We present a mathematical model to simulate transcutaneous energy transmission systems. Treating such systems as resonant power electronic converters, we develop the equivalent circuit equations, for which the circuit variables are then expanded as Fourier series and a multi-frequency averaging method was applied. Keeping terms up to first-order, the analysis produces a dynamic and harmonic model describing these energy transmission systems. With appropriate values for the circuit parameters, numerical results are compared with those of the exact time domain model. This comparison verifies that our model can adequately represent to first-order such energy-transmission systems.