Synchronous generator, peripheral speed 2

[Jensgisla]

I'm looking for information on peripheral speed design limits of synchronous generators. More specifically for 50 Hz hydrogenerators with with rated speed 100 - 300 rpm.

As far as I understand the design limits of the peripheral speed is determined by mechanical stress (centrifugal forces) on rotor poles at run-away speed. It seems that the limits mentioned in my (old) textbooks are inaccurate or outdated by development in machine design.

The textbooks mention higher peripheral speeds for turbo generators than for the slower hydro generators. Would it be safe to assume that the peripheral speed limits of slow hydros (100 rpm) would be lower than for faster hydros (300 rpm)? Would there be a correlation with core length also (assuming longer core would add to mechanical strength of rotor spider)?

The reason I ask these questions is that have to comment on possible pit diameters and heights for different options (number of units and speed) for a preliminary design of a hydro project. The final generator design would of course be done by the generator manufacturer.

 

[LionelHutz]

Wouldn't this be a question you should pose to the manufacturers?

Not sure how you can compare peripheral speeds using the rpm. If the 100rpm machine rotor had a 1.73 times larger radius then the peripheral speed would be the same as the 300rpm machine.

 

[electricpete]

Lionel - you probably realized already, but there is no square root involved. Speed = 2*pi*f*R

=====================================
(2B)+(2B)' ?

 

[7anoter4]

I don't think there is a limited peripheral speed. As you said:
"design limits of the peripheral speed are determined by mechanical stress (centrifugal forces) on rotor poles at run-away speed".
The rpm for a hydro generator driven by a hydro turbine may reach even 2.5 times rated speed or more.
But a peripheral speed for 1.8*rated speed could be limited to 90 m/sec [300 ft/sec] in order to limit the
centrifugal yield and reduce the mechanical stress to an easier solution.
Never the less, there are salient pole machine with 155 m/sec and up.
One of important variable is the tangential stress =2*torque/pi()/Dia rot^2/ideal length of core.
The torque=Pi/(2*pi()*rps).Pi=internal power approx.1.09*Srated.
The tangential stress is also proportional with air gap magnetic field density (Bd) and with linear current density distributions [A].
Usually we state the stator inner diameter based on recommended tangential stress for a well loaded machine
and the ratio between pole pitch and the ideal core length.
If the peripheral speed is limited then we have to take a longer core for an elevated machine power.
It is recommended to check anyway if the pole pieces are suitable bonded for the centrifugal force
The centrifugal mechanic stress S=K*Rotor dia^2*rpm^2 since S=K*speed^2.
K depends on rotor material density [ro] and the size and shape of the rotor.
The length of the rotor is chiefly restricted by the critical angular speeds of the rotor. Usually, the
ratio of the length of the machine and the air gap diameter ? = L/D is selected to operate the rotor
below the first critical rotation speed

 

[rhatcher]

The prime mover and the desired power output are the first considerations.

Turbo-generators, meaning steam or gas turbine, generally run at 3600 rpm. At this speed, less torque is required to produce a given kW output.

Hyrdo-generators generally run much slower, on the order of 100-300rpm. At this speed, much more torque is required to produce the same power output.

The diameter of the generator will generally be proportional to the square of the torque required. So, for the same power output, a turbo-generator will have a much smaller diameter that a hydro-generator.

However, a turbo-generator will be much longer than the hydro-generator of the same rating. Length is generally considered to be 1:1 proportional for power output.

Next, turbo generators generally have non-salient poles and hydro generators generally have salient poles. This is a major factor in maximum safe speed.

So...having perhaps completely complicated the discussion, I do have two questions to ask:

1. Why would you be concerned about maximum speeds? The generator should have both overspeed and overfrequency protection. Also, I cannot imagine a scenario where you would intentionally run at greater than rated speed.

2. Is this a student question? Student questions are not allowed in the forum. If you are a student then I have given you some food for thought, you have to find the answer yourself. If you are a working Engineer, then I have asked some questions that will help myself and others to help you.

 

[davidbeach]

Hydro machines on high head systems can easily exceed 1.5pu speed on load rejection. A turbo machine would not be expected to see those speeds.

 

[wolf39]

I assume that you refer to peripheral design limits, based on overspeed (run-away speed) conditions.

It is impossible to define a permissible peripheral speed (velocity) for hydro generators. The term "peripheral speed" is a bit misleading because in practice such values usually are based on the stator bore diameter, not on the mean value of the rotor rim diameter (after consideration of the field pole attachment) or the field pole gravity center. Only these diameters count for the centrifugal forces and mechanical stress calculations.

I know of a 10 pole hydro generator with a stator bore diameter of 3850 mm which has an effective rotor rim mean diameter of 2090 mm only. This results in a peripheral speed (velocity) ratio of 2090 / 3850 = 0.54. A hydro generator with 84 poles with a stator bore diameter of 18800 mm and an effective rotor rim diameter of about 17100 mm gives us a ratio of 17100 / 18800 = 0.91.

It depends entirely on the permissible rotor rim yield strength, usually 65 to 75 percent of the elastic limit, which max. diameters for a given rpm overspeed can be selected.

Wolf

http://www.hydropower-consult.com

 

[Jensgisla]

Thank you guys for the input.

