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Adequacy evaluation of a composite power system normally only considers independent outages of elements such as generating units and transmission lines/transformers. The adequacy indices are calculated after examining a predetermined sequence of outage events. The computation time increases tremendously, if the number of outage events is large. It may be possible to avoid examining high-level contingencies in relatively small power-system networks. As the size of the system increases, testing of higher-level simultaneous independent outages, particularly those of generating units, becomes an important factor. The computation time increases tremendously as the system size increases because of both the number of outages that are to be examined and the time required to solve the network under each outage situation. It becomes important therefore to appreciate the effect of contingency level selection on the calculated adequacy indices. This paper illustrates the effect of including higher-level outages on the adequacy of three power systems, a small hypothetical 6-busbars test system, the standard IEEE Reliability Test System (RTS) and a model of the existing power-system network of the Saskatchewan Power Corporation in Canada.