A smart grid is an electricity network that uses advanced technologies to facilitate the exchange of information and electricity between utility companies and customers. Although most of the technologies involved in such grids have reached maturity, smart meters—as connected devices—introduce new security challenges. To overcome this significant obstacle to grid modernization, safeguarding privacy has emerged as a paramount concern. In this paper, we begin by evaluating the security levels of recently proposed authentication methods for smart meters. Subsequently, we introduce an enhanced protocol named PPSG, designed for smart grids, which incorporates physical unclonable functions (PUF) and an elliptic curve cryptography (ECC) module to address the vulnerabilities identified in previous approaches. Our security analysis, utilizing a real-or-random (RoR) model, demonstrates that PPSG effectively mitigates the weaknesses found in prior methods. To assess the practicality of PPSG, we conduct simulations using an Arduino UNO board, measuring computation, communication, and energy costs. Our results, including a processing time of 153 ms, a communication cost of 1376 bits, and an energy consumption of 13.468 mJ, align with the requirements of resource-constrained devices within smart grids.