In this paper, we analyse the vulnerabilities of KL scheme which is an ID-based authentication scheme for AMI network, and propose two kinds of authentication schemes which satisfy forward secrecy as well as security requirements introduced in the previous works. In the first scheme, we use MDMS which is the supervising system located in an electrical company for a time-synchronizing server, in order to synchronize smart grid devices in home, and we process device authentication with a new secret value generated by OTP function every session. In the second scheme, we use a secret hash-chain mechanism for authentication process, so we can use a new secret value every session. The proposed two schemes have strong points and weak points respectively and those depend on the services area and its environment, so we can select one of them efficiently considering real aspects of AMI environment.