جامعة سطامم ابد العزيز بن عندسة كلية ا- لكهربائيةندسة ا قسم ا( لكهربائيةت ا ا2 ) كهر( 3360 ) د مصطفى حس د. أ1 Dr. AHMED MUSTAFA HUSSEIN Chapter # 2 Cylindrical Synchronous Generator and Motor 1. Introduction Synchronous machines are named by this name as their speed is directly related to the line frequency. Synchronous machines may be operated either as motor or generator. Synchronous generators are called alternators. Synchronous motors are used mainly for power factor correction when operate at no load. Synchronous machines are usually constructed with stationary stator (armature) windings that carrying the current and rotating rotor (field) winding that create the magnetic flux. This flux is produced by DC current from a separate source (e.g. DC shunt generator). 2. Types of Synchronous Generators The type of synchronous generators depends on the prime mover type as: a) Steam turbines: synchronous generators that driven by steam turbine are high speed machines and known as turbo alternators. The maximum rotor speed is 3600 rpm corresponding 60 Hz and two poles. b) Hydraulic turbines: synchronous generators that driven by water turbine are with speed varies from 50 to 500 rpm. The type of turbine to be used depends on the water head. For water head of 400m, Pelton wheel turbines are used. But for water head up to 350 m, Francis Turbines are used. For water head up to 50 m, Kaplan Turbines are used.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
1 Dr. AHMED MUSTAFA HUSSEIN
Chapter # 2 Cylindrical Synchronous Generator and Motor
1. Introduction
Synchronous machines are named by this name as their speed is directly related to the
line frequency. Synchronous machines may be operated either as motor or generator.
Synchronous generators are called alternators. Synchronous motors are used mainly
for power factor correction when operate at no load. Synchronous machines are
usually constructed with stationary stator (armature) windings that carrying the current
and rotating rotor (field) winding that create the magnetic flux. This flux is produced
by DC current from a separate source (e.g. DC shunt generator).
2. Types of Synchronous Generators
The type of synchronous generators depends on the prime mover type as:
a) Steam turbines: synchronous generators that driven by steam turbine are high
speed machines and known as turbo alternators. The maximum rotor speed is 3600
rpm corresponding 60 Hz and two poles.
b) Hydraulic turbines: synchronous generators that driven by water turbine are with
speed varies from 50 to 500 rpm. The type of turbine to be used depends on the
water head. For water head of 400m, Pelton wheel turbines are used. But for water
head up to 350 m, Francis Turbines are used. For water head up to 50 m, Kaplan
Turbines are used.
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
2 Dr. AHMED MUSTAFA HUSSEIN
c) Diesel Engines: they are used as prime movers for synchronous generator of small
ratings.
For the type a) and c) the rotor shape is cylindrical as shown in Fig. 1, and this type is
called cylindrical rotor synchronous machines. But for type b), the rotor has salient
poles on the rotor periphery as shown in Fig. 2.
Fig.1, Cylindrical-type synchronous machine
Fig.2, Salient-pole synchronous machine
3. Relation Between Field Flux and Armature Flux
There are two types of fluxes are obtained in the air gap between the armature and
rotor;
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
3 Dr. AHMED MUSTAFA HUSSEIN
- Field flux (Ff) that produced by the DC exciter and by using the appropriate prime
mover, it can rotate at synchronous speed (Ns).
- Armature flux or armature reaction (Fa) which is produced from 3-phase armature
winding and rotate with the synchronous speed.
Therefore, both of Ff and Fa are stationary w.r.t. each other
4. Equivalent Electrical Circuit Model per Phase
Neglecting saturation, the circuit diagrams, shown in Fig. 3, illustrate the per phase
equivalent circuits of a cylindrical rotor synchronous machine in the motor and
generator mode respectively.
Fig. 3, equivalent circuit (a) synchronous Generator (b) synchronous Motor
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
4 Dr. AHMED MUSTAFA HUSSEIN
Fig. 4, equivalent circuit including leakage reactance and air-gap voltage
Ra armature resistance
XL Leakage reactance (Leakage flux) saturation doesn't affect its value
Xa armature reactance (corresponding to Linkage flux) saturation affects its value
Ef the field voltage (Exciter DC voltage induced at the armature side)
Er the air-gap voltage which is the resultant between Ef and Ea
The leakage reactance XL and the armature reactance Xa may be combined to give
synchronous reactance XS.
