synchronous machines - o nás | katedra elektrických...
TRANSCRIPT
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
Loading of a Synchronous Motor Increase of load torque Mp
S
J
n1 Φa
J S
n Φf
n = n1
Loading of a Synchronous Motor Increase of load torque Mp
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
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
Loading at a Constant Power while Connected to a Strong Grid
U
I=Iw
Uif
jXdIw
δ
~
Xd I
U Uif
Loading at a Constant Power while Connected to a Strong Grid
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
Loading at a Constant Power while Connected to a Strong Grid
All currents are recalculated to stator
V-curve of a synchronous machine
Loading at a Constant Power while Connected to a Strong Grid
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.
Loading at a Constant Excitation while Connected to a Strong Grid
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
=
Synchronizing factor:
Loading at a Constant Excitation while Connected to a Strong Grid
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
=
Synchronizing factor:
Loading at a Constant Excitation while Connected to a Strong Grid
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 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
Excitation Systems of Synchronous Machines
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