6 Lecture Synchronous Machines3
Transcript of 6 Lecture Synchronous Machines3
-
8/11/2019 6 Lecture Synchronous Machines3
1/48
Synchronous Machines
-
8/11/2019 6 Lecture Synchronous Machines3
2/48
-
8/11/2019 6 Lecture Synchronous Machines3
3/48
Constructional Features of Synchronous Machines
Basic parts of a synchronous generator:
Rotor - dc excited winding
Stator - 3-phase winding in which the ac emf is generated
Machine physical size and structure:
The severe electric and magnetic loadings in a synchronous
machine produce heat that must be properly dissipated
The manner in which the active parts of a synchronousmachine are cooled determines its overall physical size and
structure
-
8/11/2019 6 Lecture Synchronous Machines3
4/48
Various Types
Salient-pole synchronous machine
Cylindrical or round-rotor synchronous machine
-
8/11/2019 6 Lecture Synchronous Machines3
5/48
1. Most hydraulic turbines have to turn at low speeds
(between 50 and 300 r/min)2. A large number of poles are required on the rotor
Hydrogenerator
Turbine
Hydro (water)
D 10m
Non-uniform
air-gapN
S S
N
d-axis
q-axis
Salient-Pole Synchronous Generator
-
8/11/2019 6 Lecture Synchronous Machines3
6/48
Salient-Pole Synchronous Generator
Stator
-
8/11/2019 6 Lecture Synchronous Machines3
7/48
L 10 m
D 1mTurbine
Steam
Stator
Uniform air-gap
Stator winding
Rotor
Rotor winding
N
S
High speed
3600 r/min2-pole
1800 r/min4-pole
Direct-conductor cooling (usinghydrogen or water as coolant)
Rating up to 2000 MVA
Turbogenerator
d-axis
q-axis
Cylindrical-Rotor Synchronous Generator
-
8/11/2019 6 Lecture Synchronous Machines3
8/48
Cylindrical-Rotor Synchronous Generator
Stator
Cylindrical rotor
-
8/11/2019 6 Lecture Synchronous Machines3
9/48
Operation Principle
The rotor of the generator is driven by a prime-mover
A dc current is flowing in the rotor winding which
produces a rotating magnetic field within the machine
The rotating magnetic field induces a three-phasevoltage in the stator winding of the generator
-
8/11/2019 6 Lecture Synchronous Machines3
10/48
Electrical Frequency
Electrical frequency produced is locked or synchronized tothe mechanical speed of rotation of a synchronous
generator:
where fe= electrical frequency in Hz
P= number of poles
nm
= mechanical speed of the rotor, in r/min
120
Pn
f
m
e
-
8/11/2019 6 Lecture Synchronous Machines3
11/48
Generated Voltage
The generated voltage of a synchronous generator is given by
where = flux in the machine (function of IF)
w= angular speed
Kc= synchronous machine constant
Saturation characteristic (generated voltage vs field current) of
a synchronous generator.
wf KEA
IF
EA
-
8/11/2019 6 Lecture Synchronous Machines3
12/48
Voltage Regulation
A convenient way to compare the voltage behaviour of two
generators is by their voltage regulation (VR). The VR of asynchronous generator at a given load, power factor, and at rated
speed is defined as
%100
fl
flnl
V
VV
VR
Where Vflis the full-load terminal voltage, and Vnl(equal toEf)
is the no-load terminal voltage (internal voltage) at rated speed
when the load is removed without changing the field current.For lagging power factor (PF), VR is fairly positive, for unity
PF, VRis small positive and for leadingPF, VRis negative.
-
8/11/2019 6 Lecture Synchronous Machines3
13/48
Equivalent Circuit_1
o The internal voltage EA produced in a machine is not usually
the voltage that appears at the terminals of the generator.
o The only time EA is same as the output voltage of a phase is
when there is no armature current flowing in the machine.
o There are a number of factors that cause the difference between
EAand Vf:
The distortion of the air-gap magnetic field by the current flowing
in the stator, called the armature reaction
The self-inductance of the armature coils.
The resistance of the armature coils.
