SIR - Synchronous inertial response of generators with different inertia constants H 2

[Carlos Melim]

Good afternoon

Suppose I have two synchronous generators. One rated 10 MVA with H=4s and the other 20 MVA with H=2s.

I understand that the SIRs of the generators don’t depend on their operating point.

But if both are working at, let’s say, 5 MVA, and there’s an outage of another generator in the grid, wouldn’t the 20 MVA generator contribute instantaneously with more MVAs than the 10 MVA, even for a shorter period of time?

Can the higher MVA rating compensate for the lower inertia constant?

I’m looking forward to hearing from you.

Carlos Melim

 

[waross]

It depends.
What was the power factor of the two sets in question?
What is the connected MVA of the grid?
How fast do the governors of all the remaining sets on the grid respond?
What was the power factor of the set that was lost?
How distant was the set that was lost?
You must consider MW and VAR effects separately.
Loss of MVAR capacity;
If the lost set was running at unity PF then there may be no change in the MVAR production.
VAR production is voltage dependent and inertia has little or no effect.
MW production.
With a block drop in grid capacity, all sets will pick up their share of the increased MW load.
That is the instantaneous result.
With increased load, all the sets will start to slow down.
The slight drop in frequency will cause a slight drop in loading from inductive loads, mostly motors.
As the sets drop in frequency, their governors will be responding and supplying more fuel or steam.
The sets with lower inertia will lose speed quicker and thus contribute less, but their governors will be acting to increase their MW production.
The swing set will be acting to pick up the load increase and the load on the sets in question will soon drop back to the original level of MW production.
We are considering fairly small numbers.
If the grid consists of only the three sets:
With the loss of a guesstimated 4 MW,
The remaining sets are producing 4 MW and 4 MW.
When 4 MW capacity is lost, the 20 MVA set will pick up 2.67 MW and the 10 MVA set will pick up 1.33 MW.
Each set will pick up 13.3% of its capacity.
with 5% droop, that will represent a 0.67% frequency error.
With no swing set, the resulting frequency after correction will be 60 Hz x (1 - 0.0067) = 59.6 Hz.
With no swing set, the droop is more often set to 3%.
With 3% droop, the final frequency will be 59.76 Hz.

The only time that I can see this as an issue is when a short lived overload is dropped on both sets.
If the overload pushes both sets to within a very close margin of tripping their protection on instantaneous trip. then a set with higher inertia may "hog" enough extra load to trip on instantaneous.
This is a very small window of opportunity.
I have had issues with mismatched governors trying to start a large motor.
The set with the electronic governor responded faster to the motor starting current and hogged the load, and tripped.
This threw the load onto the set with the hydraulic governor which also tripped.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Carlos Melim]

Good afternoon Waross.

Thanks for your quick reply.

I live in Madeira island and our isolated grid is only 120 MW worth, isolated.
We have natural gas and fuel thermal power plants. Also, hydro, windpower and photovoltaic power plants.
The natural gas power plant is equipped with three 21 MVA generators with inertia H of 1.3 s.
The fuel power plants, much older, are equipped with 14 MVA but with inertia H of 2 s.

Normally the dispatch center team prefers to use the older fuel power plants, with mechanical governors, all because of the highest inertia figures.

The natural gas plant is new and its electronic governors assure a quicker response to a generator outage.
That’s why I ask if the older generators highest inertia justifies its use over the new ones.
I’m only concerned with the initial synchronous inertial response.
The power factor of the generators is normally around 0,95.

People tell me that the SIR of the generators is not limited by its MVA rating. Just like in a short circuit response with current way higher than its nominal one.

Please share your thoughts.

Best regards.

Carlos Melim

 

[waross]

I think that this is what you are looking for.
For example, consider the load acceptance (25% load step event) of a 1.5MVA diesel generator with varying inertia constants:

Notice that the frequency stabilizes slightly lower than the base frequency.
This is a characteristic of droop control.
If there is a swing set, it will initially act in droop and will then increase its output so as to correct the frequency back to the base frequency.
However a swing set on a small grid may cause more problems than it solves.
When I was responsible for a small island grid, (1.5 MW to 2 MW) our operators checked the frequency every 15 minutes and if it had drifted would correct it back to the base frequency.
We considered using a swing set and rejected the idea.
How does the price per KWHr of running a diesel set compare with the cost per KWHr of running a natural gas set?
Is there a large cost differential between running on natural gas versus running on diesel?


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Carlos Melim]

I work for the utility so the difference costs of fuel and natural gas is not really an issue.

Of course we want to stop the fuel thermal power plants in due time for ecological reasons.

We don’t have what we call an isochronous machine. All work on 3% droop. That’s the primary control. Then we have a GPS-based secondary control that drives the system frequency back to 50 Hz after an imbalance.

I was familiar with the frequency chart you’ve shown. But do you have a power production chart that shows the contribution of several generators with different inertia constants H?

The SIR depends only on the generator rated apparent power, the rpm and the rotating mass.
It doesn’t relate to the prime-mover or the governors faster or slower response.

My doubt is, if we have a 21 MVA machine , with low inertia figure, running at 11 MVA, I think it will, if needed, provide instantaneously 21-10=10 MVA.
For the 14 MVA machine, with higher inertia figure, running also at 11 MVA, it will provide instantaneously 14-11=3 MVA. Even if its contribution lasts longer.

It brings me back to the idea that, following and outage, the frequency will decrease and, both 21 and 14 MVA generators, will supply the grid with currents much higher that the nominal ones. Like in a short circuit.

