Expressing motor loads in polar form

In summary, Dumbkiwi explains that the form impedance of a load in an AC current is a complex number, Z = R + jX where R is the resistance of the load and X is its reactance. Polar form is the form rejθ, or in this case Z = |Z|ejφ. Dumbkiwi also explains that voltage leads current by a phase angle φ, so Z = |Z|cosφ + j|Z|sinφ. Finally, he says that he is too tired to try and work through the problem himself but will post again when he has had time to look at it.
  • #1
dumbkiwi
5
0

Homework Statement


I am having difficulty with a question on my Electrical course and the expressing a motor load voltage and current in polar form. The motor is single phase 2.8 KW efficiency 70% and 80% of full load runs with a power factor of 0.8 lagging. Voltage 400v.

Express the motor loads as impedances in polar and complex number forms assuming the motors are operating at 400v. This "express" has me baffled and have spent 4 hours trying to get past this bit of the problem. My notes are not clear on the form this should take and I am now stuck as it were.



Homework Equations





The Attempt at a Solution


I have worked out that 80% of 2.8 Kw is 2.24kw which with a voltage of 400v gives a current of 7amps. With a power factor of 0.8 I get a Cos of 36.86 degrees. The current is lagging. If current is expressed as 7xCos38.86 is voltage then 400xCos38.86? My notes are not very clear on these two expressions and can't progress until I have this information.

Many thanks, Dumbkiwi.
 
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  • #2
Welcome to PF!

Hi dumbkiwi! Welcome to PF! :smile:
dumbkiwi said:
Express the motor loads as impedances in polar and complex number forms assuming the motors are operating at 400v. This "express" has me baffled and have spent 4 hours trying to get past this bit of the problem. My notes are not clear on the form this should take and I am now stuck as it were.

The impedance of a load (a combination of components) in an AC current is a complex number Z = R + jX where R is the resistance of the load and X is its reactance.

For a load for which the voltage leads the current by a phase angle φ:

Z = |Z|cosφ + j|Z|sinφ.​

Polar form is the form rejθ, or in this case Z = |Z|ejφ :wink:
 
  • #3
Hi Tiny Tim,

Thanks for your reply, I think it will help but I am too tired to try and work through it just now but will post again when I have had time to look at.

Regards Dumbkiwi.
 
  • #4
hello dumbkiwi,

Is that you Calum If it is I am struggling on this assignment too! fancy meeting up and putting our heads together?

salv
 
  • #5
Hey Salv,

Yeah could do that. I'll send you a pm with my phone number.

See you soon mate.

Regards Callum.
 

1. What is the concept of expressing motor loads in polar form?

Expressing motor loads in polar form is a way to represent the characteristics of a motor load in terms of magnitude and angle. It is a mathematical representation that helps in analyzing and understanding the performance of a motor load.

2. Why is it important to express motor loads in polar form?

Expressing motor loads in polar form allows for easier analysis and calculation of the motor's performance. It also helps in understanding the effects of different parameters on the motor's operation, such as voltage and current.

3. How is the polar form of a motor load determined?

The polar form of a motor load can be determined by converting the rectangular form of the load parameters (real and reactive power) into polar form using trigonometric functions.

4. Can motor loads be expressed in polar form for both AC and DC motors?

Yes, motor loads can be expressed in polar form for both AC and DC motors. However, the calculations may differ slightly due to the different characteristics of these types of motors.

5. What are the advantages of using polar form to express motor loads?

Using polar form to express motor loads allows for a simpler and more intuitive understanding of the motor's performance. It also makes it easier to analyze and compare different motor loads and their effects on the overall system.

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