Transcript Chapter 7 - AC Machine Fundamentals

BASIC ELECTRICAL TECHNOLOGY
DET 211/3
Chapter 7
AC Machines
Fundamentals &
Synchronous Machines
Synchronous Machines
(Introduction)
A synchronous machine rotates at a constant speed in
the steady state.
Unlike induction machine, the rotating air gap field and
the rotor in the synchronous machine at the same
speed, called the synchronous speed.
Synchronous machine can operate as both a
generator and a motor.
Synchronous machines are
generators of electrical power.
used
primarily
as
Synchronous machine can be used to compensate the
reactive power in the power system.
Synchronous Machines
(Introduction)
Synchronous Generator
Synchronous Motor
Synchronous Machines
(Introduction)
A synchronous motor can draw either lagging or
leading reactive current from the ac supply.
A synchronous machine is a double excited machine.
Its rotor poles are excited by a dc current and its stator
windings (armature winding) are connected to the ac
supply.
The air gap flux is the resultant of the fluxes due to
both rotor current and stator current.
Construction of Three Phase Synchronous Machines
The stator winding of the three phase synchronous
machines has a three phase distributed winding similar
to that of the three phase induction machine.
Unlike the dc machine, the stator winding, which is
connected to ac supply system is called the armature
winding.
The rotor winding has a winding called the field
winding, which is carries direct current. The field
winding on the rotating structure is fed from an external
dc source through slip rings and brushes.
Construction of Three Phase Synchronous Machines
Two common approaches to supplying the dc supply
to the rotor winding (field winding):
• Supply the power from an external dc source to the
rotor by means of slip rings and brushes.
• Supply the dc power from a special power source
mounted directly on the shaft of the generator.
On the larger synchronous machine, brushless
exciter are used to supply the dc field current to the
machines. A brushless exciter is a small ac
generator with its field circuit mounted on the stator
and its armature circuit mounted on the rotor shaft.
Construction of Three Phase Synchronous Machines (A
Brushless Exciter Circuit)
A small three phase current is rectified and used to supply the
field circuit of the exciter, which is located on the stator. The
output of the armature of the exciter (on the rotor) is then
rectified and used to supply the field current of the main
winding.
Construction of Three Phase Synchronous Machines
Synchronous machines can be divided into two groups:
1. High speed machines with cylindrical (or non salient
pole) rotor.
2. Low speed machines with salient pole rotors.
The cylindrical or non salient pole rotor has one
distributed winding and essentially uniform air gap while
salient pole rotors have concentrated winding on the
poles and a uniform air gap.
Round Rotor Generator
Generator
Exciter
View of a two-pole round rotor generator and exciter
Round Rotor Generator
Cross-section of a large turbo generator. (Courtesy
Westinghouse)
Round Rotor Generator
Metal frame
Laminated iron
core with slots
Insulated copper
bars are placed in
the slots to form
the three-phase
winding
Details of a generator stator
Round Rotor Generator
Rotor block of a large generator. (Courtesy Westinghouse)
Round Rotor Generator
Generator rotor with conductors placed in the slots
Round Rotor Generator
Steel
retaining
ring
Shaft
Shaft
Wedges
DCcurrent
current
DC
terminals
terminals
Large generator rotor completely assembled. (Courtesy
Westinghouse)
Salient pole generator
Stator of a large salient pole hydro generator; inset shows
the insulated conductors and spacers
Salient pole generator
Large hydro generator rotor with view of the vertical poles
Salient pole generator
Slip
rings
Pole
Fan
DC excitation
winding
Rotor of a four-pole salient pole generator
Synchronous generator
Mechanism of ac voltage generation
• Rotor flux is produced by a dc field current If.
• Rotor is driven by a prime mover, producing rotating
field in the air gap.
• A voltage is induced in the stator winding due to
the rotating field.
Induced voltage is sinusoidal due to the sinusoidal
distributed flux density in the air gap.
