A smart grid, considered the next-generation type of power grid, combines a traditional power grid with information and communication technologies to effectively facilitate power generation and ensure transmission security and reliability in real-time. Only authorized consumers should be able to access the smart grid because the information gathered by smart meters includes users' private information. However, smart grid security is still a challenge. Motivated by this challenge, in this paper, we propose a heterogeneous signcryption (HSC) scheme for secure communication between smart meters and the utility. We demonstrate that this scheme is indistinguishable against adaptive chosen-ciphertext attacks (IND-CCA2), existentially unforgeable against adaptive chosen-message attacks (EUF-CMA) and ciphertext-anonymous against adaptive chosen ciphertext attacks (ANON-CCA2) under the computational Diffie-Hellman (CDH) problem in the random oracle model. Our scheme simultaneously achieves confidentiality, integrity, authentication, non-repudiation and ciphertext anonymity in a single logical step. It supports heterogeneous systems, allowing a meter in an identity-based cryptography (IBC) environment to transmit electrical usage data to a utility in a public key infrastructure (PKI) environment. Compared with other existing related schemes, our scheme has the lowest communication overhead and energy consumption for the smart grid. Based on these features, our scheme is highly suitable for secure power transmissions in a smart grid.