Cable model

A three-phase cable system consisting of three single-core (SC) cables becomes a six-conductor circuit. If its sheath voltages can be neglected, the cable is can be expressed by a three-phase circuit. The voltage drop due to the cable-series impedance is expressed by the following equation  

Where the first subscripts f and f denote core and sheath, and the second subscripts J g, and f express phases, respectively. The voltage and current vector in Equation 4.8 is defined as 

In the same manner, the admittance matrix of the line can be reduced to a 3 by 3 matrix  

For a steady-state analysis, a cable can be expressed by a single or a cascaded r-equivalent circuit instead of a disfribufed paramefer line. In fhe EMTP, even if a cable is represenfed by a consfanf-paramefer line model (Dommel s line model) or a frequency-dependenf line model (Semiyen s or 

Marti s line model), the distributed parameter line is internally converted to a t-equivalent circuit and is passed to a steady-state analysis routine. 

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Figure 9. The cable model for the structure of concentrated calcium pectate gels. Egg-box dimers link single-chains segments (top left) and are themselves ed together by larger aggregates of either egg-box or 3i helical chains (lower right)...

Thus pectins in muro contain most elements of the cable model but have additional features due to esterification (acetyl- as well as methyl-) and branching. The ionic junction zones are similar to those of calcium pectate gels in vitro but also contam methyl-esterified junctions, and most of the single chains probably have a relatively high degree of methyl-esterification. 

Zhang, D., Cowin, S.C., and Weinbaum, S. (1997) Electrical signal transmission and gap junction regulation in bone cell network a cable model for an osteon. Annals of Biomedical Engineering 25 357-374... 

Figure 6.234 Cable models with concentrated and differential cable parameters.

Bidomain A two- or three-dimensional cable model that takes into account the resistance of both the intracellular and the extracellular spaces. 

Electrical circuits are used to model the electrical behavior of neurons. These electrical-equivalent circuits, often referred to as cable models, represent the neuron as a series of cylindrical elements. Each cylinder is in turn replaced by a compartment, representing the neuronal membrane, and a resistor representing the intracellular space. Thus the model becomes a series of membrane compartments, connected by resistors. Each compartment is itself an electrical circuit that includes a capacitor representing the membrane capacitance of the lipid bilayer, resistors representing the ionic conductances of the transmembrane... 

The response of a cable model, representing a CNS neuron, to extracellular electrical stimulation is shown in Figure 30.5. The transmembrane potential as a function of time, in different segments of the neuron, is shown for a cathodic electrode positioned over the axon (Figure 30.5a), for a cathodic electrode positioned over the cell body (Figure 30.5b), and for an anodic electrode positioned over the cell body (Figure 30.5c). 

Figure 1. (A) Discrete cable model of cylindrical cardiac cells, each 100// in length and 16// in diameter, interconnected by an intercalated disc structure of 80A. (B) Core conductor network utilized for the intercalated disc interaction between two adjacent cells.

A Motori, F Sandrolini, GC Montanari. Degradation and electrical behavior of aged XLPE cable models. Proceedings of IEEE International Conference on Conduction and Breakdown in Solid Dielecterics, Trodheim, 1989, pp 352-358. 

Figure 3.10 shows the physical and electrical data of a 400-kV cable used for comparison. An existence of semiconducting layers introduces an error in the charging capacity of the cable. The relative permittivity of the insulation (XLPE) is converted from Equations 2.4 to 2.7, according to Equation 3.72, in order to correct the error and achieve a reasonable cable model [10] ... 

Modes 1-3 in the solidly bonded cable shown in Table 3.3a-4 are coaxial modes and are the same as mode 3 in the homogeneous cross-bonded cable model. Although the attenuations of the inter-core modes (modes 1 and 2) shown in Table 3.3b-4 are almost identical to that of the coaxial mode of the solidly bonded cable, the velocities are lower. The velocity of the coaxial mode is determined by the permittivity of the main insulator = 2.3 shown in Table 3.2 ... 

The attenuation and velocity of the earth-return mode (mode 4) in both cable models are identical. 

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