P= 1.732 X 230V X 42A X 0.85 = 10,731.06 W or 10.73 kW

In summary, a 15 hp/230V, three phase induction motor with a full load current of 42A per terminal has a full load kVA input of 16kVA and a kW input of 13.5kW at a power factor of 0.85. The motor can be connected in either Wye or Delta configurations, with the calculated kVA and kW inputs differing slightly between the two. The 15 hp (11kW) stated in the original question is likely the motor's rated power, while the calculated kW input of 13.5kW is its actual input power. The wording in the problem can be ambiguous and may require clarification.
  • #1
JGrecs
14
0
3 PHASE INDUCTION MOTOR

A 15 hp/230V, three phase induction motor has a full load current of 42A per terminal.
15HP= 11kW

find:
a) Full load kVA input
b) If the full load power factor is lagging 0.85, what is the kW input.

My question: How do I know whether its connected Wye or Delta?a) kVA= 1.732 X ELine X ILine

ELine= 230V ILine=IPhase (Wye) and ILine=IPhase X 1.732 (Delta)

b) P= 1.732 X Eline X ILineX PF
 
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  • #2
A)

Wye: kVA= 1.732 X 230V X 40A

kVA= 16kVA

Delta: kVA= 1.732 X 230V X 69A

kVA= 27kVA

B)

Wye: P= 1.732 X 230V X 40A X 0.85

P= 13.5kW

Delta: P= 1.732 X 230V X 69A X 0.85

P= 23.4kWHow do these look?
 
  • #3
The problem stated the motor current as 42A per terminal. So that would be the line current. The motor is said to be 230V, so I think you can take that as the line-to-line voltage.
 
  • #4
Ok, so "per terminal" refers to "Line-to-Line"?
so Id go with these:

kVA= 1.732 X 230V X 40A
kVA= 16kVA

P= 1.732 X 230V X 40A X 0.85
P= 13.5kW

Also, the 15HP (11kW) stated in the original question. Would that be the motors rated power, while the 13.5kW calculated would be its input power?
 
  • #5
JGrecs said:
Ok, so "per terminal" refers to "Line-to-Line"?
Well, at the very least it refers to the line current since the motor's terminals are where the lines connect. I'm less certain about the interpretation of the wording for the "230V, three phase...". It could refer to the "three phase voltage", making the individual line voltages about 133V. Or it could be the line-to-line voltage. [I hate these ambiguities due to topic-specific "common-knowledge" jargon!]
so Id go with these:

kVA= 1.732 X 230V X 40A
kVA= 16kVA

P= 1.732 X 230V X 40A X 0.85
P= 13.5kW
Yeah, looks good as far as I can tell.
Also, the 15HP (11kW) stated in the original question. Would that be the motors rated power, while the 13.5kW calculated would be its input power?
That would be my interpretation.
 
  • #6
gneill said:
Well, at the very least it refers to the line current since the motor's terminals are where the lines connect. I'm less certain about the interpretation of the wording for the "230V, three phase...". It could refer to the "three phase voltage", making the individual line voltages about 133V. Or it could be the line-to-line voltage. [I hate these ambiguities due to topic-specific "common-knowledge" jargon!]

Yeah, looks good as far as I can tell.

That would be my interpretation.

Yeah my prof likes to throw us off with his wording heh.
Thanks again for your help.
I have 3 more questions to go. Ill post them in this thread If I am stuck.
 
  • #8
Nice! Good find :smile:
 

FAQ: P= 1.732 X 230V X 42A X 0.85 = 10,731.06 W or 10.73 kW

1. What is a 3 phase induction motor?

A 3 phase induction motor is a type of electric motor that uses three alternating currents to generate a rotating magnetic field, which in turn drives the rotation of the motor's rotor. This type of motor is commonly used in industrial and commercial applications due to its high reliability and efficiency.

2. How does a 3 phase induction motor work?

When three alternating currents, each 120 degrees out of phase with each other, are applied to the stator windings of a 3 phase induction motor, a rotating magnetic field is created. This magnetic field induces a current in the rotor, which in turn creates a second magnetic field. The interaction between these two magnetic fields causes the rotor to rotate, thus driving the motor.

3. What are the advantages of using a 3 phase induction motor?

There are several advantages to using a 3 phase induction motor. These include high efficiency, low maintenance, and high reliability. Additionally, these motors do not require any additional starting mechanisms, making them simple and cost-effective to use in various applications.

4. What are the common applications of 3 phase induction motors?

3 phase induction motors are commonly used in industrial and commercial applications, such as in pumps, fans, compressors, and conveyor belts. They are also used in household appliances such as washing machines and air conditioners.

5. How do you maintain a 3 phase induction motor?

Maintenance of a 3 phase induction motor includes regular inspection and cleaning of the motor's components, such as the stator and rotor windings, bearings, and cooling system. It is also important to monitor the motor's performance and address any issues or abnormalities promptly to prevent further damage.

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