An analysis of numerical procedures for treating load-flow problems is performed. It is shown that the Newton-(Raphson) method and a Z-matrix method yield the unique solution provided that a characteristic number λof the network is not larger than 0.25. The number λcorresponds to the losses. We form an a priori estimate for the number of iterations which are sufficient to achieve a prescribed accuracy of the numerical solution. Modifications of the Newton method for treating networks with larger losses are given.
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Braess et al. (1981) studied this question.
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