The integration of information and communication technology (ICT) with traditional power grids has led to the emergence of smart grids. Advanced metering infrastructure (AMI) plays a crucial role in smart grids by facilitating two-way communication between smart meters and the utility provider. This bidirectional communication allows intelligent meters to report fine-grained consumption data at predefined intervals, enabling accurate billing, efficient grid monitoring and management, and rapid outage detection. However, the collection of detailed consumption data can inadvertently disclose consumers' daily activities, raising privacy concerns and potentially leading to privacy violations. To address these issues and preserve individuals' privacy, we propose a lightweight privacy-preserving smart metering protocol specifically designed to support real-time tariff billing service with dynamic policy adjustment. Our scheme employs an efficient data perturbation technique to obscure precise energy usage data from internal adversaries, including the intermediary gateways and the utility provider. Subsequently, we validate the efficiency and security of our protocol through comprehensive performance and privacy evaluations. We examined the computational, memory, and communication overhead of the proposed scheme. The execution time of our secure and privacy-aware billing system is approximately 3.94540 seconds for a complete year. Furthermore, we employed the Jensen-Shannon divergence as a privacy metric to demonstrate that our protocol can effectively safeguard users' privacy by increasing the noise scale.