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An application of a functionally graded material (FGM) to the solid spacer in gas insulated switchgears (GISs) can reduce the electric field concentration at the specific region, for example, the anode or the interface between the spacer and the gas. However, the electric field stress near the triple junction of the grounded electrode with a rounded shape, which remarkably affects the insulation capability of the GIS, inversely related. Therefore, in order to prevent this, it is necessary to modify the grounded electrode geometry in the common Cubicle-GIS and apply the elliptical FGM spacer with a reverse-direction variation unlike the permittivity variations of the existing unidirectional or bidirectional distributions. In this paper, we found the proper distribution of dielectric permittivity, dug a groove in the grounded electrode near the triple junction, and performed the optimization of this grounded electrode configuration by using the design of experiments (DOE). Consequently, the electric field stress in the triple junction of the grounded electrode can be effectively reduced by using the optimally designed grounded electrode shape applying the FGM spacer.