The effect of salient-pole rotor shapes.
-
8/11/2019 6 Lecture Synchronous Machines3
14/48
generator
motor
IA
IA
EA Eres Vf
jX jXl RA
++
+
Equivalent Circuit_2
Equivalent circuit of a cylindrical-rotor synchronous machine
-
8/11/2019 6 Lecture Synchronous Machines3
15/48
Phasor Diagram
Phasor diagram of a cylindrical-rotor synchronous generator,for the case of lagging power factor
Lagging PF: |Vf||EA| for underexcited condition
-
8/11/2019 6 Lecture Synchronous Machines3
16/48
Three-phase equivalent circuit of a cylindrical-rotor
synchronous machine
The voltages and currents of the three phases are 120oapart in angle,
but otherwise the three phases are identical.
+
IA1
EA1 jXs RA+
VL-L
VL-L=1.41Vf
Vf
-
8/11/2019 6 Lecture Synchronous Machines3
17/48
Determination of the parameters of the equivalent
circuit from test data
The equivalent circuit of a synchronous generator that has beenderived contains three quantities that must be determined in order
to completely describe the behaviour of a real synchronous
generator:
The saturation characteristic: relationship betweenIF
and f(and
therefore betweenIF andEA)
The synchronous reactance,Xs
The armature resistance,RA
The above three quantities could be determined by performing the
following three tests:
Open-circuit test
Short-circuit test
DC test
-
8/11/2019 6 Lecture Synchronous Machines3
18/48
Open-circuit test
The generator is turned at the rated speed
The terminals are disconnected from all loads, and the field currentis set to zero.
Then the field current is gradually increased in steps, and the
terminal voltage is measured at each step along the way.
It is thus possible to obtain an open-circuit characteristic of a
generator (EAor VfversusIF) from this information
+
Vdc
IF
Vt
-
8/11/2019 6 Lecture Synchronous Machines3
19/48
Short-circuit test
Adjust the field current to zero and short-circuit the terminals ofthe generator through a set of ammeters.
Record the armature currentIscas the field current is increased.
Such a plot is called short-circuit characteristic.
A
A+
Vdc
IF
Isc
-
8/11/2019 6 Lecture Synchronous Machines3
20/48
then
If the stator is Y-connected, the per phase stator resistance is
If the stator is delta-connected, the per phase stator resistance is
DC Test
The purpose of the DC test is to determineRA. A variable DC voltage
source is connected between two stator terminals. The DC source is adjusted to provide approximately rated stator current,
and the resistance between the two stator leads is determined from the
voltmeter and ammeter readings
DCDC
DC
VR
I
2
DC
A
R
R
DCA RR2
3
-
8/11/2019 6 Lecture Synchronous Machines3
21/48
Determination of Xs
For a particular field currentIFA, the internal voltageEA (=VA) could
be found from the occ and the short-circuit current flowIsc,Acouldbe found from the scc.
Then the synchronous reactanceXscould be obtained using
IFA
EAor Vt(V)Air-gap line
OCC Isc(A)
SCC
IF(A)
Vrated
VA Isc,B
Isc, A
IFB
scA
AAunsatsAunsats
I
EVXRZ
2,2
,
22,, Aunsatsunsats RZX
scA
oct
scA
Aunsats
I
V
I
EX
,
,
:RAis known from the DC test.
SinceXs,unsat>>RA,
-
8/11/2019 6 Lecture Synchronous Machines3
22/48
Xsunder saturated condition
IA
EA Vf=0
jXs RA
++
EAVf=0
jIAXs
IARA
IA
scB
Aratedsa tsAsa ts
I
EVXRZ
2,2
,
At V=
V
rated,
22
,, Asa tssa ts RZX : R
Ais known from the DC test.
