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A multi-objective approach for solving transmission expansion planning problem considering wind power uncertainty

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Abstract

Security-constrained transmission expansion planning (SCTEP) is a vital power system problem. In last years, to attain energy sustainability, wind power has received significant attention as one of the popular renewable energy resources. This paper solves multi-objective optimization of TEP considering uncertainty of wind power. The uncertainty is modelled by Weibull probability distribution function and Monte-Carlo simulation is employed to consider the uncertainty into the problem. In the problem, the objectives are investment cost of new lines and expected energy not supplied obtained by N-1 security constraint criterion. Since SCTEP is a complex, large-scale, mixed-integer and non-linear combinatorial optimization problem, multi-objective crow search algorithm and multi-objective particle swarm optimization are utilized to find Pareto front. On modified 24-bus IEEE system, the optimization framework is investigated and the results are discussed.

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Abbreviations

\(f_{1} \left( x \right)\) :

Total investment cost

\(c_{i,j}\) :

Investment cost of adding a new line between buses i and j

\(n_{i,j}\) :

Number of added lines between buses i and j

EENS jk :

Expected energy not supplied by demand j due to contigency k

\(\Gamma_{jk}\) :

Involuntary load shedding of demand j due to contigency k

\(\rho_{k}\) :

Probability of contingency k

u k :

State of new component

\(\rho_{all} \) :

Probability of no contigency

FOR k :

Forced outage rate of component k

MTTF :

Mean time to failure

MTTR :

Mean time to repair

λ :

Outage rate

\(n_{i,j}^{0}\) :

Number of lines between buses i and j

\(P_{i,j}^{max}\) :

Maximum power flow between buses i and j

\(P_{i,j }\) :

Power flow between buses i and j

\(n_{i,j}^{max}\) :

Maximum number of lines which can be added between buses i and j

\(b_{i,j }\) :

Susceptance of the line between buses i and j

\(\theta_{i}\) :

Voltage phase angle at bus i

\(\theta_{j}\) :

Voltage phase angle at bus j

\(f\left( {v, c,k} \right)\) :

Weibull PDF

\(F\left( {v, c,k} \right)\) :

Weibull CDF

v :

Wind speed

k :

Shape parameter

c :

Scale parameter

P w :

Output power of wind generator

v rated :

Rated speed

v ci :

Cut-in wind speed

v co :

Cut-out wind speed

\(x_{i}^{iter}\) :

Current position of crow i

\(x_{i}^{iter + 1}\) :

New position of crow i

iter :

Iteration number

\(m_{j}^{iter}\) :

Memorized position of crow j

r :

Random number

\(m_{i}^{iter + 1}\) :

Memorized position of crow i at iteration iter + 1

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Authors and Affiliations

  1. Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran

    Basir Rashedi & Alireza Askarzadeh

Authors
  1. Basir Rashedi
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  2. Alireza Askarzadeh
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Correspondence to Alireza Askarzadeh.

Appendix

Appendix

See Tables

Table 5 Transmission line data for modified IEEE 24-bus system (base = 100 MVA)
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5,

Table 6 Transformer data for modified IEEE 24-bus system (base = 100 MVA)
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6 and

Table 7 Data of new lines added to existing branches of modified IEEE 24-bus system (base = 100 MVA) [23]
Full size table

7.

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Rashedi, B., Askarzadeh, A. A multi-objective approach for solving transmission expansion planning problem considering wind power uncertainty. Evol. Intel. 15, 497–511 (2022). https://doi.org/10.1007/s12065-020-00525-2

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  • DOI: https://doi.org/10.1007/s12065-020-00525-2

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