Methods for calculating leakage inductances

Knowledge of leakage inductances is essential for predetermining the electromechanical characteristics of electrical machines. These leakage inductances are used in equivalent diagrams, and are indispensable in the study of the association between the machine and the power source. The latter is not simply the mains, with its practically infinite power and constant frequency; it is often a variable-frequency source, driven by control laws imposed by the structure of the machine and the nature of the load.

These few considerations demonstrate the importance of properly predetermining leakage in electrical machines.

• Before moving on to the actual calculation, we need to define the notion of leakage flux. We'll call leakage flow any flow that doesn't directly contribute to electromechanical conversion. The leakage flux of a machine has several terms, depending on the region of space where it develops. We distinguish between notch leakage, differential leakage, zigzag leakage, coil head leakage, etc. Each of these types of leakage defines an inductance whose value depends on the geometry of the zone concerned. All these leaks are involved in equivalent schematics and are the cause of voltage drops of varying magnitude.

  As a rule, leakage fluxes take a relatively long air path. It can be assumed that the value of the corresponding inductances is very little affected by the magnetic state of the machine, and remains constant whatever the operating regime.

• Calculating leakage inductances is not always easy. It assumes that the path of the induction lines is known. In certain cases of simple geometry, we can perform a calculation that leads to an analytical expression, depending on the geometric dimensions of the region under study. This is the case, for example, with rectangular slots containing divided or solid conductors. The expressions obtained are then used to predetermine the characteristics of the machine, according to its geometry; they are also used to optimize it, taking into account the technical and economic constraints imposed by the user.

  When the path of the induction lines is not known, it is essential to make simplifying assumptions which, combined with laboratory validation tests, lead to empirical analytical expressions whose accuracy is sufficient for most practical applications. In the following paragraphs, we will develop the essentials of these methods, which will be the subject of the first part of our article.

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