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

#### carlosduarte

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

#### ControlsGuy25

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

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
Good night ALL,

Carlos Duarte,

Could you tell us, what kind of prime, is coupled with these generators??
As I want also, to know more on the SIR theme .
There are bunch of documentation, on the web treating on SIR , most of them are Wind turbine generator case studies.

Here is one very intersting article to read:
https://books.google.fr/books?id=pY...rs with different inertia constants H&f=false

Controlsguy25

#### carlosduarte

Hello Controlsguy25.

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 prefer, with low load, 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.

#### ControlsGuy25

Hello Controlsguy25.

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 prefer, with low load, 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.
Hello Carloduarte,

Here is some read before we can exchange more on this subject:
https://www.sciencedirect.com/science/article/pii/S2352484719307097

I do not know if you got, flywheel ( variable or fixed inertia ) but it can be useful, to have read on this article.

Tomorrow i will post some notes, to get better overview of what is the best choice for you !

Perhaps somebody else on this great forum, can contribute and share with us his (her) opinion!

Controlsguy25.

#### ControlsGuy25

Hello Controlsguy25.

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 prefer, with low load, 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.
Hello Carlosduarte,

I had a strong read, on two differents articles treating, on AGC and low inertia consequence.

The thing is that it is clearly, mentionned that the larger the generator is, the more it will compensate changes in system power demand.

There are formulas used, by Dispatching center that you can follow for confirming what, you partner in dispatch center told you.

Also you can clear, lot of doubts by reading these "excelllents" articles.

I am sure that, these informations can give you, some higlights!

Controlsguy25.

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#### carlosduarte

Merci beaucoup. I‘ll keep you updated on the subject.

Au revoir

#### ControlsGuy25

Merci beaucoup. I‘ll keep you updated on the subject.

Au revoir
Merci a vous, de meme cher Carlos.
Thanks for keeping update !

Kind regards,
Controlsguy25.
Merci beaucoup. I‘ll keep you updated on the subject.

Au revoir

#### carlosduarte

Hello Controlsguy25.

I’ve been studying the docs that you’vê provided which were really enlightening.
I’m from Portugal, Madeira island. I guess our grid is similar to French possessions like Martinique or Guadeloupe. An island.

Equations 3 and 4 caught my attention:

The RoCoF depends on the kinetic energy, which depends on the size of the generator. I will study it in depth.

Our grid is small and I can calculate the RoCoF. I’ve had the chance to study an outage and the frequency behaviour. The calculated figure was around 0.72 Hz/s. The measured one was around 0.6 Hz/s.
I think the difference maybe related to the load damping, considered in equation 4.

Your documents consider Dload=1%. But what figure should I use in fm?

Equation 4 presents the rate of change of frequency (RoCoF) but depends on the frequency figure, fm.

Do you have any information about the typical RoCoF and Dload figures in French possessions?

I’m looking forward to hearing from you.

Best regards.

Carlos Melim

#### CSA

Good day,

Dispatch operators have all kinds of preferences, they are, after all, human. Most of them are thinking human beings that use their experiences to form their preferences. (Some (more and more, actually) just do what they've been told, which is usually, "We've always done it that way.") But, it really takes a long conversation, usually over several visits and exchanges to get to what experiences formed their preferences.

"My colleagues of the Dispatch Center prefer, with low load, 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."

I don't really understand this statement. It is my experience that it's the prime mover governor that really defines the response of a "generator" to grid frequency. A generator just converts torque (supplied by a prime mover coupled to the generator) into amperes. Wires connected to the generator output terminals connect the generator (driven by the prime mover) to loads--many of them are induction motors (refrigerators; fans; pumps (water; sewage; etc.); air conditioners; etc.) which convert the amperes back into torque to power compressors (in refrigerators and air conditioners) and pump water and sewage and move air (fans). It's actually the prime mover(s) driving the generator(s) that are doing the work of powering compressors and pumping water and sewage and moving air--electricity is just the "medium" for transmitting torque from a place where it is available (a power plant with reciprocating engines or turbines) to places where torque is required (refrigerators, air conditioners, water and sewage plants, homes and businesses with fans, etc.). Generators convert torque to amperes, and motors convert amperes to torque.

If it weren't for electricity it would be necessary to have reciprocating engines and small turbines driving refrigeration compressors and pumps and fans everywhere refrigerators and pumps and fans are located. OR, there would have to be many overhead or underground shafts (VERY long shafts, with bearings) and wheels to which belts could be looped over to get torque from to drive refrigeration compressors and pumps and fans.

But, it's not the motors that do the work, or even the generators--it's the prime movers.

