A novel modelling method and a stability analysis procedure for weak power networks with high penetration of power electronics converters are proposed in this paper. The modeling approach can be applied to any network topology and in order to model of the complete network it introduces small-signal state-space models for each network component including power lines, loads, power converters and their control algorithms. The proposed linearized model was validated by comparing its response with the response of the non-linear model. In order to identify the critical network and control parameters of the weak grid in presence of disturbances the developed small-signal model was then used in the stability analysis based on the frequency response of singular values. Finally, the existence of the identified resonance modes was confirmed by using the original non-linear model of the network.