This article is concerned with the power-balanced simulation of analog audio circuits, governed by nonlinear differential algebraic equations (DAE). The proposed approach is to combine principles from the port-Hamiltonian and Brayton-Moser formalisms to yield a skew-symmetric gradient system. The practical interest is to provide a solver, using an average discrete gradient, that handles differential and algebraic relations in a unified way, and avoids having to pre-solve the algebraic part. This leads to a structure-preserving method that conserves the power balance and total energy. The proposed formulation is then applied on typical nonlinear audio circuits to study the effectiveness of the method.