How reactor sizes effect circuit current and voltage

[mull982]

I want to determine what happens to a circuits current and voltage when different size reactors/inductors are connected in series in each circuit to the same size load.

For instance lets say I have circuits 1 and 2 fed from a 480V supply each with a 100kVA transformer loaded to the the exact same amount. Now lets say that for particular reasons we insert an reactor in series with each transformer however the reactor size for circuit 1 is larger than that of circuit 2. Lets assume its double the size for the sake of conversation.

So with the two transformers loaded to the same amount would I have less current flowing in circuit 1 due to the fact that reactor would caused increased circuit impedance? Would I therefore also have reduced voltage on the primary of the transformer in the first circuit due to the fact that there would be a larger voltage drop across the reactor in the first circuit?

For either circuit, if the reactor was sized so it was 50% of transformer impedance then would % of circuit voltage would drop across reactor and what % would be left across transformer?

 

[Cold Fusion]

It's kind of late. But here is a start. We'er going t use these models. They are from Chapman, Electric Machinery Fundamentals

You work on these. If I get some time tomorrow, I'll find some more.

cf

 

[mivey]

I want to determine what happens to a circuits current and voltage when different size reactors/inductors are connected in series in each circuit to the same size load.

For instance lets say I have circuits 1 and 2 fed from a 480V supply each with a 100kVA transformer loaded to the the exact same amount. Now lets say that for particular reasons we insert an reactor in series with each transformer however the reactor size for circuit 1 is larger than that of circuit 2. Lets assume its double the size for the sake of conversation.

I made some sample calcs for a 100 kVA unit:

Add a 75 kW load at unity pf: V=474.1<-1.29?, I=158.2<-1.29?.

Circuit 1: Add enough inductance to get 37.1 kW load at 70.7% pf (52.4 kVA). V=471.6<-0.33?, I=111.2<-45.36?.

Circuit 2: Halve the inductance of circuit 1: You get 59.2 kW load at 89.4% pf (66.2 kVA). V=471.0<-0.77?, I=140.5<-27.36?.

So with the two transformers loaded to the same amount would I have less current flowing in circuit 1 due to the fact that reactor would caused increased circuit impedance?

Yes

Would I therefore also have reduced voltage on the primary of the transformer in the first circuit due to the fact that there would be a larger voltage drop across the reactor in the first circuit?

I doubt you will have much impact on the primary side as it is usually much stiffer. As for the secondary: You would think Less current = Less voltage drop but you have to consider the power factor as well. The circuit with resistor alone has a higher current but less drop than the scenario with inductance. Adding inductance causes the current to drop. It also causes the voltage drop to increase until the inductance becomes appreciable in size. When the inductance dominates the resistor in size, it determines the voltage drop and if it becomes very large, the load current will approach zero as will the voltage drop.

For either circuit, if the reactor was sized so it was 50% of transformer impedance then would % of circuit voltage would drop across reactor and what % would be left across transformer?

If the impedance of the load is on the order of the transformer size, the transformer will be overloaded and you will essentially have a fault. Here is what you get if the load impedance is 1/2 of the transformer impedance: You get 301.5 kW load at 44.9% pf (672.0 kVA). V=159.9<-0.01?, I=4202.7<-63.35?. So you have 320.1 dropped across the transformer and 159.9 across the load. The transformer is trying to dissipate about 123 kW of heat as opposed to 4.6 kW at full load.

These calcs used some estimated values for the internal impedances but the relative values are certainly valid.

 

[mivey]

..The transformer is trying to dissipate about 123 kW of heat as opposed to 4.6 kW at full load...

Looking at my numbers again, that might should have been:

The transformer is trying to dissipate about 606 kW of heat as opposed to 4.6 kW at full load.

 

[jghrist]

So with the two transformers loaded to the same amount would I have less current flowing in circuit 1 due to the fact that reactor would caused increased circuit impedance? Would I therefore also have reduced voltage on the primary of the transformer in the first circuit due to the fact that there would be a larger voltage drop across the reactor in the first circuit?

What do you mean by the transformers loaded to the same amount? If the loads are constant power type loads like motors, then the current will increase with higher circuit impedance to keep the power the same. If the load is a constant impedance load like resistance heating, then the current will decrease with higher circuit impedance because the voltage across the load will decrease.

 

[mull982]

Attached is a a schematic representing the circuits that I am referring to showing the reactors, transformer and load in each circuit. For the purpose of this exercise lets assume a resistive load on the secondary.

Hopefully this clears up what I was referring to.

 

[mull982]

Sorry Forgot Attachment

 

[mivey]

Attached is a a schematic representing the circuits that I am referring to showing the reactors, transformer and load in each circuit. For the purpose of this exercise lets assume a resistive load on the secondary.

Hopefully this clears up what I was referring to.

In my calcs, I put the added impedance on the load side of the transformer.

 

[mull982]

In my calcs, I put the added impedance on the load side of the transformer.

O.k. I was wondering about your calcs.

I should have been more specific I apoligize, but I was looking for the effects on the primary of the transformer such as primary current, and voltage effects on the transformer primary.

 

[Cold Fusion]

I made some sample calcs for a 100 kVA unit:

Add a 75 kW load at unity pf: V=474.1<-1.29?, I=158.2<-1.29?.

Circuit 1: Add enough inductance to get 37.1 kW load at 70.7% pf (52.4 kVA). V=471.6<-0.33?, I=111.2<-45.36?.

Circuit 2: Halve the inductance of circuit 1: You get 59.2 kW load at 89.4% pf (66.2 kVA). V=471.0<-0.77?, I=140.5<-27.36?. ...

