Overvew Electrcal achnes an Drves 7-9 1: Introucton, axwell s equatons, magnetc crcuts 11-9 1.2-3: agnetc crcuts, Prncples 14-9 3-4.2: Prncples, DC machnes 18-9 4.3-4.7: DC machnes an rves 21-9 5.2-5.6: I ntroucton, I prncples 25-9 Guest lecture Emle Brnk 28-9 5.8-5.10: I equvalent crcuts an characterstcs 2-10 5.13-6.3: I rves, S 5-10 6.4-6.13: S, PAC 12-10 6.14-8.3: PAC, other machnes 19-10: rest, questons 9-11: exam 1
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 2
Constructon Stator comparable to I: lamnate strbute stator wnngs Rotor hgh-spee: cylnrcal (p 4) wth strbute wnng low-spee lentpole (p 4) wth concentrate wnng 3
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 4
Synchronous generator p n 1 2 60 2 n 60 1 p or 1 50Hz requency o the stator voltage or exctaton voltage synchronous spee o the rotor p 2 4 6 8 10 60 n s (rpm) 3000 1500 1000 750 600 100 5
P-pole machnes p s the number o poles (n some other books: number o pole-pars) N p N a ( θ ) sn( θ ) ˆ p B s ( θ, t) B cos( θ ωt) 2 2 2 p θ θ 2 e m 6
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 7
Open crcut characterstc E 2π 1kw 1N1 2 Φ p 8
Poston n the gr 9
Connectng to the gr (nnte bus) Beore a synchronous machne can be connecte to the nnte bus, 1. voltage 2. requency 3. phase sequence 4. phase o the synchronous machne an the gr must be the me. 10
Synchronous motor connecte to the gr Not sel startng, thereore: - amper cage or asynchronous startng an ampng oscllatons - requency converter 11
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 12
Dervaton o voltage equatons The sketche stator an rotor wnngs are concentrate, but they represent strbute wnngs How can we erve voltage equatons an equvalent crcuts? 13
14 Voltage equatons t R u λ sr sc sb b b sc sr sc b sb b sb sr sc b sb b L L L ) ( ) ( ) ( 3 4 3 2 π θ λ π θ λ θ λ 0 sc sb sr sc b sc sr sb b sb sr b L L L ) ( ) ( ) ( ) ( ) ( ) ( 3 4 3 2 π θ λ π θ λ θ λ axwell, Faraay: No star-pont connecton
15 Voltage equatons, equvalent crcut c sc s sc sr sc s sc sc b sb s sb sr sb s sb sb a s sr s e t L R t t L R u e t L R t t L R u e t L R t t L R u ) ( ) ( ) ( 3 4 3 2 π θ π θ θ b s L L Usng
Armature reacton The rotatng magnetc el conssts o two parts 1. the el create by the three-phase stator currents 2. the el create by the rotor exctaton Φ r Φ Φ a Generator conventon: λ E t E jωλ 16
Equvalent crcuts Generator conventon: λ E t E jωλ 17
easurng the synchronous nuctance 18
Phasor agrams Generator: V E RI jωl I t a s a otor: V E RI jωl I t a s a 19
Synchronous conenser Synchronous machne that behaves lke a capactor or nuctor may use or reactve power compenton n power systems has no mechancal loa Can you sketch the phasor agrams or capactve an nuctve operaton? 20
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 21
Power characterstcs R 0 Vt Vt E E (cos( δ ) jsn( δ )) s S V I V S (cos( δ ) jsn( δ )) V * t 3 t a 3 t j X s V E sn( δ ) V E cos( δ ) V 3 3 j X X 2 t t t s E s * Vt E P 3 sn( δ ) X s 22
Torque characterstcs T P ω m Vt E 3 sn( δ ) Tmax sn( δ ) ω X m s Stablty lmts Also or negatve loa angle 23
Torque-spee characterstc 24
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 25
Complex power locus S V E sn( δ ) V E cos( δ ) V 3 3 j X X 2 t t t s s What happens the power s ncrease? What happens the el current s ncrease? 26
Capablty curves Capablty s lmte by armature heatng el heatng steay-state stablty lmt 27
Synchronous machnes Introucton, constructon Synchronous generators / motors Voltage equatons, equvalent crcuts an phasor agrams Power an torque characterstcs Capablty curves Spee control 28
Spee control o synchronous machnes How can the spee o synchronous machnes be controlle? 29
Frequency control VSI s mportant. The cycloconverter s not scusse n ths course. 30
Flux weakenng 31
Overvew Electrcal achnes an Drves 7-9 1: Introucton, axwell s equatons, magnetc crcuts 11-9 1.2-3: agnetc crcuts, Prncples 14-9 3-4.2: Prncples, DC machnes 18-9 4.3-4.7: DC machnes an rves 21-9 5.2-5.6: I ntroucton, I prncples 25-9 Guest lecture Emle Brnk 28-9 5.8-5.10: I equvalent crcuts an characterstcs 2-10 5.13-6.3: I rves, S 5-10 6.4-6.13: S, PAC 12-10 6.14-8.3: PAC, other machnes 19-10: rest, questons 9-11: exam 32