XS =XL + Xa
Also, Ra + JXS is called synchronous impedance ZS
If the mutual inductance between the rotor and armature (Laf) is considered as shown
in Fig. 4, then the rms value of the induced voltage Ef can be given as:
𝐸𝑓 =2𝜋𝑓 𝐿𝑎𝑓 𝐼𝑓
√2
Therefore, the excitation current (If) can be calculated as:
𝐼𝑓 = √2 𝐸𝑓
2𝜋𝑓 𝐿𝑎𝑓
5. Phasor Diagram of Unsaturated Cylindrical Alternators
5.1 Lagging power factor
Assume that the synchronous generator is loaded with a lagging power factor load.
From the phasor diagram shown in Fig. 5, it is clear that the terminal voltage is
decreased from its no-load value Ef to its loaded value Va (for a lagging power factor).
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
5 Dr. AHMED MUSTAFA HUSSEIN
This is because of: Drop due to armature resistance, IRa & drop due to leakage
reactance, IXL and drop due to armature reaction IXa.
Fig. 5, Phasor diagram for synchronous generator (p.f. Lag)
The angle () between the no-load voltage (Ef) and the terminal voltage (Va) is called
the load angle or (power angle) and it is positive value in case of alternators.
The DC voltage (Excitation voltage) produces a flux (f) or (field mmf Ff). If the
armature circuit is closed by an electric load, the armature reaction (a) or (armature
mmf Fa) is produced. These two fluxes may support each other or oppose each other
depend on the load power factor to produce the air-gap or resultant flux (r) or
(resultant mmf Fr).
From the phasor diagram shown in Fig. 5,
Since Fr < Ff this means that Fa oppose Ff
Since Va < Ef this is called over-excited alternator
5.2 Leading power factor
Assume that the synchronous generator is loaded with a leading power factor load.
From the phasor diagram shown in Fig. 6, it is clear that the terminal voltage is
increased from its no-load value Ef
𝐸𝑓 = 𝑉 + 𝐼𝑎(𝑅𝑎 + 𝐽𝑋𝑆)
Fa
Ff Fr
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
6 Dr. AHMED MUSTAFA HUSSEIN
Fig. 6, Phasor diagram for synchronous generator (p.f. Lead)
From the phasor diagram shown in Fig. 6,
Since Fr > Ff this means that Fa support Ff
Since Va > Ef this is called under-excited alternator
5.3 Unity power factor
Assume that the synchronous generator is loaded with a unity power factor load.
From the phasor diagram shown in Fig. 7, it is clear that the terminal voltage is
decreased from its no-load value Ef (similar to lagging power factor)
Fig. 7, Phasor diagram for synchronous generator (p.f. unity)
From the phasor diagram shown in Fig. 7,
Since Fr < Ff this means that Fa oppose Ff
Since Va < Ef this is called over-excited alternator
6. Analytical Representation of Phasor Diagram
Consider the phasor diagram of 3-phase alternator at lagging p.f. as shown in Fig. 8-
(a).
Ia XL
Ia Xa
Fr
Ff
Fa
Fa
Ff Fr
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
7 Dr. AHMED MUSTAFA HUSSEIN
Fig. 8-(a), Alternator phasor diagram at lagging p.f
We can describe this phasor diagram by two equations:
Horizontal Analysis:
𝐸𝑓 cos(𝛿) = 𝑉 + 𝐼𝑎𝑅𝑎 cos(𝜑) + 𝐼𝑎𝑋𝑠 sin(𝜑) … (1)
Vertical Analysis:
𝐸𝑓 sin(𝛿) = 𝐼𝑎𝑋𝑠 cos(𝜑) − 𝐼𝑎𝑅𝑎 sin(𝜑) … (2)
By dividing (2) over (1), we obtain:
tan(𝛿) =𝐼𝑎𝑋𝑠 cos(𝜑) − 𝐼𝑎𝑅𝑎 sin(𝜑)
𝑉 + 𝐼𝑎𝑅𝑎 cos(𝜑) + 𝐼𝑎𝑋𝑠 sin(𝜑)
Once the angle (𝛿) is known, we can obtain the excitation voltage Ef.
Now, if Ra is neglected, the phasor diagram is shown in Fig. 8(b).
Equations (1) and (2) can be rewritten by replacing Ra=0 as:
Horizontal Analysis:
𝐸𝑓 cos(𝛿) = 𝑉 + 𝐼𝑎𝑋𝑠 sin(𝜑) … (3)
Vertical Analysis:
𝐸𝑓 sin(𝛿) = 𝐼𝑎𝑋𝑠 cos(𝜑) … (4)
By dividing (4) over (3), we obtain:
Ef
Ia Xs
φ
φ
V
δ
Ia Fig. 8(b), Approximate phasor at lag p.f
Ef
Ia Xs
φ
φ
V
δ
Ia
Ia Ra φ
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
8 Dr. AHMED MUSTAFA HUSSEIN
tan(𝛿) =𝐼𝑎𝑋𝑠 cos(𝜑)
𝑉 + 𝐼𝑎𝑋𝑠 sin(𝜑)… (5)
Once the angle (𝛿) is known, we can obtain the excitation voltage Ef.
