# 20210213224813solutions

Content type
User Generated
Subject
Engineering
School
The University of Texas at Dallas
Type
Homework
Rating
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Question 1
Solution:
Data:
V
L
=570V
PF=0.5
P=41KW
No of induction motors=8
The total power consumed by the power system:
  
 
Power consumed by the system is given by:

 
  
 

   


Question 2
Solution:
Using the Line diagram;


 
Delta-connected

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Power consumed by the Y-connected load:
 


 (For a Y-connected generator connected to a Y-connected load their
phase voltages are the same)


 
 

 
The power factor is   






   

Power Consumed by the Delta-connected load:
 

  

(Since the load is delta connected, its phase voltage is equal to the line
voltage of the generator)

    


 
 
 
The power consumed by the load:
The power factor is   

 




    


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Question 1 Solution: Data: VL=570V PF=0.5 P=41KW No of induction motors=8 The total power consumed by the power system: 𝑃 = 𝑁𝑜 𝑜𝑓 𝑖𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑚𝑜𝑡𝑜𝑟𝑠 × 𝑃𝑜𝑤𝑒𝑟 𝑜𝑓 𝑒𝑎𝑐ℎ 𝑖𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑚𝑜𝑡𝑜𝑟 𝑃 = 8 × 41𝐾𝑊 = 328𝐾𝑊 Power consumed by the system is given by: 𝑃 = √3𝑉𝐿 𝐼𝐿 × 𝑃𝐹 𝐼𝐿 = 𝐼𝐿 = 𝑃 √3 × 𝑉𝐿 × 𝑃𝐹 328𝐾𝑊 √3 × 570 × 0.5 𝐼𝐿 = 664.5𝐴𝑚𝑝𝑠 𝐼𝑚 = 𝐼𝐿 = 664.5𝐴𝑚𝑝𝑠 Question 2 Solution: Using the Line diagram; Y-connected load 𝑉𝜃𝐺 = 𝑉𝑎𝑛 = 270 < 0° Delta-connected load Power consumed by the Y-connected load: 𝑍 = 23 < 30° 𝑉𝜃𝐿𝑜𝑎𝑑 = 𝑉𝑎𝑛 = 270𝑉 (For a Y-connected generator connected to a Y-connected load their phase voltages are the same) Phase current in load: 𝐼𝜃𝐿𝑜𝑎𝑑 = 𝑉𝑎𝑛 270 < 0° = 𝑍 23 < 30° 𝐼𝜃𝐿𝑜𝑎𝑑 = 11.74 < −30°𝐴𝑚𝑝𝑠 The power consumed by load: The power factor is 𝑃𝐹 = cos(0 − (−30)) = 𝑐𝑜𝑠30° 𝑃1 = 3𝑉𝜃𝐿 𝐼𝜃𝐿 𝑐𝑜𝑠30 𝑃1 = 3 × 270 × 11.74𝑐𝑜𝑠30 𝑃1 = 8.235𝐾𝑊 Power Consumed by the Delta-connected load: 𝑍 = 10 < −30° 𝑉𝜃𝐿𝑜𝑎𝑑 = √3 × 𝑉𝑎𝑛 (Since the load is delta connected, its phase voltage is equal to the line voltage of the genera ...
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