scholarly journals Optimization of Cable Layout Design in a Wind Farm: A Hybrid Approach

2015 ◽  
Vol 11 (2) ◽  
Keyword(s):  
Convex Hull ◽  
Steiner Tree ◽  
Wind Farm ◽  
Multicast Routing ◽  
Hybrid Approach ◽  
Steiner Tree Problem ◽  
Steiner Minimal Tree ◽  
Minimal Graph ◽  
Short Time ◽  
Optimal Graph

In this paper, a hybrid algorithm based on modified Ants Colony Optimization (ACO) and Artificial Immune Algorithm (AIA) for solving the Steiner Minimal Tree Problem (SMTP) is introduced. Since the Steiner Tree Problem is NP-hard, we design an algorithm to construct high quality Steiner trees in a short time which is suitable for real time multicast routing in networks. After the breadth - first traversal of the minimal graph obtained by ACO, the terminal points are divided into different convex hull sets, and the full Steiner tree is structured from the convex hull sets partition. The Steiner points can be vaccinated by AIA to get an optimal graph. The average optimization effect of AIA is shorter than the minimal graph obtained using ACO, and the performance of the algorithm is shown. We give an example of application in wind farm network design.

scholarly journals Optimization for Onshore Wind Farm Cable: Connection Layout using ACO-AIA algorithm

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 67-82
Author(s):  
Mohamed Tifroute ◽  
Hassane Bouzahir
Keyword(s):  
Convex Hull ◽  
Steiner Tree ◽  
Wind Farm ◽  
Multicast Routing ◽  
Mathematical Problem ◽  
Steiner Tree Problem ◽  
Minimal Graph ◽  
Onshore Wind ◽  
Wind Farm Layout Optimization ◽  
Short Time

The wind farm layout optimization problem is similar to the classical mathematical problem of finding the Steiner Minimal Tree Problem (SMTP) of a weighted undirected graph. Due to the cable current-carrying capacity limitation, the cable sectional area should be carefully selected to meet the system operational requirement and this constraint should be considered during the SMTP formulation process. Hence, traditional SMTP algorithm cannot ensure a minimal cable investment layout. In this paper, a hybrid algorithm based on modified Ants Colony Optimization (ACO) and Artificial Immune Algorithm (AIA) for solving SMTP is introduced. Since the Steiner Tree Problem is NP-hard, we design an algorithm to construct high quality Steiner trees in a short time which is suitable for real time multicast routing in networks. After the breadth - first traversal of the minimal graph obtained by ACO, the terminal points are divided into different convex hull sets, and the full Steiner tree is structured from the convex hull sets partition. The Steiner points can then be vaccinated by AIA to get an optimal graph. The average optimization effect of AIA is shorter than the minimal graph obtained using ACO, and the performance of the algorithm is shown. We give an example of application in optimization for onshore wind farm Cable. The possibility of using different sectional area’s cable is also considered in this paper.

GENERALIZED MELZAK'S CONSTRUCTION IN THE STEINER TREE PROBLEM

2002 ◽  
Vol 12 (06) ◽  
pp. 481-488 ◽  
Author(s):  
JIA F. WENG
Keyword(s):  
Steiner Tree ◽  
Euclidean Plane ◽  
Steiner Tree Problem ◽  
Minimal Tree ◽  
Steiner Minimal Tree ◽  
The Core ◽  
Steiner Minimal Trees ◽  
Minimum Networks ◽  
Set Of Points ◽  
The Given

For a given set of points in the Euclidean plane, a minimum network (a Steiner minimal tree) can be constructed using a geometric method, called Melzak's construction. The core of the Melzak construction is to replace a pair of terminals adjacent to the same Steiner point with a new terminal. In this paper we prove that the Melzak construction can be generalized to constructing Steiner minimal trees for circles so that either the given points (terminals) are constrained on the circles or the terminal edges are tangent to the circles. Then we show that the generalized Melzak construction can be used to find minimum networks separating and surrounding circular objects or to find minimum networks connecting convex and smoothly bounded objects and avoiding convex and smoothly bounded obstacles.

A GRASP for the Steiner Tree Problem in Graphs to Support Multicast Routing

2015 ◽  
Vol 13 (12) ◽  
pp. 3873-3878 ◽  
Author(s):  
C.R. Costa ◽  
V. Rosset ◽  
M.C.V. Nascimento
Keyword(s):  
Steiner Tree ◽  
Multicast Routing ◽  
Steiner Tree Problem

scholarly journals Wind Farm Cable Connection Layout Optimization with Several Substations

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3615
Author(s):  
Adelaide Cerveira ◽  
Eduardo J. Solteiro Pires ◽  
José Baptista
Keyword(s):  
Energy Production ◽  
Wind Farm ◽  
Programming Model ◽  
Optimal Solution ◽  
Wind Farms ◽  
Green Energy ◽  
Fossil Energy ◽  
Proposed Model ◽  
Short Time ◽  
Cable Connection

Green energy has become a media issue due to climate changes, and consequently, the population has become more aware of pollution. Wind farms are an essential energy production alternative to fossil energy. The incentive to produce wind energy was a government policy some decades ago to decrease carbon emissions. In recent decades, wind farms were formed by a substation and a couple of turbines. Nowadays, wind farms are designed with hundreds of turbines requiring more than one substation. This paper formulates an integer linear programming model to design wind farms’ cable layout with several turbines. The proposed model obtains the optimal solution considering different cable types, infrastructure costs, and energy losses. An additional constraint was considered to limit the number of cables that cross a walkway, i.e., the number of connections between a set of wind turbines and the remaining wind farm. Furthermore, considering a discrete set of possible turbine locations, the model allows identifying those that should be present in the optimal solution, thereby addressing the optimal location of the substation(s) in the wind farm. The paper illustrates solutions and the associated costs of two wind farms, with up to 102 turbines and three substations in the optimal solution, selected among sixteen possible places. The optimal solutions are obtained in a short time.

scholarly journals Solving the Steiner tree problem in graphs by chaotic search

2020 ◽  
Vol 11 (1) ◽  
pp. 90-108
Author(s):  
Misa Fujita ◽  
Takayuki Kimura ◽  
Tohru Ikeguchi
Keyword(s):  
Steiner Tree ◽  
Steiner Tree Problem ◽  
Chaotic Search
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