𝑝𝑏𝑏𝑆𝑆𝑝𝑝𝑒𝑒 𝑆𝑆𝑜𝑜 𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏 𝑝𝑝𝑒𝑒𝑒𝑒 𝑜𝑜𝑜𝑜 𝑏𝑏𝑆𝑆𝑜𝑜𝑝𝑝𝑏𝑏𝑜𝑜𝑒𝑒𝑒𝑒𝑐𝑐 𝟑𝟑 Similarly, 𝐸𝐸 =𝐸𝐸 +𝐸𝐸 +𝐸𝐸 +𝐸𝐸 & 𝐸𝐸 =𝐸𝐸 +𝐸𝐸 +𝐸𝐸 +𝐸𝐸 𝐵𝐵 5 6 7 8𝐶𝐶 9 10 11 12  the phase belt or phase band may be defined as the group of adjacent slots belonging to one phase under one pole-pair Conductors 1, 2, 3 and 4 constitute first phase group Conductors 5, 6, 7 and 8 constitute second phase group Conductors 9, 10, 11 and 12 constitute third phase group  the angle subtended by one phase group is called phase spread, symbol σ 𝑜𝑜 𝜎𝜎 =𝑞𝑞𝛾𝛾 = 4 × 30 where 𝑆𝑆 𝑞𝑞 =𝑒𝑒𝑐𝑐𝑚𝑚𝑏𝑏𝑝𝑝𝑝𝑝 𝑜𝑜𝑜𝑜 𝑆𝑆𝑆𝑆𝑜𝑜𝑆𝑆𝑆𝑆 𝑝𝑝𝑝𝑝𝑝𝑝 𝑜𝑜𝑆𝑆𝑝𝑝𝑝𝑝 𝑝𝑝𝑝𝑝𝑝𝑝 𝑝𝑝ℎ𝑆𝑆𝑝𝑝 = 𝑃𝑃𝑚𝑚 7 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl Sequence of phase-belts (groups) Let 12-conductors can be used to obtain three-phase single – layer winding having a o 𝑜𝑜 phase spread of 60 (𝜎𝜎 = 60 ) 𝑆𝑆 12  coil pitch or coil span y = pole pitch τ = = = 6 𝑃𝑃 2 o  for 12 slots and 2 poles, slot angular pitch γ =30 𝑜𝑜  for 𝜎𝜎 = 60 , two adjacent slots must belong to the same phase A ′ 1 B 12 2 N 11 E 3 12 E 1 ′ E 2 C E 11 E 3 E 10 10 E 4 4 E 9 E 5 E C 6 E E 8 7 S 9 5 6 8 B 7 ′ A o 3-phase winding, phase spread is 60 8 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl a b a b 1 4 6 7 10 12 2 3 5 8 9 11 ′ ′ ′ ′ ′ A A ′ B C A C C B A B C B o γ=30 o o 120 120 c d c d B A B C C 1 1 A 2 1 2 2 (a) -E 8 A E 2 E 7 E 1 o 120 E 5 -E 11 E 9 C -E -E E 4 E 3 6 10 -E 12 B (b) o Phase spread of 60 , 12 slots,2 pole winding arrangement (b) Time-phase diagram for the emfs generated in (a) 9 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl Double Layer Winding  synchronous machine armatures and induction –motor stators above a few kW, are wound with double layer windings 𝑺𝑺  if the number of slots per pole per phase 𝒒𝒒 = is an integer, then the 𝒎𝒎𝑷𝑷 winding is called an integral-slot winding  in case the number of slots per pole per phase, q is not an integer, the winding is called fractional-slot winding. For example  a 3-phase winding with 36 slots and 4 poles is an integral slot 36 winding, because 𝑞𝑞 = = 3 𝑆𝑆𝑖𝑖 𝑏𝑏𝑒𝑒 𝑒𝑒𝑆𝑆𝑝𝑝𝑝𝑝𝑝𝑝𝑖𝑖𝑖𝑖 3×4  a 3-phase winding with 30 slots and 4 poles is a fractional slot 30 5 winding, because 𝑞𝑞 = = 𝑖𝑖𝑆𝑆 𝑒𝑒𝑜𝑜𝑆𝑆 𝑏𝑏𝑒𝑒 𝑝𝑝𝑝𝑝𝑖𝑖𝑒𝑒𝑆𝑆𝑝𝑝𝑖𝑖 3×4 2  the number of coils C is always equal to the number of slots S, C=S 1- Integral Slot Winding Example: make a winding table for the armature of a 3-phase machine with the following specifications: Total number of slots = 24 Double – layer winding o Number of poles = 4 Phase spread=60 Coil-span = full-pitch (a) Draw the detailed winding diagram for one phase only o (b) Show the star of coil-emfs. Draw phasor diagram for narrow-spread(σ=60 ) connections of the 3-phase winding showing coil-emfs for phases A and B only. 𝑜𝑜 4×180 𝑜𝑜 Solution: slot angular pitch, 𝛾𝛾 = = 30 24 𝑜𝑜 Phase spread, 𝜎𝜎 = 60 24 Number of slots per pole per phase, 𝑞𝑞 = = 2 3×4 24 Coil span = full pitch = = 6 4 10 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl (a) Detailed double layer winding diagram for phase A for 3-phase armature o having 24 slots, 4 poles, phase spread 60 11 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl (c) The star of coil emfs can be drawn similar to the star of slot emfs or star of conductor emfs Phasor diagram showing the phasor sum of coil-emfs to obtain phase voltages A and B 12 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl 2. integral slot chorded winding  Coil span (coil pitch) pole pitch (y τ)  The advantages of using chorded coils are:  To reduce the amount of copper required for the end-connections (or over hang)  To reduce the magnitude of certain harmonics in the waveform of phase emfs and mmfs  The coil span generally varies from 2/3 pole pitch to full pole pitch Example. Let us consider a double-layer three-phase winding with q = 3, p = 4, (S = pqm = 36 slots), chorded coils y/τ = 7/9 The star of slot emf phasors for a double-layer winding p = 4 poles, q = 3 slots/pole/phase, m = 3, S = 36 13 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl Double-layer winding: p = 4 poles, q = 3, y/τ = 7/9, S = 36 slots. 