In 1978, it was found that, using the rectangular coordinates, the Taylor-series expansion of the load-flow equation could be expressed completely up to the 2nd-order term and that the term had the same form as, but a different variable from, the first term. Using this fact, the following applications are described: a fast load-flow algorithm, a method for preventing oscillation and divergence of solutions, a method for finding multiple solutions, and the relationship between multiple solutions and voltage sensitivity.