Original Paper

Energy Systems

, Volume 5, Issue 1, pp 179-207

First online:

Complexity of transmission network expansion planning

NP-hardness of connected networks and MINLP evaluation
  • David OertelAffiliated withKarlsruhe Institute of Technology Email author 
  • , R. RaviAffiliated withTepper School of Business, Carnegie Mellon University

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Transmission network expansion planning in its original formulation is NP-hard due to the subproblem Steiner trees, the minimum cost connection of an initially unconnected network with mandatory and optional nodes. By using electrical network theory we show why NP-hardness still holds when this subproblem of network design from scratch is omitted by considering already (highly) connected networks only. This refers to the case of extending a long working transmission grid for increased future demand. It will be achieved by showing that this case is computationally equivalent to \(3\)-SAT. Additionally, the original mathematical formulation is evaluated by using an appropriate state-of-the-art mixed integer non-linear programming solver in order to see how much effort in computation and implementation is really necessary to solve this problem in practice.


Transmission network expansion planning NP-hard Mixed-integer non-linear programming Electrical network