To address the problems that the ratio-error series of current-transformers，affected by environmental disturbance， operating condition variations and random noise，exhibit nonstationary and multi-scale characteristics，and it is difficult to balance point prediction and interval estimation，this paper proposes an interval forecasting method integrating complete ensemble empirical mode decomposition（CEEMD），dual-scale temporal convolutional network（DTCN）and bias-corrected residual bootstrap（BCRB）.Firstly，The CEEMD is adopted to decompose and reconstruct the original ratio-error series to suppress high-frequency noise and mode mixing.Secondly， the DTCN is used to extract short-term fluctuation and long-term drift features to realize point prediction of ratio errors.Finally，prediction intervals under different confidence levels are constructed based on the residual bootstrap method. Case studies show that the proposed method achieves a high interval coverage probability at the confidence level of 0.99. This work is supported by National Key Research and Development Program of China（No.2023YFB2405903）.