So, if you want fast response to grid frequency deviations you want prime mover governors (and prime movers) that can respond quickly to speed changes (because in an AC power distribution and transmission system, prime mover speed (remember--prime movers are directly coupled to generators) and generator frequency are directly related (directly proportional). Need to change frequency quickly? The prime mover, controlled by its governor, better be able to respond quickly.

Now, this business about "contributing" to a grid frequency disturbance is really related to the droop speed regulation of each prime mover governor. AND, it' also related to the amount of load on a prime mover and its generator at the time the grid frequency deviation (speed deviation) occurs. Grid regulators and designers use many things in determining which assets (prime movers and their generators) get used for power generation depending on the time of day (or night), expected load fluctuations, required spinning reserve (which is also very important to operators--and grid regulators and designers). And, I'm sure when they are building and configuring their grid models they use a lot of very intricate maths and calculations and values--but for actual operators (the people who start and stop and load and unload) machines--or who direct power plant operators to start and stop and load and unload machines, I doubt very seriously if they even know anything about SIR and H values. Very seriously. (And I'm NOT one to use the word 'doubt' unless I mean I don't believe what I'm being told--and this is one of those cases.)

Most grid regulators and operators are going to choose generating resources (assets) based on economics--which assets are least expensive to start and run--especially at loads less than rated. (Which is where generating assets need to be run if they are to respond to grid frequency deviations.... We're back to the droop regulation thing again.) This idea of a "time delay" attributable to the SIR and H value and MVA rating of a generator is kind of, well, ..., it just doesn't make much sense to me (who's NOT a maths whiz and doesn't care about theoretical values and calculations). To me, it's about how fast the governor prime mover is going to respond to the speed deviation--and that has a LOT to do with the type of prime mover more than the SIR and H value and MVA rating of the generator. Yes; when analyzing a grid frequency disturbance (AFTER it happens) all of these "little" things usually get brought up and bandied about and discussed. But, I have never seen a SIR meter or an H value meter. I do see power factor meters, and VAr meters and Watt meters and frequency meters.

It's like trying to equate the resistance of pipes and hoses to the flow of water. It is what it is (the pipe and hose resistance). It's more about the build-up of dirt and sediment and rust and scale on the inside of pipes and hoses that ultimately degrades the flow to the point that it becomes necessary to start discussing the possible causes of low flow-rate through the pipes and hoses.

It's the current load on the generator set (prime mover and generator)--which is determined by the amount of energy flowing into/through the prime mover!--and the response of the energy delivery system and the energy delivery control system, and the way the energy delivery control system (the prime mover governor) is configured (the droop regulation setpoint) that determines more than anything how the asset (generator set) is going to respond to a frequency (speed) deviation. Sure, the OVERALL inertia of the generator set is important (the prime mover's inertia and the generator's inertia), but when it comes down operating generator sets (generators and their prime movers), it's more about the prime mover governors than anything. The generator doesn't have any controls that make it respond faster or slower--but the prime mover governor does. And, it's the overall inertia of the generator set that's also important.

Maybe you were meaning to include the prime mover when you were talking about the generator--but without a prime mover the generator does nothing. It's the voltage in a car battery--it doesn't do anything by itself. It has to be connected to a circuit, and amperes have to flow for the battery voltage to "do" anything. It's about amperes.

I'm oversimplifying and understating the effects of SIR and H and MVA ratings--I'm sure. But, those things are fixed, and the controllable variable is the energy flow-rate into the prime mover, which changes the torque applied to the generator which the generator converts to amperes (as long as the generator breaker is closed and there are load circuits and loads connected to the transmission and distribution system).

#### CSA

By the way, when you finish with all the maths, can you post the results--indicating how much (in percent) each genrators SIR and H value and MVA rating contribute to Frequency response?

Is it 45%, or 72%?

Or 2%, or 0.73%?

Thanks!

#### CSA

"Synchronous generators respond to load-generation imbalances by accelerating or decelerating (changing speeds). For example, when load increases, generation slows down, effectively releasing some of its inertial energy to compensate for the load increase. Likewise, when load decreases, generation speeds up, absorbing the oversupply as increased inertial energy.

Because load is constantly changing, an unregulated synchronous generator has highly variable speed resulting in highly variable system frequency, ..."

It's ivory tower drivel like this that contributes to the mystique of droop speed control. On which planet Earth do generators appreciably change speed and operate in a wide range??? It just does't happen if the generator prime mover speed control works. And, if the grid uses AGC (or some variant) to properly control ("regulate") grid frequency (as most do, even during grid disturbances), frequency deviations of 0.1 Hz are uncommon--not the norm.

