**2. Materials and Methods**

#### *2.1. Experimental Determination of Current Asymmetry for Single-Phase Systems*

A laboratory stand was developed for the experimental examination of several spatial configurations of single-phase cable systems. The photograph of the stand is shown in Figure 2, whereas in Figure 3, the considered configurations are depicted. Five of them included the strands made of YAKXS 1 × 70 cables, whereas the remaining two were made using YAKXS 1 × 240 cables. All considered configurations were excited from a single phase. For each setup, three values of excitation current were preset, that is, 200 A, 300 A, and the maximal value, possible to be obtained for the transformer used.

**Figure 2.** A photograph of the laboratory setup for examination of current distribution in the flat setup.

Ahead of the current measurements, the measurements of resistances of individual strands were carried out. The difference between extreme values was smaller than 1%. The measurements were made using the MMR-620 device from Sonel. The temperature of each strand before the measurements was the same and remained practically constant during the measurements (taking into account relatively small current magnitudes and short measurement time). Temperature recording for each strand was made individually for each phase. A control measurement of the ambient temperature was also carried out. Considering very small values of cable resistances (4.42 mΩ for YAKXS 1 × 70 cables, 1.21 mΩ for YAKXS 1 × 240 cables), it was crucial to prepare the cable endings properly and to minimize the values of contact resistances. The screw connections were applied and the cable endings were pressed from both sides using aluminum bars. Additionally, between the cable ending and the bar, the silver-based contact paste MG Chemicals 8463 was applied. After the connections were made, the measurements of contact resistance were carried out using the MMR-620 device. The average value of resistance for the 70 mm<sup>2</sup> cable ending was 27.6 μΩ, for the 240 mm<sup>2</sup> cable ending—15.4 μΩ. The deviation between the measured extreme values did not exceed 5%.

In order to compare the obtained measurement results for each spatial configuration, the ratio of currents in the extremely loaded strands (the asymmetry coefficient) was determined, as in Equation (1):

$$\mathbf{C\_{AS}} = \frac{\mathbf{I\_{max}}}{\mathbf{I\_{min}}} \mathbf{\prime} \tag{1}$$

where Imax is RMS current value in the most loaded strand and Imin is RMS current value in the least loaded strand.

Table 1 presents the measurement results for the maximal attainable excitation current value, whereas Table 2 includes the values of asymmetry coe fficient for di fferent models, both for the maximal excitation current value and for the preset value 200 A. (Notation: S1—strand 1, etc., M1—model 1, etc.)


**Table 1.** Current of individual strands—summary for the maximal attainable excitation current.


The analysis of the obtained measurement results indicates that the current distribution in parallel lines is highly dependent on spatial configuration. More uneven distributions are obtained for bigger cable cross-sections. Strand separation, as well as the increase of their amount in the flat configuration, leads to the increase of asymmetry coe fficient. For the considered physical models, the most uniform current distribution was obtained for model No. 5.
