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This paper studies the consequences of a human-initiated targeted attack on the national electric power system. We consider two kinds of attacks: ($i$) an attack by an adversary that uses a tactical weapon and destroys a large part of the grid, by physically targeting a large geographic region; ($ii$) a targeted attack by an adversary that takes out a small number of critical components in the network simultaneously. Our analysis uses ($i$) a realistic representation of the underlying power grid, including the topology, the control and protection components, ($ii$) a realistic representation of the targeted attack scenario, and ($iii$) a dynamic stability analysis, that goes beyond traditional work comprising structural and linear flow analysis. Such realistic analysis is expensive, but critical since it can capture cascading failures that result from transient instabilities introduced due to the attack. Our model acknowledges the presence of hidden failures in the protection systems resulting in relay misoperations. We analyze the extent of cascading outages for different levels of hidden failures. Our results show that: ($i$) the power grid is vulnerable to both these attacks, ($ii$) the tactical attack has significant social, economic and health damage but need not result in a regional cascade; on the contrary the targeted attack can cause significant cascade and lead to power outage over a large region. Our work shows the necessity to harden the power grid not just to cyber-attacks but also to physical attacks. Furthermore, we show that realistic representations and analysis can lead to fundamentally new insights that simplified models are unlikely to capture. Finally, the methods and results help us identify critical elements in the grid; the system can then be hardened in a more precise manner to reduce the vulnerabilities.