These kinds of descriptions should include a statement about the conditions when this occurs. Simply saying "unregulated" generator is incorrect. One doesn't regulate a generator; one regulates the generator's prime mover. A generator doesn't do anything except convert torque to amperes. And, on an AC power system the torque has to be supplied at a constant speed or the frequency isn't constant. And if the frequency isn't pretty constant, is it a "good" grid?

Sorry; I have tried for decades to explain droop speed control to people (even grid regulators and designers), and they always point me to drivel like this which says generator speed changes when load changes as their basis for their "understanding" of droop speed control. When I was in university learning about AC power generation and transmission and distribution I struggled mightily with the same explanations. I went to multiple texts and references and I just could NOT reconcile the descriptions with my experience in the lab where we had generator sets that we practiced on (with DC motors driving synchronous generators that we "boiled crabs" (heated salt water using resistance heaters made of reinforcing bar) to simulate load). It all had to be done at a constant speed--to produce power at a constant frequency, which is what the instructor was always emphasizing. Unbeknownst to us students at the time, the DC motor control (the prime mover's "governor") was doing that, except when he tweaked the droop regulation or the speed bias signal he controlled with a potentiometer.

It's not about the generator--it's about the prime mover driving the generator. One doesn't have a knob connected to the generator that controls the load it's producing (carrying, actually!)--one has a knob connected to the generator's prime mover to control the load it's producing (carrying). A synchronous generator requires a prime mover--that delivers torque at a relatively constant speed to produce power at a relatively constant frequency. On the plant Earth I live on, anyway.

Some might say I'm being too literal, or too picky. But for people who are trying to learn and understand AC power generation and droop speed control (because you can't have one without the other--or at least SOME kind of speed control, and by convention it's either droop or Isochronous) it is misleading not to include the prime mover and a discussion of speed and frequency--and to say that speed changes in a wide range when load changes when a generator set (prime mover and generator) are SYNCHRONIZED to a power distribution and transmission system (grid--large or small) that doesn't use some kind of speed control is even worse. And what generator set doesn't use a prime mover governor with some kind of speed control?

On the planet Earth I live on--they all do.

#### ControlsGuy25

Merci a vous, de meme cher Carlos.
Thanks for keeping update !

Kind regards,
Controlsguy25.
Carlosduarte,

Hello Controlsguy25.

I’ve been studying the docs that you’vê provided which were really enlightening.
I’m from Portugal, Madeira island. I guess our grid is similar to French possessions like Martinique or Guadeloupe. An island.

Equations 3 and 4 caught my attention:

View attachment 253

The RoCoF depends on the kinetic energy, which depends on the size of the generator. I will study it in depth.

Our grid is small and I can calculate the RoCoF. I’ve had the chance to study an outage and the frequency behaviour. The calculated figure was around 0.72 Hz/s. The measured one was around 0.6 Hz/s.
I think the difference maybe related to the load damping, considered in equation 4.

Your documents consider Dload=1%. But what figure should I use in fm?

Equation 4 presents the rate of change of frequency (RoCoF) but depends on the frequency figure, fm.

Do you have any information about the typical RoCoF and Dload figures in French possessions?

I’m looking forward to hearing from you.

Best regards.

Carlos Melim
Please read carrefully the 2 documents, as it contains concretes examples of Experiments with a One-Area & 2 areas Power System Model.
Chapter V: IMPACT OF LOW ROTATIONAL INERTIA ON POWER SYSTEM OPERATION.

I am pretty sure it contains answers of most of your questions.

I will read and study carrefully this coming week , and come back to you asap.

Till now i do not have information, on typical RoCoF & Dload for French possessions/Islands.

But here is a document about French island, Called "Ouessan" in french britain, Spanish canarians island tests & results it contains Islands Grid design cases studies , and the solutions adopted .

ps: The presented version, is limited so you must try to find a "full version" downldable, or see if you can buy it it costs around 120 \$
(cheapest price i found).
Have a read on this good document , and tell us if you can get your calculations done.

I did my best to give more valuables, informations on the subject, as I am also interested to know your opinion.

With best regards,
Controlsguy25.

.

#### carlosduarte

Hi there ControlsGuy25 and CSA.

I’ve had the chance to study chapter V: IMPACT OF LOW ROTATIONAL INERTIA ON POWER SYSTEM OPERATION. The question is that the figures it presents relates to continental Europe.

Our grid has no tie lines and the whole system is fragile to imbalances. That’s why we focus so much on SIR and RoCoF. We have no other areas to supply us in case of outages.

The book you have suggested looks excellent to help me on my analysis. I will order it.

