Many of the practically adopted methods for feeder reconfiguration in distribution networks are based on classical switch exchange. Switch exchange has been originally developed for legacy distribution networks, and does not account for many of the complexities associated with active grids. This paper extends the classical reconfiguration method to account for reverse power flows from distributed generation, controllable loads from prosumers, and a multiphase network representation. To comply with the distribution management system real time computing requirements, previous techniques adopt a positive sequence network model so that formulas to approximately evaluate the intermediate solutions could be used without recourse to repeated power flow. This paper proposes a compensation technique for switch exchange in the power flow solution of multiphase network representations, but without requiring matrix re-factorization; the proposed technique gives an exact solution, which serves as an alternative to the approximation formulas that are usually employed with the positive sequence network representation. The proposed compensation approach is used in extending the practically adopted feeder reconfiguration method from the single-phase equivalent circuit model to the multiphase model of active grids, while being three times as fast as the approach that employs repeated power flow and matrix re-factorization.