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EXPERIMENT 2
To determine the direct axis reactance (Xd) and quadrature axis reactance (Xq) of
synchronous machine
Fig 2.1 Connection Diagram for Slip Test
Fig 2.2 Connection Diagram for Static Test
Link reference:
https://youtu.be/5fB-17hCe9w
https://vp-dei.vlabs.ac.in/Dreamweaver/videos/video2.mp4
The slip test is a method for determining the direct axis reactance (Xd) and quadrature
axis reactance (Xq) of an alternator. During this test, a three-phase power supply is
applied to the alternator's armature with a voltage significantly lower than its rated voltage,
while the field winding circuit is kept open. This setup causes the armature to draw three-
phase currents, creating a rotating magnetic flux, similar to what occurs in an induction
motor. Since the air gap in the alternator is not uniform, the reactance varies, causing
cyclic fluctuations in armature current at twice the slip frequency. The root mean square
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(rms) current is minimal when the machine reactance is Xd and maximum when it's Xq.
The varying reactance leads to cyclic changes in voltage drops, alternator impedance,
and terminal voltage. This test helps determine key parameters for understanding the
alternator's behavior under various conditions.
A static test is a thorough evaluation procedure used to determine parameters of
synchronous machines, primarily direct axis reactance (Xd) and quadrature axis
reactance (Xq). It's conducted in a controlled setting, often a lab, with specific test
conditions and a no-load test to find synchronous reactance (Xs). The excitation system
is adjusted to control field current (If), enabling control over internal voltage and armature
current (Ia). Measurements of terminal voltage (Vt), If, Ia, power factor, and rotor speed
are recorded. Xd and Xq calculations are complex, often requiring machine geometry and
mathematical models. Results inform machine behavior under various conditions,
documented in a report, crucial for machine performance assessment and power system
applications, following industry standards.
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Simulation 1: Checking the Phase Sequence of Synchronous Machine
Procedures 1-2 (Clockwise)
RESULT:
DISCUSSION:
When the synchronous machine rotates in a clockwise direction, it implies that the
phase sequence is initially correctly matched with the bus bar. This is important
because the phase sequence must be synchronized with the grid or bus bar for
the machine to operate correctly.
Procedure 4 (Anticlockwise)
RESULT:
DISCUSSION:
In the first instance of anticlockwise rotation, the phase sequence is incorrect or
does not match the bus bar's phase sequence. This is a problem because the
machine will not operate properly in this state.
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Procedure 5-10 (Anticlockwise)
RESULT:
DISCUSSION:
After changing the phase sequence to match the bus bar, the rotation remains
anticlockwise. This is correct because once the phase sequence is correctly
synchronized with the grid or bus bar, the machine should rotate anticlockwise as
expected.
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Simulation 2: Simulation for Xd and Xq
RESULT:
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Xd = Lmax - Lmin
Xq = Lmax – Lmin
Self-Inductance (mH) Mutual-Inductance (mH) Max
Angle(rad)
S. No. Xd Xq Xd Xq
1 0.3 0.3 2 2 1
2 0.3 0.3 7.92 7.92 2
3 0.4 0.4 8 8 3
DISCUSSION:
The variations in self-inductance with angle provide crucial insights into the machine's
electrical self-interaction. They are a direct measure of how the machine's own coils (L)
change as the rotor angle varies. By calculating Xd and Xq based on these variations, we
essentially determine how the machine's direct axis inductance (Ld) and quadrature axis
inductance (Lq) change in response to the rotor angle.
The variations in mutual inductance with angle inform us about how the machine's
different coils interact with each other as the rotor angle changes. This is essential in
understanding how the machine affects the flow of electrical energy.
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RESULT:
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DISCUSSION:
The waveforms of voltage induced in rotor, terminal voltage and current drawn by
armature are shown in the Figures above. The armature current (Ia) is a crucial element
in the experiment, offering valuable insights into the behavior of a synchronous machine.
The observed changes in armature current over time provide significant implications for
the machine's operation. The "closeness" of the armature current waveforms as time
advances hints at the machine's transient response and its ability to stabilize during
disturbances, a fundamental aspect of transient stability. This behavior also suggests
synchronization of the rotor angle and effective voltage regulation, crucial for maintaining
a stable electrical grid and ensuring power supply quality. In essence, the armature
current's behavior signifies the machine's capacity to adjust and stabilize its electrical
output, vital for reliable and stable power system operation.
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EXPLANATION FOR QUIZ
1. Ratio of Xd/Xq for cylindrical alternator is ------- Xd/Xq of salient pole
machine:
Answer: less than
Explanation: The ratio Xd/Xq indicates the relative values of the direct-axis
reactance (Xd) to the quadrature-axis reactance (Xq) in an alternator. In
cylindrical alternators, where the rotor has a uniform cross-section and is
symmetric, Xd is generally less than Xq. In contrast, in salient pole
machines, where the rotor has projections or poles, Xd is often greater than
Xq.
