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

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Introduction

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:

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

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  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.

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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.

The links between the nodes of the MV grid are described by the complex impedance z_n, where n is the index of connecting nodes. Each impedance contains of real and imaginary part z_n=R_n+jx_n, 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 I_n is the value of the effective current in the n-th section of the grid, and R_n 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.