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Fig. 2 | Earth, Planets and Space

Fig. 2

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

Fig. 2

(a) Norm of the earthing GIC column matrix for a three-node network when the pe current column matrix is normalised to unity. The earthing resistances of the nodes are S1 = 0.96 Ω, S2 = 1.10 Ω and S3 = 0.80 Ω, and the line resistances are R1 (line 1−2) = 1.62 Ω, R2 (line 2−3) = 0.97 Ω and R3 (line 3−1) = 0.82 Ω. All these resistance values are chosen randomly in reasonable ranges. The pe current column matrix is also 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 two of the eigenvalues of the transfer matrix between pe currents and earthing GIC (while the third eigenvalue equals one). It is seen that the values of the norm of the earthing GIC cover the range between the two eigenvalues very accurately. (b) Scalar product between the pe current column matrices used in Fig. 2(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 cover the whole range from − 1 to +1 very well.

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