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State estimation is a key element in today's power systems for reliable system operation and control. State estimation collects information from a large number of meter measurements and analyzes it in a centralized manner at the control center. Existing state estimation approaches were traditionally assumed to be able to tolerate and detect random bad measurements. They were, however, recently shown to be vulnerable to intentional false data injection attacks. This paper fully develops the concept of load redistribution (LR) attacks, a special type of false data injection attacks, and analyzes their damage to power system operation in different time steps with different attacking resource limitations. Based on damaging effect analysis, we differentiate two attacking goals from the adversary's perspective, i.e., immediate attacking goal and delayed attacking goal. For the immediate attacking goal, this paper identifies the most damaging LR attack through a max-min attacker-defender model. Then, the criterion of determining effective protection strategies is explained. The effectiveness of the proposed model is tested on a 14-bus system. To the author's best knowledge, this is the first work of its kind, which quantitatively analyzes the damage of the false data injection attacks to power system operation and security. Our analysis hence provides an in-depth insight on effective attack prevention with limited protection resource budget.