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Earth, Planets and Space
Fig. 3 | Earth, Planets and Space

Fig. 3

From: Eigenvalues and eigenvectors of the transfer matrix involved in the calculation of geomagnetically induced currents in an electric power transmission network

Fig. 3

(a) Norm of the earthing GIC column matrix for the Finnish 400 kV test model (see Pirjola, 2009) when the pe current column matrix is normalised to unity. The pe current column matrix is determined randomly for every run of the calculation program requiring that the sum of the elements of the pe matrix is zero. The total number of the runs is 100000. The horizontal lines show the eigenvalues of the transfer matrix between pe currents and earthing GIC. It is seen that the values of the norm of the earthing GIC are clearly between the smallest eigenvalue and the largest (=1) eigenvalue, both of which are plotted with thicker lines. (b) Scalar product between the pe current column matrices used in Fig. 3(a) for the 100000 runs and a fixed reference column matrix normalised to unity and having elements whose sum is zero. It is seen that the scalar product values do not cover the range from −1 to +1, which means that the 100000 runs do not include all possible pe current matrices.

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