Synchronous Machine

Synchronous Machines - Structure

Synchronous Machines - Structure

Non-salient pole generator

• high speed (2 - 4 poles)• large power (100 - 400 MVA)• steam and nuclear power plants

Salient pole generator

• small and mid-size power ( 0 - 100 MVA)• small motors for electrical clocks and other domesticdevices

• mid size generators foremergency power supply

• mid size motors for pumps and ship propulsion

• large size generators in hydro-electric power plants

• rotates at constant speed.

• primary energy conversion devices of the word’s electricpower system.

• both generator and motoroperations

• can draw either a lagging or a leading reactive current from the supply system.

Synchronous Generators – No-load

• excitation voltages

120 fnp

=120npf = wf f4.44E f NKΦ= f fE nΦ∝

• open circuit characteristics• magnetization characteristics

• frequency depends on the speed

Synchronous Generators - loaded

• the stator currents will establish a rotating field in the air-gap• armature reaction flux Φa• resultant air-gap flux

r afΦ Φ Φ= +

Synchronous Machines – The Infinite Bus

Synchronous Machines – Paralleling with The Infinite Bus

• synchronizing lamps

• same • voltage• frequency • phase sequence• phase

1. Same f and phase sequence

2. Same V and phase sequence

1. Same V and f

Synchronous Motor - Starting

• variable-frequency supply • start as an induction motor

• high inertia of the rotor prohibits direct connection into supply net

Synchronous Machines – Per Phase Equivalent Circuit Model

r ar fE E E= +

a ar rfE I jX E= +

r arf ( ) ( )f aI IΦ Φ Φ= +

a ar alΦ Φ Φ= +

• armature flux, armature reaction flux, armature leakage flux

•magnetizing reactance Xar , (reactance of armature)

• synchronous reactance Xs =Xar + Xal• synchronous impedance Zs =Ra + jXs

ar ar aE jX I− =

Synchronous Machines – Equivalent Circuit Model

ff

s

EIX

′ = arf f

s

XI nIX

′ = re

se

23NnN

=

• Norton equivalent circuit

Equivalent Circuit Model – Determination of the Synchronous Reactance

• open circuit test• synchronous speed• stator open-circuited• measure Vt(If) • open-circuit characteristic• air-gap line

• short circuit test• synchronous speed• stator short-circuited• measure Ia(If)• short-circuit characteristic• straight line• flux remains at low level

a sR X• Ia lags the Ef by almost 90 because

Equivalent Circuit Model – Determination of the Synchronous Reactance

daas(unsat) s(unsat)

ba

EZ R jXI

= = + das(unsat)

ba

EXI

• unsaturated value from the air-gap line

Equivalent Circuit Model – Determination of the Synchronous Reactance – Saturated

r t a a tal( )E V I R jX V= + + ≈

caas(sat) s(sat)

ba

EZ R jXI

= = +

cas(sat)

ba

EXI

• at infinite bus operation the saturation level is defined by terminal voltage• operation point c• if the field current is changed the excitation voltage will change along

modified air-gap line OC

Synchronous Machines – Phasor Diagram

t a a a sf fE V I R I jX E δ= + + =

t a a a sfV E I R I jX= + +

• generator• power angle positive

• motor• power angle negative

• terminal voltage taken as the reference vector

t a a a sf

f

0E V I R I jXE δ

= ° − −= −

convention: generating current flows out of the machine

Synchronous Machines – Power and Torque

t t 0V V= °

f fE E δ=

s a s s sZ R jX Z θ= + =

*t aS V I=

δθ θ

θ δ θ

−⎛ ⎞= = −⎜ ⎟⎝ ⎠

−= −

− −

= − −

* **f t* tf

a * *s s s

tf

s s s s

tfs s

s s

0

E V VEIZ Z Z

VEZ Z

VEZ Z convention: lagging reactive power positive


2t tf

s ss s

V E VS

Z Zθ δ θ= − −

2t tf

s ss s

cos( ) cosV E V

PZ Z

θ δ θ= − −

2t tf

s ss s

sin( ) sinV E V

QZ Z

θ δ θ= − −

• real power

• reactive power

• complex power


t f3 max

s

3sin sin

V EP P

Xφ δ δ= =

2t tf

3s s

3 3cos

V E VQ

X Xφ δ= −

• Ra neglected

φ δ δω ω

= = = ⋅3 t fmax

syn syn s

3 sin sin N mP V E

T TX

• real power

• reactive power

• torque

Synchronous Machines – Complex Power Locus

t f3 max

s

3sin sin

V EP P

Xφ δ δ= =2

t tf3

s s

3 3cos

V E VQ

X Xφ δ= −

Synchronous Machines – Capability Curves

• armature heating, length of OM• field heating, length of YM• steady-state stability δ

