Question

A balanced 3 phase system is given with the following specifications:

- The balanced system has a single delta-connected source and a single Y-connected load side.

- Between the source and the load side there is the line_impedance = R_linr+ jX_line.

- The average power and reactive power delivered form the source is P_in = 500 Watt and Q_in = 500 VAR respectively.

- The source side line voltage is V_{line_source}=100 Volt (rms).

- The load side average and reactive powers are P_load = 400 Watt and Q_load = 0 VAR respectively

a) Draw the circuit diagram of this three phase system

b) Find source side line current I_{line_source}

c) Find R_line and X_line values of line_impedance

d) Find the load side line voltage V_{line_load} and load side phase voltage V_{phase_load}

Answer 1

@ 3-phase system: Riine & jx line A IA د Van Zy Nab 24 IB to mm +B Consider 100 Lo (b) we have Pin = 500 in complex power a Total Qin = 500 VAR Pin + j Qin 500 + j 500 = 500 52 L45 V.A. x Total ap complex V power = √3 Vinne (I line) 5000 Lus' = B(100 Lo ) ( I sinek 4.082 245° ( I nine) 4.082 L-45 A Iirne (0) 4.082 L-45° A IA= If I line 4.082 L-165 A. then IB = 4.082 L-45 x 1 L-120 Side A boad At have we Total active power Pin = 500w and Pload 400w generated by source is equal to active power absorbed by line and load, Pin Prine + Pload, * Pline Sum of the = 100 W Prine + uoo 500 -

where Pline 31IAP Rane 100 Rline 252 3(4.082)² Simillenly Qin 500WAR. 500 to Qline + Groad Qline * Qline 31 IAR Xine 500 where Qline = 102 Xline 3 (4.082) (2+; 10) .. » Line impedence Zrine Star Connected currents flow in phases of d) The same line load. Ian = I line = 4.082 L-45A Total complex power in load side Sload - Pload & j Qload = 400+ j(0) 400 LO (or) Sload B (Voine) (Ian) Sload = 3(Van) (Jan)* 400 Loo 3(Van) (4.082 L-45% Van = 32.664 L-45° v. → Vab= B 230 X 32. Van = 3 £30 x 32 664 45° 56.58 L-15°v. 56.58 L-15°V Vline- lead 32.664 L45°v, * Load side line Voltage phase voltage Uphase-load