Equivalent circuit and phasor diagram under SC condition
IFA
EAor Vf(V)Air-gap line
OCC Isc(A)
SCC
IF(A)
Vrated
VA Isc,B
Isc, A
IFB
-
8/11/2019 6 Lecture Synchronous Machines3
23/48
Short-circuit Ratio
Another parameter used to describe synchronous generators is the
short-circuit ratio (SCR). The SCR of a generator defined as theratio of thefield current required for the rated voltage at open
circuitto thefield current required for the rated armature current
at short circuit. SCRis just the reciprocal of the per unit value of
the saturated synchronous reactance calculated by
..1
_
_
_
upinX
I
ISCR
sats
IscratedF
VratedF
EA or Vf(V)Air-gap line
OCC
Isc(A)
SCC
IF(A)
Vrated
Isc,rated
IF_V
rated
IF_Isc rated
-
8/11/2019 6 Lecture Synchronous Machines3
24/48
Example 5-1 (pp.287-288)
A 200 kVA, 480-V, 60-Hz, 4-pole, Y-Connected synchronousgenerator with a rated field current of 5 A was tested and the
following data was taken.
a) from OC test terminal voltage = 540 V at rated field
current
b) from SC testline current = 300A at rated field currentc) from Dc testDC voltage of 10 V applied to two terminals,
a current of 25 A was measured.
1. Calculate the speed of rotation in r/min
2. Calculate the generated emf and saturated equivalent circuitparameters (armature resistance and synchronous reactance)
-
8/11/2019 6 Lecture Synchronous Machines3
25/48
Solution to Example 11.
fe= electrical frequency = Pnm/120
fe= 60Hz
P = number of poles = 4
nm= mechanical speed of rotation in r/min.
So, speed of rotationnm =120fe/ P
= (120 x 60)/4 = 1800 r/min
2. In open-circuit test,IA = 0andEA = VfEA= 540/1.732
= 311.8 V (as the machine is Y-connected)
In short-circuit test, terminals are shorted, Vf= 0
EA= IAZsorZs =EA/IA =311.8/300=1.04 ohm
From the DC test,RA=VDC/(2IDC)= 10/(2X25) = 0.2 ohm
Synchronous reactance2,
2, sa tsAsa ts XRZ
02.12.004.1
2222
,, Asa tssa ts RZX
IA
EA Vf
j1.02 0.2
+
+
-
8/11/2019 6 Lecture Synchronous Machines3
26/48
Parallel operation of synchronous generators
There are several major advantages to operate generators inparallel:
Several generators can supply a bigger load than one machineby itself.
Having many generators increases the reliability of the powersystem.
It allows one or more generators to be removed for shutdownor preventive maintenance.
S h i i
-
8/11/2019 6 Lecture Synchronous Machines3
27/48
Before connecting a generator in parallel with another
generator, it must be synchronized. A generator is said to be
synchronized when it meets all the following conditions:
The rms line voltages of the two generators must be
equal.
The two generators must have the samephase sequence.
Thephase anglesof the two aphases must be equal.
The oncoming generator frequency is equal to the
running system frequency.
Synchronization
Load
Generator 2
Generator 1
Switch
ab
c
a/
b/
c/
S h i ti
-
8/11/2019 6 Lecture Synchronous Machines3
28/48
Synchronization
LoadGenerator
Rest of the
power system
Generator
Xs1
EA1
Xs2
EA2
Xsn
EAn
Infinite bus
V,fare constant
Xs eq =0
G
-
8/11/2019 6 Lecture Synchronous Machines3
29/48
Concept of the infinite bus
When a synchronous generator is connected to a power system,
the power system is often so large that nothing the operator of the
generator does will have much of an effect on the power system.
An example of this situation is the connection of a single
generator to the Canadian power grid. Our Canadian power gridis so large that no reasonable action on the part of one generator
can cause an observable change in overall grid frequency. This
idea is idealized in the concept of an infinite bus.An infinite bus
is a power system so large that its voltage and frequency do not
vary regardless of how much real or reactive power is drawnfrom or supplied to it.
-
8/11/2019 6 Lecture Synchronous Machines3
30/48
Active and reactive power-angle characteristics
P>0: generator operation
P
-
8/11/2019 6 Lecture Synchronous Machines3
31/48
Active and reactive power-angle characteristics
The real and reactive power delivered by a synchronous
generator or consumed by a synchronous motor can be
expressed in terms of the terminal voltage Vt, generated voltage
EA, synchronous impedanceZs, and the power angle or torqueangle d.
