The large disturbance behaviour of power systems often involves complex interactions between continuous dynamics and discrete events. The paper proposes a differential-algebraic-discrete (DAD) model structure which captures those interactions in a systematic way. It is shown that the model is a realization of a general hybrid system model. The DAD model opens up opportunities for the application to power systems of hybrid system results in stability analysis and control. The paper presents a practical approach to implementing the DAD model structure.