Due to the low biodegradability of mineral oil, intense research is conducted to define alternative liquids with comparable dielectric properties. Natural ester liquids are an alternative in focus; they are used increasingly as insulating liquid in distribution and power transformers. The main advantages of natural ester liquids compared to mineral oil are their good biodegradability and mainly high flash and fire points providing better fire safety. The dielectric strength of natural ester liquids is comparable to conventional mineral oil for homogeneous field arrangements. However, many studies showed a reduced dielectric strength for highly inhomogeneous field arrangements. This study investigates at which degree of inhomogeneity differences in breakdown voltage between the two insulating liquids occur. Investigations use lightning impulses with different electrode arrangements representing different field inhomogeneity factors and different gap distances. To ensure comparisons with existing transformer geometries, investigations are application-oriented using a transformer conductor model, which is compared to other studies. Results show significant differences in breakdown voltage from an inhomogeneity factor of 0.1 (highly inhomogeneous field) depending on the gap distance. Larger electrode gaps provide a larger inhomogeneity at which differences in breakdown voltages occur.
This paper gives a detailed presentation of the Substitution-Newton-Raphson method, suitable for large sparse non-linear systems. It combines the Successive Substitution method and the Newton-Raphson method in such way as to take the best advantages of both, keeping the convergence features of the Newton-Raphson with the low requirements of memory and time of the Successive Substitution schemes. The large system is solved employing few effective variables, using the greatest possible part of the model equations in substitution fashion to fix the remaining variables, but maintaining the convergence characteristics of the Newton-Raphson. The methodology is exemplified through a simple algebraic system, and applied to a simple thermodynamic, mechanical and heat transfer modeling of a single-stage vapor compression refrigeration system. Three distinct approaches for reproducing the thermodynamic properties of the refrigerant R-134a are compared: the linear interpolation from tabulated data, the use of polynomial fitted curves and the use of functions derived from the Helmholtz free energy
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