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The long-term operation planning problem is generally solved by a chain of computational models based on Stochastic Dual Dynamic Programming (SDDP) considering a period of 5–10 years ahead. A recent issue that has arisen concerning this problem is to define a convergence criterion when using conditional value-at-risk (CVaR) with SDDP due to the lack of good upper bound estimators. The main contribution of this paper is to propose a convergence criterion in which including CVaR does not hinder convergence analysis. Also, the proposed method does not increase the computational burden. Moreover, this paper provides a method that allows forward paths to be individually assessed, which can then either be discarded to reduce computational time or even replaced in an alternative resampling scheme in the SDDP. Based on aggregate reservoir representation, the proposed method of convergence was applied on long-term operation planning problems related to the Brazilian Power System. Results showed improvements in both the SDDP technique and the effectiveness of the proposed convergence criterion when CVaR was used. [ABSTRACT FROM AUTHOR]