Optimal Placement of the Wind Generators in the Medium Voltage Power Grid

Optimal Placement of the Wind Generators in the Medium Voltage Power Grid

Andrzej Jordan (The State College of Computer Science and Business Administration in Lomza, Poland and University of Bedfordshire, UK), Carsten Maple (University of Bedfordshire, UK) and Ryszard Szczebiot (The State College of Computer Science and Business Administration in Lomza, Poland)
Copyright: © 2012 |Pages: 10
DOI: 10.4018/jdst.2012040106


The minimization of power losses in the medium voltage (MV) grid requires adjustment of network of power sources. This problem is particularly important for renewable energy sources, for example for the farms of wind generators. Their placement and nominal power should be selected according to the configuration of the network and the largest loads. The presented problem is solved using a genetic algorithm (GA). The formulation of the GA algorithm and its performance for different numbers of power sources is analyzed. The optimal placements of wind generators were computed for some case problems. The algorithm is validated with a medium sized electrical grid. The formulation of the parallel version of the genetic algorithm is presented. Its properties are verified on the cluster of workstations environment.
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The development of Renewable Energy Sources (RES) has become a priority for EU energy policy in recent years (Paska, Salek, & Surma, 2009; Pienkowski, 2010). One of the main sources of renewable energy can be wind farms (e.g., about 60·103 MWh in Great Britain in 2009; Sobolewski, 2009).

The wind turbines are often connected to medium voltage (MV) grids at nodes that can be accessible for turbine installation. The connection of these generators to the medium voltage power grid is associated with a number of different limitations, which include:

  • The relationship between the generator’s switching power and the short-circuit power in the linking node,

  • The location of wind generators in the MV power grid in such a way as to ensure minimal active power losses (Sobolewski, 2009; Jordan & Pienkowski, 2010; Cieslik, Zakrzewski, Bielinski, & Drechny, 2010).

The paper is an extended version of the publication that appeared in the conference materials PARELEC 2011 titled “ Optimal placement of wind generators in medium voltage power grids – investigation of generic algorithm”. The problem presented in this paper consists in determining optimal placement of wind turbines in a chosen part of the medium voltage power grid. To determine the optimal placement of wind turbines a genetic algorithm (Butrylo, Jordan, & Skorek, 2001; Goldberg, 1995) and a parallel program developed on its basis (Butrylo, Jordan, & Skorek, 1999) are used.


Mathematical Model Of The Power Grid

The analyzed part of the MV power grid is separated and it is placed on the area of 81 square kilometers (S=9×9 km). The network consists of 23 grid nodes to which the wind generators with a maximum number of 23 can be connected (Figure 1). In the further analysis we assume, that the connection of wind generators to fixed grid nodes does not result in exceeding the values of either short circuit or rated currents determined on the basis of a fixed grid topology and cross sections of the wires. Simultaneously we disregard such technical problems as, for instance, a choice of location conditioned by the existence of access roads or a possibility to acquire location site from private landowners, etc.

Figure 1.

The diagram of the analyzed part of the power grid


The links between the nodes of the MV grid are described by the complex impedance zn, where n is the index of connecting nodes. Each impedance contains of real and imaginary part zn=Rn+jxn, which characterize both the active and passive losses of power in a section of the network. Total active power losses in the grid are described by formula

(1) where In is the value of the effective current in the n-th section of the grid, and Rn is the value of the electrical resistance calculated on the basis of the length and cross section of the power lines.

The mathematical description of the grid is reduced to a large system of algebraic equations, which determines power losses after switching on the wind power generators (Niebrzydowski, 2000)

(2) where Y is the admittance matrix representing the network segments between the nodes, V is the nodal complex vector potential, whereas vector I represents the complex currents of wind power generators in the nodes during the operation of the algorithm. The sizes of the components are stated by the number of the nodes in the analyzed network: dim Y= 23×23, dim V = dim I = 23. During the calculations of the currents in the network, limitations resulting from the values of both admissible and short circuit currents are imposed in respective sections of the grid.

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