14 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl 3. Fractional Slot Windings If the number of slots qof a winding is a fraction, the winding is called a fractional slot winding. Advantages of fractional slot windings when compared with integral slot windings are: 1. a great freedom of choice with respect to the number of slot a possibility to reach a suitable magnetic flux density 2. this winding allows more freedom in the choice of coil span 3. if the number of slots is predetermined, the fractional slot winding can be applied to a wider range of numbers of poles than the integral slot winding the segment structures of large machines are better controlled by using fractional slot windings 4. this winding reduces the high-frequency harmonics in the emf and mmf waveforms Let us consider a small induction motor with p = 8 and q = 3/2, m = 3. The total number of slots S = pqm = 833/2= 36 slots. The coil span y is y = (S/p) = (36/8) = 4slot pitches Fractionary q (q = 3/2, p = 8, m = 3,S = 36) winding- emf star, 15 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl  The actual value of q for each phase under neighboring poles is 2 and 1, respectively, to give an average of 3/2 Fractionary q (q = 3/2, p = 8, m = 3, S = 36) winding slot/phase allocation & coils of phase A Single – Layer Winding  One coil side occupies one slot completely, in view of this, number of coils 𝟏𝟏 C is equal to half the number of slots S, 𝑪𝑪 =𝑺𝑺 𝟐𝟐  The 3-phase single –layer windings are of two types 1. Concentric windings 2. Mush windings Concentric Windings  The coils under one pole pair are wound in such a manner as if these have one center  the concentric winding can further be sub-divided into 1. half coil winding or unbifurcated winding 2. Whole coil winding or bifurcated winding 16 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl Half coil winding For phase A only  The half coil winding arrangement with 2-slots per pole per phase and for o σ=60  A coil group may be defined as the group of coils having the same center  The number of coils in each coil group = the number of coil sides in each phase belt (phase group)  The carry current in the same direction in all the coil groups whole coil winding For phase A only  The whole coil winding arrangement with 2-slots per pole per phase  The number of coil sides in each phase belt (here 4) are double the number of coils (here 2) in each coil group  There are P coil groups and the adjacent coil groups carry currents in opposite directions Example. Design and draw (a) half coil and (b) whole coil single layer o concentric windings for a 3-phase machine with 24-slots, 4-poles and 60 phase spread. 17 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl Solution: (a) half coil concentric winding 𝑜𝑜 4×180 𝑜𝑜 𝑜𝑜𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑏𝑏𝑒𝑒𝑖𝑖𝑐𝑐𝑆𝑆𝑏𝑏𝑝𝑝 𝑝𝑝𝑖𝑖𝑆𝑆𝑏𝑏ℎ,𝛾𝛾 = = 30 24 24 𝐹𝐹𝑐𝑐𝑆𝑆𝑆𝑆 𝑝𝑝𝑖𝑖𝑆𝑆𝑏𝑏ℎ 𝑝𝑝𝑜𝑜 𝑜𝑜𝑆𝑆𝑝𝑝𝑝𝑝 𝑝𝑝𝑖𝑖𝑆𝑆𝑏𝑏ℎ = = 6 𝑆𝑆𝑆𝑆𝑜𝑜𝑆𝑆𝑆𝑆 𝑝𝑝𝑖𝑖𝑆𝑆𝑏𝑏ℎ𝑝𝑝𝑆𝑆 4 o Half-coil winding diagram for 24 slots, 4 poles, 60 phase spread single layer concentric winding (two – plane overhang) 18 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl (b) Whole-coil concentric winding o o For slot pitch γ = 30 & phase spread σ = 60 ,  The number of coils per phase belt = 2  The number of coils in each coil group = 1  The pole pitch=6  The coil pitch of 6 slot pitches does not result in proper arrangement of the winding  In view of this, a coil pitch of 5 is chosen o Whole-coil winding arrangement of 24 slots, 4 poles, 60 phase spread, single layer concentric winding (three-plane overhang) Mush Winding  The coil pitch is the same for all the coils  Each coil is first wound on a trapezoidal shaped former. Then the short coil sides are first fitted in alternate slots and the long coil sides are inserted in the remaining slots  The number of slots per pole per phase must be a whole number  The coil pitch is always odd 19 Introduction to AC Machines Dr. Suad Ibrahim Shahl Introduction to AC Machines Suad Ibrahim Shahl For example, for 24 slots, 4 poles, single-layer mush winding, the pole pitch is 6 slots pitches. Since the coil pitch must be odd, it can be taken as 5 or 7. Choosing here a coil pitch of 5 slot pitches. o Single – layer mush winding diagram for 24 slots, 4 poles and 60 phase spread H.W: Design and draw 1. 3-phase, 24-slots, 2-poles single-layer winding (half coil winding) 2. a.c. winding: 3-phase, 4 -pole, 24- slots, double layer winding with full pitch coils (phase B& phase C) 3. a.c. winding: 3-phase, 4 -pole, 24- slots, double layer winding with chorded coils y/τ = 5/6 4. 10 -pole, 48- slots, fractional 3-phase double layer winding 20

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