Suppose a linear, passive network has the input and output as:
Ein=Emsin(ωt)andEout=AEmsin(ωt+α)
Here A is the attenuation or magnification factor and α is the phase shift.
Power
Power on a 1-phase circuit can be easily found using 1-phase power formula:
Pph=Vph⋅Iph∗=Pactive+jPreactive
Here Iph∗ is the complex conjugate of the current phasor.
Standard terminology
Examples:
A 3-ph, 415 V, 50 Hz, 100 kVA transformer
A 3-ph, 33 kV, 50 Hz, 1 MVA, 3-wire transmission line
A 3-ph, δ-connected, 415 V, 3.2 kW, 0.85 pf motor
Here:
Voltage specified is always line voltage
Active power or apparent power is always the total 3-ph quantity
If apparent power is given, maximum current capacity of the device can be determined
4-wire system has the neutral wire connected between the star-points of supply and load.
For motors, the power specified is the output mechanical power. The operating power factor of the motor is specified at its rated power.
Efficiency=Input Electrical PowerOutput Power
Symmetrical Components
A technique used to handle unbalanced voltages or current sources. Any unbalanced system of three-phase circuits can be decomposed into three symmetrical components:
Positive sequence (a)
Has same phase sequence as the original 3-phase system
Negative sequence (b)
Has reverse phase sequence as the original 3-phase system
Zero sequence (c)
Has equal magnitude and phase angle in all 3-phases
ABC=A0B0C0+A1B1C1+A2B2C2
The above equation can be simplified as below. Here α=1.0∠120∘.