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This paper presents a quantitative analysis method for an EIE-core variable inductor, which is applied as a voltage regulator in an electric power system. We propose a three-dimensional nonlinear reluctance network analysis (RNA) model of an EIE-core considering magnetic hysteresis. The RNA model of the core is coupled with external electric circuits, in order to simulate an EIE-core variable inductor. Using the coupled model, we can calculate the operating characteristics of the variable inductor including an iron loss. Furthermore, we describe the development of a trial 6.6 kV-300 kVA reactive power compensator using an EIE-core.