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There have been many experimental investigations into the ability of electric fields to enhance combustion by acting upon ion species present in flames . In this work, we examine this phenomenon using a one-dimensional model of a lean premixed flame under the influence of a longitudinal electric field. We expand upon prior two-step chain-branching reaction laminar models with reactions to model the creation and consumption of both a positively-charged radical species and free electrons. Also included are the electromotive force in the conservation equation for ion species and the electrostatic form of the Maxwell equations in order to resolve ion transport by externally applied and internally induced electric fields. The numerical solution of these equations allows us to compute changes in flame speed due to electric fields. Further, the variation of key kinetic and transport parameters modifies the electrical sensitivity of the flame. From changes in flame speed and reactant profiles we are able to gain novel, valuable insight into how and why combustion can be controlled by electric fields.