Dear Mohammad,

This is simply and mainly due to the fact that PMSG speed is directly depending on the pole pairs number: N = 60f/p. If you use a low speed SG, you have no choice apart from increasing p.

Regards,

Mohamed

Dear Professor Benbouzid, Salaam

Thanks a lot for your prompt response.

As you know, the output of the SG in this case need not have a frequency as high as 50 or 60 HZ. So, the frequency in your relation (N = 60f/p) could be low, making a low pole number possible for the PMSG. Am I right?

Mohammad,

If you view the question entirely from the operational perspective (as your question seems to indicate !) then what you are suggesting certainly seems to be possible.

There will be additional ripple that the DC link capacitor will need to smoothen out in case of PMSG with low pole number, and that will require a revision of the capacitor selection - but frankly, that is not much of a problem!

However, the aspect one must not overlook has to do with the PMSG design and manufacture. In order to make design of electromechanical devices economically viable, with good use of the air gap, acceptable flux-per-pole (within saturation levels of the specific core material) etc., one has to converge on an acceptable pole number.

You may wish to refer to books or manuals on PMSG design to get a better feel of this matter.

With best wishes.

-Sanjay

Dear Mohammad,

I recommend Sanjay response. Indeed, the main issue is the design of the PMSG based on some important constraints.

Regards,

Mohamed

Dear Mohammad

From your repeated question, you seem to insist on the fact that: for the pole number of PMSG to be low, why not to act on the generator frequency and keep the pole number of the PMSG to its low value low!!!!

o The answer to this question is legal and 100% right from the point of view of a pure mathematical aspect.

The equation below justifies your argument, since it indicates that the PMSG rated speed in rpm (N) is directly proportional to the electrical supply frequency (f) and inversely proportional to the number of poles (p) of the PMSG.

N = (120 x f) / (p) [Hz]

From the equation, two quantities can be varied to act on the speed either by (f using a static converter) or (by p by choosing the right PMSG with p poles). So you can mathematically reduce the frequency (below 50Hz or 60Hz) and keep the number of pole to its lowest value.

o But from a technical point of view, the equation above may not justify your argument for the reasons cited before by my two colleagues.

Increasing the number of poles as recommended in Benbouzid response is a usual easy and practical solution. Decreasing the supply frequency may also work but on the detriment of the operation of the PMSG as suggested by Sanjoy answer. One should also look at the stability of the PMSG due to frequency reduction and other aspects.

Hi Bendiabdellah,

Thanks for the interesting points.

Just a small difference of opinion though ! Though we get sort of "used to" thinking of all synchronous devices with reference to stability, that may not be a major issue here due to the controllable DC link interface.

Cheers !

-Sanjay

Mohamed Benbouzid gave a good answer.

For Variable Speed Permanent Magnet Sychronous Generator

Stator Power =electrical torque x synchronuos speed.

The speed is related to voltage rise or fall at the stator winding and terminals as result of flux linkage from PM rotor excitation.

Flux = EMF/angular frequency

The higher the number of poles, the lower the rated speed for a given frequency. So, the least number of pole you can use is 2=1-pole-pair

But remember that

Synchronous speed=angular frequency/pole pair.

So, frequency impacts on synchronous leakage inductance of the stator winding, speed, torque, power and flux density.

For high performance and efficiency, stator losses must be reduced and care should be taken at design stages to reduce over or under voltage seen by stator windings (insulation and thermal issues).

Finally, the AC power output from the inverter depends on the DC link power. DC link voltage and current depends on the power input from the turbine and its angular frequency.

I agree with Sanjoy Roy response.

Just to enrich this debate, I share a graph where I did an analysis of the influence of the number of poles on the PMSG active materials cost. Each point in the graph indicates the result of an optimal design with the objective of reducing the active materials cost of the PMSG, for different numbers of poles.

Note a well-known trend: considering the same speed, the higher the number of poles, the lower the active materials cost of the machine. From 52 poles the cost increases due to constraints on the optimal design that have been reached: minimum tooth width and maximum outer diameter.

Nice study, Thiago.

Just a couple of queries though:

Cheers !

-Sanjay

Dear professor Sanjoy Roy,

Thank you very much.

1. Yes. I used a reluctance network to compute the flux. Such a reluctance network takes into account the material saturation and several leakage flux paths. This model is attached;

2. I am glad about your interest. Yes, the main publications converning this work can be found in:

- BAZZO, THIAGO DE PAULA MACHADO; KOLZER, JOSE FABIO ; CARLSON, RENATO ; WURTZ, FREDERIC ; GERBAUD, LAURENT . Multiphysics Design Optimization of a Permanent Magnet Synchronous Generator. IEEE Transactions on Industrial Electronics, v. 64, p. 1-1, 2017. DOI: 10.1109/TIE.2017.2726983

- BAZZO, T.P.M.; KOLZER, J.F. ; CARLSON, R. ; WURTZ, F. ; GERBAUD, L. . Multidisciplinary design optimization of direct-drive PMSG considering the site wind profile. Electric Power Systems Research (Print), v. 141, p. 467-475, 2016. DOI: Article Multidisciplinary design optimization of direct-drive PMSG c...

- BAZZO, T.P.M.; GERBAUD, L. ; KOLZER, J. F. ; Renato Carlson ; WURTZ, F. . Large multidisciplinary design optimization applied to a permanent magnet synchronous generator. INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS, v. 56, p. 171-181, 2017. DOI: 10.3233/JAE-172287

Here the Reluctande network I have created.

Thanks Thiago, for all the details.

Your reluctance network looks quite detailed to me at first sight - must have taken a good amount of effort on your part ! Truly something to be appreciated...

But perhaps a bit premature for me to discuss the work right now. Thanks for the list of publications - let me first go through those.

Will get back to you in case I have any query.

With best wishes.

-Sanjay

For the designs with same power and speed, the rotor diameter (in the other word the air gap diameter) is almost identical.

But it should be noted that the flux per pole changes inversely by increasing the pole numbers. This means that by increasing the pole numbers, we can design the stator core with shorter yoke height and this leads to smaller generator.

Similar consept is considered in design of electrical motors used in electric vehicles, where one can see often an eight pole design instead of lower pole numbers, at the expense of higher supply frequency.

Also there are other aspects from static converter design points of view, which are indicated in Sanjoy's answer.