Synchronous Machines

Transcription

1 Synchronous Machines

2 Synchronous Machines n 1 Φ f n 1 Φ f I f I f I f damper (run-up) winding Stator: similar to induction (asynchronous) machine ( 3 phase windings that forms a rotational circular magnetic field ) n 1 = 60.f 1 / p Rotor: I f DC. + slip rings circular field Φ f ~ I f Rotor design: a) salient pole b) cylindrical (round / non salient pole) rotor (turbo)

3 ČKD kw, 10 kv, 2p= to 3900 min -1

4 Rotor of a Turbomotor

5 Rotor of a Salient Pole Machine Run-up squirrel cage (damper winding)

6 ČKD kw, 6 kv, 2p=4 Synchronous Motor

7 ČKD kw, 6 kv, 2p=4

8 ČKD kva, 11 kv, 2p=8 Synchronous Generator

9 ČKD 2500 kw 10 kv, 2p=40 synchr.

10 Rotor of a Turbomachine Cross Section

11 Detail of a Nonmagnetic Armature of a Turbomachine

12 Rotor of a Slow Speed Machine Magnet wheel Hub Shaft

13 Magnetic Flux within a Salient Pole Machine

14 Fluxes and Reactances Resulting field is excited by the electromotive force produced by currents in three phase windings of the stator and DC current in excitation (field) winding in the rotor. Resulting fictional magnetizing current: In stator: Uˆ Uˆif I ˆ = Iˆ + µ - Supply (power grid) voltage - Voltage induced by excitation current I f U ˆ ˆ creates current Î, that flows through resistance U if and longitudinal synchronous reactance X d. X d = X ad + Φ ad main flux, Iˆ f X 1σ (interacts with rotor winding) Φ 1σ leakage (stray) flux X ad - longitudinal reactance of backelectromotive force of the rotor Similarly, the lateral synchronous reactance X q can be derived.

15 Synchronous Alternator with a Cylindrical Rotor Assumptions: a) Air gap is constant along the whole circumference δ = konst. R = m δ konst. b) Stator and rotor electromotive forces are sinusoidal distributed in space F m = F max π sin α τ p c) Angular velocity of rotor rotation is equal to d) Permeability ω = 2πf = konst. µ = konst. Φ ~ F m

16 Voltage Equations Uˆ = RIˆ + jx Iˆ σ + U = R I f f f ˆ U i If equation U i =4,44 f 1 Φ µ N 1 k v1 ~ Φ µ ~ F µ is valid, then also equations Fˆ = Fˆ f + Fˆ µ a are valid. Φ ˆ =Φ ˆ + Φˆ µ Uˆ = Uˆ + Uˆ i f f a a

17 For cylindrical rotor: X d = X q = X s = X ad + X 1σ Voltage equation has following form: or U ˆ = RIˆ + jx Iˆ + ˆ d U if U ˆ RIˆ + jx Iˆ + jx Iˆ + Uˆ = σ ad if

18 Phasor Diagram of a Turboalternator

19 Asynchronous Run-up of a Synchronous Motor n n 1 A A n n' < n 1 Synchronization: S of rotor tightens to J of stator Permanent coupling betweenφ f a Φ a : n = n 1 = konst = f (f ) M

20 Asynchronous run-up of synchronous motor n' n'' n n 1 A A' A'' n'' < < n 1 No synchronization M

21 Loading of a Synchronous Motor Increase of load torque M p S J n 1 Φ a n S Φ f J n = n 1

22 Loading of a Synchronous Motor Increase of load torque M p S n 1 Φ a J δ n = n 1 Rotor field is delayed behind the stator field of torque angle δ.

23 Loading of a Synchronous Motor Increase of load torque M p S n 1 Φ a J n = n 1

24 Loading of a Synchronous Motor Increase of load torque M p S n 1 Φ a J S n Φ f J n = n 1

25 Loading of a Synchronous Generator - Alternator Increase of driving torque M p S J n 1 Φ a n S Φ f J n = n 1

26 Loading of a Synchronous Generator - Alternator Increase of driving torque M p S n 1 Φ a J n = n 1

27 Loading of a Synchronous Generator - Alternator Increase of driving torque M p S n 1 Φ a J n = n 1

28 Loading of a Synchronous Generator - Alternator Increase of driving torque M p S n 1 Φ a J S Φf n J n = n 1

29 Basic Equivalent Circuit of a Turbomachine ~ U if X d I U X d - synchronous reactance (respests existence of stray flux and flux generated by current I ) R 1 = 0 - negligible compared to X d Uˆ = Uˆ + if jx d Iˆ

30 Loading at a Constant Power while Connected to a Strong Grid X d I jx d I w ~ U if U jx d.i q U I w φ I U if Important: I w = I cosφ ~ M X d I w = U if sinδ δ p I I q p U

