Synchronous Machines - Structure
Nov 22, 2014
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
Synchronous Machines – Power and Torque
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
Synchronous Machines – Power and Torque
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
Speed Control of Synchronous Motors
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
Speed Control of Synchronous Motors
• 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