LionelHutz: I will ask the manufacturer when the projects get to that stage. But I would like to be able to give somewhat educated guestimate of stator diameter and core length of units at an early design state of hydro projects, long before a machine manufacturer has been contracted. At this stage of our projects the rated power and rated speed are known (but run-away speed is unknown at this stage).

7anoter4: Thank you for a detailed answer. I will have to study it better at a later time.

ratcher: Thank you for your seeds of wisdom. Perhaps my question was not detailed enough. You asked 2 questions, here are the answeres:
1) I'm ultimately interested in the stator bore diameter. As far as I can understand from my textbooks on electrical machine design the upper limits of rotor diameter are set by the mechanical stresses of the rotor poles set on the rotor spider and frame.
Actually the overfrequency (ANSI 81) protections are for load projection, not for generator projection, the electrical- and mechanical overspeed protections suffice, some seeds of wisdom for you too ;-)

2) As I mentioned in the original post, I'm not a student, although sometimes I wish I was.

Wolf: Thank you for the input. Have you wondered why your 88 pole machine has a stator bore of 18800 mm and not 20000 or 16000 mm (with the same number of poles, but different stator core length)?

 

[Jensgisla]

7anoter4: Thank you again for the informative post. It has put many pieces of information I have in perspective.
You say:
"Usually we state the stator inner diameter based on recommended tangential stress for a well loaded machine
and the ratio between pole pitch and the ideal core length."
I assume you are referring to the electrical- and magnetic loading of the machine by "well loaded machine".
Would you say that it was a reasonable assumption to assume that the electrical and magnetic loading of hydro generators from the same manufacturer would be constant (let's say within the limits of rated power: 50-500 MVA and rated speed 100-300 rpm, and ignoring the restrictions caused by the 1st critical speed of the rotor?. If I could make this assumption (with reasonable approximation) it would be the solution to my problem.

 

[7anoter4]

I cannot say you can neglect the first critical speed even you take into consideration the "well loaded" machine parameters.
But you can avoid the critical speed to interfere the operating range of the machine speed.
Here are some remarks from different authors published by IEEE:
"A rotor dynamic analysis of the entire shaft system should be performed. This analysis should include the prime mover, generator, and any other rotating components. This analysis should include lateral and torsional shaft system response to the various excitations that are possible within the operational duties allowed by the standards.
When the turbine generator is purchased as a set, it would be typical that the manufacturer should perform this analysis..
When shaft components are purchased from different manufacturers, the purchaser should arrange to have this analysis.
The first Critical speed of the generator rotor assembly should be at least 10-15% higher than the maximum runaway speed of turbine and not cause unsatisfactory operation within the speed range corresponding to the frequency range agreed.
The generator rotor assembly should also operate satisfactorily for a reasonable period of time at speeds between standstill and rated speed set by the prime mover and generator designers.
The turbine generator set shaft vibration at operating speed should be limits specified by ISO 7919-5 for machine sets in hydraulic power generating and pumping plants".
For more than 20 years I am not involved in generators design but, as I remember the critical speed has to be
at least 1.8*rated speed for salient poles synchronous generator. This is the high first critical speed.
But a critical speed less than operating range it is possible if it stays out of operating range and if the amplification factor of interfering critical speed will be acceptable.
If you would take into consideration in the critical speed calculations not only the rotating mass and the stiffness of assembly but also the bearing elasticity [instead of ball bearing using white metal sleeve bearings, which are not a rigid, but a flexible mounting, for instance] you could get a more low critical speed and shift the critical speed from the operating range.
As an idea [it is turbogenerator!] see:

http://www.dresser-rand.com/techpapers/tp108.pdf

:......

 

[Jensgisla]

Thank you for another informing post.

I agree that the rotor dynamic analysis is important and will be performed at a later design stage by the machine manufacturer.

 

[wolf39]

jensgisla:

When it comes to hydro generators: I never wonder, because I know.

Wolf

http://www.hydropower-consult.com

 

[wolf39]

Jensgisla:

You may not have noticed but the two examples I've mentioned in my response dated June 03 are data of actual hydro generators in operation.

The 10 pole/50 Hz unit at the run-away speed of 1070 rpm has a peripheral speed of 216 m/s, based on the stator bore diameter of 3850 mm.

The 84 pole/60 Hz unit at the run-away speed of 158 rpm has a peripheral speed of 156 m/s, based on the stator bore diameter of 18800 mm.

For a proper centrifugal force and rotor rim stress calculation one at first has to apply the rotor rim mean diameter. With a mean value of 2090 mm you arrive at a peripheral speed of 117 m/s for the 10 pole unit and with 17100 mm rotor rim mean diameter you get a peripheral speed of 142 m/s for the 84 pole generator. All of a sudden it seems that the rotor rim of the 84 pole generator is higher stressed than the one of the 10 pole unit. After considering the centrifugal forces of the field poles for the final rim calculation, the 10 pole generator again is the higher stressed unit.

From your post dated May 31 I understand that you intend to comment/advise? on possible unit numbers, unit speed data and pit diameters for a certain project. This is a very complex issue and requires a lot of experience to deal with. Our forum is a group of competent professionals who are willing to share their experience and know-how with others free of charge. But even the combination of their comments together with your (old) text book information most certainly will not enable you to address this topic adequately. Therefore, don't forget the legal liability issue. If your comments lead to a costly power plant lay-out you may face a court case. Because of this you better have concluded a sufficient liability insurance.

Wolf