Transmission Expansion Planning with Re-design

Luciano S Moulin (1) , Michael Poss (2) , Claudia Sagastizábal (1)

1 Cepel - Electrical Energy Research Center
2 MAORE - Methods, Algorithms for Operations REsearch

Expanding an electrical transmission network requires heavy investments that need to be carefully planned, often at a regional or national level. We study relevant theoretical and practical aspects of transmission expansion planning, set as a bilinear programming problem with mixed 0-1 variables. We show that the problem is NP-hard and that, unlike the so-called Network Design Problem, a transmission network may become more efficient after cutting-off some of its circuits. For this reason, we introduce a new model that, rather than just adding capacity to the existing network, also allows for the network to be redesigned when it is expanded. We then turn into different reformulations of the problem, that replace the bilinear constraints by using a "big-M" approach. We show that computing the minimal values for the "big-M" coefficients involves finding the shortest and longest paths between two buses. We assess our theoretical results by making a thorough computational study on real electrical networks. The comparison of various models and reformulations shows that our new model, allowing for redesign , can lead to sensible cost reductions.

Mots clés: "big-M" formulation; transmission network; network design

Domaines: Recherche opérationnelle [math.OC]

Luciano S Moulin, Michael Poss, Claudia Sagastizábal. Transmission Expansion Planning with Re-design. Energy Systems, 2010, 1 (2), pp.113-139. ⟨10.1007/s12667-010-0010-9⟩. ⟨hal-02399898⟩