Referring to Fig. 8, it is convenient to adopt a convention that
makes positive real powerPand positive reactive power Q
delivered by an overexcited generator.
The generator action corresponds to positive value of d, while
the motor action corresponds to negative value of d.
PmP
e
, Qe
Vt
-
8/11/2019 6 Lecture Synchronous Machines3
32/48
The complex power output of the generator in volt-amperes per phase is given by
*_
AIVjQPS f
where:
Vf=terminal voltage per phaseIA
* =complex conjugate of the armature current per phase
Taking the terminal voltage as reference
0
_
jVV ff
the excitation or the generated voltage,
dd sincos_
jEE AA
Active and reactive power-angle characteristics
PmP
e
, Qe
Vf
-
8/11/2019 6 Lecture Synchronous Machines3
33/48
Active and reactive power-angle characteristics
Pm Pe, Qe
Vt
and the armature current,
s
AA
s
AA
jX
jEVE
jX
VEI
dd ff sincos___
whereXsis the synchronous reactance per phase.
s
A
s
A
s
A
s
A
s
AAtA
X
VEVQ
X
EVP
X
VEVj
X
EV
jXjEVEVIVjQPS
2
2
*__
cos
&sin
cossin
sincos
ff
f
fff
ff
d
d
d
d
dd
-
8/11/2019 6 Lecture Synchronous Machines3
34/48
Active and reactive power-angle characteristics
PmP
e
, Qe
Vf
s
A
s
A
X
VEVQ
X
EVP
2cos&
sin fff dd
The above two equations for active and reactive powers holdgood for cylindrical-rotor synchronous machines for negligibleresistance
To obtain the total power for a three-phase generator, the aboveequations should be multiplied by 3 when the voltages are line-to-
neutral If the line-to-line magnitudes are used for the voltages, however,
these equations give the total three-phase power
-
8/11/2019 6 Lecture Synchronous Machines3
35/48
Steady-state power-angle or torque-angle characteristic of a
cylindrical-rotor synchronous machine (with negligible
armature resistance).
d
Real power or torque
generator
motor
pp/2
p/2
0
p
Pull-out torque
as a generator
Pull-out torque
as a motor
d
Steady state stability limit
-
8/11/2019 6 Lecture Synchronous Machines3
36/48
Steady-state stability limit
Total three-phase power: d f sin3
s
A
X
EVP
The above equation shows that the power produced by a synchronous
generator depends on the angle d between the Vf and EA. The maximum
power that the generator can supply occurs when d=90o.
s
A
X
EV
P
f
3
max
The maximum power indicated by this equation is calledsteady-state stability
limit of the generator. If we try to exceed this limit (such as by admitting
more steam to the turbine), the rotor will accelerate and lose synchronism
with the infinite bus. In practice, this condition is never reached because the
circuit breakers trip as soon as synchronism is lost. We have to resynchronize
the generator before it can again pick up the load. Normally, real generators
never even come close to the limit. Full-load torque angle of 15o to 20o are
more typical of real machines.
-
8/11/2019 6 Lecture Synchronous Machines3
37/48
Pull-out torque
The maximum torque orpull-out torqueper phase that a two-pole
round-rotor synchronous motor can develop is
p
w
602
maxmaxmax
sm n
PP
where ns
is the synchronous speed of the motor in rpm
P
d
P orQ
Q
Fig. Active and reactive power as a function of the internal angle
-
8/11/2019 6 Lecture Synchronous Machines3
38/48
Example 5-2 (pp.291-294)
A 480 V, 60 Hz, -connected, four pole synchronous generator has the OCCshown below. This generator has a synchronous reactance of 0.1 ohm andarmature resistance of 0.015 ohm. At full load, the machine supplies 1200 Aand 0.8 pf lagging. Under full-load conditions, the friction and windagelosses are 40 kW, and the core losses are 30 kW. Ignore field circuit losses.
a) What is the speed of rotation of the generator?
b) How much field current must be supplied to the generator to make theterminal voltage 480 V at no load?
c) If the generator is now connected to a load and the load draws 1200 A at 0.8pf lagging, how much field current will be required to keep the terminalvoltage equal to 480 V?
d) How much power is the generator now supplying? How much power issupplied to the generator by the prime-mover?
