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Robust Static Transmission Expansion Planning Considering Contingency and Wind Power Generation

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Abstract

This paper proposes a framework based on the Benders decomposition to obtain a scenario-based robust static transmission expansion planning by considering N-1 security criterion, transmission losses and uncertainties in wind power generation. The model is solved by a bi-level approach that seeks to minimize investment cost as well as penalty costs of wind spill and load curtailment. The wind uncertainty is modeled by grouped historical wind series through k-means clustering technique maintaining the wind correlation between different geographic regions. Case studies are performed in the well-known power systems: IEEE-RTS 24-bus test system and an equivalent Brazilian Southern 46-bus system. In addition, a detailed tutorial case is also presented with a modified version of Garver 6-bus test system.

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Abbreviations

i :

System bus

ij :

Branch between terminal buses i and j

kij :

Transmission line in branch ij

c :

Operational state

w :

Wind scenario

s :

Iteration number

\(pg_{{iwc}}\) :

Active power generation at bus i, scenario w and state c (MW)

\(rd_{{iwc}}\) :

Load shedding at bus i, scenario w and state c (MW)

\(rw_{{iwc}}\) :

Wind spilled at bus i, scenario w and state c (MW)

\(\theta _{{ijwc}}\) :

Angular difference between terminal buses i and j in scenario w and state c (rad)

\(f^E_{{kijwc}}\) :

Active power flow of existing line k in branch ij, for scenario w and state c (MW)

\(f^C_{{kijwc}}\) :

Active power flow of candidate line k in branch ij, for scenario w and state c (MW)

\(\varPhi _{{iwc}}\) :

Active power flow coming out of the bus i through the lines connected to it for scenario w and state c

\(L_{kijwc}\) :

Half of active losses of line k in branch ij, for scenario w and state c (MW)

\(S_{{kijwc}}\) :

Sensitivity of candidate line k in branch ij, scenario w and state c (\({{{\$}}}\))

\(\mathrm{OBF}_{wc}\) :

Objective function value in scenario w and state c (\({{{\$}}}\))

\(\mathrm{IC}\) :

Investment cost (\({{\$}}\))

\(X_{{kij}}\) :

Expansion decision (binary variable) for reinforcement in line k in branch ij

\(\lambda _{{iwc}}\) :

Lagrange multiplier of power balance constraint at bus i for scenario w and state c ($/MW)

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

Active power generation capacity at bus i (MW)

\(pw_{{iw}}\) :

Sampled generation from wind farm at bus i and scenario w (MW)

\(d_{{i}}\) :

Active demand at bus i (MW)

\(b_{{kij}}\) :

Susceptance of line k (\(\mho \))

\(g_{{kij}}\) :

Conductance of line k (\(\mho \))

\(\bar{f}^E_{{kij}}\) :

Active power flow limit of existent line k (MW)

\(\bar{f}^C_{{kij}}\) :

Active power flow limit of candidate line k (MW)

\(ce_{{kij}}\) :

Investment cost of candidate line k in branch ij (\({{{\$}}}\))

\(N_W\) :

Number of wind scenarios

\(N_L\) :

Number of operational states, including the base case and contingencies

B :

System buses

E :

Existing lines

C :

Candidate lines

\(\varOmega ^E_{{i}}\) :

Existing lines connected to bus i

\(\varOmega ^C_{{i}}\) :

Candidate lines connected to bus i

L :

Operational states

W :

Wind scenarios

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Acknowledgements

The authors thank the “Coordination for the Improvement of Higher Education Personnel” (CAPES), “Brazilian National Research Council” (CNPq), “Foundation for Supporting Research in of Minas Gerais” (FAPEMIG) and “Postgraduate Program in Electrical Engineering of the Federal University of Juiz de Fora” (PPEE/UFJF) for supporting this work.

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Authors and Affiliations

  1. Federal University of Juiz de Fora, Rua José Lourenço Kelmer, s/n, Juiz de Fora, MG, 36036-900, Brazil

    Arthur N. de Paula, Edimar J. de Oliveira, Leonardo W. de Oliveira & Leonardo M. Honório

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  1. Arthur N. de Paula
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  2. Edimar J. de Oliveira
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  3. Leonardo W. de Oliveira
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  4. Leonardo M. Honório
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Correspondence to Arthur N. de Paula.

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de Paula, A.N., de Oliveira, E.J., de Oliveira, L.W. et al. Robust Static Transmission Expansion Planning Considering Contingency and Wind Power Generation. J Control Autom Electr Syst 31, 461–470 (2020). https://doi.org/10.1007/s40313-019-00556-w

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