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Vulnerability assessment is a requirement of NERC's cybersecurity standards for electric power systems. The purpose is to study the impact of a cyber attack on supervisory control and data acquisition (SCADA) systems. Compliance of the requirement to meet the standard has become increasingly challenging as the system becomes more dispersed in wide areas. Interdependencies between computer communication system and the physical infrastructure also become more complex as information technologies are further integrated into devices and networks. This paper proposes a vulnerability assessment framework to systematically evaluate the vulnerabilities of SCADA systems at three levels: system, scenarios, and access points. The proposed method is based on cyber systems embedded with the firewall and password models, the primary mode of protection in the power industry today. The impact of a potential electronic intrusion is evaluated by its potential loss of load in the power system. This capability is enabled by integration of a logic-based simulation method and a module for the power flow computation. The IEEE 30-bus system is used to evaluate the impact of attacks launched from outside or from within the substation networks. Countermeasures are identified for improvement of the cybersecurity.