Question 16.20: An average power of 20 kW is delivered to a balanced Δ-conne......
An average power of 20 kW is delivered to a balanced Δ-connected load with Z_{Δ} = 30 + j45 Ω/phase. Find the line voltage V_{L} at the load and the complex power delivered to the load.
In a balanced Δ-connected load the phase current I_{P} passes through all three of the phase impedances. The total average power delivered to the load is P_{L} = 3I^2_{P}R_{Δ}, where R_{Δ} is the resistive part of the phase impedance Z_{Δ}. Solving for I_{P} yields
I_{P} =\sqrt{\frac{P_{L}}{3R_{Δ}}}=\sqrt{\frac{20 × 10^3}{3 × 30}}= 14.9 A (rms)
The total complex power delivered to a delta load is then found as
S_{L} = 3I^2_{P}Z_{Δ} = 3(14.9)^2 (30 + j45)
= 20 × 10³ + j30 × 10³ VA
Given the phase current, the line current is I_{L} =\sqrt{3} × 14.9 = 25.8 A(rms). The apparent power delivered to any balanced load is |S_{L}| =\sqrt{3}V_{L}I_{L}. Solving for the line voltage gives
V_{L} =\frac{|S_{L}|}{\sqrt{3}I_{L}}=\frac{|20 × 10^3 + j30 × 10^3|}{\sqrt{3} × 25.8} =807 V (rms)