Magnetic core dimensionning limits in hydro generators

We believe that the understanding of magnetic core dimensioning limits demands knowledge of the theory of magnetic circuits applied to hydro-generators. For this reason, the Technical Brochure was developed as a consolidation of history, papers and several books.

To conduct this task, certain premises were stated related to technical documentation in general:

• The bibliography should be in public domain;
• State a transparent evolution of formulation throughout the text;
• A computational program will not be delivered as an output, although all the formulation was programmed, and the results were fully validated;
• As an Annex of the technical brochure, a benchmark model will be introduced with calculated results aiming to support the elaboration of customized routines.

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Structure of the Technical Brochure

After finding a detailed magnetic circuit theoretical exposition, based on Figure 1 the reader is introduced on the universe of magnetic flux leakage which approach is very hard to find in traditional books or papers. As illustrated Figure 2, from a 1903 paper the concept of “leakage-flux-tubes” was extracted. This is an attempt to confine the dispersed leakage magnetic flux (like ϕσ_sh and ϕσ_bd in Figure 1) inside of imaginary tubes where they can be quantified.

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Once the concept of pole leakage coefficient is clearly defined, the procedure for calculating no-load excitation current is introduced. With that, the theory is extended to calculate the machine no-load characteristic.

As saturation is highly dependent on material properties, an exhaustive analysis on the real nature of silicon-steel sheets is developed for stating the “state of the art” of its properties, revisiting the concept of anisotropy. As shown in Figure 3, this analysis demonstrates that non-grain-oriented silicon steel is actually isotropic whose impact in the excitation current calculation may elucidate some “inexplicable” deviations.

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Complementarily, the application of grain-oriented silicon steel is debated. The pros and cons are tabled based on practical applications.

As it can be appreciated in Figure 4, a saturation index is presented as the conjugation rate of two excitation current points. The one over the air-gap line (I_f0) to the other over the saturation curve (I_fg), both at rated no-load voltage. The goodness of this proposed index lays in the fact that these two excitation points are commonly informed in every technical machine description.

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Finally, aiming to motivate the reader to implement his own calculation routine, as an Annex to the Technical Brochure is presented:

1. A benchmark reference machine data;
2. The pole magnetic flux density over the air-gap line and its Fourier series harmonics;
3. Typical core materials magnetic characteristics; and
4. The benchmark machine expected results.

Conclusion

The author’s hope is to contribute to a better understanding of salient pole synchronous machine magnetic dimensioning analytical process.