Example
A 4-pole, 3-phase synchronous generator is rated 250 MVA, its terminal voltage is 24
kV, the synchronous reactance is: 125%. • Calculate the synchronous reactance in
ohm. • Calculate the rated current. • Calculate the induced voltage, Ef , at rated load
and pf = 0.8 lag.
250×106 = √3×24000×𝐼𝑎 → 𝐼𝑎 = 6014.0653𝐴
𝑍𝑏𝑎𝑠𝑒 =𝑉𝑝ℎ𝑎𝑠𝑒
𝐼𝑝ℎ𝑎𝑠𝑒=
24000/√3
6014.0653= 2.304 Ω
The actual value of the synchronous reactance = Xs (in PU) * Zbase =
1.25*2.304=2.88Ω
The load angle can be obtained based on eqn. (5):
tan(𝛿) =𝐼𝑎𝑋𝑠 cos(𝜑)
𝑉 + 𝐼𝑎𝑋𝑠 sin(𝜑)=
6014.0653×2.88×0.8
13856.4065 + 6014.0653×2.88×0.6= 0.57143
𝛿 = 29.745
By substituting with this value in eqn. (3) as:
𝐸𝑓×0.868242 = 13856.4065 + 6014.0653×2.88×0.6
Ef = 27928.52
By the same way, we can describe the phasor diagram in case of leading power factor
givenin Fig. 9-(a) by two equations:
Fig. 9-(a), Alternator phasor diagram at leading p.f
V
Ef Ia Xs
φ
φ
δ
Ia
φ Ia Ra
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
9 Dr. AHMED MUSTAFA HUSSEIN
Horizontal Analysis:
𝐸𝑓 cos(𝛿) = 𝑉 + 𝐼𝑎𝑅𝑎 cos(𝜑) − 𝐼𝑎𝑋𝑠 sin(𝜑) … (6)
Vertical Analysis:
𝐸𝑓 sin(𝛿) = 𝐼𝑎𝑋𝑠 cos(𝜑) + 𝐼𝑎𝑅𝑎 sin(𝜑) … (7)
By dividing (7) over (6), we obtain:
tan(𝛿) =𝐼𝑎𝑋𝑠 cos(𝜑) + 𝐼𝑎𝑅𝑎 sin(𝜑)
𝑉 + 𝐼𝑎𝑅𝑎 cos(𝜑) − 𝐼𝑎𝑋𝑠 sin(𝜑)
Once the angle (𝛿) is known, we can obtain the excitation voltage Ef.
Now, if Ra is neglected, the phasor diagram is shown in Fig. 9(b).
Equations (6) and (7) can be rewritten by replacing Ra=0 as:
Horizontal Analysis:
𝐸𝑓 cos(𝛿) = 𝑉 − 𝐼𝑎𝑋𝑠 sin(𝜑) … (8)
Vertical Analysis:
𝐸𝑓 sin(𝛿) = 𝐼𝑎𝑋𝑠 cos(𝜑) … (9)
By dividing (9) over (8), we obtain:
tan(𝛿) =𝐼𝑎𝑋𝑠 cos(𝜑)
𝑉 − 𝐼𝑎𝑋𝑠 sin(𝜑)
Once the angle (𝛿) is known, we can obtain the excitation voltage Ef.
From the explained phasor diagrams given in Figs 5 to 9, we notice that V is always
behind Ef, this means the power angle (δ) is always positive, and this is the remarkable
notice on the phasor diagram of synchronous generators.
Ef
Ia Xs
φ
φ
V
δ
Ia
Fig. 9-b, Approximate phasor at leading p.f
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
10 Dr. AHMED MUSTAFA HUSSEIN
7. Experimental Determination of Circuit Parameters
In the per phase equivalent circuit model illustrated in section 1, there are three
parameters need to be determined: armature winding resistance Ra, synchronous
reactance Xs, and induced emf in the phase winding Va. The phase winding resistance
Ra can be determined by measuring DC resistance of the winding using volt-ampere
method (DC test), while the synchronous reactance and the induced emf can be
determined by the open circuit and short circuit tests.
