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The new converter transformer and harmonic suppression scheme Filter Commutated Converter (FCC) has a unique connection mode. It is very hard to establish the coupled circuit mathematical model when the FCC only contains unaccompanied voltage sources or voltage controlled voltage sources (VCVSs), because some of their elements have no branch admittances or the impedances equals to zero. However the double-graph modified nodal method can solve the above problems, which removes some redundancy variables by making topological graphs separate into two parts. Based on the orient graph of the coupled circuit, a basic double-graph modified nodal model is established according to the coupled circuit principle and the actual design parameter. Furthermore, two examples are given to verify the accuracy of the mathematical model introduced in this paper, such as admittance continuation and controlled source continuation of the basic model. Their simulation results show that the mathematical model established by double-graph modified nodal method is accurate and effective. The proposed method can be selected flexibly in practical project and will have general significance and broad application prospects.