Analyze 3ϕ Circuits

BC Electrical Level 3, Analyze 3ϕ Circuits Chapters 1-9

CEC colours for phase

A: Red

B: Black

C: Blue

Neutral: White or natural grey

Advantages of 3ϕ over 1ϕ

• Possible to produce smaller machines with the same kVA capacity. (Can have a rating of about 1.5 times a 1ϕ machine.)

• 3ϕ requires about ¾ as much copper to distribute the same energy with same efficiency at the same voltage as a 1ϕ.

• Power delivered to a 3ϕ load is constant at all times due to the spacing of the sin waves being 120° apart.

• 3ϕ Motors are much simpler in design, they are also self starting and do not require a starting winding.

You can reverse a phase sequence (A-B-C or C-B-A) by:

• Interchanging any of the two line leads. (Eg. B-C-A)

• Changing the direction of the prime mover.

Current phasors are normally shown with

Closed arrowheads

Voltage phasors are normally shown with

Open arrowheads

Voltage rise

• Emf

• Circuit Receives energy from something outside the circuit.

• Source

• The first subscript is more positive

• E

Voltage drop

• Potential difference

• Dissipates energy to something outside the circuit.

• Load

• The first subscript is more negative.

• V

First subscript

always represents the end of the circuit component at which the current tracing loop enters.

Second subscript

always represents the end of the circuit component from which the current tracing loop leaves.

What does the term polyphase mean?

A system with more than one phase.

What is the phase angle between the three generated voltages of a three-phase alternator?

120°

What are the two possible configurations for the leads of a three-phase alternator?

WYE (Y) and Delta (Δ)

The length of the phasor is most often used to represent the

RMS/effective value of the sine wave.

The postitive direction of phasor rotation is:

Counter clockwise.

Reversing the order of the subscripts causes the direction of the phasor to change by:

180°

In a purely resistive, balanced Y-connected Δ-connected system, the magnitude of the phase angles between the line voltages and the line currents is:

30°

Mathematical relationship between the line currents and the phase currents in a Y-connected system.

I_{Line}=I_{Phase}

Mathematical relationship between the line voltages and the phase voltages in a Y-connected system is:

E_{Line}=E_{Phase}\cdot\sqrt3

Reasons for grounding the neutral in a three-phase, four-wire, Y-connected system.

• Reduces the magnitude of transient over voltages.

• Lightning protection.

• Ground faults may be more easily located and eliminated.

• More effecting system and equipment fault protection may be used.

• Reduces the stress on electrical insulation and extends the life of the electrical equipment.

• Maximum voltage-to-ground is limited to phase voltage in a grounded system.

Mathematical relationship between the line currents and the phase currents in a Δ-connected system.

I_{Line}=I_{Phase}\cdot\sqrt3

Mathematical relationship between the line currents and the phase currents in a Δ-connected system.

E_{Line}=E_{Phase}

Three wire Δ systems are typically:

Ungrounded

In a three phase, four wire, grounded Δ system, the phase conductor required to be the one with the higher voltage to ground is:

A Phase (high leg)

Putting the grounded and the high leg of a three-phase, four-wire, Δ system in the same panel compartment is:

Not permissable. (To prevent it from being confused for a Y system.)

Power Total formula with Line Voltage and Line Current

P_{T}=E_{L}\cdot I_{L}\cdot\sqrt3\cdot PF

Power Total formula with Phase Voltage and Phase Current

P_{T}=E_{P}\cdot I_{P}\cdot3\cdot PF

VA Total formula with Line Voltage and Line Current

VA_{T}=E_{L}\cdot I_{L}\cdot\sqrt3

VA Total formula with Phase Voltage and Phase Current

VA_{T}=E_{P}\cdot I_{P}\cdot3

Neutral Amperage shortcut formula

\frac{C-A}{2}\cdot\sqrt3