Impedance matrix cross-bonded cable

It is often observed in practice that the number of conductors changes at a boundary, as shown in Figure 1.53, where phases a and b are short-circuited at node 1. In the case of a cross-bonded cable, three-phase metallic sheaths are rotated at every cross-bonding point. In such a case, it is required to reduce the order of an impedance matrix and/or to rotate the matrix elements. 

The calculation process in the case of a cross-bonded cable using the proposed formulas is shown as follows (the 6x6 impedance matrix Z is obtained using cable constants [1,11,12]) ... 

The capacitance matrix looks similar to the impedance matrix in Table 3.3a-2. The capacitance between the core and sheath of the homogeneous model is identical to that of the solidly bonded cable. The equivalent capacitance Q4 of the cross-bonded cable in Table 3.3b-2 is given as the sum of the elements as shown in Equations 3.44 and 3.45. 

In Table 3.3a-l, the upper 3x3 matrix expresses three-phase core impedance [ZJ, the right upper and the left lower matrices are three-phase core to sheath [ZJ and sheath to core impedance [Z J = [ZJ and the lower 3x3 matrix is three-phase sheath impedances [ZJ. The upper line is the resistance [Q/km] and the lower one is the inductance [mH/km]. The [ZJ matrix of the solidly bonded cable in Table 3.3a-l is the same as that of fhe cross-bonded cable in Table 3.3b-l. The impedance in the last column,... 

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