# Three-phase circuit.

#### cdummie

Joined Feb 6, 2015
124
So i have a three phase circuit with effective value of line voltage Ul=220sqrt(3) V (voltages are symmetric), other known values are R=ωL=1/(ωC) = 10Ω. I have to find the active power of receiver. The only problem for me in this example is the way resistors are connected in circuit. I really don't know what kind of connection is this, are resistors in parallel with coils and if the are, then, could anyone explain me how is that so?

#### Johann

Joined Nov 27, 2006
190
The resistors are connected in Delta. They are not in parallel with the coils. The coils are connected in Star (wye).
In short, the coils are subjected to the line voltage divided by square root of 3 = phase voltage.
The resistors are subjected to full line voltage each.

#### cdummie

Joined Feb 6, 2015
124
The resistors are connected in Delta. They are not in parallel with the coils. The coils are connected in Star (wye).
In short, the coils are subjected to the line voltage divided by square root of 3 = phase voltage.
The resistors are subjected to full line voltage each.
What would happen if i transform resistors R into star? Then they would be subjected to phase voltage, right? And, the most important, since i want to find active power how can i do it with this circuit, i mean i need current through every element, how can i find them, since the current through C is not the same as through the L and R?

#### WBahn

Joined Mar 31, 2012
24,974
So i have a three phase circuit with effective value of line voltage Ul=220sqrt(3) V (voltages are symmetric), other known values are R=ωL=1/(ωC) = 10Ω. I have to find the active power of receiver.

View attachment 100152

The only problem for me in this example is the way resistors are connected in circuit. I really don't know what kind of connection is this, are resistors in parallel with coils and if the are, then, could anyone explain me how is that so?
1) What are you referring to when you say "line voltage"? Are you referring to the line-to-line voltage?

2) The statement "R=ωL=1/(ωC) = 10Ω" is pretty sloppy, but strictly speaking correct.

3) What part of the circuit constitutes the "receiver" that you are trying to find the "active power" of?

4) What do you mean by "active power"? Do you mean "real power"?

#### WBahn

Joined Mar 31, 2012
24,974
The resistors are connected in Delta. They are not in parallel with the coils. The coils are connected in Star (wye).
In short, the coils are subjected to the line voltage divided by square root of 3 = phase voltage.
The resistors are subjected to full line voltage each.
Even if you removed the resistors entirely the coils would not be subjected to the voltage you describe due to the presence of the capacitors.

Similarly, the resistors are not subjected to the full line voltage due to the capacitors.

#### WBahn

Joined Mar 31, 2012
24,974
The only problem for me in this example is the way resistors are connected in circuit. I really don't know what kind of connection is this, are resistors in parallel with coils and if the are, then, could anyone explain me how is that so?
If you consider the capacitors as part of the generator circuits, then you have a delta-connected load and a star-connected load. If you look a the whole thing as a single load, then you have a hybrid.

#### WBahn

Joined Mar 31, 2012
24,974
What would happen if i transform resistors R into star? Then they would be subjected to phase voltage, right? And, the most important, since i want to find active power how can i do it with this circuit, i mean i need current through every element, how can i find them, since the current through C is not the same as through the L and R?
No, they won't be subject to the phase voltage because of the presence of the capacitors -- your transformed resistor load will NOT be connected directly to the power lines.

If by "active power" you mean "real power", then you only need the current in the resistors, right? The other elements dissipate no real power.

• Johann

#### cdummie

Joined Feb 6, 2015
124
1) What are you referring to when you say "line voltage"? Are you referring to the line-to-line voltage?

2) The statement "R=ωL=1/(ωC) = 10Ω" is pretty sloppy, but strictly speaking correct.

3) What part of the circuit constitutes the "receiver" that you are trying to find the "active power" of?

4) What do you mean by "active power"? Do you mean "real power"?
1)If Ur and Us are phase-voltages then U= Ur - Us is line voltage, i don't know the actual name of it, so i thought it's line voltage

3)Reciever - all the elements in the circuit that don't generate current or voltage (resistor, inductor and capacitor)
4)active power is real power

#### cdummie

Joined Feb 6, 2015
124
No, they won't be subject to the phase voltage because of the presence of the capacitors -- your transformed resistor load will NOT be connected directly to the power lines.

If by "active power" you mean "real power", then you only need the current in the resistors, right? The other elements dissipate no real power.
So i only need to find current through the resistors to find real power? Can i use one of the standard methods to do this?

#### WBahn

Joined Mar 31, 2012
24,974
So i only need to find current through the resistors to find real power? Can i use one of the standard methods to do this?
A three-phase circuit is just a circuit and any and all general analysis techniques apply. You can just often greatly simplify the analysis by using techniques that apply to balanced three-phase systems.

#### cdummie

Joined Feb 6, 2015
124
A three-phase circuit is just a circuit and any and all general analysis techniques apply. You can just often greatly simplify the analysis by using techniques that apply to balanced three-phase systems.
Ok, now i know, but, what if i transformed inductors into triangle, would that mean that every inductor is in parallel with corresponding resistor?

#### WBahn

Joined Mar 31, 2012
24,974
Ok, now i know, but, what if i transformed inductors into triangle, would that mean that every inductor is in parallel with corresponding resistor?
Yes. And then you could transform that back into a wye and combine it with the capacitors. Then you could transform that single load back into a delta. At that point it will be trivial to determine the current in one of the branches and, from there, to find the real power in one branch.

Note that, because it is balanced, you could get away with transforming the resistors into a wye and then use symmetry arguments to say that they are virtually in parallel with the inductors. But it is important to understand that this would ONLY be valid for the balanced case.

• cdummie

#### MrAl

Joined Jun 17, 2014
6,817
Hi,

Just to note, in 3 phase systems it is common to refer to either the line to line voltage or the line to neutral voltage. These are often abreviated as L-L and L-N or just LL and LN.
"line" voltage by itself would be taken to mean the line to neutral voltage, but it's better to specify only one of the two above rather than just "line" by itself.

• cdummie