Question

Given a Three-Phase Y Connection load:

V LL =208<30∘V
P=7500 W
Power Factor =0.9 Leading
Find: Q, Complex I line, and Complex I phase, S3-Ø, Complex S3-Ø in polar and rectangular, and the Impedance per phase.

Answer 1

To solve for various elements in a three-phase Y-connected load system, one must apply the power triangle, complex power calculations, and Ohm's law for AC circuits, involving the use of the power factor to determine reactive power and subsequently finding the impedance per phase.

Step-by-step explanation:

The task is to find the reactive power (Q), complex line current (Complex I line), complex phase current (Complex I phase), the three-phase apparent power (S3-Ø), and the three-phase complex power (Complex S3-Ø) both in polar and rectangular forms, as well as calculate the impedance per phase for a given three-phase Y-connected load.

Step-by-step calculation:

1. Use the given power factor (power factor = 0.9 leading) to calculate Q using the power triangle relationship where the apparent power (S) is the hypotenuse.
2. Calculate the complex power (S = P + jQ) using the power (P) and the reactive power (Q) obtained from step 1.
3. Calculate the line-to-line voltage and line current from the complex power.
4. Obtain the Complex I phase by dividing the line current by √3 (since it's a Y-connection).
5. Convert the complex power S to polar and rectangular forms.
6. Finally, calculate the per-phase impedance (Z) by dividing the line-to-neutral voltage by the phase current.

The per-phase impedance will give an insight into the resistance and reactance in the circuit which determine how the voltage and current are related in terms of phase.

Answer 2

The student's question involves calculating reactive power (Q), line and phase currents (Complex I line and I phase), total complex power (S3-Ø) in polar and rectangular form, and per-phase impedance (Z phase) for a Three-Phase Y Connection load with given specifications.

Step-by-step explanation:

The student is asked to calculate various parameters related to a Three-Phase Y Connection AC circuit with a given line-to-line voltage (VLL), total real power (P) and power factor (cos φ) that is leading.

To find the reactive power (Q), we use the formula Q = P * tan(acos(cos φ)). Since the power factor is leading, this implies that the circuit has more capacitive reactance than inductive reactance.

The line current (Complex Iline) and phase current (Complex Iphase) can be calculated based on the real power (P), power factor and the line to line voltage. Considering the Y configuration, the phase voltage (Vphase) is VLL/√3. The complex power (S3-Ø) in both polar and rectangular forms is found using P and Q, and it is denoted as S = P + jQ, where j is the imaginary unit.

The impedance per phase (Zphase) is determined by the relationship Z = Vphase/Iphase, and the complex power S also relates to Z as S = Iphase² * Z*. Finally, these values can be represented graphically on a phasor diagram.