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The purpose of this paper is to shed light on and compare the second-order load-flow (SOLF) methods. To do this, the mismatch theorem is developed, which relates the neglected terms for a Taylor series, during an iteration to the mismatches at the end of that iteration. This theorem suggests improvements on the reported SOLF methods. It is shown that all these second-order methods propose either reusing the matrix of coefficients until convergence, or using it more than once before updating it. The examined SOLF algorithms and other suggested algorithms are tested using 5, 13, 14 and 30-node systems, each one with different loading conditions. Guidelines for selecting the best algorithm for a particular network can be derived from the presented results.