## 1 Introduction  
The Advanced Metering Infrastructure (AMI) plays a pivotal role in modernizing traditional power distribution systems by enabling bidirectional communication and data exchange between utility providers and end-users. This transformation is a critical element of the Smart Electrical Grid, enhancing energy efficiency and grid reliability and enabling the integration of renewable energy sources. However, with an increasing reliance on interconnected digital technologies, the AMI system also becomes vulnerable to various cyber threats, making robust security management an indispensable aspect of its successful implementation [1]. The fundamental objective of an AMI system is to collect real-time data from Smart Meters (SMs) installed at consumer premises and communicate this information back to utility companies for billing, load balancing, and demand response purposes. The data transmitted through the AMI system include sensitive information about energy consumption patterns, user behavior, and potentially private details of consumers. Consequently, the confidentiality and integrity of these data are paramount to protecting the privacy and security of consumers and maintaining the overall stability of the electrical grid [1, 2]. To safegu guard the AMI system against potential cyber-attacks, it is essential to establish a comprehensive and robust Security Management framework. The Security Management approach for AMI should encompass various aspects, including but not limited to authentication, access control, encryption, and key management. In this paper, we focus on discussing the modeling of Security Management for the Advanced Metering Infrastructure (AMI) system of Smart Electrical Grids with specific emphasis on the Key Management Scheme (KMS) that is designed to address the unique security challenges of AMI [3]. Security considerations for AMI differ significantly from conventional IT systems due to several distinct features. First, Smart Meters (SMs) often have limited storage and computational capabilities, necessitating the development of lightweight cryptographic techniques to ensure secure key generation, distribution, and management. Second, the AMI system employs a hybrid message transmission approach that combines unicast, broadcast, and multicast modes, introducing complexities when managing encryption keys effectively. Finally, the participation of consumers in Demand Response (DR) projects can vary over time, demanding flexible key refreshing policies to accommodate changes in the AMI ecosystem [4]. SMs are a major component of modern smart grids (SG). Since SMs have limited computation power and are positioned at an exceedingly long distance from the utility, Advanced Metering Infrastructure (AMI) is an essential component in the SG that represents the structure of a complex communication network. It integrates SMs, Monitoring Systems (MS), sensing devices, and the Meter Data Management System (MDMS) [1]. Through AMI, utilities can congregate their fundamental targets for revenue protection and load management. AMI gathers instantaneous information about individual and aggregated demand, puts caps on consumption, and performs various revenue models to control their costs. The application of AMI in the SG enables greater control and operation with smaller margins. This scheme requires a sort of communication and coordination between the different components of the power grid. For years, data exchanged in traditional power line communications were only electrical system measurements, such as voltage measurements, and these data were not considered to be as valuable as financial information [2; 3]. However, with the changing paradigms in modern power system operations, financial information is currently exchanged in power system communications for the purpose of deregulated energy markets. In these energy markets, a small error in the power information (both electrical and financial) can lead to a disruption in the bids of highly competitive electricity markets.