7.1 DC Test
The purpose of the DC test is to determine Ra. 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. Then
𝑅𝐷𝐶 = 𝑉𝐷𝐶
𝐼𝐷𝐶
If the stator is Y-connected, the per phase stator resistance is
𝑅𝑎 = 𝑅𝐷𝐶
2 ×1.15
If the stator is delta-connected, the per phase stator resistance is
𝑅𝑎 = 3
2𝑅𝐷𝐶×1.15
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
11 Dr. AHMED MUSTAFA HUSSEIN
Here, we take the skin effect of 15% to calculate the AC value of Ra
7.2 Open Circuit Test
Drive the synchronous machine at the synchronous speed using a prime mover when
the stator windings are open circuited. Vary the rotor (field) winding current (If) , and
measure stator winding terminal voltage (V). The relationship between the stator
winding terminal voltage and the rotor field current obtained by the open circuit test is
known as the open circuit characteristic (O.C.C.) of the synchronous machine as
shown in Fig. 10.
Fig. 10, Open-Circuit Characteristic (O.C.C.)
From the OCC shown in Fig. 10, the effects of magnetic saturation can be clearly
seen; the characteristic bends downward with increasing the field current. As
saturation of the magnetic material increases, the permeability decreases and as a
result, the reluctance of the flux paths is increases and reduces the effectiveness of the
field current in producing magnetic flux. As can be seen from Fig. 10, the open-circuit
characteristic is initially linear as the field current is increased from zero. This portion
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
12 Dr. AHMED MUSTAFA HUSSEIN
of the curve (and its linear extension for higher values of field current) is known as the
air-gap line. It represents the machine open-circuit voltage characteristic
corresponding to unsaturated operation. Deviations of the actual open-circuit
characteristic from this air-gap line are a measure of the degree of saturation in the
machine.
Note that with the machine armature winding open-circuited, the terminal voltage is
equal to the generated voltage Ef. Thus the open-circuit characteristic is a
measurement of the relationship between the field current If and Ef. It can therefore
provide a direct measurement of the field-to-armature mutual inductance Laf.
Example
An open-circuit test performed on a three-phase, 60-Hz synchronous generator shows
that the rated open-circuit voltage of 13.8 kV is produced by a field current of 318 A.
Extrapolation of the air-gap line from a complete set of measurements on the machine
shows that the field current corresponding to 13.8 kV on the air-gap line is 263 A.
Calculate the saturated and unsaturated values of Laf.
Ef = 13800/√3 = 7967.434 V
To calculate the unsaturated value of Laf, we use the air-gap quantity of field current
𝐿𝑎𝑓|𝑈𝑛𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑
= √2 𝐸𝑓
2𝜋𝑓 𝐼𝑓|𝑎𝑖𝑟 𝑔𝑎𝑝
𝐿𝑎𝑓|𝑈𝑛𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑
= √2×7967.434
2𝜋×60×263 = 113.644 𝑚𝐻
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
13 Dr. AHMED MUSTAFA HUSSEIN
To calculate the saturated value of Laf, we use the O.C quantity of field current
𝐿𝑎𝑓|𝑆𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑
= √2 𝐸𝑓
2𝜋𝑓 𝐼𝑓|𝑜𝑝𝑒𝑛 𝑐𝑖𝑟𝑐𝑢𝑖𝑡
𝐿𝑎𝑓|𝑆𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑
= √2×7967.434
2𝜋×60×318 = 93.989 𝑚𝐻
The saturation reduces the magnetic coupling between field and armature windings by
113.644 − 93.989
113.644×100% = 17.295 %
7.3 Short Circuit Test
Reduce the field current to a minimum value, using the field rheostat, and then open
the field supply circuit breaker. Short the stator terminals of the machine together
through three ammeters; Close the field circuit breaker; and raise the field current
gradually to the value noted in the open circuit test at which the open circuit terminal
voltage equals the rated voltage, while maintain the synchronous speed. Record the
three stator currents. (This test should be carried out quickly since the stator currents
may be greater than the rated value). Plot the relation between the field current and the
armature current as shown in Fig. 11. Such kind of relation is called Short Circuit
Characteristics (S.C.C.). It is clear from the S.C.C. shown in Fig. 11, the relation
between the field current and the short-circuit armature current is straight line passing
through origin. Ef = Ia (Ra + jXs)
if Ra is negligible, Ia will lag Ef by nearly 90 elec. deg.
Fig. 11, Short-circuit characteristics S.C.C.
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
14 Dr. AHMED MUSTAFA HUSSEIN
7.4 Calculation of synchronous reactance XS
Following procedural steps are involved in this calculation:
1. O.C.C is plotted from the given data as shown in Fig. 10.
2. Similarly, S.C.C. is drawn from the data given by the short-circuit test as shown in
Fig. 11. It is a straight line passing through the origin.
