Question

Two balanced three-phase loads that are connected in parallel are fed by a three-phase line having a series impedance of (0.4+????2.7) Ω per phase. One of the loads absorbs 560 kVA at 0.707 power factor lagging, and the other 132 kW at unity power factor. The line-to-line voltage at the load end of the line is 2200√3 V. Compute (a) the line-to-line voltage magnitude (in RMS value) at the source end of the line, (b) the total real and reactive power losses in the three-phase line, and (c) the total real and reactive power supplied at the sending end of the line.

Answer 1

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Step-by-step explanation:

a)

S1 560 e^(j acos 0.707 ) ⋅kVA S1 = ( ) 395.92 396.04j kW+ ⋅

S2 := 132 kW⋅ S2 = 132 kW⋅

Sd S1 +S2 :=

Sd = 527.92 396.04j kW

Sd = 660 kVA ⋅

arg Sd = 36.877 deg ⋅

Vd 2.2 e^(− j⋅0⋅deg)⋅kV

current in the line =(Sd/3 Vd) ⋅

⎯

:=

I Line = 79.988 60.006j A

Line = 99.994 A

arg I( ) Line = −36.877⋅deg

r Line := 0.4⋅Ω resistance in the line xLine := 2.7⋅Ω

Vsan Vd+ (r Line+ j xLine) ILine

Vsan = ( ) kV 2.394 0.192j + ⋅ Vsan = 2.402 kV⋅ arg V( ) san = 4.584 deg ⋅

Vsab 3 e

j 30 ⋅ ⋅deg ⋅ Vsan := ⋅

Vsab = ( ) kV 3.425 2.361j + ⋅ Vsab = 4.16 kV⋅ arg V( ) sab = 34.584 deg

b)

PLine 3 I ( ) Line

2 ⋅ r

Line := ⋅

PLine = 12 kW⋅

QLine 3 I ( ) Line

2 ⋅ xLine := ⋅ QLine = 80.99 kVAR ⋅

c)

Ss 3 Vsan ⋅ I

Line := ⋅

⎯ Ss = ( ) kVA 539.919 477.03j + ⋅

Ss = 720.5 kVA ⋅ arg S( )s = 41.461 deg ⋅

Ps Re S( )s := Ps = 540 kW⋅

Qs Im S( )s := Qs = 477 kVAR ⋅

S1 S2 + PLine + j QLine + ⋅ = ( ) kVA 539.919 477.03j + ⋅ Check