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In this paper we present two new algorithms for solving the power flow equation. The algorithms are modifications of the BX and XB algorithms, obtained by explicitly treating lines with "high" rlx ratios. An analytical justification of the algorithm is given together with test results comparing the performance of the new algorithms with that of the Newton algorithm, the constant Jacobian Quasi-Newton algorithm and the BX and XB algorithms. The test results indicate that the new algorithms have greatly increased robustness properties over the BX and XB algorithms.

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