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Earth, Planets and Space
Fig. 1 | Earth, Planets and Space

Fig. 1

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

Fig. 1

(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 = 1.00 Ω, S2 = 0.64 Ω and S3 = 0.88 Ω, and the line resistances are R1 (line 1–2) = 0.50 Ω, R2 (line 2–3) = 1.20 Ω and R3 (line 3–1) = 0.87 Ω. Altogether 32660 runs of the calculation program are included by changing the pe current column matrix slightly and systematically between the runs and requiring that the sum of the elements of the pe matrix is zero. The horizontal lines show two of the eigenvalues of the transfer matrix between pe currents and earthing GIC (while the third eigenvalue equals one). (b) Scalar product between the pe current column matrices used in Fig. 1(a) for the 32660 runs and a fixed reference column matrix normalised to unity and having elements whose sum is zero.

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