Convexification method for bilinear transmission expansion problem

Abstract

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.

A LP and MILP methodology to support the planning of transmission power systems

“…[21]), bilinearization (e.g. [22]), or semidefinite programming (e.g. [23]) show the same limits of the MINLP in terms of complexity of the solution algorithm and also introduce approximations which errors should be compared with the errors that can be obtained with the adoption of DC-load flow models.…”

Dynamic generation and transmission expansion planning in the power market-based on a multiobjective framework

“…Since the solution methodology usually begins from a feasible point, local minima issue is very probable particularly when many variables are included in the formulation. Some of the most important mathematical‐based methods are linear programming, nonlinear programming, mixed‐integer linear programming, and benders decomposition . On the other hand, the free‐derivative metaheuristic methods have straightforward process that are constructed based on elitism and competitive selection.…”

Probabilistic multi-objective transmission investment and expansion planning

“…In [25], Gram-Charlier series is used to control the risk which is time consuming when used in TEP, which is inherently a time-consuming procedure. A convexification technique is used in [27] to deal with the non-linearity of the TEP problem. However, a two-node system is used to test the method, and the application of the method for large-scale networks is not evaluated.…”