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EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
Chapter 5
Synchronous Generators
(Alternators)
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5.1 Synchronous Generator
Construction
Types of Windings and Rotors
Type of windings:
Stator (armature) windings (sinusoidally distributed): three-phase
AC voltages are induced by the rotating magnetic field produced
by the rotor windings.
Rotor (field) windings: supplied by DC current by means of slip
rings and brushes, producing the rotating rotor magnetic field.
The permanent magnets can be used for small AC generator. The
rotor winding is rotated by prime mover.
Type of rotors:
Salient pole: 4-pole or more. Low speed.
Nonsalient (cylindrical) pole: 2- or 4-pole. High speed.
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Salient and Nonsalient Rotors
Salient pole: (non-uniform air-gap)
Nonsalient pole: (uniform air-gap)
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5.2 The Speed of Rotation of a
Synchronous Generator
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Synchronous Speed
Synchronous generators are by definition synchronous, meaning
that the (stator) electrical frequency produced is locked in or
synchronized with the mechanical rate of rotation of the
generator.
fe = nmP/120
…(4-34)
where fe = electrical frequency (Hz)
nm = mechanical speed of magnetic field or rotor speed (rpm)
P = number of poles
For example, to generate 50-Hz with 4-pole machine, the
synchronous generator must turn at 1500 rpm
nm = 120*50/4 = 1500 rpm (synchronous speed)
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5.3 The Internal Generated
Voltage of a Synchronous
Generator
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The Internal Generated Voltage
of a Synchronous Generator
From Chapter 4, the induced (internal generated) voltage in a
given stator phase
EA = √2 πNCφf
…(4-50)
In simpler form,
EA = Kφω
…(5-1)
where K = constant representing the construction of the machine.
Thus, the internal generated voltage, EA, is directly proportional to
1. Flux (without frequency change of EA): φ ∝ IF
2. Rotor speed (with frequency change of EA)
Plot of IF vs EA is called as magnetization curve or open-circuit
characteristic of the machine.
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The Internal Generated Voltage
of a Synchronous Generator
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5.4 The Equivalent Circuit of a
Synchronous Generator
Factors That Cause the
Difference Between EA and Vφ
EA = internal generated voltage of synchronous generator
Vφ = terminal voltage of synchronous generator
Factors that cause the difference between EA and Vφ.
1. Distortion of the air-gap magnetic field 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 effects of salient-pole rotor shapes. (relatively
minor, and ignored in this Chapter)
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Armature Reaction
The stator magnetic field produced by the stator current
distorts the original rotor magnetic field, changing the
resulting phase voltage. This effect is called “armature
reaction”. The armature reaction voltage is defined as
Estat.
Total terminal voltage in a phase,
Vφ = EA + Estat
…(5-4)
Net magnetic field Bnet, summing of rotor and stator
magnetic field,
Bnet = BR + Bs
…(5-5)
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Armature Reaction
Initially, the two-pole rotor spinning inside a three-phase stator.
- Now the generator is connected
to a lagging load.
- The peak current will occur at an
angle behind the peak voltage.
- Initially, there is no current load
connected to the stator.
- The rotor magnetic field BR
produces an internal generated
voltage EA, which peak value
coincides with the direction of BR.
- No armature reaction happens at
this time.
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Armature Reaction
- With two voltages present in the
stator windings, the total voltage in a
phase, Vφ is the sum of EA and Estat.
- The sum of the rotor and stator
magnetic fields, Bnet= BS + BR.
- The angle of the resulting magnetic
field Bnet will coincide with the net
voltage, Vφ.
- The stator current produces the stator
magnetic field, BS. The direction of BS is
given by the right-hand rule.
- Then, the Bs produces a voltage of its
own in the stator, called as Estat.
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Armature Reaction
From Figure 5-8d,
1. Estat lies at an angle of 90o behind the current IA.
2. Estat is directly proportional to the current IA.
Then, model the armature reaction voltage as
Estat = -jXIA
…(5-6)
Thus, this voltage can be modeled as an inductor in the
series with the internal generated voltage. The negative
sign appears because Estat lags IA 90o.
So, total terminal voltage in a phase becomes
Vφ = EA - jXIA
…(5-7)
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Self-Inductance and Stator
Resistance Voltages
In addition to the effects of armature reaction, the stator
coils have a self-inductance (LA) and a resistance (RA).