Synchronous generator
(The Speed of Rotation of a Synchronous Generator)
Synchronous generators are by definition synchronous,
meaning that the electrical frequency produced is
locked in or synchronized with the mechanical rate of
rotation of the generator.
The rate of rotation of the magnetic fields in the
machined is related to the stator electrical frequency is
nm P
fe 
120
Where fe = electrical frequency (Hz)
nm = mechanical speed of the magnetic field, rpm (=
speed of rotor)
P = number of poles
The Internal Generated Voltage of a Synchronous
Generator
The magnitude of the voltage induced in a stator phase
is
EA  2NC f
or
EA  K
Where
NC = no of conductors at an angle of 00
NC
K
2
The Equivalent Circuit of a Synchronous Generator
The voltage EA is the internal voltage generated produced in
one phase of a synchronous generator. However, this
voltage EA is not usually the voltage that appears at the
terminals of the generator.
There are many factors that cause the difference between
EA and VФ.
1. The distortion of the air gap magnetic filed by the
current flowing in the stator called armature reaction.
2. The self inductance of the armature coils.
3. The resistance of the armature coils.
4. The effect of salient pole rotor shapes.
The Development of a Model for Armature Reaction
Figure (a) shows a two pole rotor spinning inside a three
phase stator. A rotating magnetic field produces the internal
generated voltage EA.
There is no load connected to the stator. The rotor
magnetic field BR produces an internal generated voltage
EA whose peak value coincides with the direction of BR.
With no load on the generator, there is no armature current
flow, and EA will be equal to the phase voltage VФ.
The Development of a Model for Armature Reaction
Figure (b): The resulting voltage produces a lagging
current flow when connected to a lagging load
The Development of a Model for Armature Reaction
Figure (c): The stator current produces its own magnetic
filed BS, which produces its own voltage Estat in the stator
windings of the machine
The current flowing in the stator in the stator windings
produces a magnetic field of its own. This stator magnetic
filed is called BS and its direction is given by the right hand
rule. The stator magnetic filed Bs produces a voltage of its
own in the stator, and this voltage is called Estat.
The Development of a Model for Armature Reaction
Figure (d): The field BS adds to BR, distorting it into Bnet. The voltage
Estat adds to EA, producing VФ at the output of the phase.
With two voltages present in the stator windings, the total
voltage in a phase is just the sum of the internal generated
EA and the armature reaction voltage Estat:
V  E A  Estat
The Development of a Model for Armature Reaction
The net magnetic field Bnet is just the sum of the rotor
and the stator magnetic fields:
Bnet  BR  BS
Since the angles of EA and BR are the same and the
angles of Estat and Bs, are the same, the resulting
magnetic field Bnet will coincide with the net voltage VФ.
We know, the voltage Estat is directly proportional to the
current IA. If X is a constant of proportionality, then the
armature reaction voltage can be expressed as:
Estat   jXI A
The Development of a Model for Armature Reaction
The voltage on a phase is
V  E A  jXI A
The Development of a Model for Armature Reaction
In addition to the effects of armature reaction, the stator
coils have a self inductance and a resistance. If the
stator self inductance is called LA (and its corresponding
reactance is called XA) while the stator resistance is
called RA, then the total difference between EA and VФ is
given by
V  E A  jXI A  jX A I A  RA I A
Combine the armature reaction effects and the self
inductance in the machine
XS  X  X A
The Development of a Model for Armature Reaction
So
V  E A  jX S I A  RA I A
The Development of a Model for Armature Reaction
If the machine is Wye (Y ) connection
VT  3V
If the machine is Delta (Δ) connection
VT  V
The Per Phase Equivalent Circuit of a Synchronous
Generator
The Phasor Diagram of A Synchronous Generator
The Phasor Diagram of A Synchronous Generator at
Unity Power Factor
The Phasor Diagram of A Synchronous Generator
(a) Lagging (b) Leading
Power and Torque in Synchronous Generator
Input mechanical power
Pin   appm
Power converted from mechanical to electrical is
Pconv  ind m  3E A I A cos 
Where γ is the angle between EA and IA
Power and Torque in Synchronous Generator
The difference between the input power to the
generator and the power converted in generator is
mechanical (friction & windage), core and stray losses.
