11/20/2012 - drhenrylouie

1 11/20/2012 1 31-AC Machine Construction text: to ECEGR 450 Electromechanical Energy Conversion Overview Introduction Physical Construction Armature Windings Pitch Factor Distribution Factor Winding Connections Rotor Dr. Louie 2 Introduction Recall that DC machines: armature windings in rotor AC machines: armature windings in the stator AC machines (generators, motors) have similar stators Rotors are different Induction Synchronous Analyze physical construction of AC machines Dr. Louie 3 Introduction Advantages of armature windings in the stator: Larger coils can be used since they are located in the stator High power rated slip rings can be avoid Easier to cool stator than rotor Easier to construct the armature winding if it is in the stator Easier to electrically insulate the stator Dr.

2 Louie 4 Stator Houses armature windings Contains large gauge coils (low R) Conductors are symmetrically arranged to form a balanced poly-phase winding Induced emf can be in kV range Power ratings can be in MVA range Dr. Louie 5 Armature Windings Common for the armature (stator) windings to be three-phase Windings are identical, but displaced by 120o electrical Can be delta or wye connected (generators) wye is common if higher voltage is needed neutral point is grounded Windings are commonly double layer Equal number of slots and windings Dr. Louie 6 11/20/2012 2 Salient vs Cylindrical Early machines used salient pole stators Salient poles still used in rotors Modern machines use cylindrical stators Dr.

3 Louie 7 salient pole cylindrical Salient-Pole vs Cylindrical Dr. Louie 8 a-axis b-axis c-axis b-axis a-axis c-axis Armature Windings Mechanical slot span: Electrical slot span: Example: 24 slot, 4 pole machine m = 15o = 30o Dr. Louie 9 m360# of slotsm360PP# of slots 22mArmature Windings Balanced three phase: Number of coils connected in series and in parallel in each phase must be equal Total number of coils must be an integer multiple of the number of phases Coils are distributed equally among the poles Number of coils (slots) per pole must be an integer Number of coils per phase must be an integer Dr. Louie 10 Armature Windings Mathematically S: number of armature slots P: number of poles q: number of phases n: number of coils per pole per phase (integer) P x q = is the number of phase groups (phase coils under the same pole) n is also equal to the number of coils per phase group Dr.

4 Louie 11 SnPqArmature Windings Example: a three-phase, 4-pole synchronous generator has 24 slots. P = 4 (poles) S = 24 (slots) q = 3 (phases) therefore 24/4 = 6 coils per pole 24/3 = 8 coils per phase 6/3 = 2 coils per pole per phase 4 x 3 = 12 phase groups (4 phase groups per phase) Dr. Louie 12 S24n2Pq 4 311/20/2012 3 Armature Windings 24 total coils (24 slots) A-phase: 8 coils total 4 phase groups 2 coils per phase group B-phase: 8 coils total 4 phase groups 2 coils per phase group C-phase: 8 coils total 4 phase groups 2 coils per phase group Dr. Louie 13 m = 15o = 30o Armature Windings Coils in each phase group are connected in series A-phase windings shown (4 phase groups) Dr.

5 Louie 14 A1 A2 A3 A4 four-poles, 24 slots Note: phase group coils must be series connected. Coil Span Each coil spans 5 slots 75 degrees (mechanical) 150 degrees (electrical) Coil span: angular span of each coil m: coil span (mechanical) : coil span (electrical) Dr. Louie 15 A1 1 5 3 4 2 6 7 m mP2m = 15o = 30o Coil Span If = 180o, then known as full pitch coils If < 180, then known as fractional pitch or partial pitch coils Typical coil span strategy: Dr. Louie 16 180(# of coils in each phase group-1)Pitch Factor Example of full pitch coils Fractional pitch is used: Reduces harmonics (have a sinusoidal voltage output) Shortens length of end connections (less copper, less resistance) Reduces leakage and magnetizing losses Reduces the induced emf (disadvantage) Dr.

