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The dynamic operation of power transmission systems requires the acquisition of reliable and accurate measurement and state information. The use of TCP/IP-based communication protocols such as IEEE C37.118 or IEC 61850 introduces different gateways to launch cyber-attacks and to compromise major system operation functionalities. Within this study, a combined network intrusion and phasor data anomaly detection system is proposed to enable a secure system operation in the presence of cyber-attacks for dynamic control centers. This includes the utilization of expert-rules, one-class classifiers, as well as recurrent neural networks to monitor different network packet and measurement information. The effectiveness of the proposed network intrusion and phasor data anomaly detection system is shown within a real-time simulation testbed considering multiple operation and cyber-attack conditions.