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Transmission expansion planning with re-design

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Abstract

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 re-designed 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 re-design, can lead to sensible cost reductions.

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Abbreviations

S :

bus-circuit incidence matrix

i∈B:

index bus, in the set of buses

\(\overline{g}_{i}\) :

maximal generation at bus i

d i :

load at bus i

Ω=Ω0∪Ω1 :

set of all circuits

Ω0 :

set of existing circuits

Ω1 :

set of candidate circuits

|Ω1|:

cardinality of set Ω1

i(k), j(k):

terminal buses of circuit k

γ k :

susceptance of circuit k

\(\overline{f}_{k}\) :

capacity of circuit k

c k :

investment cost of circuit k

k 1 ∦ k 2 :

not parallel circuits

k 1 ∥ k 2 :

parallel circuits

E=E0∪E1:

set of all “fat” edges

E 0 :

set of “fat” edges containing existing circuits

E 1 :

set of “fat” edges containing candidate circuits

\(\overline{x}_{ij}\) :

maximum number of circuits that can be built between i and j

x ij :

existing number of circuits between i and j

(ij):

“fat” edge between i and j

ℓ∈ℒ ij :

index circuit among all circuits belonging to “fat” edge (ij)

SP i−j :

shortest path between buses i and j

LP i−j :

longest path between buses i and j

\(\mathit{LP}_{i-j}^{l}\) :

longest path between buses i and j not passing through bus l

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Authors and Affiliations

  1. Eletrobrás Group, CEPEL, Electric Energy Research Center, Rio de Janeiro, Brazil

    Luciano S. Moulin & Claudia Sagastizábal

  2. Department of Computer Science, Université Libre de Bruxelles, Brussels, Belgium

    Michael Poss

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  1. Luciano S. Moulin
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  2. Michael Poss
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Correspondence to Michael Poss.

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C. Sagastizábal on leave from INRIA Rocquencourt, France.

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Moulin, L.S., Poss, M. & Sagastizábal, C. Transmission expansion planning with re-design. Energy Syst 1, 113–139 (2010). https://doi.org/10.1007/s12667-010-0010-9

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