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An induction motor operating at 0.8 pf lag consuming 500 kW. A zero real power consuming synchronous motors is connected across the induction motor raise the power factor to unity. The reactive power drawn by synchronous motor is___ (kVAR)
Correct answer is between '374,376'. Can you explain this answer?
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An induction motor operating at 0.8 pf lag consuming 500 kW. A zero re...
P = 500 kW, Power factor = 0.8
KVA = 500/0.8 = 625 KVA
Reactive power drawn = 625 × 0.6 = 375 kVAR
To rise the power factor to unity, the total kVAR drawn by induction motor should be supplied by synchronous motor. KVAR drawn by synchronous motor is 375 kVAR.
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An induction motor operating at 0.8 pf lag consuming 500 kW. A zero re...
Given information:
- Induction motor operating at 0.8 power factor (lagging)
- Power consumed by the induction motor = 500 kW
- Zero real power consuming synchronous motor is connected across the induction motor to raise the power factor to unity
To find:
The reactive power drawn by the synchronous motor
Solution:
Step 1: Calculate the apparent power of the induction motor
Apparent power (S) = Real power (P) / Power factor (pf)
Given P = 500 kW and pf = 0.8 (lagging)
So, S = 500 kW / 0.8 = 625 kVA
Step 2: Calculate the reactive power of the induction motor
Reactive power (Q) = √(S^2 - P^2)
Q = √(625^2 - 500^2)
Q = √(390625 - 250000)
Q = √140625
Q = 375 kVAR (approximately)
Step 3: Calculate the reactive power of the synchronous motor
Since the synchronous motor is connected to raise the power factor to unity (1), it compensates for the reactive power drawn by the induction motor.
Reactive power drawn by the synchronous motor = - Reactive power drawn by the induction motor
Therefore, the reactive power drawn by the synchronous motor is -375 kVAR.
Step 4: Calculate the total reactive power
Since the synchronous motor is connected across the induction motor, the total reactive power is the sum of the reactive powers of both motors.
Total reactive power = |Reactive power of induction motor| + |Reactive power of synchronous motor|
Total reactive power = |375 kVAR| + |(-375 kVAR)|
Total reactive power = 375 kVAR + 375 kVAR
Total reactive power = 750 kVAR
Conclusion:
The reactive power drawn by the synchronous motor is 375 kVAR, which falls within the range of 374-376 kVAR as specified in the correct answer.
- Induction motor operating at 0.8 power factor (lagging)
- Power consumed by the induction motor = 500 kW
- Zero real power consuming synchronous motor is connected across the induction motor to raise the power factor to unity
To find:
The reactive power drawn by the synchronous motor
Solution:
Step 1: Calculate the apparent power of the induction motor
Apparent power (S) = Real power (P) / Power factor (pf)
Given P = 500 kW and pf = 0.8 (lagging)
So, S = 500 kW / 0.8 = 625 kVA
Step 2: Calculate the reactive power of the induction motor
Reactive power (Q) = √(S^2 - P^2)
Q = √(625^2 - 500^2)
Q = √(390625 - 250000)
Q = √140625
Q = 375 kVAR (approximately)
Step 3: Calculate the reactive power of the synchronous motor
Since the synchronous motor is connected to raise the power factor to unity (1), it compensates for the reactive power drawn by the induction motor.
Reactive power drawn by the synchronous motor = - Reactive power drawn by the induction motor
Therefore, the reactive power drawn by the synchronous motor is -375 kVAR.
Step 4: Calculate the total reactive power
Since the synchronous motor is connected across the induction motor, the total reactive power is the sum of the reactive powers of both motors.
Total reactive power = |Reactive power of induction motor| + |Reactive power of synchronous motor|
Total reactive power = |375 kVAR| + |(-375 kVAR)|
Total reactive power = 375 kVAR + 375 kVAR
Total reactive power = 750 kVAR
Conclusion:
The reactive power drawn by the synchronous motor is 375 kVAR, which falls within the range of 374-376 kVAR as specified in the correct answer.
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An induction motor operating at 0.8 pf lag consuming 500 kW. A zero real power consuming synchronous motors is connected across the induction motor raise the power factor to unity. The reactive power drawn by synchronous motor is___ (kVAR)Correct answer is between '374,376'. Can you explain this answer?
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An induction motor operating at 0.8 pf lag consuming 500 kW. A zero real power consuming synchronous motors is connected across the induction motor raise the power factor to unity. The reactive power drawn by synchronous motor is___ (kVAR)Correct answer is between '374,376'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about An induction motor operating at 0.8 pf lag consuming 500 kW. A zero real power consuming synchronous motors is connected across the induction motor raise the power factor to unity. The reactive power drawn by synchronous motor is___ (kVAR)Correct answer is between '374,376'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An induction motor operating at 0.8 pf lag consuming 500 kW. A zero real power consuming synchronous motors is connected across the induction motor raise the power factor to unity. The reactive power drawn by synchronous motor is___ (kVAR)Correct answer is between '374,376'. Can you explain this answer?.
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