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Three Phase A.C. Circuit Study Notes for GATE and Electrical Engineering Exams
By BYJU'S Exam Prep
Updated on: September 25th, 2023
Introduction to Three Phase A.C. Circuit
 A phase is carried out to the periodic modifications of a few quantities, which includes the voltage in an AC circuit.
 An electrical segment is measured in degrees, with 360° comparable to an entire cycle.
 A sinusoidal voltage is proportional to the cosine or sine of the section.
 Threephase, abbreviated 3φ, refers to three different voltages and currents.
 It is a system produced by a generator that includes three sources that contain the same amplitude and frequency but out of phase from each other by 120°.
 The three phases should be supplied over sixwire, with two wires used for each phase. However, they are generally supplied over three wires
 The phase or line currents are the currents in each wire.
 AC Voltages and currents are expressed as RMS values
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Table of content
 A phase is carried out to the periodic modifications of a few quantities, which includes the voltage in an AC circuit.
 An electrical segment is measured in degrees, with 360° comparable to an entire cycle.
 A sinusoidal voltage is proportional to the cosine or sine of the section.
 Threephase, abbreviated 3φ, refers to three different voltages and currents.
 It is a system produced by a generator that includes three sources that contain the same amplitude and frequency but out of phase from each other by 120°.
 The three phases should be supplied over sixwire, with two wires used for each phase. However, they are generally supplied over three wires
 The phase or line currents are the currents in each wire.
 AC Voltages and currents are expressed as RMS values
Following requirements must be satisfied in order to be a alanced 3phase set
 All 3 variables have the same amplitude
 All 3 variables have the same frequency
 All 3 variables are 120^{o} in phase
Balanced System
Following requirements must be satisfied for a 3phase system or circuit to be balanced.
 All 3 sources are represented by a set of balanced 3phase variables.
 All loads are 3phase with equal impedances(balanced load).
 Line impedances are equal in all 3 phases.
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Unbalanced System
A system is unbalanced if either the source is unbalanced or the load is unbalanced. Practically for an unbalanced system, the source is always balanced and the load is unbalanced.
Advantages of 3 Phase Circuits
 Electric power is generated and distributed in the threephase system only.
 The instantaneous power in a threephase system is always constant.
 The amount of wire required for a 3phase system is lesser than that required for an equivalent 1phase system.
 For Similar power, the threephase system is more economical than the singlephase.
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ThreePhase Circuit Connections
 The Y or wye connection joints neutrals of each phase at a common junction.
 The Δ or delta connection is a triangle whose vertices form the buses, and there is no neutral bus available.
Star or “Y” (also known as the “T”) configuration:
 The star connection is made by connecting one end of each of phase windings together (as shown in the above figure).
 The voltage measured across a single winding or phase is known as the phase voltage.
 The voltage measured between the lines is known as the linetoline voltage or simply as the line voltage.
 In a star connected system, the line voltage is greater than the phase voltage
 In a star connected system, phase current and line current are the same.
Delta, or Δ (also known as the “Pi,” or π) configuration:
 In a delta connection, line voltage and phase voltage are the same.
 The line current of a delta connection is higher than the phase current
Balanced Three‐Phase Connections
 YY connection
 Y∆ connection
 ∆∆ connection
 ∆Y connection
Wye‐Delta transformation
 WyeDelta transformation is also called as stardelta transformation.
 WyeDelta Transformation is a technique to reduce common resistor connections that are neither in series nor on parallel.
 Conversion from Delta (Δ) to Wye (Y)
 Conversion from Wye (Y) to Delta (Δ)
Transformations
Note: Both Star Delta Transformation and Delta Star Transformation permits us to transform one sort of circuit connection into some other kind so as for us to without difficulty examine the circuit. These transformation strategies may be used to precise impact for star or delta circuits containing resistances or impedances.
Now, it is easy to compute the total resistance between points A and B.
StarDelta Transformation
Note: Both Star Delta Transformation and Delta Star Transformation allow us to convert one type of circuit connection into another type in order for us to easily analyze the circuit. These transformation techniques can be used to good effect for either star or delta circuits containing resistances or impedances.
ThreePhase Power:
If line values of voltage and current are known, the power (watts) of a purely resistive load is:
If the phase values of voltage and current are known, the apparent power is:

3 Phase A.C. Circuit Part 1, Download PDF

3 Phase A.C. Circuit Part 2, Download PDF

3 Phase A.C. Circuit Part 3, Download PDF
The ThreePhase AC Circuit is an important topic for GATE EE, SSC JE EE, ESE IES EE, ISRO EE, and other electrical engineering exams.
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