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[rakarskiy]

Here is a method for calculating a synchronous generator (Russian site), I think you can use a translator, but a translator is not needed for formulas.

https://studbooks.net/2116779/matematika_himiya_fizika/raschet_sinhronnogo_generatora

Introduction
Rating Calculation
Stator sizing
Calculation of the tooth zone of the stator. Segmentation
Calculation of slots and stator winding
Air gap selection. Rotor pole calculation
Calculation of the damper winding
Magnetic circuit calculation
Determination of the parameters of the stator winding for steady state operation
Calculation of the MMF of the excitation winding under load. vector diagram
Excitation winding calculation
Determination of parameters and time constants of windings
Calculation of masses of active materials
Determination of losses and efficiency
Stator winding temperature rise calculation
Determination of short circuit currents
Calculation and construction of generator characteristics
List of sources used

[bistander]

... let's use Tom Lipo's book which you referenced a week or so ago. Here's a link to a preview which in fact has a few complete sections in chapter 1 pertinent to the subject at hand.
https://tinyurl.com/mrxt867h

Re. Magnetic Circuits.
I apologize that tiny url link was corrupted in the quoted post. Dr. Lipo has a couple sections in chapter 1 on this subject, 1-24 and 1-28. Hopefully this link will take you to the book preview. Unfortunately the preview only goes thru 1-19. https://tinyurl.com/TomLipoBook
bi

[SolarLab]

Lots of good Magnetic Circuit information is available
but it is not really a subject in and of itself - it's more inter-related
by its nature!  pdfdrive_dotcom  e.g practical_transformer_handbook...
Some others as well - see above post(s).
Within your literature - target a search [within a document] 
for "magnetic circuit" etc...

[SolarLab]

HAPPY NEW YEAR !

Best Wishes and Good Times for 2023

[SolarLab]

The fact that the field is stronger in iron is clear. But we need not in iron, but in another, secondary winding. Probably when the field enters the iron, it intensifies, and when it exits towards the other winding, it weakens again. Is this the problem?

That first answer wasn't very good, was it?  "Magnetic Circuit" kind of explains the phenomena,
what ever that is. Had to think on that one abit for a {hopefully} more fundamental view.

Try this -> The magnetic field "in" the iron is like the magnetic field in a bar magnet.

The field, - ""as we see it"" - , is not really "in" the "iron" or "bar;" it's the field in close proximity to, or
around, the iron or around a permanent bar magnet.  If 'the field were only inside the iron or bar, it would
not do us much good. Atomic Magnetic Domains reside within the iron (a.k.a. sort iron or electrical steel)
and is easily magnetized and de-magnetized, whereas a permanent magnet bar will maintain it's magnatism.

The magnetic field will also "couple" between other unattached "iron" close by. The space
seperating these two, or more, "irons" (the gap) results in losses - that's where the "Magnetic Circuit" analysis
helps us to determine those losses and adjust our design accordingly (e.g. saturation, etc.).

Note we can control the (magnetic) field around the iron but the (magnetic) field around the
permanent bar magnet is always there. Also, since the "u" in air is a lot less than that found in metals, often
times it's almost invisible in CAE simulation cartoons, even for small "gaps," but the Field will traverse
from one "iron" to another close adjacent "iron," and in some cases the gap loss with not be much.

The field rapidly falls in air (air u~0) so we configure our pick-up windings (induced) in the "close
adjacent" iron in some fashion that affords good/reasonable magnetic field coupling with the windings.

If we left the pick-up windings in the air close to the "inducing iron" the coupling would be very inefficient,
plus the field would be partially blocked by the close copper layer and the outer copper layes would see
much less of the magnetic field. This appears to have been a drawback in the early Gramme generators.

Instead, we surround (as best we can) the pick-up coils (LAP) by the coupled magnetic field from the Rotor
Coil Poles to capture as much of the field as we can (e.g. by using stator slots). Lots of various schemes
for this but that's the basic idea.

Sounds simple enough; but these basic things seem to stump, it appears, even some of the experts here!

Edit: added clairifications and corrected spelling errors.