Nowadays, power systems are vulnerable to stealthy false data injection attacks (FDIAs). These meticulously crafted attacks can bypass the bad data detection (BDD) module and mislead operators. Load redistribution (LR) is a type of FDIA, which maliciously manipulates load measurements such that a falsified power flow is perceived by the operator. The most severe stealthy LR attacks are often determined by solving a bi-level optimization problem. In these problems, however, the effects of the contingency analysis (CA) module and the physical constraints of generators are usually ignored. On this basis, this paper proposes improved modeling of power systems in bi-level optimization problems to investigate the economic vulnerabilities of power systems to LR attacks. Simulation results obtained from the IEEE 30-bus test system demonstrate that if the CA module and generator physical constraints are not accurately modeled, the imposed costs by LR attacks are underestimated, especially when power systems are congested.