Synchronous Machines - O nás | Katedra elektrických...

Synchronous Machines

If

Synchronous Machines

Stator: similar to induction (asynchronous) machine ( 3 phase windings that forms a rotational circular magnetic field )

Rotor: If DC. + slip rings → circular field Φf ~ If Rotor design: a) salient pole

b) cylindrical (round / non salient pole) rotor (turbo)

If

Φf n1 Φf n1

If

n1 = 60.f1 / p

damper (run-up) winding

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: fIII ˆˆˆ +′=µ

In stator: UifU

- Supply (power grid) voltage - Voltage induced by excitation current If

ifUU ˆˆ − creates current , that flows through resistance and longitudinal synchronous reactance Xd .

I

σ1XXX add +=

Φad main flux,

(interacts with rotor winding)

Φ1σ leakage (stray) flux

Xad - longitudinal reactance of back-electromotive force of the rotor

Similarly, the lateral synchronous reactance Xq can be derived.

Synchronous Alternator with a Cylindrical Rotor

Assumptions: a) Air gap is constant along the whole circumference

.. konstRkonst m == δδb) Stator and rotor electromotive forces are sinusoidal distributed in space

ατπ

pm FF sinmax=

c) Angular velocity of rotor rotation is equal to

.2 konstf == πωd) Permeability

µ = konst. Φ ~ Fm

Voltage Equations

iUIjXIRU ˆˆˆˆ ++= σ

fff IRU =

If equation Ui=4,44 f1ΦµN1kv1 ~ Φµ ~ Fµ

are valid.

af FFF ˆˆˆ +=µ

ˆˆ ˆ Φf aµΦ = Φ +

afi UUU ˆˆˆ +=

is valid, then also equations

For cylindrical rotor: Xd = Xq = Xs = Xad + X1σ

Voltage equation has following form:

ifd UIjXIRU ˆˆˆˆ ++=or

ifda UIjXIjXIRU ˆˆˆˆˆ +++= σ

Phasor Diagram of a Turboalternator

→ M

→ n

n1

Asynchronous Run-up of a Synchronous Motor

A

A’ n’

n' < n1

Synchronization: S of rotor tightens to J of stator

Permanent coupling betweenΦf a Φa :

n = n1 = konst = f (f )

→ M

→ n

n1 A

A' n'

A'' n''

n'' < < n1

No synchronization

Asynchronous run-up of synchronous motor

S

J

n1 Φa

J

S

n Φf

n = n1

Increase of load torque Mp

Loading of a Synchronous Motor

S

J

n1 Φa

Rotor field is delayed behind the stator field of torque angle δ.

δ n = n1

Loading of a Synchronous Motor Increase of load torque Mp

S

J

n1 Φa

n = n1


S

J

n1 Φa

J S

n Φf

n = n1


S

J

n1 Φa

J

S

n Φf

Increase of driving torque Mp

n = n1

Loading of a Synchronous Generator - Alternator

S

J

n1 Φa

n = n1

Loading of a Synchronous Generator - Alternator Increase of driving torque Mp

S

J

n1 Φa

J S

n Φ

f n = n1

Loading of a Synchronous Generator - Alternator Increase of driving torque Mp

Basic Equivalent Circuit of a Turbomachine

~

Xd I

U Uif

Xd - synchronous reactance (respests existence of stray flux and flux generated by current I )

R1 = 0 - negligible compared to Xd

IjXUU difˆˆˆ +=

Loading at a Constant Power while Connected to a Strong Grid

U φ

I

Uif

jXd.Iq

jXdIw

Iq

δ

Iw = I cosφ ~ M

pU

Iw pI

Important:

XdIw = Uif sinδ

~

Xd I

U Uif


U

I=Iw

Uif

jXdIw

δ

~

Xd I

U Uif


U

φ

Uif

jXd.Iq jXdIw

Iq

Iw δ I

Advantages of a synchronous motor: n = n1 = konst.

Change of cos φ

~

Xd I

U Uif

U Uif

jXd.Iq jXd.Iw

Iq δ

Iw I

φ

Iw

U Uif

jXd.Iq jXdIw

Iq

δ

~

Xd I

U Uif

Phasor Diagram of an Overexcited Turbomachine

motor generator

I

Regulation of Real and Reactive Power


All currents are recalculated to stator

V-curve of a synchronous machine


Loading at a Constant Excitation while Connected to a Strong Grid

Iμ 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

Pm = m U I cosφ = M ω1m

Xd Iw = Uif sinδ δ

ωsin

1 d

if

m XUUmM =

Static stability a overload capacity

0>δd

dPStable run:

δδ

cos11

d

if

XUU

mddP

=

Synchronizing factor:

Determines ability of the machine to stay in synchronism. Maximum at δ = 0.


Synchronizing power: δδ∆

ddP

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

Static stability and overload capacity

0>δd

dPStable run:

δδ

cos11

d

if

XUU

mddP

=



Power overload capacity:

NNM M

MP

Pp maxmax ==

Motor pM ≥ 1,5 Alternator pM ≥ 1,25

Synchronizing power: δδ∆

ddP

Static stability and overload capacity

0>δd

dPStable run:

δδ

cos11

d

if

XUU

mddP

=



Power (Torque) Overload Capacity

NNM M

MP

Pp maxmax == Motor pM ≥ 1,5 Alternator pM ≥ 1,25

NN

kN

NN

d

if

m

NN

dm

if

M II

IXU

mUIX

mUU

pϕϕ

ωϕ

ωcoscoscos

1

1 ===

IkN is steady short-circuit current that corresponds to an excitation current IfN

NNf

fNk

NfkN

fNM I

Ii

II

pϕϕ coscos 0

==

Overload capacity is bigger when short-circuit ratio ik is higher and cosφN is lower

≈≈d

k Xi 1

bigger air gap ≈ higher excitation power ≈ larger dimensions

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 cosφN = 0,8 big ones up to 0,85 ÷ 0,9.

Power (Torque) Overload Capacity

Torque of a Salient Pole Synchronous Machine

If

U0

No-load characteristics

I = 0, n = konst.

Stand-alone Alternator

External characteristics

If = const.

cos φ = const.

n = const.

Stand-alone Alternator

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

If

U0

60. 1npf =

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 from alternate driver

4 – system for excitation current control


Excitation with carried rectifier

(brushless excitation system)


Excitation from a system with a rotary transformer

4 – AC voltage controller


Excitation from a static converter


Excitation with permanent magnets


S J Pole extenders

Permanent magnet

Small synchronous machines

Reluctance motor (without excitation winding)

Clutches generator (Klauenpol maschine, drápkový generátor)

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.

Load

Commutation and control

Power supply

Electrical part

Electronic part

Mechanical part

commands

Hall probes encoder

Components of a BLDC drive

1 2

5

15°

6 4

3

Course of commutation

15°

Course of commutation Coil

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) PN=450 W

Synchronous Machines - O nás | Katedra elektrických...

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