Supplied complex power from source vs consumed by load

[eehelp150]

Homework Statement

Homework Equations

S= 3VaIa*

The Attempt at a Solution

After transformation:

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?

 

[cnh1995]

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?

 

[eehelp150]

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
?

 

[cnh1995]

Load impedance = 5 + j6
Load current = 12<-53.13A
I*I*Z
?

Yes. Take magnitudes only.
S=I²Z.

 

[eehelp150]

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?

 

[cnh1995]

So 144 * (5+j6)

Yes.

Is it right for these values to not match?

Yes. Can you say why?

 

[eehelp150]

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?

 

[cnh1995]

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.

 

[eehelp150]

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?

 

[cnh1995]

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.

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*).

 

[eehelp150]

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?

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)?

 

[cnh1995]

Calculate the total complex power consumed by the load and determine the load's power factor

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.

So magnitude of (5+j6) = sqrt(61)?

Yes.

 

[eehelp150]

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?

 

[cnh1995]

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?