31 Loading at a Constant Power while Connected to a Strong Grid X d I jx d I w ~ U if U U U if I=I w δ

32 Loading at a Constant Power while Connected to a Strong Grid X d I jx d I w jx d.i q ~ U if U U U if φ I I w δ I q Advantages of a synchronous motor: n = n 1 = konst. Change of cos φ

33 Phasor Diagram of an Overexcited Turbomachine X d I motor ~ U if U generator φ U jx d.i w U if jx d.i q jx d.i q U if jx d I w U I I w δ δ I q I q I I w

34 Regulation of Real and Reactive Power

35 Loading at a Constant Power while Connected to a Strong Grid All currents are recalculated to stator

36 Loading at a Constant Power while Connected to a Strong Grid V-curve of a synchronous machine

37 Loading at a Constant Excitation while Connected to a Strong Grid I μ is a magnetizing current in stator needed for excitation of a nominal voltage in idle run. It is constant if connected to a strong grid.

38 Torque of a Turbomachine P m = m U I cosφ = M ω 1m X d I w = U if sinδ M = m ω UU X 1m d if sinδ

39 Loading at a Constant Excitation while Connected to a Strong Grid Static stability a overload capacity Stable run: dp > 0 dδ Synchronizing factor: dp = m dδ 1 U U 1 X d if cosδ Determines ability of the machine to stay in synchronism. Maximum at δ = 0.

40 Loading at a Constant Excitation while Connected to a Strong Grid Static stability and overload capacity dp Synchronizing factor: Stable run: > 0 dδ dp U1U if = m1 cosδ δ d X Synchronizing power: dp dδ δ Indicates size of static stability of an alternator in a given working point in torque angle if the machine is able to get stable in a new point of a power characteristics after change of power without change of excitation d

41 Loading at a Constant Excitation while Connected to a Strong Grid Static stability and overload capacity Stable run: dp > 0 dδ Synchronizing factor: dp U1U if = m1 cosδ dδ X Synchronizing power: Power overload capacity: p M = P P max = N d dp dδ δ M M max N Motor p M 1,5 Alternator p M 1,25

42 Power (Torque) Overload Capacity p p M M P P N M M max max = = Motor p M 1,5 Alternator p M 1,25 = N muu ω X mui ω 1 m d d = = N cosϕn I N cosϕn 1m if U X if I N I kn cosϕ N I kn is steady short-circuit current that corresponds to an excitation current I fn p M = I fkn I fn I fn = ik cosϕ I 0 cosϕ N f N N Overload capacity is bigger when short-circuit ratio i k is higher and cosφ N is lower 1 ik bigger air gap higher excitation power larger dimensions X d

43 Power (Torque) Overload Capacity Conclusions: Short-circuit ratio is smaller when electrical and magnetic utilization of the machine is higher. Stability is provided by fast voltage regulators. Nominal power factor depends on design of excitation winding. Synchronous generators normally have cosφ N = 0,8 big ones up to 0,85 0,9.

44 Torque of a Salient Pole Synchronous Machine

45 Stand-alone Alternator No-load characteristics U 0 I = 0, n = konst. I f

46 Stand-alone Alternator External characteristics I f = const. cos φ = const. n = const.

47 Synchronization of Generator (Connecting to the Grid) Same phase sequences of generator and grid Same frequency Same voltages Same phase in the instant of connection U 0 f = p. n 1 60 I f

48 Dimensions of Turbomachines Power Bearing span Rotor diameter (MW) (mm) (mm)

49 Excitation Systems of Synchronous Machines Excitation from rotary converters 1 synchronous machine 2 dynamo 3 auxiliary driver

50 Excitation Systems of Synchronous Machines Excitation from alternate driver 4 system for excitation current control

51 Excitation Systems of Synchronous Machines Excitation with carried rectifier (brushless excitation system)

52 Excitation Systems of Synchronous Machines Excitation from a system with a rotary transformer 4 AC voltage controller

53 Excitation Systems of Synchronous Machines Excitation from a static converter

54 Excitation Systems of Synchronous Machines Excitation with permanent magnets

55 Small synchronous machines Reluctance motor (without excitation winding) Clutches generator (Klauenpol maschine, drápkový generátor) Permanent magnet J S Pole extenders

56 Brushless DC Motor Commonly called: EC motor, BLDC motor - Properties similar to DC motor - Construction similar to a synchronous machine (3-phase stator winding, rotating manets) - Feeding according to rotor position Sources from company UZIMEX, that supplies motors of the company MAXON.

57 Components of a BLDC drive Power supply Mechanical part Load Electrical part Commutation and control Hall probes encoder commands Electronic part

58 Course of commutation

59 Course of commutation Coil 15 Coil Coil

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64 Low speed motor with outer rotor - 40 poles on rotor - 36 poles on stator W - 36 V min -1

65 High speed with planet gear to low speed Rotor inside has 4 poles

66 Friction planet gearbox

67 Planet gearbox with cogs (teeth) P N =450 W