Three Phase Circuit

The Y Connections

           -  each phase is connected between a line and the neutral.

Phase Voltage = Line to neutral voltage(Va, etc.).

Phase Currents = Line currents(Ia, etc.).

Neutrals Connect the 3 phases.

The Delta Connections

            - each phase is connected in two lines.

Phase Voltage = Line voltages(Vab, etc.).

Phase Currents = Currents from line to line(Iab, etc.).

Neutral is not present.

Definition of the following:

Phase - it is simply the branch of the circuit.

Line - wires that connect the source to the load.

Neutral - the 4th wire in the three phase system. It's where the phases of a Y connection come together.

Line Currents - the current flowing in each of the lines(Ia, Ib, Ic).

Line Voltage - the voltage between any two of the lines(Vab, Vbc, Vac).

Phase Currents & Voltages - the voltages and currents across and through a single branch (phase) of the circuit. It depends on whether the connection is Wye or Delta!



Y connected  source

 

Delta connected source

 

Y connected load

 

Delta connected load

 

Reminders:

• All 3 variables have the same amplitude
• All 3 variables have the same frequency
• All 3 variables are 120^o in phase
• All 3 sources are represented by a set of balanced 3-phase variables
• All loads are 3-phase with equal impedance's
  
• Line impedance are equal in all 3 phases

 

Balanced 3-phase circuit:

 

Power Factor

Power Factor

- the cosine of the phase difference between voltage and current.

- it is also the cosine of the angle of the load.

Consider this is a circuit:

Find the Power Factor:

• First, analyze the circuit.
• You can see to the circuit that when you convert the given load into phasor, you can get the angle.
• The formula is pf = cos(angle of Z)
• The answer must in between Zero to One. 
• If your answer is greater than 1, it means your answer is wrong.
• If it is positive, its LAGGING(inductive).
• If it's negative, its LEADING(capacitive).
• In the circuit, the complex part is positive, it means LAGGING.
• FINISH!!

Apparent Power

Apparent POWER(in VA)

- is the product of the RMS values of voltage and current.

RMS(Root Mean Square)

- arises from the need measure the effectiveness of a voltage or current source 

in delivering power to a resistive load.

The incandescent light bulb is a commonly-used resistive load.

Consider this is a circuit.

Find the apparent power of the circuit:

• For getting the apparent power.
• The formula is S = Vrms Irms
• In the formula, the Irms is also unknown.
• Therefore, to solve the Apparent Power(S) get first the Irms.
• To get the Irms, use Ohm's Law. Don't forget that! :))
• Formula for Ohm's Law: 
• I = Vrms/Z , instead of R.

•  Then, you can now solve the Apparent Power(S)
• FINISH