Synchronous Machines – Power Factor Control

t a3 cosP V I φ=

s t fajX I V E= −

t f

s3 sinV EPX

δ=

• machine connected to an infinite bus

a cos = const.I φ

• for constant power operation

• also

• reactive current can be controlled by field current

f sin constE δ =

Synchronous Machines – Independent Generators

t a sf

sc s a s

s sc a( )

V E I XI X I XX I I

= −= −= −

s scfa 2 2 2 2

L s L s

E X IIR X R X

= =+ +

t a LV I R=

2 2t a

2 2s sc sc

1( )V IX I I

+ =

• purely inductive load (Isc is short-circuit current)

• purely resistive load

• quarter ellipse

• control curves• constant terminal voltage

Salient Pole Synchronous Machines• the field mmf and flux are along the d-axis

• stator current is in phase with the excitation voltage

• armature mmf and flux are along the q-axis

• stator current is lagging the excitation voltage by 90 degrees

• armature mmf and flux act along the d-axis, directly opposing the field

• the same magnitude of the armature mmf produces more flux in d-direction than that in q-direction

• magnetizing reactance is not unique in a salient pole machine

Salient Pole Synchronous Machines

d ad alX X X= +

q aq alX X X= +

• the armature quantities can be resolved into two components – one acting along the d-axis (Fd, Id), and the other acting along the q-axis (Fq, Iq),

• these components produce fluxes along the respective axes (Φad, Φaq),

• d-axis armature reactance Xd• q-axis armature reactance Xq• leakage reactance Xal

• synchronous reactances

Salient Pole Synchronous Machines – Phasor Diagrams

t a a q qf d dE V I R I jX I jX= + + + a qdI I I= +

• the component currents (Id, Iq), produce component voltage drops (jIdXd, jIqXq)

• generator phasor diagram (Ia lagging)

• ψ internal power factor angle• φ terminal power factor angle• δ torque angle

• Ra neglected

Salient Pole Synchronous Machines – Phasor Diagrams

t q qf d dV E I jX I jX= + +

ψ φ δ= ±

a ad sin sin( )I I Iψ φ δ= = ±

q a acos cos( )I I Iψ φ δ= = ±

a q

t a q

costan

sinI X

V I Xφ

δφ

=±

tf d dcosE V I Xδ= ±

• motoring phasor diagram (Ia lagging)• ψ internal power factor angle• φ terminal power factor angle• δ torque angle

Power Transfer

*t a

*t q d

t q d

( )

( )

S V I

V I j I

V I j I

δ

δ

=

= − −

= − +

tfd

d

cosE VI

Xδ−

=

tq

q

sinVI

Xδ

=

Power Transfer

2 2t t tf

q d dsin 90 cos 90

V V E VS P jQ

X X Xδ δ δ δ δ= − + ° − − ° − = +

2t qdt f

rfqd d

( )sin sin 2

2V X XV E

P P PX X X

δ δ−

= + = +

2 22t f

tqd d

sin coscosV E

Q VX X X

δ δδ= − +

t f

dsin

V EP

Xδ=

2t tf

d dcos

V E VQ

X Xδ= −

• if Xd = Xq, then

Power Transfer - Torque

2t qdt f

rfqd d

( )sin sin 2

2V X XV E

P P PX X X

δ δ−

= + = +

Determination of Xd and Xq

td

min 2VX

i=

tq

max 2VX

i=

• slip test• rotor is driven at a small slip• field winding open-circuited• stator is connected to a balanced three phase supply• stator encounters varying reluctance path• amplitude of the stator current varies

Speed Control of Synchronous Motors

• open-loop frequency control


m4 fpπω =

t fm

s

3 sinV EP TX

ω δ= =

s s2X fLπ=

1fE K f=

t sinVT Kf

δ=

• frequency control

• field current kept constant

• voltage is changed with the frequency


• self-controlled synchronous motor• rotor position information is

used to decrease the stator frequency

• open-loop / closed-loop control

Applications

• ac generator

• constant speed operation• high efficiency

• motor-generator set, air compressor, centrifugal pump, blower, crusher, mill• power factor control, synchronous reactor, -condenser

Synchronous Machine

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