What is the machines overall efficiency?e) If the generators load were suddenly disconnected
from the line, what would happen to its terminal voltage?
0
100
200
300
400
500
600
0 2 4 6 8 10
-
8/11/2019 6 Lecture Synchronous Machines3
39/48
Problem 5-2 (p.338)
Solution to Problem 5 2 (p 338)
-
8/11/2019 6 Lecture Synchronous Machines3
40/48
Solution to Problem 5-2 (p.338)
-
8/11/2019 6 Lecture Synchronous Machines3
41/48
Solution to Problem 5-2 (p.338) Contd
-
8/11/2019 6 Lecture Synchronous Machines3
42/48
Synchronous Motors
A synchronous motor is the same physical machine as agenerator, except that the direction of real power flow isreversed
Synchronous motors are used to convert electric power tomechanical power
Most synchronous motors are rated between 150 kW (200hp) and 15 MW (20,000 hp) and turn at speed ranging from150 to 1800 r/min. Consequently, these machines are used in
heavy industry At the other end of the power spectrum, we find tiny single-
phase synchronous motors used in control devices andelectric clocks
P, Q
Vt
Motor
-
8/11/2019 6 Lecture Synchronous Machines3
43/48
Operation Principle
The field current of a synchronous motor produces a steady-
state magnetic fieldBR A three-phase set of voltages is applied to the stator windings of
the motor, which produces a three-phase current flow in the
windings. This three-phase set of currents in the armature
winding produces a uniform rotating magnetic field ofBs
Therefore, there are two magnetic fields present in the machine,
and the rotor field will tend to line up with the stator field, just
as two bar magnets will tend to line up if placed near each other.
Since the stator magnetic field is rotating, the rotor magnetic
field (and the rotor itself) will try to catch up
The larger the angle between the two magnetic fields (up to
certain maximum), the greater the torque on the rotor of the
machine
-
8/11/2019 6 Lecture Synchronous Machines3
44/48
Vector Diagram
The equivalent circuit of a synchronous motor is exactly same asthe equivalent circuit of a synchronous generator, except that the
reference direction ofIAis reversed.
The basic difference between motor and generator operation in
synchronous machines can be seen either in the magnetic fielddiagram or in the phasor diagram.
In a generator,EAlies ahead of Vf, andBRlies ahead ofBnet. In a
motor,EAlies behind Vf, andBRlies behindBnet.
In a motor the induced torque is in the direction of motion, and in a
generator the induced torque is a countertorque opposing the
direction of motion.
-
8/11/2019 6 Lecture Synchronous Machines3
45/48
Vector Diagram
d
IA
Vf
EA
jIAXs
d
IA
Vf
EA
jIAXs
d
Bs
Bnet
BR
wsync
Fig. The phasor diagram (leading PF: overexcited and |Vt||EA|).
-
8/11/2019 6 Lecture Synchronous Machines3
46/48
Application of Synchronous Motors
Synchronous motors are usually used in large sizes because in small sizes
they are costlier as compared with induction machines. The principaladvantages of using synchronous machine are as follows:
Power factor of synchronous machine can be controlled very easily
by controlling the field current.
It has very high operating efficiency and constant speed. For operating speed less than about 500 rpm and for high-power
requirements (above 600KW) synchronous motor is cheaper than
induction motor.
In view of these advantages, synchronous motors are preferred for driving
the loads requiring high power at low speed; e.g; reciprocating pumps and
compressor, crushers, rolling mills, pulp grinders etc.
Problem & Solution of 5 22 (p 343)
-
8/11/2019 6 Lecture Synchronous Machines3
47/48
Problem & Solution of 5-22 (p.343)
Problem & Solution of 5 22 (p 343)
-
8/11/2019 6 Lecture Synchronous Machines3
48/48
Problem & Solution of 5-22 (p.343)