Electrc Machnery and Apparatus 1 AE1B14SP1 Mroslav Chomát chomat@fel.cvut.cz room B3-48
Inducton Machne (IM) Applcatons Constructon Prncple Equatons Equvalent crcut Torque-speed characterstc Crcle dagram Effcency Startng Breakng Speed control Sngle-phase IM
Applcatons The overall most used motors smple, relable, cost-effectve In combnaton wth power converters can be used n almost any applcaton Ventlators, pumps, compressors, conveyers Tracton, wnd power plant generators, automaton of manufacturng Home applances, machne tools
MOTOR TERMINAL BOARD Constructon of IM TEFC = Totally Enclosed Fan Cooled motor ROTOR PLATES STATOR PLATES STATOR WINDING FAN (VENTILATOR) SHAFT BEARING ROTOR WINDING (SQUIRELL CAGE) FRAME
Prncple
Rotatng Magnetc Feld
Double Revolvng Feld Theory One Phase FF = jjff sn ωωtt + ππ vector rotatng n postve drecton vector rotatng n negatve drecton 7
Double Revolvng Feld Theory Two Phases FF = jjff sn ωωtt + ππ FF 11 = FF 1 sn ωωtt vector rotatng n postve drecton vector rotatng n negatve drecton 8
Double Revolvng Feld Theory Three Phases
Functon of Three-Phase IM
Magnetc Feld n Ar Gap τ p Φ= Bx l dx = Bmaxτ p l π 0
Magnetc Feld n Ar Gap
Magnetc Feld n Ar Gap
Magnetc Feld n Ar Gap + = = = π π τ τ p p z x x v l B v l B v B l u u u sn sn max 1 1
Stator Wndng
Stator Wndng
Ptch Factor k p ν y = snν τ p π
Dstrbuton Factor k d U = = qu c qα sn α q sn
Stator Slots
Man Speed Terms 1 = π p f 1 1 ω ( s ) 1 ω ( s ) ω s s ω ω1 ω = ω 1 = ω ω = 1 = n 1 n n 1 angular frequency at supply frequency f 1 mechancal angular frequency of rotor angular frequency of rotor relatve to mg. feld slp ω f = s angular slp frequency ω 1 = s slp frequency f 1 ( ) 1 ω = 1 s ω mechancal angular frequency of rotor
Equvalent Crcut and correspondng phasor dagram
Phasor Dagram
Equatons for Steady State 1 1 1 1 1 1 ˆ ˆ ˆ ˆ U I X j I R U + + = σ ˆ ˆ ˆ I X j I R U + = σ 1 1 1 1 44, 4 v k N f U Φ = µ 1 44, 4 v k N f U Φ = µ U = 0 ˆ ˆ ˆ I X s j I R U s + = σ Referred to the frequency n the stator: ˆ 1 ˆ ˆ ˆ ˆ ˆ I R s s I X j I R I X j I s R U + + = + = σ σ Induced voltages Analogy of transformer 1 1 ω ω = = s f s f
Fundamental voltage equatons for partcular wndngs: Equatons dψ k u k = R kk + k= uvwklm dt Equatons for magnetc fluxes: (,, /,, ) ψ u = L uu u uv v uw w uk K ul L um M ψ v = L vu u vv v vw w vk K vl L vm M ψ w = L wu u wv v ww w wk K wl L wm M ψ K = L Ku u Kv v Kw w KK K KL L KM M ψ L = L Lu u Lv v Lw w LK K LL L LM M ψ M = L Mu u Mv v Mw w MK K ML L MM M
Equatons Matrx form of equatons of resultng magnetc fluxes: L1 M1 M1 M cosϑ M cos( ϑ+ π ) M cos( ϑ π ) 3 3 ψ M1 L1 M1 M cos( ϑ π ) M cosϑ M cos( ϑ+ π ) u 3 3 ψv M1 M1 L1 M cos( ϑ+ π ) M cos( ϑ π ) M cosϑ ψ w 3 3 = ψ K M cosϑ M cos( ϑ π ) M cos( ϑ+ π ) L M M ψ L 3 3 ψ M M cos( ϑ+ π ) M cosϑ M cos( ϑ π ) M L M 3 3 M cos( ϑ π ) M cos( ϑ+ π ) M cosϑ M M L 3 3 u v w K L M
Clarke Transformaton
Clarke Transformaton
Clarke Transformaton R.H. Park Two Reacton Theory of Synchronous Machnes AIEE Transactons 48:716-730 (199).
Park Transformaton
Park Transformaton
Equatons Lnear transformaton of voltage equatons nto d,q,0 system: dψ d u d = R 1d + ω d k ψ t q dψ u q q = R 1 q + d t ωψ k q dψ 0 u 0 = R 10 + dt dψ D u D = R D ( ω k ω) ψ Q + dt dψ Q u Q = R Q + ( ω k ω) ψ D + dt dψ 0 u 0 = R 0 + dt Torque equaton for any speed ω k : m = p( ψ dq ψ qd )
Effcency Losses dstrbuton n the ar gap of an IM:
Effcency Losses dstrbuton n the ar gap of an nducton generator: Losses dstrbuton n the ar gap of an nducton brake:
Torque-Speed Characterstc Torque characterstcs of an IM: Influence of rotor resstance: Influence of frequency:
Torque-Speed Characterstc Influence of Harmoncs Generaton of harmoncs: Stepwse harmoncs Slot harmoncs
Torque-Speed Characterstc Influence of harmoncs Asynchronous torques Synchronous torques
Confguraton of Three-Phase Machne star delta
Confguraton of Three-Phase Machne u A u A u B u C u B u C star delta
Startng Reduced-voltage reactor startng: Reduced-voltage auto-transformer startng: Star-delta startng:
Star-Delta Startng M D B M Y A M p 1 0,8 0,6 s 0,4 0, 0
Startng Rotor resstance change motor wth slp rngs: SLIP RINGS BRUSHES STARTING RESISTOR
Startng Rotor resstance change specal rotor cages: Vortex cage: Double cage: LOWER BAR UPPER BAR NECK Overvew: UPPER BAR DOUBLE LOWER BAR VORTEX CAGE ROUND WIRES
Startng Drect connecton to the grd Overvew: Torque and angular speed at drect grd connecton. DOUBLE VORTEX CAGE ROUND WIRES
Speed Control Varable supply frequency Change of the number of poles Change of slp value Change of stator voltage Change of rotor resstance Slp energy recovery system (slp power control)
Speed Control Varable supply frequency
sngle layer concentrated q = double layer dstrbuted q = 3
Wndng Dstrbuton q =, y = τ p
Stator Slots double layer sngle layer
Cage Wndng n Rotor rotor bars endrng
Cage Wndng n Rotor Q For nteger p holds: m = Q N = 0,5 k v = 1 rotor phases
Change of Rotaton Orentaton u v w u v w n 1 n 1
Breakng pluggng brakng J Φ 1 M p P p n 1 M P m n ΔP j
Crcle Dagram
Crcle Dagram http://en.wkpeda.org/wk/crcle_dagram
Sngle-Phase IM Dervaton of torque of sngle-phase IM
Sngle-Phase IM Startng of sngle-phase IM Splt phase wth centrfugal swtch Shaded pole