The smart metering infrastructure plays an important role in smart grid environments. Such metering networks need to be protected against cyber attacks by using authenticated key exchange protocols, and many relevant schemes have been presented by researchers. In addition, in order to protect against the energy theft problem, it is also important to consider physical security of the smart meter. Recently, PUFs (physical uncloneable functions) have gained popularity as a primitive against physical attacks. In 2019, we proposed the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> PUF-based authentication scheme for secure smart grid communication with resilience against physical attacks on smart meters. However, recent studies have shown that PUFs are susceptible to modeling attacks. To address this issue, this paper proposes a reconfigurable authenticated key exchange scheme for secure communication in smart grids by using the concept of reconfigurable PUFs. In addition to security, the efficiency evaluation demonstrates that our new scheme has advantages in both the computation and communication costs as compared to the state-of-the-art protocols.