The authors present R²Power, an effective approach to the realizable reduction of RC networks with independent current sources. The proposed approach is based on the entrywise perturbation theory for diagonally dominant M-matrices. The accuracy of the node voltages of the reduced network, as compared to those of the original network, is maintained on the order of the entrywise perturbation performed during reduction. R²Power can be used to reduce the size of RC networks used to model the power networks of SoCs, for efficient IR-drop analysis. Experiments showed that R²Power reduced the size of industrial examples by more than 95%, with maximum relative node voltage errors of less than 0.012%.