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# System Inertia and Synchronous Inertia

## System Inertia and Synchronous Inertia

(OP)
Hi everyone, I got some questions about "System Inertia and Synchronous Inertia", while doing some study my manager asked.

Q1: Some paper mentioned that they can "update the system inertia by time". But, based on the formula of calculating system inertia [Htotal = sum of (each generators' inertia constant (H) x rated power)], if both the inertia constant (H) of and rated power (installed capacity?) of them are fixed, which means that the system inertia are the same value, how can they change the value by time?

Q2: Did anyone hear about "synchronous inertia"? Is it the same as "system inertia"? I would like to ask the difference between "synchronous inertia" and "system inertia". Also if anyone could please tell the definitions and calculating formulas of them, that's even better!

Q3: Our power system will be rich in renewable energy in the near future; that is, our system inertia will gradually reduce. If a disturbance occurs, it might cause a serious frequency drop. Then, how do I estimate "the minimum value of system inertia" to maintain a system stability like not to reach the setting point of load shedding? (Maybe you guys saw news about an earthquake that occurred in Taiwan, which also is why my manager asked me to study.)

Yu-Kai, Chung (Ken)

### RE: System Inertia and Synchronous Inertia

Not that I have al your answers, but it is possible to add inertia by the addition of synchronous condensers. Also some of those with the addition of a flywheel can continue to produce fault current for a longer time.
There is also a concept out there where IBR's can simulate inertia. It isn't real from what I have seen, but from the graphs it happens late. Although the late inertia does help in the system recovery, for a faster recovery (don't completely dismiss it).
For inertia, the best rotating machines are typically hydro units, because they have lots of mass for there size, and they don't have a low frequency limit. But they are hard to place.
I am not a planner, so take it as you will, but I have looked into it, because I see short circuit availability dropping.

### RE: System Inertia and Synchronous Inertia

Hi YKC,
Regarding Q1, although both the inertia constant and the installed capacity remain the same, different generators could be in service at different times, according to the system load and renewable generation share.
Regarding Q3, your inertia constant has to be large enough to avoid excessive Rate-Of-Change-Of-Frequency (ROCOF). Take into account, for instance, that most inverter-based resources and HVDC converters cannot withstand ROCOF higher than 2.5 Hz/s.

Si duri puer ingeni videtur,
preconem facias vel architectum.

### RE: System Inertia and Synchronous Inertia

The system inertia includes both the inertia of online synchronous generators, as well as contributions from other nonsynchronous spinning equipment such as induction motors. It will even include things like synthetic inertia programmed into IBR based resources like wind farms and battery installations.

For considering frequency drop, there are also frequency sensitive loads such as pumps and fans that contribute to frequency stability. Putting a motor onto a VFD eliminates it's contribution to system inertia.

Running underfrequency load shedding simulation is quite complex to set up.

### RE: System Inertia and Synchronous Inertia

@bacon4life,
We did have to tweak our underfrequency settings in our standalone electrical system until we had the best setup -> no nuisance trips and no observed exceedance of load limits.

### RE: System Inertia and Synchronous Inertia

(OP)
Thanks everyone very much!

Dear cranky108, about the issue of adding inertia in the grid, actually it's not the main issue I care now, but suggestion you gave is useful, I would keep in mind.

Dear FPelec, do you mean that "if the generators are not-in-service or their generation are 0 MW, I have to remove their inertia when calculating system inertia"? Also, your experience which is "the IBR and HVDC equipment could not withstand ROCOF whose value over 2.5 Hz/s" is really cool and also I did not understand that deep before, since I mainly work on doing simulation.

Dear bacon4life, it's good to meet you again, also thank you for answering my other questions. So, could I say "synchronous inertia only focuses on the inertia created by synchronous generators, while the system inertia need to consider all of the equipment in the grid which can create the inertia, such as 1) synchronous generators, 2) three-phase motor load, 3) wind turbines, so on."? As for UFLS, I am not really work on this topic, I know the frequency setting point which would trip the customers' load, and try not to reach the point.

Dear Parchie, that's true, we must design the setting point of UFLS carefully.

