Optimization of Electric Stress in a Vacuum Interrupter Using Charnes’ Big M Algorithm

Abstract

This article presents the optimization of electric stress distribution over the live electrode of an axisymmetric vacuum interrupter which is employed for 11 kV switching operations. The optimization is carried out by a classical approach using Charnes’ Big M algorithm used for solving constrained linear programming problems (LPPs). For this purpose, the objective function is obtained by applying multiple linear regression analysis by which a mathematical relationship between the maximum resultant electric field intensity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}^{\text {max}}$ </tex-math></inline-formula> ) over the surface of the live electrode and the critical dimensions affecting this stress. For this purpose, a set of 173 data is used which is prepared by varying the critical dimensions within the constraints of the overall dimension of the system and calculating the value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${E}^{\text {max}}$ </tex-math></inline-formula> over the surface of the live electrode by employing the boundary element method (BEM).