.What is the relation of the total slot leakage reactance with number of stator slots?

In electrical machines such as induction and synchronous motors, the total slot leakage reactance is related to the number of stator slots due to the leakage flux paths that are created around the stator slots. The slot leakage reactance essentially represents the inductive reactance due to the magnetic flux that does not contribute to energy conversion but instead leaks through paths surrounding the stator slots.

As the number of stator slots increases, the total slot leakage reactance usually increases as well. This is because with more slots, there are more paths for the leakage flux to follow, resulting in an increase in total slot leakage reactance. The exact relationship can be complex, as it is influenced by several factors including the geometry of the stator slots, the slot fill factor (how much of the slot is filled with conductor material), and the magnetic permeability of the materials involved.

In general, however, engineers and designers of electrical machines strive to optimize the design of the stator, including the number and configuration of slots, to achieve a balance between minimizing leakage reactance (which can decrease efficiency and performance) and meeting other design criteria such as manufacturability, cost, and mechanical strength.