6 Louie 17 A1 Pitch Factor Consequence of partial pitch is reduction of flux through each coil Must account for partial pitch coils by a de-rating factor known as pitch factor Dr. Louie 18 N N S S 11/20/2012 4 Pitch Factor Flux density is not uniform over face of rotor pole Flux density is maximum (Bm) at the face of the pole |Bm|: maximum flux density |B2|: minimum flux density |B1|: between maximum and 0 Dr. Louie 19 x Bm B1 B2 Pitch Factor Flux density of a cylindrical rotor can be approximated as Bm: maximum flux density per pole (T) Dr. Louie 20 x Bm B1 B2 (deg.)B ( )B1 Bm B2 cosmBBPitch Factor For multi-pole rotors: m: mechanical angle : electrical angle Dr. Louie 21 Bm m2 PPitch Factor Consider a full-pitch coil with coil conductors X, Y in the stator = 180o Orientation shown results in maximum flux Flux through the coil: Dr.

7 Louie 22 PsdBsBm Y X 22air gap exaggerated Pitch Factor From the geometry of the rotor (see Figure ): L: axial length of the rotor (m) r: radius of the rotor (m) P: number of poles Dr. Louie 23 mm2dLrdLrdPsL r Pitch Factor Maximum flux through a full pitch coil: Dr. Louie 24 cos()2 Pmmmms22Lr4 LrdBdBPPBsBm Y X 22air gap exaggerated 11/20/2012 5 Pitch Factor Now consider a fractional-pitch coil < 180o Dr. Louie 25 Bm Y X 22air gap exaggerated Pitch Factor For a fractional pitch coil: cm: maximal flux per coil (Wb) : span of the coil (rad) kp: pitch factor (less than or equal to 1) Dr. Louie 26 cos()sin() = sin()sin()2mcmmmms2pp pp2Lr4 LrBdBd2 PPk2k2 BsExample Calculate the pitch factor of a 48-slot, 4-pole three phase AC machine.

8 Dr. Louie 27 Example Calculate the pitch factor of a 48-slot, 4 pole three phase winding 12 slots per pole, so each slot spans 180o/12 = 15o (electrical) n = 48/(4 x 3) = 4 coils per phase group Coil 1: slot 1, slot 10 Coil 2: slot 2, slot 11 Coil 3: slot 3, slot 12 Coil 4: slot 4, slot 13 Each coil spans 9 x 15o = 135o (electrical) kp = sin(135o/2) = Dr. Louie 28 Winding Connection Coils in each phase group are series-connected Series-connected coils are windings Note the orientation of the coils under the rotor poles A1, A3 are under North A2, A4 are under South Dr. Louie 29 A1 A2 A3 A4 Polarity dots Polarity dots Winding Connection Several possible ways to connect each winding in a phase Series Parallel Series/parallel Dr.

9 Louie 30 11/20/2012 6 Winding Connections Dr. Louie 31 A1 A2 A3 A4 A1 A3 A2 A4 I 4I A1 A3 A2 A4 2I high current, low voltage low current, high voltage Winding Connections To achieve 3 phase, A, B, C phases must be displaced by 120 degrees electrical Dr. Louie 32 A1 C1 B1 (V)time (s)Distributed Windings Cylindrical stators use distributed windings Advantages (motors) Greater starting torque Quieter operation Advantages (generators) Less harmonic distortion in induced voltage Dr. Louie 33 Distributed Windings To create a sinusoidal voltage, there are more than one coil in each phase group Coils within a phase group are connected in series and are in distributed across the pole Each coil in a phase group therefore has a different induced voltage at a given point in time Dr.

10 Louie 34 Distributed Windings Dr. Louie 35 single full-pitch coil two series-connected distributed coils 1 2 1 2 Distributed Windings Dr. Louie 36 single full-pitch coil five series-connected distributed coils 1 2 1 2 end connection detail not shown 11/20/2012 7 Distribution Factor (text ) Distribution factor: kd Accounts for the different phasing of the coils De-rates induced voltage kd = 1 only if the coils in a phase group are in the same slots We can show that: : slot pitch (electrical degrees) (see Figure ) Dr. Louie 37 sin()sin()dn2kn2 Distribution Factor Distribution factor kd and pitch factor kp are combined into the winding factor kw = kdkp Winding factor accounts for the physical characteristics of the stator windings Typically: < kw < Dr.