Supplied complex power from source vs consumed by load

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Discussion Overview

The discussion revolves around the calculation of complex power supplied from a source versus the power consumed by a load in a three-phase electrical system. Participants explore the relationships between load impedance, load current, and the resulting active and reactive power, as well as the implications of using per-phase equivalents.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the total complex power supplied from the source as 2592W + j3456 VAR and seeks to determine the power consumed by the load.
  • Another participant suggests using the load impedance and load current to find the active and reactive power associated with the load, proposing the formula S = I²Z.
  • There is a discussion about whether to take magnitudes only when calculating power, with some participants affirming this approach.
  • One participant questions if the calculated values for load power should match the total complex power supplied, expressing confusion over the apparent discrepancy.
  • Another participant explains that the total power for three phases should be multiplied by 3, noting that some power is associated with line impedance and not all is fed to the load.
  • Participants discuss whether to use the calculated load power directly or multiply it by 3 for total power, with a consensus that multiplication is necessary due to the per-phase equivalent transformation.
  • There is a mention of using the single-phase equivalent network for calculating load power factor in a balanced network.
  • Questions arise regarding how to derive the power factor from the load impedance.

Areas of Agreement / Disagreement

Participants generally agree that the load power should be multiplied by 3 to account for the three-phase system. However, there is ongoing uncertainty regarding the relationship between the calculated load power and the total complex power supplied, as well as the correct approach to determining the power factor.

Contextual Notes

Some assumptions about the circuit's configuration and the nature of the load may not be fully articulated, and there are unresolved questions about the implications of line impedance on the total power consumed by the load.

Who May Find This Useful

Students and practitioners in electrical engineering, particularly those studying three-phase power systems and complex power calculations.

eehelp150
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Homework Statement


upload_2016-10-27_0-28-37.png

upload_2016-10-27_0-28-49.png


Homework Equations


S= 3VaIa*

The Attempt at a Solution


After transformation:
upload_2016-10-27_0-30-5.png

Ia = 120<0 / (6+8j) = 12<-53.13 A
Total complex power = 3 * Va * Ia* = 3*120<0 * 12<53.13 = 2592W + j3456 VAR
This is the power supplied from source. What would be the power consumed by load?
 

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eehelp150 said:
What would be the power consumed by load?
You know the load impedance and load current. How will you determine the active and reactive power associated with the load?
 
cnh1995 said:
You know the load impedance and load current. How will you determine the active and reactive power associated with the load?
Load impedance = 5 + j6
Load current = 12<-53.13A
I*I*Z
?
 
eehelp150 said:
Load impedance = 5 + j6
Load current = 12<-53.13A
I*I*Z
?
Yes. Take magnitudes only.
S=I2Z.
 
Last edited:
cnh1995 said:
Yes. Take magnitudes only.
S=I2Z.
So 144 * (5+j6)
?

power of (1+j2)= 144 * (1+2j)
and
(load) = 144*(5+j6)
combined become 864W + j1152VAR

but the total complex power is 2592W + j3456VAR

Is it right for these values to not match?
 
Last edited:
eehelp150 said:
So 144 * (5+j6)
Yes.
eehelp150 said:
Is it right for these values to not match?
Yes. Can you say why?
 
cnh1995 said:
Yes.

Yes. Can you say why?
Is it because it's 1/3 of the "actual" circuit?
Do I need to multiply by 3 to get the total complex power consumed by load?

If no, does this look correct?
720W + j864VAR

Load power factor:
S = sqrt(Q^2+P^2) = 1124VA
PF = P/S = 720/1124 = 0.64 lagging (Q>0)
correct?
 
eehelp150 said:
Is it because it's 1/3 of the "actual" circuit?
Do I need to multiply by 3 to get the total complex power consumed by load?

If no, does this look correct?
720W + j864VAR

Load power factor:
S = sqrt(Q^2+P^2) = 1124VA
PF = P/S = 720/1124 = 0.64 lagging (Q>0)
correct?
Well, you calculated the total power for three phases. So, you should multiply the load power by 3. But they are not equal because out of total input power, some power is associated with the line impedance 1+j2 ohm. Remaining power is fed to the load.
 
cnh1995 said:
Well, you calculated the total power for three phases. So, you should multiply the load power by 3. But they are not equal because out of total input power, some power is associated with the line impedance 1+j2 ohm. Remaining power is fed to the load.
If the prompt is:
Calculate the total complex power consumed by the load and determine the load's power factor

Do I use what I calculated (720W + j864VAR) or do I need to multiply that by 3?
 
  • #10
eehelp150 said:
If the prompt is:
Calculate the total complex power consumed by the load and determine the load's power factor

Do I use what I calculated (720W + j864VAR) or do I need to multiply that by 3?
You should multiply by 3. You have transformed the circuit into its per phase equivalent. Total power will be thrice the per phase power.
eehelp150 said:
power of (1+j2)= 144 * (1+2j)
and
(load) = 144*(5+j6)
combined become 864W + j1152VAR
Here, while applying S=I2Z, you should consider the magnitude only. If you want to use the phasor form, you should take the conjugate of the current i.e. (IZ)(I*).
 
  • #11
cnh1995 said:
Well, you calculated the total power for three phases. So, you should multiply the load power by 3. But they are not equal because out of total input power, some power is associated with the line impedance 1+j2 ohm. Remaining power is fed to the load.
If the prompt is:
Calculate the total complex power consumed by the load and determine the load's power factor

Do I use what I calculated or do I need to multiply that by 3?
cnh1995 said:
You should multiply by 3. You have transformed the circuit into its per phase equivalent. Total power will be thrice the per phase power.

Here, while applying S=I2Z, you should consider the magnitude only. If you want to use the phasor form, you should take the conjugate of the current i.e. (IZ)(I*).
So magnitude of (5+j6) = sqrt(61)?
 
  • #12
eehelp150 said:
Calculate the total complex power consumed by the load and determine the load's power factor
cnh1995 said:
You should multiply by 3. You have transformed the circuit into its per phase equivalent. Total power will be thrice the per phase power.
For load power factor, you can use the single phase equivalent network since it is a balanced network.
eehelp150 said:
So magnitude of (5+j6) = sqrt(61)?
Yes.
 
  • #13
cnh1995 said:
For load power factor, you can use the single phase equivalent network since it is a balanced network.

Yes.
so load would be 3 * 144*sqrt(61)?
How do i get power factor from this?
 
Last edited:
  • #14
eehelp150 said:
so load would be 3 * 144*sqrt(61)?
How do i get power factor from this?
If the load impedance is R+jX, what would its power factor?
 

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