### RE: System Inertia and Synchronous Inertia

Yes YKC,
to evaluate system inertia at a given time, you should only consider the generator connected to the grid (i.e. operating synchronously in parallel with the grid) at that time.
Note that some generators could, in principle, operate at zero active power as synchronous condensers. This is typically done with some hydro generators or steam/gas turbines equipped with a clutch to decouple the generator from the turbine shaft. In the latter case, take into account that the generator's inertia constant changes (it is much lower) when the turbine is decoupled from the generator.

Si duri puer ingeni videtur,
preconem facias vel architectum.

### RE: System Inertia and Synchronous Inertia

#### Quote:

This is typically done with some hydro generators or steam/gas turbines equipped with a clutch to decouple the generator from the turbine shaft. In the latter case, take into account that the generator's inertia constant changes (it is much lower) when the turbine is decoupled from the generator.

Hi FPelec,

I won't speak to decoupling gas or steam turbines, but separating a hydro generator from its turbine is generally quite difficult mechanically, and the utility I worked for never went that route that I'm aware of; instead, plants were as much as possible designed so that all hydro turbine runners were sited above maximum tail race level. Synchronous condenser operation was achieved by slowly closing the hydro turbine wicket gates [we had no Peltons] so the generating unit in question would not trip on reverse power, and the scroll case was vented so the water within it would fall by gravity into the draft tube, leaving the runner rotating in air. The scroll case vents were sometimes just two large check valves in series so the scroll case would auto drain on wicket gate closure; in more sophisticated designs the scroll case vents were cam operated by the wicket gate bull ring. A separate water supply was always provided to keep the runner's lower lignum vitae bearings not only wet but "submerged."

There was at one time a major change to the way our grid operated such that more synchronous condensers were needed overnight during off-peak periods, but all the hydro units in the electrical area that could have been used for this purpose had runners sited either at the minimum tailrace level or even in some cases completely below it. Since the need was dire, considerable re-engineering [at considerable expense!] incorporating tailrace suppression systems with high pressure air compressors, large receivers, piping and other associated equipment was undertaken.

The results were gratifying, and well worth the trouble, and obviated concerns about reduced inertia constant / a loss of spinning mass.

Additionally, this thread [now closed] https://www.eng-tips.com/viewthread.cfm?qid=497589 contains IMHO a great deal of valuable information, most of it provided by the very learned and experienced participants in these fora; I highly recommend it.

CR

"As iron sharpens iron, so one person sharpens another." [Proverbs 27:17, NIV]

### RE: System Inertia and Synchronous Inertia

Hi, I did some work on this area in Ireland (Eirgrid) a few years ago.
For Q3, there's an equation that relates inertia to loss of largest infeed/outfeed and ROCOF.
When operating at high values of ROCOF (>0.5Hz/s) you need to check that distribution generation doesn't start tripping off due to loss of sync/island relays. We also had a lot off issues with generators agreeing to operate with ROCOFs higher than 0.5Hz/s. A lot of studies had to be done. We eventually decided on a minimum inertia of 25000MW-seconds, and over time with pressure from wind industry, this has been reduce to about 20000MW-seconds. Important things to look at are minimum gen values of Synchronous machines, and trying to keep them running where possible. Most of our CCGTs managed to reduce their min gen values significantly.

Over time, with more and more BESS being added to the system, we find that the frequency doesn't drop anywhere near load-shedding thresholds - there's just so much fast-acting reserve.

There's some background material here: Link
and an entsoe document here: Link

Hope this is of use.

### RE: System Inertia and Synchronous Inertia

I don't think with hydro units disconnecting the turban from the generator is done. It maybe done with steam or gas, but not hydro. We can run one of our hydro's as a synchronous condenser, but it is a Pelton wheel.
Hydro turbans don't seem to over heat like steam, or gas turbans do. But watch your auxiliaries, some of those may be designed with water flow as a cooling source.

### RE: System Inertia and Synchronous Inertia

Yes cranky108, regarding clutches I was only referring to gas or steam turbines. Here in my area, for example, there are several gas turbines equipped with clutches for synchronous compensator operation. In the latter case, the inertia constant decreases dramatically to about H=1.7 s.
As far as hydraulic generators are instead concerned, many Francis turbines can also be used as a synchronous compensator, by emptying the case using compressed air and making the turbine spinning in air instead of water. Almost all large pumping units installed here (with unit powers of up to 250 MW) can be used as synchronous compensators.

