Question

A balanced Y-connected voltage source with V_ab = 480/0° V is connected to a balanced Δ- load with ZΔ = 30/40° 12. The line impedance between the source and load is Z_L = 1/85° Ω (almost an inductor) for each phase. Calculate the per-unit and actual current in phase a of the line using S_base 3ϕ = 10 kVA and V_baseLL= 480 V. (Hint: first determine the L-N base Z, L- N base voltage.)

Answer 1

To calculate the per-unit and actual current in phase a of the line, first determine the L-N base impedance and voltage. Then, calculate the per-unit and actual current using the given values and formulas.

Step-by-step explanation:

To calculate the per-unit and actual current in phase a of the line, we first need to determine the L-N base impedance and voltage. The L-N base voltage (VbaseLN) can be found by dividing the L-L base voltage (VbaseLL) by √3. In this case, VbaseLL = 480 V, so VbaseLN = 480 / √3 = 277.1 V.

The L-N base impedance (ZbaseLN) can be found by dividing the L-L base impedance (ZbaseLL) by 3. In this case, ZbaseLL = 1 ∠ 85° Ω, so ZbaseLN = (1 / 3) ∠ 85° = 0.33333 ∠ 85° Ω.

Now, we can calculate the per-unit current in phase a of the line:

Per-unit current = |Vab| / ZbaseLN = 277.1 / 0.33333 ≈ 831.3 A.

Finally, to calculate the actual current in phase a of the line, we multiply the per-unit current by the base current:

Actual current = 831.3 A * (10 kVA / 3 * 480 V) = 547.69 A.