Transmission expansion planning (TEP) is a rather complicated process which requires extensive studies to determine when, where and how many transmission facilities are needed. A well planned power system will not only enhance the system reliability, but also tend to contribute positively to the overall system operating efficiency. Starting with two mixed-integer nonlinear programming (MINLP) models, this paper explores the possibility of applying AC-based models to the TEP problem. Two nonlinear programming (NLP) relaxation models are then proposed by relaxing the binary decision variables. A reformulation- linearization-technique (RLT) based relaxation model in which all the constraints are linearized is also presented and discussed in the paper. Garvers's 6-bus test system and the IEEE 24-bus system are used to test the performance of the proposed models and related solvers. A validation process guarantees that the resultant TEP plan is strictly AC feasible. The simulation results show that by using proper reformulations or relaxations, it is possible to apply the AC models to TEP problems and obtain a good solution.