Answered: A 400-V DB in a factory hall supplies…

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter2: Fundamentals

Section: Chapter Questions

Problem 2.48P

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Question

A 400-V DB in a factory hall supplies the following 3-phase loads:
12- kVA induction motor load at PF=0.94 lag and wye connected
20- kW inductive heating load at PF=0.90 lag and delta-connected
(a) Determine line current phasors of each load.and also total line current phasor.
(b) Draw current phasors found in part (a) for only R-phase on the graph given below.
(c) Determine the total complex powers S drawn from the source.
(d) Determine also the total P and Q components of the complex power.

Expert Solution

Step 1

Given Data:

VL = 400 V

Sload1 = 12 kVA

Pload2 = 20 kW

$\cos ϕ 1 = 0.94 l a g \cos ϕ 2 = 0.90 l a g$

Step 2

Answer A

$I (l o a d 1) = \frac{S l o a d 1}{\sqrt{3} x V l} = \frac{12000}{\sqrt{3} x 400} = 17.32 i n p h a s o r f o r m I (l o a d 1) = 17.32 ∠ - \cos^{- 1} 0.94 = 17.32 ∠ - 19.94 A P (l o a d 2) = \sqrt{3} x V l o a d 2 x I l o a d 2 x \cos \emptyset 2 20000 = \sqrt{3} x 400 x I l o a d 2 x 0.9 I l o a d 2 = 32.07 i n p h a s o r f o r m I l o a d 2 = 32.07 ∠ - \cos^{- 1} 0.9 = 32.07 ∠ - 25.84 A T o t a l c u r r e n t I S = I l o a d 1 + I l o a d 2 = 49.33 ∠ - 23.77 A$

Step 3

Answer B

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