Conic Programming for Circuit Equations with Rational Current Controlled Resistors

This brief considers special nonlinear resistors are where the voltage is controlled by a polynomial of the current with arbitrary rational exponents, called rational current controlled resistors (RCCRs). It is discovered that nonlinear circuit equations with these special nonlinear resistors can be isomorphic to the Karush-Kuhn-Tucker (KKT) conditions of a convex optimization model. Moreover, three-dimensional rotated cones using the 'tower of variables' technique are utilized to exactly reformulate the convex optimization model into tractable conic programming (CP). Through the proposed approach, the solution of the nonlinear circuit equations can be exactly obtained by solving the CP. Simulation results on several test systems with RCCRs demonstrate the effectiveness of the proposed method.