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Cyber security is becoming an area of growing concern in the electric power industry with the development of smart grid. False data injection attack, which is against state estimation through SCADA network, has recently attracted wide research interests. This paper further develops the concept of load redistribution (LR) attack, a special type of false data injection attack. The damage of LR attacks to power system operations can manifest in an immediate or a delayed fashion. For the immediate attacking goal, we show in this paper that the most damaging attack can be identified through a max-min attacker-defender model. Benders decomposition within a restart framework is used to solve the bilevel immediate LR attack problem with a moderate computational effort. Its effectiveness has been validated by the Karush-Kuhn-Tucker (KKT)-based method solution in our previous work. For the delayed attacking goal, we propose a trilevel model to identify the most damaging attack and transform the model into an equivalent single-level mixed-integer problem for final solution. In summary, this paper enables quantitative analysis of the damage of LR attacks to power system operations and security, and hence provides an in-depth insight on effective attack prevention when resource budgets are limited. A 14-bus system is used to test the correctness of the proposed model and algorithm.