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The distributed radial basis function neural networks (RBF NN) can effectively solve fault section estimation (FSE) in large-scale power networks. However when the network expands or topology changes, the RBF NN has to be totally retrained, which is time-consuming and becomes a bottleneck in its applications. In this paper, functional equivalence between a RBF NN and a companion fuzzy system (CFS) is built up throughout the neural network training process, therefore the RBF NN retraining issue under network expansion and topology change can be solved effectively and efficiently through useful knowledge extraction from the old CFS and insertion back to the new CFS piece by piece. The corresponding FSE system has been implemented and tested in the IEEE 118-bus power system. The simulation results show that the suggested approach for RBF NN retraining works successfully and efficiently in the case of power network expansion and topology change, which significantly improves the application potential of RBF NN in FSE of real power systems.