Synchronous Machines

Synchronous Machines

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)

ČKD - 25000 kw, 10 kv, 2p=2 2600 to 3900 min -1

Rotor of a Turbomotor

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

ČKD - 6300 kw, 6 kv, 2p=4 Synchronous Motor

ČKD - 14000 kw, 6 kv, 2p=4

ČKD - 3250 kva, 11 kv, 2p=8 Synchronous Generator

ČKD 2500 kw 10 kv, 2p=40 synchr.

Rotor of a Turbomachine Cross Section

Detail of a Nonmagnetic Armature of a Turbomachine

Rotor of a Slow Speed Machine Magnet wheel Hub Shaft

Magnetic Flux within a Salient Pole Machine

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.

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

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

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

Phasor Diagram of a Turboalternator

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

Regulation of Real and Reactive Power

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

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

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.

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

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.

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

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

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

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.

Torque of a Salient Pole Synchronous Machine

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

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

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

Dimensions of Turbomachines Power Bearing span Rotor diameter (MW) (mm) (mm) 500 10300 1125 800 11780 1200 1200 13000 1250

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

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

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

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

Excitation Systems of Synchronous Machines Excitation from a static converter

Excitation Systems of Synchronous Machines Excitation with permanent magnets

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

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.

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

Course of commutation 1 2 15 3 6 5 4

Course of commutation Coil 15 Coil Coil

Low speed motor with outer rotor - 40 poles on rotor - 36 poles on stator - 300 W - 36 V - 230 min -1

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

Friction planet gearbox

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