**Title: Analysis of a Balanced Three-Phase Delta-Wye System** **Problem Statement:** In the balanced three-phase delta-wye system shown below: - \( V_{ab} = 440 \angle 0^\circ \) V rms - \( V_{bc} = 440 \angle -120^\circ \) V rms - \( V_{ca} = 440 \angle -240^\circ \) V rms - \( Z_Y = 4.5 + j10.5 \, \Omega \) - \( Z_F = 0.5 + j1.5 \, \Omega \) Find the (a) magnitude of line current and (b) the average power delivered to the load. **Diagram Explanation:** 1. The diagram depicts a balanced delta-wye (Δ-Y) electrical network. 2. Points a, b, and c represent the connection points in the delta configuration. 3. \( Z_F \) represents the impedance in the delta configuration. 4. Points A, B, and C represent the connection points in the wye (Y) configuration. 5. \( Z_Y \) represents the impedance in the wye configuration. 6. The line current \( I_a \) flows from point a to A. **Solution Steps:** 1. **Convert Delta Impedances to Wye:** - Use the transformation formulas to convert \( Z_F \) into equivalent wye impedances. This enables the analysis of line and phase currents. 2. **Calculate Line Current Magnitude:** - Use the phase voltages \( V_{ab}, V_{bc}, \) and \( V_{ca} \) to determine the phase currents through \( Z_Y \). - Apply Ohm’s Law in the wye connection. 3. **Determine Average Power Delivered:** - Use the formula for power in a three-phase system: \[ P_{\text{avg total}} = \sqrt{3} \times V_L \times I_L \times \cos(\theta) \] - Calculate the power factor using the impedance angles. By following these steps, you can solve for the line current and average power delivered to the load in a balanced delta-wye system.

11 B/s A load of 120 MW at a power factor of 0.9 lagging can be delivered by a 3-phase transmission line. The voltage at the receiving end is to be maintained at 42 kV and the loss in the transmission is 8 % of the power delivered. (Consider the line to be a short transmission line) Find Single phase Power delivered Per phase voltage Current flowing through the transmission line 3 Phase Losses in the transmission line Per phase resistance of the transmission line II