Dynamic Security Assessment (DSA) consists in the quantification of the risk of electricity supply interruption. It relies on dynamic simulations which need a reliable initial point. In case of a major incident or in case of systematic DSA (run in quasi real-time), the latter is not necessarily an equilibrium (load-flow) one and thus needs to be dynamically estimated. For this task, one can rely on static state estimator data and on real-time grid measures. However, internal states of the dynamic devices (like generators) are not accessible for measure and should thus be estimated. The related observability issue is studied here and a solution to estimate these states is proposed, taking into account the nonlinearities of the regulations of the dynamic devices (mainly related to the saturations of the actuating variables like excitation voltages and mechanical torque of the generators). It is shown that numerical solutions can be obtained despite the weak observability.