Both these curves are drawn on a common field-current base as shown in Fig. 12, from
which, the value of ZS is not constant but varies with saturation. At low saturation, its
value is larger because the effect of a given armature ampere-turns is much more than
at high saturation. Now, under short-circuit conditions, saturation is very low, because
armature m.m.f. is directly demagnetising. Different values of ZS corresponding to
different values of field current are also plotted
Fig. 12, Determination of saturated and unsaturated values of Xs using S.C.C. and
O.C.C.
Consider a field current If. The O.C. voltage corresponding to this field current is Oa.
When winding is short-circuited, the terminal voltage becomes zero. Hence, it may be
assumed that the whole of this voltage Oa is being used to circulate the armature
short-circuit current O'b against the synchronous impedance ZS.
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
15 Dr. AHMED MUSTAFA HUSSEIN
Based on both O.C.C. and S.C.C. given in Fig. 12, at any convenient field current (If),
the saturated synchronous impedance ZS can be calculated by:
𝑍𝑆 = 𝑂. 𝐶. 𝑉𝑜𝑙𝑡𝑎𝑔𝑒
𝑆. 𝐶. 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 ]
𝑎𝑡 𝑠𝑎𝑚𝑒 𝑓𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑍𝑆 = 𝑂𝑎 (𝑓𝑟𝑜𝑚 𝑂. 𝐶. 𝐶. )
𝑂′𝑏 (𝑓𝑟𝑜𝑚 𝑆. 𝐶. 𝐶. )
𝑋𝑆 = √𝑍𝑆2 − 𝑅𝑎
2 (𝑆𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)
The unsaturated synchronous impedance ZS can be calculated by:
𝑍𝑆 = 𝑂. 𝐶. 𝑉𝑜𝑙𝑡𝑎𝑔𝑒
𝑆. 𝐶. 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 ]
𝑎𝑡 𝑠𝑎𝑚𝑒 𝑓𝑖𝑒𝑙𝑑 𝑐𝑢𝑟𝑟𝑒𝑛𝑡
𝑍𝑆 = 𝑂𝑐 (𝑓𝑟𝑜𝑚 𝑎𝑖𝑟𝑔𝑎𝑝 𝑙𝑖𝑛𝑒)
𝑂′𝑏 (𝑓𝑟𝑜𝑚 𝑆. 𝐶. 𝐶. )
𝑋𝑆 = √𝑍𝑆2 − 𝑅𝑎
2 (𝑢𝑛𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒)
The resistive element of the machine can simply be found from the DC test explained
before. Value obtained in this test (Ra) may increase the XS accuracy.
* Notes on this method
The important comment on the determination of saturated and unsaturated values of Xs
using S.C.C. and O.C.C. is as follows;
Ef is taken from the OCC whereby the core would be partially saturated for large field
currents, while Ia is taken from the SCC where the core is not saturated at all field
currents. Therefore Ef value taken during the OCC may not be the same Ef value in the
SCC test. Hence the value of XS is only an approximate.
Hence to gain better accuracy, the test should be done at low field currents which
looks at the linear region of the OCC test.
Example 1
From the following tests, determine the synchronous reactance, assuming Ra is 0.8Ω.
S.C.C: a current of 100 A is produced on short-circuit by a field excitation of 2.5A.
O.C.C: An e.m.f. of 500 V (phase) is produced on open-circuit by the same excitation.
بن عبد العزيز األمري سطامجامعة
قسم اهلندسة الكهربائية - كلية اهلندسة
(3360)كهر (2اآلالت الكهربائية )
د. أمحد مصطفى حسني
16 Dr. AHMED MUSTAFA HUSSEIN
𝑍𝑆 = 500
100= 5 Ω
𝑋𝑆 = √𝑍𝑆2 − 𝑅𝑎
2 = √52 − 0.82 = 4.936 Ω (Saturated value)
7.5 Short Circuit Ratio (SCR)
SCR is defined as the ratio of the field current required for the rated voltage at open
circuit to the field current required for rated armature current at short circuit. Based on
Fig. 13, the SCR can be obtained as:
𝑆𝐶𝑅 = 𝑂𝑓′
𝑂𝑓′′
The saturated synchronous reactance (in per unit) can be calculated as the inverse of
SCR
𝑋𝑆(𝑠𝑎𝑡𝑢𝑟𝑎𝑡𝑒𝑑 𝑖𝑛 𝑃𝑈) = 1
𝑆𝐶𝑅=
𝑂𝑓′′
𝑂𝑓′
Fig. 13, Short Circuit Ratio (S.C.R.)
Example 2
The following data are taken from the open- and short-circuit characteristics of a 45