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Reliability-constrained dynamic transmission expansion planning considering wind power generation

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Abstract

This paper proposes a two-stage framework to solve the long-term transmission network expansion planning (TNEP) problem ensuring user-defined reliability levels and wind curtailment over the planning horizon. In the first stage, the static TNEP (S-TNEP) problem is solved to define where a set of new lines must be installed at the end of planning horizon. In the second stage, a multistage procedure is performed to solve the dynamic TNEP (D-TNEP) in order to determine the moment that each transmission line should be built. Both S-TNEP and D-TNEP are decomposed into investment decision and performance assessment through a bi-level scheme based on Benders decomposition; thus, the reliability is considered and evaluated over the planning process. The reliability and performance indexes are obtained through the non-chronological Monte Carlo simulation considering the random behavior of transmission lines failures, load fluctuations and uncertainties over wind availability. The loss of wind probability performance index is introduced to measure the probability of wind curtailment in each connection point of the system, and it is used to prevent wind farms from being underused. The proposed methodology is tested in modified versions of the 24-bus IEEE reliability test system and the IEEE 118-bus test system.

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Abbreviations

B :

Set of system buses

E :

Set of existing lines

C :

Set of candidate lines

\(\varOmega ^\mathrm{E}_{i}\) :

Set of existing lines connected to bus i

\(\varOmega ^\mathrm{C}_{i}\) :

Set of candidate lines connected to bus i

i :

System bus

ij :

Line between buses i and j

k :

Existing or candidate transmission lines

s :

Operative state

\(\mathrm{pg}_{i, s}\) :

Active power generation at bus i in state s, MW

\(\mathrm{rd}_{i, s}\) :

Active power deficit equivalent to the load shedding at bus i in state s, MW

\(\mathrm{rw}_{i, s}\) :

Active power surplus equivalent to the wind energy spillage at bus i in state s, MW

\(\theta _{ij, s}\) :

Angular difference between terminal buses i and j in state s, rad

\(\mathrm{f}^\mathrm{E}_{k, s}\) :

Active power flow of existing line k in state s, MW

\(\mathrm{f}^\mathrm{C}_{k, s}\) :

Active power flow of candidate line k in state s, MW

\(\varPhi _{i, s}\) :

Active power flow from bus i through the lines connected to it, in state s, MW

\(S_{k, s}\) :

Sensitivity index for line k in state s, $

IC:

Investment cost, $

\(\mathrm{OBF}_s\) :

Objective function for state s, $

\(X_{k}\) :

Expansion parameter for reinforcement decision in line k, which is a binary variable 0/1

\(u_{k, s}\) :

Operative state s for existing line k, which is a binary variable 0/1

\(\lambda _{i, s}\) :

Lagrange multiplier of power balance constraint at bus i in state s, $/MW

\(\mathrm{LOLP}_i\) :

Loss of load probability in bus i

\(\mathrm{LOWP}_i\) :

Loss of wind probability in bus i

EENS:

Expectation of energy not supplied, MWh/year

EWES:

Expectation of wind energy spilled, MWh/year

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

Active power generation capacity at bus i, MW

\(\mathrm{pw}_{i, s}\) :

Sampled generation from wind farm at bus i in state s, MW

\(d_{i, s}\) :

Active demand at bus i in state s, MW

\(b_{k}\) :

Susceptance of line k, \(\varOmega ^{-1}\)

\(g_{k}\) :

Conductance of line k, \(\varOmega ^{-1}\)

\(\mathrm{FOR}_{k}\) :

forced outage rate of line k

\(\bar{\mathrm{f}}^\mathrm{E}_{k}\) :

Active power flow limit of existing line k, MW

\(\bar{\mathrm{f}}^\mathrm{C}_{k}\) :

Active power flow limit of candidate line k, MW

\(\mathrm{ce}_{k}\) :

Investment cost of candidate line k, $

NS:

Number of sampled states

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Acknowledgements

The authors acknowledge CAPES, CNPq, FAPEMIG and INERGE for their support.

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Authors and Affiliations

  1. Department of Energy, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    A. N. de Paula, E. J. de Oliveira, L. W. Oliveira & C. A. Moraes

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  1. A. N. de Paula
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  2. E. J. de Oliveira
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  3. L. W. Oliveira
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Correspondence to A. N. de Paula.

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de Paula, A.N., de Oliveira, E.J., Oliveira, L.W. et al. Reliability-constrained dynamic transmission expansion planning considering wind power generation. Electr Eng 102, 2583–2593 (2020). https://doi.org/10.1007/s00202-020-01054-y

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