Finally, total terminal voltage in a phase becomes
Vφ = EA – jXIA – jXAIA – RAIA
…(5-9)
Traditionally, the reactances of armature reaction and selfinductance are combined into a single reactance, called
as “synchronous reactance” of the machine.
XS = X + XA
…(5-10)
Finally, total terminal voltage in a phase becomes
Vφ = EA – jXSIA – RAIA
…(5-11)
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The Equivalent Circuit of a
Synchronous Generator
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Three-phase Stator Windings
are Y- or ∆-connected
VT = √3 Vφ
IL = IA
…(5-12)
V T = Vφ
...(5-13)
IL = √3 IA
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Per-Phase Equivalent Circuit of
Synchronous Generator
The per-phase equivalent circuit is used to analyze when
1. Three-phases have the same magnitude of voltages
and currents.
2. The balanced loads (equal loads) are attached to threephases.
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Phasor Diagram of a Synchronous
Generator at Unity Power Factor
Induced voltage in a phase can be expressed as
EA = Vφ + jXSIA + RAIA
Unity power factor ⇒ Vφ and IA are in phase
(purely resistive load)
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5.5 The Phasor Diagram of a
Synchronous Generator
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The Phasor Diagram of a
Synchronous Generator
Phasor diagram is used to analyze the AC circuits with a
fixed frequency at steady-state time. It represents only
magnitude and angle for quantities (such as voltage,
current, etc).
EA = Vφ + jXSIA + RAIA
Vφ < EA
Vφ > EA
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5.6 Power and Torque in
Synchronous Generator
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Power Flow Diagram
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Powers in Synchronous
Generator
Input power:
Pin = τappωm
Internally converted power (from mechanical to electrical
form):
Pconv = τindωm
…(5-14)
= 3EAIAcos γ
…(5-15)
where γ is the angle between EA and IA.
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Powers in Synchronous
Generator
Output power:
Pout = √3 VTILcos θ
= 3VφIAcos θ
…(5-16)
…(5-17)
where θ is the angle between Vφ and IA.
Reactive output power:
Qout = √3 VTILsin θ
= 3VφIA sin θ
…(5-18)
…(5-19)
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Simplified Phasor Diagram
(RA = 0, since XS >> RA)
IAcos θ = [EA sin δ]/XS
Pout = 3VφIAcos θ …(5-17)
Pout = [3VφEAsin δ]/XS …(5-20)
In this case,
1. No copper losses of RA.
2. Pout = Pconv = [3VφEAsin δ]/XS
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Maximum Power in
Synchronous Generator
When δ = 90o, the output power is maximum
Pmax = [3VφEAsin 90o]/XS
Pmax = [3VφEA]/XS
…(5-21)
At the maximum power point is the static stability limit
of the generator. In practice, real generators never even
come close to that limit. Full-load torque angles of 15o20o are more typical of real machines.
If Vφ is assumed constant,
Pout ∝ IAcos θ
Qout ∝ IAsin θ
[or EA sin δ]
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Torque in Synchronous
Generator
From Chapter 4, the induced torque in this generator
τind = k (BR × BS)
τind = k (BR × Bnet)
…(4-58)
…(4-60)
Magnitude of induced torque,
τind = k BRBS sin α
…(4-52)
τind = k BRBnet sin δ
…(4-61)
where δ is angle between rotor and net magnetic fields
(so called torque angle).
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Torque in Synchronous
Generator
Since BR produces the voltage EA and
Bnet produces the voltage Vφ,
so the angle δ between BR and Bnet is the same as the
angle δ between EA and Vφ.
Because Pconv = τindωm , then
τind = Pconv/ωm
= [3VφEAsin δ]/[ωmXS]
for RA = 0
…(5-22)
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5.7 Measuring Synchronous
Generator Model Parameters
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Measuring Synchronous
Generator Model Parameters
Model parameters to be measured:
1. The relationship between field current and flux
(and therefore between the field current and EA)
2. The synchronous reactance, XS
3. The armature resistance, RA
There are two tests to extract these model parameters:
1. Open-circuit test
2. Short-circuit test
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Open-circuit Test
(find IF-EA curve)
To perform this test,
1. The generator is turned at the rated speed.
2. The generator terminals are disconnected from all
loads.
