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A method is given for computing matrix reductions for power flow equivalents that is many times faster than presently used methods and produces extremely sparse equivalents. It is possible to embed the method in a power flow solution algorithm so that equivalencing can be performed automatically and transparently. The method is based on a property of sparse matrix factorization. When a matrix has been factorized, most of the operations for any reduction of the matrix have already been performed. Any desired reduction can be computed from the factors with relatively few additional operations. The performance of the method has been verified on large practical problems.