## 1 Introduction
This raised the likelihood of cyber security issues and necessitated the integration of security protocols within SG for comprehensive security functionality [4; 5]. SG's evolution to a cyber-physical system by deploying AMI makes it prone to cyber threats aside from SCADA vulnerabilities. AMI cyber security, from an oriented threat perspective, impacts data confidentiality, integrity, availability, and accountability [6]. The most crucial security issues that must be resolved before AMI can be deployed are message confidentiality for user privacy and behavior, message authentication for meter readings (DR), and load control communications. Using encryption and authentication methods that rely on the safety of cryptographic keys can resolve confidentiality and integrity difficulties. In AMI systems, key management for several devices is essential for security. The key management scheme consists of a key organizational structure, key generation, updating, distribution, storage laws, etc. (KMS). Recently, a number of studies on the key management of AMI systems were released. An example of a complete system for secure AMI communications, including secrecy and authentication, is presented in [7]. Using mutual authentications, this system can provide trust services, data privacy, and integrity. A survey on key management and authentication approaches in smart metering systems is presented in [8], including security measures like the Advanced Encryption Standard (AES) [8], encryption, and public-key infrastructure authentication. The focus of this paper is on-device authentication, data secrecy, and message authentication mechanisms for Advanced Metering Infrastructure (AMI) applications. The outcomes have effects on key management. There is not a complete solution yet for man aging keys in AMI systems for various smart devices. If the AMI network is constructed on a wireless sensor network, the authors in [9] propose a key establishment and security technique based on public-key cryptography. Depending on the stage of smart grid development in various nations, different AMI network types exist [10; 11]. The significance of key management for a large number of devices in AMI is important for the security preservation of cryptographic keys [12]. Moreover, a few KMSs have been set up to enable secure communication between SCADA systems and wide-area protection systems: two examples of power control systems [13; 14]. However, because of the differences in these systems' architectures, message characteristics, and needs, these KMSs, along with those utilized in general IT systems, have difficulty when immediately adapted to an AMI system. We may infer from the findings of the available study that the suggested KMSs are for a certain AMI system. When application functions, communications, and information technology change, the KMS can no longer be appropriate. However, the majority of AMI systems have still been in the experimental stage until recently; therefore, the future is still unknown. Additionally, there are regional and national differences in the design and development of an AMI system. The functionalities that must be deployed are different from the standpoint of the application's needs. The applications are quite straightforward, like metering, measuring, and monitoring; the other applications are overly complicated and focus on DR and load management applications. According to the needs of the program and user desire, there are several communication options as well. Due to these aforementioned issues, we are attempting to recommend a more widespread KMS for AMI systems. To summarize AMI's characteristics and development, we believe that its structure and constituent parts are stable. In other words, key management's primary, ongoing goal is securing SMs. In order to manage the keys of several SMs, a key management framework based on a key graph is suggested. Although the AMI's functions are not set in stone, we can create a KMS to hold all of the potential functions.