What am I missing here?

 

[redlinej]

SIR is how the rotor will response to a change in frequency, because inertia is a resistance to change.
Although, SIR is important in the grid stability studies, the response of the generator during a frequency excursion is controlled by the governor. During a deviation from the nominal frequency the governor will response according to the active power and frequency droop curve.

 

[waross]

The response will be a curve.
The initial instantaneous response will be dependent on the inertia.
Once the frequency starts to decay, the governor will become active.
The inertia will act to dampen the original frequency decay and also to dampen the governor recovery.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[bacon4life]

Carlos-A generator rated 10 MVA with H=4s and one with rated 20 MVA with H=2s both contain the same amount of kinetic energy. Assuming both of these are attached to the same bus, they would experience identical frequency deviations, and thus would contribute equal decreases in kinetic energy. In terms of initial additional MW, the contribution would be the same from both generators. In terms of per unit contribution on the generator base, the smaller unit would contribute 2x PU more power. Note that this only applies prior the moment the system deviates from steady state.

The instantaneous power leaving a generator is not limited by the nameplate MVA. For example, a 20 MVA unit operating at 20 MW will obviously momentarily exceed 20 MVA whenever frequency declines.

I am puzzled why you want to focus solely on inertial response characteristics, while ignoring the rest of system dynamics such as:
1) Fast acting governors will begin responding while the frequency is still dropping.
2) Gas turbines have a reduction in capacity as the frequency drops. This is due to the compressor slowing down and forcing less air mass through the engine.
3) Governor action in a thermal plant to increase generation may momentarily reduce output before eventually increasing output. This is because dumping a bunch more cold water into the boiler will temporarily reduce steam pressure.

-Bill, I don't get why the generator sets with lower inertia will lose speed quicker.
My understanding is that generators within a interconnection operate at the same frequency, except for slight speed variations that account for no more than 180 degrees of angular difference. During transients the angular difference between generators tends to correspond with their electrical distance rather than the inertia of any specific unit. As an example, during an interconnection frequency drop taking 1 second, two individual units would go out of synchronism if the two units deviated by more than 0.008 Hz for the 1 second period.

 

[waross]

Bill, I don't get why the generator sets with lower inertia will lose speed quicker.

I stand corrected.
I was considering the action of one set alone with block loading.
With two sets in parallel, they will be locked to the same frequency as you pointed out.
The basic response is a the classic control theory damped waveform seen with any step change in set point or loading in a system with proportional control.
The inertia acts as a further damper on the damped waveform.

I work for the utility so the difference costs of fuel and natural gas is not really an issue.

Ahh, the classic MBA belief that a manager has no need to understand the system that he is managing.
If the bean counters ever become aware of the difference in costs of fuel and natural gas it may quickly become an issue.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Carlos Melim]

Bacon4life let me clarify my concern.

I’m not focusing only on inertial response. I work for the power generation department.

We have old 14 MVA fuel generators, with mechanic speed governors, with 2 s H inertia constants.
Then we have modern 21 MVA natural gas generators, with digital speed governors, but with only 1.34 s H inertia constants.

My colleagues of the Dispatch Center, with low load, prefer to use the old fuel generators because of their higher H constants.
They say that, in case of an outage with frequency decline, the higher inertia will allow the necessary delay to assure that the governors, even old mechanic ones, will fulfill their role.

My doubt is if the higher H, with lower MVA rating, justifies its usage.

 

[bacon4life]

The inertia is close enough such that much more detailed analysis of the rest of the grid dynamics would be needed to determine the relative value of each options. Do you have any recording of how the grid has responded to past outages? Do you have someone running dynamic stability analysis simulations? Do the simulation results fit the recordings?

It is possible that the system operators have spent years observing the system and have determined by observation that the older units work better. It is also possible the operators initially had an non fact based opinion of the new units, and over time, have succumbed to confirmation bias. Hopefully can do some simulations to prove which units will be better, all factors included.

Are these turbines or internal combustion generators? There may be other differences between the generators such as part load efficiency, minimum load levels, or emissions.

 

[waross]

Were the inertia constants calculated or were they measured in response to a step change in system loading?

When you say thermal, I visualize steam boilers and steam turbines.
Is this correct?

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Carlos Melim]

Hello waross,

The inertia constants were calculated. When I refer thermal power plants I mean fuel or natural gas prime-movers.

Based on bacon4life infos, I think I´ve made a step forward on the subject. One should consider the Kinetic Energy which is H x S.

A 2s inertia constant, 10MVA generator will be the same as a 5s inertia constant, 4MVA generator.

Am I missing something here?

Best regards.

Carlos Melim

 

[waross]

For practical applications I would use a figure derived from the response to a load upset, or several load upsets at different levels of load.
That will take into account the governor response and the prime mover's response to increased fuel.
Using a calculated value may be omitting one or more pertinent factors.
Looking at the response to actual load bumps will tell you what the actual effect on system stability is with all factors in play.
Use a range of load bumps as some of the factors may not be linear, some may follow unique characteristic curves.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[bacon4life]

Yep, you are on the right track with kinetic energy.

Furthering what Bill said, the calculated H value on probably based on a load rejection test or manufacturer calculations. Keep in mind that a load rejection test is an open loop system. When the generator is added to the grid, the closed loop response can be quite different. Hence the need to see how the generators behave in the overall system.

In figure 6 showing a load rejection test, you can see that the governor begin affecting adjusting the control gates within fractions of a second.