2. Steady state direct axis reactance is ---------- transient direct axis reactance:
Answer: greater than
Explanation:
Steady-state direct-axis reactance is usually greater than transient direct-
axis reactance. The steady-state reactance represents the reactance during
normal, continuous operation, which is typically higher due to factors like
core saturation. Transient reactance reflects the reactance during transient
events like sudden changes in load or short circuits, where the core doesn't
saturate to the same extent.
3. In a hydro alternator, if Xd=1.15 then the value of Xq will be approximately:
Answer: 0.75
Explanation: In hydro alternators, the value of Xq is generally less than Xd.
So, if Xd is 1.15, Xq would be approximately 0.75, indicating that Xd is
greater than Xq.
4. In Salient pole alternator the rotor diameter is -------- its length:
Answer: greater than
Explanation: In a salient pole alternator, the rotor has poles or projections
that extend outward from the rotor surface. These poles often make the
rotor diameter greater than its length, contributing to the saliency of the
machine.
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5. While conducting slip test, the synchronous machine runs at a slip �s� and
stator supply frequency �f�, the frequency of
i. voltage induced across open field terminals
ii. envelope of the armature terminal voltage
iii. envelope of the armature current, and
iv. armature current
will be respectively:
Answer: f, sf, sf, and f
Explanation: During a slip test; The frequency of voltage across open field
terminals remains at the stator supply frequency (f). The envelope of the
armature terminal voltage is modulated by (1-s)f. The envelope of the
armature current is also modulated by (1-s)f. The armature current itself has
a frequency of sf.
6. When a synchronous motor is running at synchronous speed, the damper
winding produces:
Answer: Damping torque
Explanation: When a synchronous motor is running at synchronous speed
(zero slip), the damper winding primarily produces damping torque. This
torque acts to dampen any oscillations and ensures that the motor remains
in synchronism with the supply frequency.
7. The reactance of any machine is ------------- proportional to reluctance of flux
path and ---------- proportional to square of the number of turns:
Answer: inversely, directly
Explanation: Reactance is inversely proportional to the reluctance of the
magnetic flux path. Lower reluctance in the magnetic circuit results in higher
reactance. Additionally, reactance is directly proportional to the square of
the number of turns in the coil, meaning that more turns lead to higher
reactance.
8. The armature reactance of salient pole synchronous machine:
Answer: is equal to Xd
Explanation: The armature reactance of a salient pole synchronous
machine is often approximately equal to Xd, indicating that they are close
in value in this type of machine.
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9. The ratio of Xd to Xq in salient pole machine varies in the range:
Answer: 0.9 to 1.0
Explanation: The ratio of Xd to Xq in salient pole machines typically falls in
the range of 0.9 to 1.0. This range is a characteristic of salient pole
machines and represents the relative values of Xd and Xq in such
machines.
10. By which test synchronous machine can be recognized as cylindrical or
salient pole type?
Answer: Slip Test
Explanation: The slip test is used to determine whether a synchronous
machine is of the cylindrical or salient pole type. The test relies on changes
in slip to observe how the machine responds, and the behavior differs
between these two types, making it a recognition test.
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CONCLUSION
Overall, this experiment shows and explains the direct axis reactance (Xd) and
quadrature axis reactance (Xq) of synchronous machine. For the first simulation, this
basically states that checking the phase sequence of the synchronous machine is a
crucial step to ensure proper synchronization with the grid. The initial result of clockwise
rotation and the subsequent adjustment to achieve anticlockwise rotation indicate that the
phase sequence is correctly set, which is essential for the reliable and efficient operation
of the synchronous machine in an electrical system. As for the second simulation, Xd and
Xq serve as indicators of how my machine reacts to different electrical scenarios. Xd
shows me how the machine copes with abrupt changes, like when sudden electrical
disruptions occur (we call these transient events). Xq, on the other hand, gives me insight
into how my machine operates under normal, steady-state conditions, such as when it's
consistently supplying power.
To sum up, the laboratory experiment and the quiz provide insights into various
aspects of synchronous machines. They cover topics such as the Xd/Xq ratios, where
cylindrical alternators typically have a ratio less than that of salient pole machines,
emphasizing balanced reactances. The distinction between steady-state and transient
direct axis reactances is highlighted, with steady-state reactance usually greater due to
core saturation. Hydro alternators are characterized by Xd being greater than Xq,
approximately 0.75 for Xq when Xd is 1.15. Salient pole alternators feature a rotor design
with greater diameter than length. During a slip test, the behavior of voltage, armature
terminal voltage, armature current, and frequency is described. When synchronous
motors run at synchronous speed, the damper winding primarily produces damping
torque. Reactance is inversely proportional to reluctance and directly proportional to the
square of the number of turns. In salient pole machines, the armature reactance can be
approximately equal to Xd, and the Xd/Xq ratio typically falls in the range of 0.9 to 1.0.
Lastly, the slip test is used to recognize whether a synchronous machine is cylindrical or
salient pole type based on its response to changes in slip.
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