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SUMMARY The paper presents a finite‐element model for the evaluation of the ampacity of an underground 110‐kV three‐phase system of cables in normal operation and in case of emergency. The proposed model takes the effects of convection, radiation, and solar heating at the trench surface into account, which enhances the previous approaches. The calculations performed have shown that these phenomena affect the heating of cables and that the IEC approach that treats the trench surface as an isothermal plane at ambient temperature, widely used in practice, might underestimate the ampacity of cables in certain cases. The model considers in detail the shape and construction of the cable trench, and the thermal properties of backfilling materials and concrete and asphalt covers including the effects of the drying out of soil. The effects of various approximations have been also investigated. The model has been applied to a real life example, and the calculation results have been compared to some experimental data. Copyright © 2011 John Wiley & Sons, Ltd.

A probabilistic approach for the determination of the optimum number of spare transformers is presented providing minimum annual cost consisting of capital cost for spares and transformer outage costs. The model suggested can cover any transformer unit lifetime and renewal time probability distribution. This makes it possible to account for the effects of transformer deterioration due to aging and to realistically, based upon empirical data, assess the impacts of the renewal time by treating it as a stochastic rather than as a deterministic variable lasting the entire planning period. The comparison of the model presented with the Poisson distribution based approach, widely used in sparing analyses in the past, has shown that the negligence of aging and of the stochastic nature of renewal times can lead to worse than optimal solutions. Index Terms-Distribution network transformers, optimal sparing, probabilities of unit and system states.

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