3. The field current is set to zero.
4. Then, the field current is gradually increased in steps.
5. The terminal voltage is measured at each step along
the way.
6. Plot of EA versus IF, so called open-circuit characteristic
(OCC) of a generator.
With terminals open, IA = 0, so EA is equal to Vφ.
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Open-circuit Test
(find IF-EA curve)
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Short-circuit Test (find XS)
To perform this test,
1. The generator is turned at the rated speed.
2. Adjust the field current to zero.
3. Short-circuit the terminals of the generator through a
set of ammeters.
4. Then, the armature current IA or the line current IL is
measured as the field current IF is increased.
5. Plot of IA versus IF, so called short-circuit characteristic
(SCC) of a generator.
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Short-circuit Test (find XS)
Only magnitude:
IA = EA/(RA + jXS)
…(5-23)
IA = EA/√(RA2 + XS2)
…(5-24)
ZS = √(RA2 + XS2) = EA/IA
XS >> RA, then
XS ≈ EA/IA = Vφ,OC /IA
…(5-25)
…(5-26)
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Short-circuit Test (find XS)
EA = IARA + jXSIA
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Approximating Method for
Determining the Synchronous
Reactance, XS
At a given field current, IF
1.Get the internal generated voltage EA
from the OCC at that field current.
2.Get the short-circuit current flow IA,SC at
that field current from the SCC.
3.Find XS by applying Equation (5-26).
XS ≈ EA/IA,SC
…(5-26)
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Approximating Method for
Determining the Synchronous
Reactance, XS
This approach is accurate
up to the point of
saturation.
The XS can be found by
applying Equation (526) at any field current
in the linear portion of
the OCC curve.
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Measuring the Armature Resistance
The armature (stator) resistance can be approximated by
applying a DC voltage to the windings while machine
is stationary and measuring the resulting current flow.
The use of DC voltage means that the reactance of the
windings will be zero during the measurement
process.
The AC resistance is slightly larger than DC resistance
due to skin effect.
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The Short-Circuit Ratio
The short-circuit ratio of a generator is
defined as the ratio of the field current
required for the rated voltage at open
circuit to the field current required for
the rated armature current at short
circuit.
It is occasionally encountered in industry.
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Example Problem
Example 5-1 on page 287
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5.8 The Synchronous Generator
Operating Alone
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Effect of Load Changes on a
Synchronous Generator Operating
Alone
An increase in the load is an increase in the real and/or
reactive power drawn from the generator.
Since the flux φ and the speed ω are constant, the
magnitude of internal generated voltage, EA = Kφω
constant.
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Lagging Power Factor Load
RA Ignored
EA = Vφ + jXSIA
EA = Kφω constant
As IA increases,
Vφ decreases rather sharply
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Unity Power Factor Load
RA Ignored
EA = Vφ + jXSIA
EA = Kφω constant
As IA increases,
Vφ decreases only slightly
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Leading Power Factor Load
RA Ignored
EA = Vφ + jXSIA
EA = Kφω constant
As IA increases,
Vφ increases
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Effect of Load Changes on a
Synchronous Generator Operating
Alone
1. If lagging loads (+Q or inductive reactive power loads)
are added to a generator, Vφ decreases significantly.
2. If unity-power-factor loads (no reactive power) are
added to a generator, Vφ decreases slightly.
3. If leading loads (-Q or capacitive reactive power loads)
are added to a generator, Vφ increases.
Voltage regulation (VR) = [(Vnl – Vfl)/Vfl]100 % …(4-67)
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Voltage Regulation
To control the terminal voltage, Vφ , constant as load
changes (in this case, load is inductive.)
• Decreasing the field resistance (RF) increases its field
current (IF).
• An increase in the field current increases the flux (φ)
in the machine.
• An increase in the flux increases the internal
generated voltage, EA = Kφω.
• An increase in EA increases Vφ of the generator.
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Example Problem
Example 5-2 on page 291
Example 5-3 on page 294
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EEE 118: Energy Conversion
Dr. Mongkol Konghirun
Department of Electrical Engineering
King Mongkut’s University of Technology Thonburi
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