Question

A balanced, positive-sequence, wye-connected source has V- 220/0 V rms and supplies an unbalanced wye-connected load ZAN-7 10 Ω, ZBN-8 +j6 Ω, and ZCN 10-j12 Ω via transmission lines with impedances ZA-2 +jl Ω, ZB-2-j0.5 Ω, and ZC-2 +j | Ω (a) Label all node voltages and loop currents (b) Determine the currents IaA? IbB, and 1cC. (c) Determine the voltages VAN, N, and VCN (d) Determine the voltages VAR, VRc, and VCA (e) (i) Determine the total complex power absorbed by the load (ii) Determine the total complex power of the source (f) Determine the total complex power losses in the transmission line 220/0° V( 220-120° V AN ZB 220/120 V BN C. Z Fig. P1.1

Explain Please.

Answer 1

Figure (i) Given V_an = 220 angle 0 degree V, V_bn = 220 angle -180 degree, Z_cn = 220 angle 120 Z_A = 2 + j 1 ohm, Z_B = 2 - j 0.5 ohm, Z_C = 2 + j 1 ohm Z_AN = 7 + j 10 ohm, Z_BN = 8 + j 6 ohm, Z_CN = 10 - j 12 ohm Apply KVL for loop 1, V_an - Z_A i_1 - Z_AN i_1 - Z_BN (i_1 + i_2) - Z_B (i_1 + i_2) = V_bn (- Z_A - Z_B - Z_AN - Z_BN) i_1 - (Z_BN + Z_B) i_2 = V_bn - V_an (-2 - j 1 - 2 + j 0.5 - 7 - j 10 - 8 - j 6) i_1 - (8 + j 6 + 2 - j 0.5) i_2 = 220 angle -120 degree - 220 angle 0 degree (- 19 - j 16.5) i_1 - (10 + j 5.5) i_2 = -330 - j 190.5 -(1) Apply KVL for loop 2, V_cn - Z_C i_2 \r\n < null