But my doubt about equation n°4, still stands:

On the suggested book, the presented equation, n°5, is different:

The load damping contribution either gets multiplied by fm, or not. The difference could be the Dload formula. I will check it as soon as I get the book.

I work for Madeira island utility and its a real pleasure to discuss these subjects with experts as you are.

Thanos for your help and I will keep you updated.

Best regards ControlsGuy25 and CSA.

#### ControlsGuy25

Hi there ControlsGuy25 and CSA.

I’ve had the chance to study chapter V: IMPACT OF LOW ROTATIONAL INERTIA ON POWER SYSTEM OPERATION. The question is that the figures it presents relates to continental Europe.

Our grid has no tie lines and the whole system is fragile to imbalances. That’s why we focus so much on SIR and RoCoF. We have no other areas to supply us in case of outages.

The book you have suggested looks excellent to help me on my analysis. I will order it.

But my doubt about equation n°4, still stands:
View attachment 256

On the suggested book, the presented equation, n°5, is different:

View attachment 257

The load damping contribution either gets multiplied by fm, or not. The difference could be the Dload formula. I will check it as soon as I get the book.

I work for Madeira island utility and its a real pleasure to discuss these subjects with experts as you are.

Thanos for your help and I will keep you updated.

Best regards ControlsGuy25 and CSA.
Carlos Duarte,

Thank you for the feeback!

I knew that the documents, would be useful!

I will keep you updated asap.

I wish you the Best for you research/studies !

I just have found/read and attached here, 2 more interesting documents.

Read carefully you will see, how they also calculate/elaborate with Dload/Fm/Wm figures.

Best regards,
Controlsguy25.

#### Attachments

• 1.9 MB Views: 10
• 352.5 KB Views: 10

#### ControlsGuy25

Carlos Duarte,

Thank you for the feeback!

I knew that the documents, would be useful!

I will keep you updated asap.

I wish you the Best for you research/studies !

I just have found/read and attached here, 2 more interesting documents.

Read carefully you will see, how they also calculate/elaborate with Dload/Fm/Wm figures.

Best regards,
Controlsguy25.
Carlos Duarte,

It talks abouts islanded system RoCof and other swing equations, Load damping definitions ....

Most of one need to learn and know about that subject is there:
https://www.researchgate.net/post/w...rtia_in_virtual_synchronous_generator_control

Last but not least!

I got that document which explaining, very well how Swing equations and some controls system mode, applied for islanded grid with synchronous generator!

You got as the other documents that i attached, some controls scheme block, explained and formulas develloped, in this document.

Best regards .
Controlsguy25.

#### carlosduarte

Hello Controlsguy25.

The subject is now much clearer. I´m working on a report to my Dispatch Center colleagues.

When finished, I will gladly share it.

I have developed an excel macro-file that is capable to calculate, compare and optimize our grid scenarios to minimize the RoCoF.

We´ll keep in touch.

Best regards.

CSA

#### ControlsGuy25

Hello Controlsguy25.

The subject is now much clearer. I´m working on a report to my Dispatch Center colleagues.

When finished, I will gladly share it.

I have developed an excel macro-file that is capable to calculate, compare and optimize our grid scenarios to minimize the RoCoF.

We´ll keep in touch.

Best regards.
Hello Carlos Duarte,

I am glad to know, that the documents helped you on these studies.

It would be nice, to share here the results, of this interesting case study.

Thanks for your feeback, it is my pleasure to try to help, as best as i can.

Best regards,
ControlsGuy25.

CSA

#### PhilCorso

Carlos Duarte, ControlsGuy25
Aren't you comparing apples to oranges. Since you are discussing transient stability, and not Steady-State or Dynamic-Stability, recovery capability for the old fuel-Generator is 7 MVA per second, while that of the GTG is 15.7 MVA per second ?
Regards, Phil Corso

#### ControlsGuy25

Carlos Duarte, ControlsGuy25
Aren't you comparing apples to oranges. Since you are discussing transient stability, and not Steady-State or Dynamic-Stability, recovery capability for the old fuel-Generator is 7 MVA per second, while that of the GTG is 15.7 MVA per second ?
Regards, Phil Corso
Phil Corso,

My Goal (when I come on this forum), is to support and share with people , on any issues that they have in several domains.

Carlos Duarte posted the thread, and I wanted to be sort of assistance, for his case studies.

The case is well described on his original post.

Carlos (as you may have read on the posts) is satisfied with informations shared, for improving his modelization and studies.

Steady state /Dynamic stability are also related with SIR ( according to some documents ).

Now let Carlos Duarte reply, to your question on the subject .

Regards,
Controlsguy25.

CSA

#### PhilCorso

Controlsguy25!
I apologize for offending you!
Phil