A multi-objective approach for solving transmission expansion planning problem considering wind power uncertainty
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RESEARCH PAPER
A multi‑objective approach for solving transmission expansion planning problem considering wind power uncertainty Basir Rashedi1 · Alireza Askarzadeh1 Received: 20 February 2020 / Revised: 15 October 2020 / Accepted: 6 November 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Transmission expansion planning · Multi-objective optimization · Wind energy · Expected energy not supplied Abbreviations f1 (x) Total investment cost ci,j Investment cost of adding a new line between buses i and j ni,j Number of added lines between buses i and j EENSjk Expected energy not supplied by demand j due to contigency k Γjk Involuntary load shedding of demand j due to contigency k 𝜌k Probability of contingency k uk State of new component 𝜌all Probability of no contigency FORk Forced outage rate of component k MTTF Mean time to failure MTTR Mean time to repair λ Outage rate n0i,j Number of lines between buses i and j Maximum power flow between buses i and j Pmax i,j Pi,j Power flow between buses i and j
Maximum number of lines which can be added nmax i,j between buses i and j bi,j Susceptance of the line between buses i and j 𝜃i Voltage phase angle at bus i 𝜃j Voltage phase angle at bus j f (v, c, k) Weibull PDF F(v, c, k) Weibull CDF v Wind speed k Shape parameter c Scale parameter Pw Output power of wind generator vrated Rated speed vci Cut-in wind speed vco Cut-out wind speed xiiter Current position of crow i xiiter+1 New position of crow i iter Iteration number Memorized position of crow j miter j r Random number Memorized position of crow i at iteration miter+1 i iter + 1
* Alireza Askarzadeh [email protected]; [email protected] 1
Department of Energy Management and Optimization, Institute of Science and High Technology and Environmental Sciences, Graduate University of Advanced Technology, Kerman, Iran
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1 Introduction In modern power systems, transmission expansion planning (TEP) is a vital optimization problem since there is a complex and large-scale in
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