Wind Generation Impact in Transmission Expansion Planning

  • Camile Arêdes MoraesEmail author
  • Edimar José de Oliveira
  • Daniel Fioresi Botelho
  • Leonardo Willer de Oliveira
  • Milena Faria Pinto


This research proposes a post-stage investment analysis in the transmission expansion network planning problem considering the intermittence of renewable energy sources, especially wind power sources. The main goal of this study is to analyze the voltage profiles in all the system buses and the level of electrical losses in the lines using AC flow for impact evaluation of renewable energy insertion. This research also performs an additional analysis considering wind energy insertion during the planning stage. This analysis is to demonstrate the effect in the stage of investment in transmission lines. The variability of these sources is represented through scenarios obtained by the K-means classification algorithm that allows the preservation of the correlation among generating stations. The methodology performance is tested using the IEEE 24-bus system, which is modified to include a significant share of wind energy.


Transmission expansion planning Renewable energy sources Voltage profiles DC network model AC network model 

List of Symbols

Sets and Subscripts


Set of branches with existing transmission lines


Set of branches with candidate transmission lines


Set of branches with fictitious transmission lines


Set of load buses


Set of generation buses


Set of candidate reinforcements of branch ij


Set of existing transmission lines of branch ij


Set of fictitious transmission lines of branch ij

\(\varOmega E_i\)

Set of existing lines connected to bus i

\(\varOmega C_i\)

Set of candidate lines connected to bus i


Index for existing or reinforcement transmission line


Index for wind generation scenario


\({\hbox {pg}}_{i,w}\)

Active power generation at bus i and wind generation scenario w (MW)

\({\hbox {pw}}_{i,w}\)

Active wind power generation at bus i and wind generation scenario w (MW)

\({\hbox {pd}}_{i,w}\)

Active power deficit at bus i and wind generation scenario w (MW)

\({\hbox {EP}}_{k,ij}\)

Expansion binary 0/1 parameter for reinforcement k in branch ij

\(\theta _{ij,w}\)

Angular difference between terminal buses i and j at wind generation scenario w


Active power flow (MW) of transmission line k in branch ij, at wind generation scenario w


Active power flow (MW) of candidate transmission line k for branch ij, at wind generation scenario w


Active power flow (MW) of fictitious line k for branch ij, at wind generation scenario w


\({\hbox {dc}}_i\)

Specific deficit generation cost at bus i ($/MW)

\({\hbox {pg}}_i^{\mathrm{min}}\)

Inferior limit of \(\hbox {pg}_{i,w}\) (MW)

\({\hbox {pg}}_i^{\mathrm{max}}\)

Superior limit of \(\hbox {pg}_{i,w}\) (MW)


Demand at bus i (MW) at wind generation scenario w


Active power flow limit of an existing transmission line k (MW)


Active power flow limit of a candidate transmission line k (MW)

\({\hbox {ce}}_k\)

Investment cost of a candidate transmission line k ($)


Susceptance of line k

\(\gamma _k\)

Susceptance of fictitious line k, considered as 0.001 per unit (pu)


Conductance of line k


Number of clusters to the K-means method



The authors would like to thank the Brazilian Research Agencies: CAPES, CNPq, FAPEMIG and INERGE for supporting this research.


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Copyright information

© Brazilian Society for Automatics--SBA 2019

Authors and Affiliations

  1. 1.Federal University of Juiz de ForaJuiz de ForaBrazil
  2. 2.Federal Center for Technological Education of Rio de JaneiroRio de JaneiroBrazil

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