Real output power is
Pout  3VT I L cos 
(Line quantities)
Pout  3V I A cos 
(Phase quantities)
Reactive output power is
Qout  3VT I L sin 
(Line quantities)
Qout  3V I A sin 
(Phase quantities)
Power and Torque in Synchronous Generator
If the armature resistance RA is ignored (since Xs >> RA)
Power and Torque in Synchronous Generator
Since the resistances are assumed to be zero
Pconv  Pout  P 
3V E A sin 
Xs
Where torque angle, δ is the angle between VФ and EA
The power of the generator is maximum when δ = 900
Pmax 
3V E A
Xs
The maximum power indicated by this equation
called static stability limit of the generator.
The induced torque is
ind 
3V E A sin 
m X s
EXAMPLE 1
A 25kVA, 230V, three phase, 4 pole, 60Hz, wye connected synchronous
generator has a synchronous reactances of 1.5Ω/phase and negligible
stator resistance. The generator is connected to an infinite bus (of
constant voltage magnitude and constant frequency) at 230V and 60Hz.
a) Determine the excitation voltage, EA when the machine is
delivering rated kVA at 0.8 pf lagging.
b) The field excitation current If increased by 20% without changing
the power input from the prime mover. Find the stator current IA,
power factor, and reactive power Q supplied by the machine.
c) With the field excitation current If as in part (a), the input power from
the prime mover is increased very slowly. What is the steady state
limit? Determine stator current IA, power factor, and reactive power
Q.
Measuring synchronous generator model parameter
The behavior of a real synchronous generator is determine by
• The relationship between field current and flux (and therefore between
field current and EA)
• The synchronous reactance, Xs
• The armature resistance, RA
The quantities above are determined by open circuit test and short
circuit test
Open Circuit Test
First step:
• To perform this test, the generator is turned at the rated speed.
• The terminals are disconnected from all loads.
• The field current is set to zero.
Second step:
The field current is gradually increased in steps, and the terminal
voltage is measured at each step along the way with the terminals
open. (IA = 0, so EA is equal to VФ)
Plot EA or VA versus IF from this information
Open Circuit Test
Air gap line
The curve almost perfectly linear, until
some saturation is observed at high field
currents.
The unsaturated iron in the frame of the
synchronous machine has a relunctance
several thousand times lower than the air
gap reluctance, so at the first almost all the
magnetomotive force is across the air gap,
and the resulting flux increase is linear.
When the iron finally saturates, the
reluctance
of
the
iron
increases
This plot called open circuit characteristics dramatically, and the flux increases much
more slowly with an increase in
magnetomotive forces. The linear portion
of an OCC is called the air gap line of
characteristic.
Short Circuit Test
Adjust the field current to zero again and short circuit terminals of the
generator through a set of ammeters. Then the armature current IA or the
line current IL is measured as the field increased.
Short Circuit Test
When the terminals are short circuited, the armature currents IA is
EA
IA 
RA  jX S
Its magnitude is
IA 
EA
R A2  jX S2
Refer to Figure (b), BS almost cancels BR, the net magnetic field Bnet is
very small, so the machine is unsaturated and the SCC is linear.
Short Circuit Test
The internal machine impedance is
Z S ( unsat )  R  X
2
A
2
S ( unsat )
EA

IA
If XS >> RA, this equation reduces to
E A V ,OC
XS 

IA
IA
Therefore, an approximate method for determining the synchronous
reactances at a given field current is
1) Get the internal generated voltage EA from the OCC at the field
changing.
2) Get the short circuit current flow IA,SC at that field current from SCC.
3) Find XS by equation above.
The saturated synchronous reactance may also found by taking the
rated terminal voltage (line to line) measured on the OCC and dividing
by the current read from SCC corresponding to the field current that
produces at rated terminal voltage.
Z S ( sat )  RA  jX S ( sat )
E A,rated E A


I A ,SC
I ba