Modern electro-mechanical systems are often subjected to Pulse-Width-Modulated (PWM) power signals which are produced by power electronics: typical examples are electrical drives or actuators. Pulse-Width-Modulation is based on sampling a reference signal $x(t)$ with a carrier signal $c(t)$ via $b(t) = \textrm{sign}\left( x(t)-c(t) \right)$. Often, both individual signals are periodic, where $\omega$ is the base frequency of the reference and $\Omega$ the base frequency of the carrier. Since both frequencies are usually incommensurable the resulting PWM-signal $b(t)$ will almost always be quasi-periodic: consequently, the frequency spectrum of PWM-signals will be a line-spectrum, which contains linear combinations of both base-frequencies. Moreover, due to the non-smooth character of the $\textrm{sign}$-function, the spectrum may also contain very high frequencies. Both aspects are problematic in the context of direct time integration (DTI) approaches: quasi-periodicity may cause beating like oscillations which demand for simulating over very long time intervals, whereas the non-smooth character of PWM-signals as well as the high spectral contents demand for very small time steps. Moreover, the analysis of mechanical systems subjected to such PWM-excitations may involve a large number of degrees of freedom as well as pronounced nonlinearities (e.h. due to friction, etc.). To overcome the problems arising in time-based analyses, this contribution presents an approach based on invariant manifolds. Consider an electromechanical system $\dot{\bf z} = {\bf f}({\bf z},t)$. To calculate the stationary solution directly, the underlying invariant manifold may be found by solving a corresponding PDE, which is referred to as invariance equation. This contribution discusses several technical details of the using the theory of invariant manifolds in the context of non-smooth quasi-periodic excitations due to PWM-signals stemming from power electronics. In particular, the numerical analysis of simple electromechanical examples will be demonstrated and compared to direct time integration.