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SUMMARY This research presents a method for convexifying the non‐linear constraints and the objective function for the Transmission Network Expansion Planning Problem (TNEP). The TNEP seeks to identify the best set of transmission capacity additions to meet a future electric power demand. The TNEP is a non‐convex Mixed Integer Non‐linear Programming problem for which a variety of primal solution methods have been designed. In this paper, the TNEP is formulated as a bilinear programming problem subject to bilinear constraints. This allows resolving the non‐linearities through convexification of the non‐linear objective function and the constraints for a relaxation of the TNEP in which integrality requirements are removed. The final solution for the original TNEP problem is obtained by using a branch and bound strategy. It was found by using a two‐node test case that the convexification method presented in this paper in conjunction with a brand and bound strategy identifies the optimal solution. Successfully solving a small‐scale test problem through convexification presents a promising scenario to solve larger scale problems. This primal‐dual method allows identifying the duality gap which is a limitation of primal methods. Further multidisciplinary research is needed to extend the method presented here to larger cases and real life networks. Copyright © 2013 John Wiley & Sons, Ltd.

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