Si duri puer ingeni videtur,
preconem facias vel architectum.

### RE: System Inertia and Synchronous Inertia

Although system inertia clearly includes all sources of inertia, I suspect the term synchronous inertia is used in a variety of ways. Depending on the context, synchronous inertia could either be synonym of system inertia or it could be used to just a specific component of the overall inertia.

### RE: System Inertia and Synchronous Inertia

System inertia I believe shouldn't be looked at as providing fault current because fault current is very reactive. I think the best way to think about system inertia is that it is conceptually something that provides or stores energy instantly when there is a difference between generation and load. This typically comes from synchronous generators just due to the amount of spinning metal involved but load itself has inertia too. Renewables struggle to provide inertia because not a lot of energy is stored on the capacitive bus of type 4 wind turbine farms or solar farms. Remember that inertia is storing or injecting real power into the grid during imbalance. Intertial energy can be pulled from the spinning wind turbines but it is rather limited in comparison to synchronous generation. The reason why inertia is needed is that it slows down the rate of frequency change there is during a load to generation imbalance (fast or slow). This is needed to give the automatic controls time to increase or decrease generation to match the load so that the grid frequency doesn't stray too much. In places with high penetrations of renewables, frequency control can be an issue due to not having enough inertia and inside of these regions there are often mechanisms to compensate battery storage for helping with inertia or frequency control since they can inject or absorb real energy very quickly. Real inertia or artificial inertia is just references a feature of the grid that allows energy to be stored or injected quickly to help control the grid frequency.

If you want an idea as to how much inertia is provided per MW, the H value gives you an idea of what types of synchronous generation provide the most inertia. The amount of inertia on a grid is in the range of around 5-10 seconds of peak load. That doesn't mean the frequency will hold for that long but that is about how much inertia you might expect.

https://qph.cf2.quoracdn.net/main-qimg-9aafb55d4a1...

### RE: System Inertia and Synchronous Inertia

There is a difference between real and artificial inertia, in that real inertia reacts faster (with present technology), and at the time it tends to droop (a few cycles) artificial inertia tends to be picking up. So for best response, some of both is best for the system. It is not either or, it should be both. That said, over sizing real inertia can help with that, but in todays environment, it may not make since.

Besides that IBR's generally don't generate negative sequence, which is used for some protection systems. So some real inertia is not a bad thing.

### RE: System Inertia and Synchronous Inertia

Cranky,

It doesn't operate faster. It operates instantly just due to physics. There is no lag. It is just energy put into or taken out of tons of spinning metal. The response after like 15 seconds isn't inertial but of governor valves opening up to pass more steam to increase generation. Artificial inertia kind of gets conflated with response time because batteries and such can have a much faster response time to increase power output than synchronous generation which has to ramp up. Artificial inertia isn't really inertia but just something with an incredibly fast ramp rate that can prevent the grid frequency from changing much, like what real inertia sort of did. If you ask me what the biggest difference between real and "artificial" inertia, it is just that real interia didn't require any controls and just existed due to physics. Artificial inertia needs controls.

### RE: System Inertia and Synchronous Inertia

(OP)
Hi guys, thank you for response, what an interesting topic!

Also I saw another description between system inertia and synchronous inertia.
Since syn. inertia only considered the machines with inertia and work "synchronously" with the grid, the syn. inertia should be calculated by "Hsyn = sum of (each generators' inertia constant (H) x rated power)"

On the other hand, since system inertia considered all components with inertia in the grid, it could not directly sum by the above equation. Then, we should calculate the system inertia by "ROCOF" and "power loss". Assume a disturbance occurs and cause 100 MW power unbalance in 60 Hz system and ROCOF is -0.05 Hz/s. The way to calculate the system inertia is as "(2H/f)*(|ROCOF|)=power unbalance", in this case, which would be (2H/60)*(0.05)=100 -> H = 60 GWs. Thus, it can consider each components with inertia in the power grid.

I would like to discuss with these two equation, please feel free to response, thanks!

YKC

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