Optimum design of core blocks and analyzing the fringing effect in shunt reactors with distributed gapped-core

• This paper investigates fringing effects in shunt reactors to optimize core blocks.
• Running the three-dimensional FEM shows that there is an optimum height for each core block.
• An analytical equation is presented using the results of the three-dimensional FEM.
• Schwarz-Christoffel transformation is used to calculate the fringing flux permeance.
• A new equation is developed for calculation of the optimum height of core blocks.

Shunt reactors are designed in the form of cores with air gaps which are distributed along the legs. It is crucial to determine the height of blocks based on its impact on the magnitude of the fringing flux, the number of blocks and other size-related parameters. This study has applied three-dimensional finite element method to a single-phase reactor which is calculated by well-known equations of magnetic circuit theory. This is done to analyze the effects of the fringing flux on the inductance.In this work, air gaps are distributed along the legs in order to determine the effects of the number and height of core blocks on the inductance. The analytical equations, which are used to calculate the optimum heights of core blocks based on the Schwarz-Christoffel transformation, are developed.These equations are derived from the size-related parameters of the reactor and their validity has been fully confirmed by the outcomes of the finite element analysis. There is a good agreement between the height calculated by empirical relations and that estimated using the proposed method in this paper.