Using mathematical programming duality, explicit conditions are found which characterize the set of substation loads that can be served with the available generation resources without overloading the transmission lines or transformers. This feasibility set is a convex polyhedron in the space of substation load vectors, when the distribution of power flow through the network is represented either by the DC load flow or the transportation flow model. The impact on the feasibility set of changes in the generation and transmission system is analyzed. This analysis is then used to construct a probabilistic supply reliability measure.
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Dersin et al. (1982) studied this question.
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