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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Balanced Voltage magnitude & phase shift in three-phase induction machine means, ___________ & __________ respectively
A) Equal RMS value of all phases & Equal phase shift (120°) between any phases
B) Equal Peak value of all phases & Equal phase shift (120°) between all phases
C) Equal DC value of all phases & Equal phase shift (180°) between all phases
D) Equal Peak value of all phases & Equal phase shift (180°) between all phases
Equal Peak value of all phases & Equal phase shift (120°) between all phases
A three-phase voltage system is considered balanced when all three line/phase voltages have equal peak (or RMS) magnitudes and are displaced from each other by equal electrical phase angles of 120° (2π/3 radians). Equal peak values ensure uniform amplitude across all phases, while a exact 120° phase displacement produces a smoothly rotating magnetic field in an induction machine.
A three-phase voltage system is considered balanced when all three line/phase voltages have equal peak (or RMS) magnitudes and are displaced from each other by equal electrical phase angles of 120° (2π/3 radians). Equal peak values ensure uniform amplitude across all phases, while a exact 120° phase displacement produces a smoothly rotating magnetic field in an induction machine.
va(t)=Vmsin(ωt) — Phase A Instantaneous Voltage
vb(t)=Vmsin(ωt−120°) — Phase B Instantaneous Voltage
vc(t)=Vmsin(ωt−240°)=Vmsin(ωt+120°) — Phase C Instantaneous Voltage
Vrms=2Vm — Relationship between RMS and Peak Magnitude
In a three-phase induction motor, when balanced three-phase AC voltages with equal peak values and 120° phase shift are applied to the three-phase stator winding, balanced three-phase currents flow. These currents produce three-phase pulsating magnetic fluxes displaced by 120° in time and 120° in space, which superimpose to create a constant-magnitude Rotating Magnetic Field (RMF) rotating at synchronous speed ns=P120f.
A balanced set of three-phase voltages has identical peak (or RMS) magnitudes across all three phases.
The electrical phase displacement between any two adjacent phases in a balanced 3-phase system is always 120° (or 2π/3 radians).
Balanced voltages generate a constant-amplitude rotating magnetic field with magnitude FR=23Fm.
Unbalanced magnitudes or unequal phase shifts lead to negative-sequence components, causing pulsating torque, excess heat, and losses.
Produces a uniform, constant-magnitude rotating magnetic field without torque pulsations.
Eliminates neutral current in star-connected systems with balanced loads.
Ensures maximum efficiency and minimal vibration/noise during induction machine operation.
Any magnitude imbalance or angular tilt causes double-frequency torque ripples.
Unbalanced supply voltages cause large negative-sequence currents due to low negative-sequence impedance.
3-phase induction motor drives and industrial manufacturing systems.
Synchronous generators producing balanced power for the grid.
Option A uses RMS value instead of peak value as stated in standard definitions, but RMS and Peak are proportional (Vrms=Vm/2). Option B explicitly states 'Equal Peak value... & Equal phase shift (120°) between all phases' which accurately defines both magnitude equality and phase symmetry.
Options C and D incorrect: DC value of pure sinusoidal AC is zero, and 180° phase displacement corresponds to single-phase or two-phase anti-phase arrangements, not a balanced 3-phase system.
B is correct — Balanced three-phase system requires equal peak magnitudes (Vm) for all phase voltages and a uniform electrical phase displacement of 120° between adjacent phases.
Remember that time displacement of 120° between balanced phase currents combined with 120° spatial displacement of windings creates a rotating magnetic field of magnitude 1.5Φm rotating at synchronous speed.