Mivey -
I'm a little slow on this. As it happens, I'm looking at a job that looks like it will be modeled as a transformer feeding a resistive load load (9+j0) with a series inductor (j0.5) - so, I am real interested.

The models/calculations look real similar to distribution problems. And, I expect youare fairly wellup on that.

So, first a couple of questions about your calcs:

"Add a 75 kW load at unity pf: V=474.1<-1.29?, I=158.2<-1.29?."
For this one you are using a transformer feeding a straight resistive load. "V" is the voltage at the load. It appears you are modeling the circuit as 480v single phase. Where did you get the R, X values for the transformer? What were the R, X values you used?

"Circuit 1: Add enough inductance to get 37.1 kW load at 70.7% pf (52.4 kVA). V=471.6<-0.33?, I=111.2<-45.36?."
I'm not sure you I get this one at all. The inductance appears to be far larger than the 50% of the transformer impedance that mull asked for. You put the inductance in series with the load? "V" = the voltage at the trnsformer output, not at the resistive load?

Let me know if I am even close. I'm trying to see if I understand the model.

cf

 

[Cold Fusion]

Mull -
Maybe I got it - maybe not. Perhaps mivey will jump in and critique - hope so.

I made some guesses as to the numbers mivey was using for his example. But I changed the added reactance to the same value as the xfm inductive impedance.

See attached for what I got. For the model, I used figure 27a for the phasor diagram and fig 18b or 18c for the transformer. i just used a turns ratio of a = 1.

See what you think. If I understood your OP, sheet 3 is what you are looking for. Anyone is welcome to give some clues. I actually need to understand this for work

 

[mull982]

Mull -
Maybe I got it - maybe not. Perhaps mivey will jump in and critique - hope so.

I made some guesses as to the numbers mivey was using for his example. But I changed the added reactance to the same value as the xfm inductive impedance.

See attached for what I got. For the model, I used figure 27a for the phasor diagram and fig 18b or 18c for the transformer. i just used a turns ratio of a = 1.

See what you think. If I understood your OP, sheet 3 is what you are looking for. Anyone is welcome to give some clues. I actually need to understand this for work

CF

Yest sheet 3 is what I was looking for. Let me take a look at these calcs to try to digest before I comment or ask any more questions.

 

[mivey]

Mivey -
I'm a little slow on this. As it happens, I'm looking at a job that looks like it will be modeled as a transformer feeding a resistive load load (9+j0) with a series inductor (j0.5) - so, I am real interested.

The models/calculations look real similar to distribution problems. And, I expect youare fairly wellup on that.

So, first a couple of questions about your calcs:

"Add a 75 kW load at unity pf: V=474.1<-1.29?, I=158.2<-1.29?."
For this one you are using a transformer feeding a straight resistive load. "V" is the voltage at the load. It appears you are modeling the circuit as 480v single phase. Where did you get the R, X values for the transformer? What were the R, X values you used?

I made them up based on some per-unit assumptions. It came out to 7.7+j15.3 ohms on the primary side. I made no attempt to look up any actual values up and they will probably not match mull's transformer. I just used about 0.74% R and 1.48% for X for high & low side impedances.

"Circuit 1: Add enough inductance to get 37.1 kW load at 70.7% pf (52.4 kVA). V=471.6<-0.33?, I=111.2<-45.36?."
I'm not sure you I get this one at all. The inductance appears to be far larger than the 50% of the transformer impedance that mull asked for.

the 50% was part of the last question. With that size inductance, you don't get a reasonable load

You put the inductance in series with the load? "V" = the voltage at the trnsformer output, not at the resistive load?

yes to both

add: Z transformer is 0.0341+j0.068 ohms on the secondary side

 

[mivey]

Mull -
Maybe I got it - maybe not. Perhaps mivey will jump in and critique - hope so.

I made some guesses as to the numbers mivey was using for his example. But I changed the added reactance to the same value as the xfm inductive impedance.

See attached for what I got. For the model, I used figure 27a for the phasor diagram and fig 18b or 18c for the transformer. i just used a turns ratio of a = 1.

See what you think. If I understood your OP, sheet 3 is what you are looking for. Anyone is welcome to give some clues. I actually need to understand this for work

Your calcs and answers look fine to me.

If you are interested in what might happen in a more complex model, I made some calcs using a fairly heavy-loaded source and some feeder impedance plus your loads. You can see it has results that are consistent with yours:

Circuit 0: 3 ohm load: 74.3 kW load at unity pf: Vpri= 7,172.4<-3.71?, Ipri=10.95<-7.98?,Vload=472.3<-5.01?, Iload=157.4<-5.01?. 478.8 volts unloaded.

Circuit 1S: Add j0.068 ohm inductance to secondary circuit 0 to get 74.2 kW load at unity pf: Vpri=7,171.9<-3.71?, Ipri=10.95<-9.21?, Vload=471.9<-6.29?, Iload=157.3<-6.29?.

Circuit 2S: Add j0.034 ohm inductance to secondary circuit 0 to get 74.3 kW load at unity pf: Vpri=7,172.2<-3.71?, Ipri=10.95<-8.60?, Vload=472.1<-5.65?, Iload=157.4<-5.65?.

Circuit 1P: Add j15.3 ohm inductance to primary circuit 0 to get 74.0 kW load at unity pf: Vpri=7,157.6<-5.04?, Ipri=10.92<-9.31?,Vload=471.3<-6.33?, Iload=157.1<-6.33?.

Circuit 2P: Add j7.65 ohm inductance to primary circuit 0 to get 74.2 kW load at unity pf: Vpri=7,165.5<-4.38?, Ipri=10.94<-8.66?,Vload=471.8<-5.67?, Iload=157.3<-5.67?.