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# Generator Damage Curve Understanding

## Generator Damage Curve Understanding

(OP)
Within SKM to model the damage/decrement curve of a generator, I have noticed that the two variables which have the greatest impact on where the damage curve lies (on the TCC curve) are the If and the Ifg.

The defaults for a  generator within SKM are If=3 and Ifg=1.00.  I usually just leave these as-is...

I will give 'my' understanding of the situation, which sometimes matches reality and sometimes not.  I am thinking back to some of my core engineering courses and differential equations for modeling the transient response of systems that are first order, second order, etc.  I would think that the system of a generator driving a load is a second order DE, and the Xd'' and Xd' and etc that come off the generator cutsheets are 'constants' in the simplified solution to the differential equation.  This all ties into the transient modeling, or TMS module of the SKM software (which I really haven't fiddled with much).

I want to confirm this and get any additional information anyone has on this..

and

I understand the If and Ifg to only impact the TCC damage curve of the generator, which I understand to basically represent what amount of current the generator is capable of sustaining for a given amount of time without damaging itself.

So the follow-up and what I am concerned with is: where do If and Ifg come from, what do they mean, and where can I get information on the theoretical framework to understand these two variables?

Thanks much

### RE: Generator Damage Curve Understanding

The generator fault current decrement curve is not a damage curve.   It is just an approximation of the generator's short circuit output for a close-in fault, based on certain assumptions on the generator field current.  Classically it is assumed that the excitation remains constant during the fault.  But in reality, field forcing is often used to boost the generator voltage and fault contribution.

The generator impedance and time constants are based on Parks transformation that provides an approximation of the generator's dynamic fault response based on a series of impedance models.

### RE: Generator Damage Curve Understanding

I believe the Ifg is the steady state pre-fault excitation current, and If is the peak exciation current. With a ratio of 3, if I follow the logic correctly, it implies a short time after the fault begins, with a rate of rise based on an exponential rise and settling that somehow comes out of other time constants you enter, the field current rises to 3 times the prefault current, and hence you get 3 times as much internal voltage and a related rise in fault current. I think it is only the ratio between Ifg and If that affects the shape of the decrement curve, but I am not sure.

The decrement curve is based on a three phase fault at the generator terminals, but I think you can calculate terminal SLG and ph-ph faults using the same logic.

You compare the decrement curve to the generator damage curve. It is really a guestimation because the generator damage curve is for steady state currents, but the current magnitude is changing due to excitation system response.

### RE: Generator Damage Curve Understanding

(OP)
Without going too crazy researching, dpc, I would assume that Parks transformation is a way to model and get the constants of impedances/reactances and time constants of a system by experimentally gathering data on the systems' response to a given input.  IE: load a generator up to a purely resistive load of various sizes, see what happens, and various configurations of other loads and see what happens to the transient response (dependant and independant variables).  I am understanding the Parks transformation to be able to go from this data to establishing what those constants are.  Please correct me if I am wrong.

Also dpc please give more information on If and Ifg and their impact on the generator's response and decrement curve.

### RE: Generator Damage Curve Understanding

If field current is increased, the fault current produced by the generator will increase, primarily impacting the fault current in the synchronous impedance region.  Without some type of current boost or field forcing the sustained fault current contribution from a synch generator is generally less than the full load current, since the synchronous reactance is generally greater than 1.0 pu. In many generators, the sustained fault current can be increased to as much as 3.0 pu.

Parks transformation is similar to symmetrical components and it converts all of the variables to a new coordinate system.

It eliminates the time-varying inductances that occur due to the rotational energy of the machine.

But you don't need to understand all the theory to use the constants.

### RE: Generator Damage Curve Understanding

The impedance of a generator is slightly different depending on the load level and power factor of the load it feeds. It has something to do with the air gap and rotor is not uniform, and the rotor can be at varying angles relative to the fault or load current wave forms. Parks equations breaks the generator effective impedance down into the direct axis and quadrature axis. If a fault occurs, the generator sees a very inductive current, and you use the Xd, Xd', and Xd" impedances, but loads are resistive, things are moving more slowly, and the Xq impedance is more applicable; maybe there is an Xq' and Xq" but I have not run into using it. Beyond that, the story is tough. I have a pretty minimal understanding of the matter. I am now drained.

### RE: Generator Damage Curve Understanding

(OP)
So is my understanding correct in that the Xd, Xq, etc are all used to only model the transient response, and that they have nothing to do with the decrement curve?

And:

When it comes to the decrement curve, it sounds as though this is a 'rough' area in terms of modeling the available fault current that a generator can provide, as you say this varies from between 1pu to 3pu.   Is it really that unimportant and unexact?  After all, literally the only thing that affects the shape of the decrement curve is the If and Ifg variables.  I don't see the point to including a decrement curve if everysingle decrement curve will look the same after adjusted on a per unit basis.

Also, please advise on the relationship between the decrement curve and the protective relay that is protecting the curve.  What I had originally thought was a damage curve caused me to believe that it was not in the right area, because it was to the left of the protective relay curve for most (thus causing the gen to get damaged before the relay picked up).  But even still, if the decrement curve is meant to show the available fault current of the generator, it still wouldnt make sense for the decrement to be on the left of the protective relay curve, because a generator would then feed a fault indefinitely.

### RE: Generator Damage Curve Understanding

The decrement curve IS the transient response.

For generator protection, you have to consider the full range of protection provided, not just overcurrent relaying.  You have not given us any information on the generators and the protective relaying will depend on the generator size.

But normally, overcurrent relaying is considered backup protection.  To account for the decrement curve, a voltage-controlled (51C) or voltage-restrained (51V) overcurrent relay is normally used.  This allows the relay to respond to current less than the generator full load current.

You need to get a good text or paper on generator protection and review that if you are trying to do relay coordination for generators.

### RE: Generator Damage Curve Understanding

Maybe you meant, "....they have nothing to do with the damage curve?"

It is the internal voltage that varies from 1pu to 3 pu, not the current. Use this varying voltage to calculate I over time.

The excitation response time varies from generator to generator, and the Td" and Td' time constantants vary from generator to generator, so each generator decrement curve is a tad different.

You are darn right it is rough. VERY rough. You cannot really plot a decrement curve vs a relay curve. The relay curve is based on a fixed current level, that you do not have. You need to integrate the relay response cycle by cycle to somehow figure out when the relay is really going to trip. And that is if you believe your decrement curve. To make it simple sometimes make wild assumptions of current staying at some constant level, such as V/Xd' and see when all the relays in the string respond given that constant current.

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