04_article_nonlinear - F E A T U R E A R T I C L E...

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November/December 2004 — Vol. 20, No. 6 27 F E A T U R E A R T I C L E Introduction dielectrics are nonlinear if subjected to sufficiently high electric fields. For example, Figure 1 shows fits to data for the conductivity of two cable dielectrics, one with an activation energy of 0.56 eV and the other with an activation energy of 0.98 eV. The former would be appropriate for a DC cable, while the latter would be typical of an AC cable insulation. At low fields, charge carriers are detrapped thermally, and the field simply makes hopping more likely in the direction of the field than against the field. However, as energy is gained from the field as a charge carrier travels from one trap to the next, it becomes comparable to the thermal energy; the energy gained from the field becomes a significant factor in detrapping, which results in the conductivity becoming an exponential function of field. The thermal energy at room temperature is about 0.025 eV, and the typical distance between traps is about 2.8 nm. Thus, the energy gained from the field in moving between traps be- comes equal to the thermal energy at a field of about 9 kV/mm, which is in good agreement with the transition from constant to exponentially increasing conductivity seen in Figure 1. While hopping theory predicts a hyperbolic sine relationship between the current density and electric field, i.e., constant con- ductivity at low fields with a transition to an exponential increase in conductivity with field at higher fields, the actual low field conductivity can be more complex, as seen in Figure 2. Of the four dielectrics shown, only EPR2 (ethylene propylene rubber) and biaxially oriented polypropylene capacitor film (BOPP) fit the model reasonably well. The conductivity of (degassed) TRXLPE (tree retardant crosslinked polyethylene) has a large field-dependence in the low field region, and EPR1 has a rela- tively small field dependence. Nonlinear dielectric properties can be used to control the elec- tric field as in a distribution cable termination that must operate under both AC and impulse conditions. Under AC conditions, capacitive grading is likely to be employed; however, under im- pulse conditions, where the voltage can be nearly 10 times greater, capacitive grading may not be adequate, and nonlinear grading becomes beneficial. On the other hand, nonlinear resistive grad- ing may dissipate energy at levels not acceptable under normal operating conditions but that are not problematic during the few tens of microseconds of an impulse. In other situations, nonlin- ear conduction “overcomes” the large temperature dependence in the conductivity that would otherwise cause highly nonlinear grading under DC operating conditions. This occurs in DC cables as well as in ZnO arrester elements when heat sinks are present between the elements, which results in an axial temperature gra- dient under impulse-current conditions.
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This note was uploaded on 06/08/2011 for the course ELECTRICAL 124 taught by Professor Ghjk during the Spring '11 term at Institute of Technology.

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04_article_nonlinear - F E A T U R E A R T I C L E...

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