Power system dynamic analysis and security assessment are becoming more significant today due to increases in size and complexity from restructuring, emerging new uncertainties, integration of renewable energy sources, distributed generation, and micro grids. Precise modeling of all contributed elements/devices, understanding interactions in detail, and observing hidden dynamics using existing analysis tools/theorems are difficult, and even impossible. In this chapter, the power system is considered as a continuum and the propagated electromechanical waves initiated by faults and other random events are studied to provide a new scheme for stability investigation of a large dimensional system. For this purpose, the measured electrical indices (such as rotor angle and bus voltage) following a fault in different points among the network are used, and the behavior of the propagated waves through the lines, nodes, and buses is analyzed. The impact of weak transmission links on a progressive electromechanical wave using energy function concept is addressed. It is also emphasized that determining severity of a disturbance/contingency accurately, without considering the related electromechanical waves, hidden dynamics, and their properties is not secure enough. Considering these phenomena takes heavy and time consuming calculation, which is not suitable for online stability assessment problems. However, using a continuum model for a power system reduces the burden of complex calculations. Finally, a new power system emergency control framework based on descriptive study of electrical measurements and electromechanical wave propagation in large electric power systems is introduced. Since, fast and accurate detection of instability is essential in initiating certain emergency control measures, the proposed methodology could be also useful to detect the contingency condition and performing the well-known islanding and load shedding techniques. The chapter is supplemented by some illustrative nonlinear simulations on large scale test systems.