Power systems are fundamental to state development, and measuring the security of the power information system is crucial. In existing power information systems, most security methods rely on encryption algorithms like RSA algorithm, which face growing threats from the increasing computing power of the Internet and quantum computers. With recognizing the urgent need for information security in power systems and the unconditional security offered by quantum communication, this paper explores the application of quantum security communication in power information systems. Specifically, through a detailed analysis of the procedure and security factors of the standard SSL protocol, this paper proposes a security enhancement method that is compatible with existing Internet protocol foundations. The proposed method enhances the source of random numbers by incorporating preset quantum random numbers, based on either a quantum random number generator or a quantum key distribution network. Implemented on the OPENSSL VPN evaluation platform, experiments show that the proposed security enhancement method can improve the security level of power information systems without significantly increasing system complexity or cost.