As quantum computing technology continues to advance towards a cryptographically relevant scale, cybersecurity for critical infrastructure such as electrical power systems must prepare for an existential threat. A crucial step to mitigating the potential damage a quantum computer-aided attack may cause is identifying quantum-vulnerable algorithms that are currently used in the standards for the security of power system control centres and communication networks. The IEC 62351 is a series of standards for protecting data in power automation systems and includes several quantum-vulnerable cryptographic primitives. Parts 7, 8, and 9 of the IEC 62351 are dedicated to network and system management, role-based access control, and key management. In this work, we conduct a comprehensive vulnerability assessment of the cryptographic algorithms selected in these parts of IEC 62351.