We suggest a statistical estimator to quantify the propagation of cascading transmission line failures in large blackouts of electric power systems. We use a Galton-Watson branching process model of cascading failure and the standard Harris estimator of the mean propagation modified to work when the process saturates at a maximum number of components. If the mean number of initial failures and the mean propagation are estimated, then the branching process model predicts the distribution of the total number of failures. We initially test this prediction on failure data generated by a simulation of cascading transmission line outages on two standard test systems. We discuss the effectiveness of the estimator in terms of how many cascades need to be simulated to predict the distribution of the total number of line outages accurately.
Nozzle clogging during continuous casting of Ti-ULC (Ultra Low C) steel was investigated by inspections of plant-used SENs and laboratory scale experiments using a rotating finger method. Various Al/Ti ratios in the steel and different kinds of nozzles (with or without CaO) were employed. Clog deposits found in the used SENs were composed of complicated oxide (CaO-Al 2 O 3-TiO x-…), Fe drops and chunks. Increasing Ti concentration increased amount of the deposit the metallic deposits. In the laboratory scale experiments, increasing Al/Ti ratios was effective to suppress the formation of the deposit and the oxidation loss of Ti in the steel. When a refractory without CaO was used, increasing Al/Ti ratio decreased the portion of Ti oxide in the deposit. Almost no Fe drops were observed, except for a thin layer of Fe on surface of the oxide deposit. When CaO-lined refractory was used, many numbers of Fe drops were found inside the deposit. Increasing Al/Ti ratio lowered Ti peak in the oxide deposit. The present results lend a strong support that Ti-ULC steel is oxidized by CO gas from nozzle refractory, forming Fe t O-containing liquid oxide and solid alumina. The liquid oxide is reduced to leave Fe drops and Al 2 O 3-TiO x layer. If CaO presents in the nozzle, then a complicated oxide of CaO-Al 2 O 3-TiO x forms, as was found in the SEN from the practical operation. KEY WORDS: Ti-ULC steel casting; nozzle clogging; Al/Ti ratio; Fe t O-Al 2 O 3-TiO x ; nozzle refractory.
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