transformer inrush - multiple transformers

[magoo2]

An earlier thread talked about selecting a high side for to protect a single transformer from inrush. It referred to 12 X normal at 0.1 seconds and 25 X normal at 0.01 seconds.

I'm looking at a case where you have 5 identical kVA transformers (medium voltage) arranged in a daisy chain fashion. Each transformer is spaced out approximately 500 to 1000 ft apart. You have one branch fuse to protect the group of 5 transformers. How do you size that branch fuse?

There are smaller individual fuses for each transformer to isolate them in case of short circuit failures so we can ignore them for this issue.

My first approach was to add up all the transformer kVAs to get one equivalent transformer. I suspect that applying the 12 X and 25 X factors at the 0.1 and 0.01 s points would be too conservative and the resulting fuse would probably be too large. Does anyone have experience doing something like this? If so, what multiples of full load were used for the 0.1 and 0.01 second inrush points?

I suspect some of the wind farms have run into this issue.

 

[davidbeach]

Well, if there is one factor the determines the magnitude of the inrush it seems to be the phase angle of energization vs. the phase angle of deenergization. Since all your transformers will have been deenergized together and will be energized together the safe thing is to assume you are dealing with a a pseudo transformer who's size is the sum of the individual transformers.

 

[prc]

Inrush current comes down with increase in kVA rating.In large power transformers it may be 5X If instead of 12 X IF. In control transformers it may be 20x If.So you have to add up the inrush currents of individual trfs instead of taking the inrush current of an equivalent transformer.

 

[magoo2]

I agree with you David that it's the safe thing to do. I just think it's too conservative. I just don't have any data to suggest changing at this point.

prc - I'm not sure i understand your suggestion. Whether it's 5 X or 12 X normal for a given transformer, with 5 identical transformers, adding up the contribution of each one is equal to what you get when you make an equivalent transformer.

 

[prc]

What I meant was -you have to take 5 times 12x full load current of P MVA transformer. Inrush current of a 5P MVA transformer will be less than the total inrush of 5 nos P MVA Transformers. for a 250 VA transformer inrush may be 20times If, for a 250 kVA it may be 12 timesIf, for a 250 MVA 5times If.

 

[magoo2]

OK, prc, I see what you mean.

In my equivalent transformer, I still retain the multiples (like 12X normal) based on the individual transformers and add them up to get my sum or equivalent kVA. I would not go with somthing like 5X if that were what was typical for the total kVA.

The equivalent or total kVA is helpful because you can see what the limiting connected kVA is for a given fuse rating. Many utilities have a typical maximum fuse size that they use on branch circuits (or taps) and the equivalent kVA math makes it easier to see how many transformers can ultimately be connected.

 

[TSun]

The issue is actually surprisingly complicated and getting an accurate maximum inrush current for multiple transformers usually takes specialized software and a great deal of information on the system and transformers.

The issue boils down to the voltage at each transformer's primary terminals. This voltage will drop as you draw more current through the system. At the system's available fault current, the voltage would be zero. A transformer's inrush current is dependent upon the degree of saturation the core experiences when energized. The degree of saturation is dependent upon the flux density in the core. The flux density is proportional to the voltage at the transformer's primary terminals plus any residual flux left over from the last time the transformer was on. So in short, the less voltage the transformer sees, the lower the inrush current. Some generator step up transformers nearly eliminate inrush current by bringing the generator on line with it connected to the transformer. Slowly increasing the voltage from zero to 100% as the generator starts keeps the core from saturating.

If you had a system with unlimited available fault current, an infinite bus, the maximum total inrush current would be equal to the sum of each transformer's maximum inrush current. Since any real system will have a finite available fault current, the transformer inrush current will, through voltage drop, reduce the applied voltage at the transformer primary terminals. Since this voltage is reduced, so is the maximum level of saturation and hence the maximum inrush current.

The problem is further complicated by the fact that transformer saturation is not linear. And for medium voltage transformers, the saturation curves are not typically available. You will also need to know the flux density the transformer is designed to operate at and know the maximum remnant flux the core can retain. Keep in mind that actual voltage drop, the kind you're interested in will also require the system X/R ratios as well as the available fault current. Even if you did have all the necessary info, without specialized software you will likely have to rely on an iterative guess and check method to approximate the maximum inrush for all of the transformers. The calculations will also be fairly complicated as all of the values you are dealing with are vectors. If you have access to power system modeling software you could make things a little easier by modeling the system but just plug in a load of your best guess as the the maximum transformer inrush then do a load flow study to determine the voltage drop, compare it to the saturation curves, adjust the inrush current values and repeat.