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Unnoticed breakdowns in capacitor voltage transformers (CVTs) result in accuracy degeneration, even explosions. Thus, detecting breakdowns in time is critical. Existing methods have made unsatisfactory progress as labeled data is insufficient. We propose an unsupervised end-to-end method, including domain knowledge-assisted feature extraction, problem formulation, and optimization. First, an estimator is proposed to obtain the extra ratio error with detailed breakdown information. Second, a new feature, i.e., distance to the clustered voltage (DCV), is introduced. Third, the detection task is reformulated into an optimization problem. Details about breakdowns are the decision variables, aiming to minimize the differences between DCV and the estimated ratio error. An optimization algorithm called the DCV-lead grid search (DCV-GS) is designed for acceleration. Experiments and practical implementations demonstrate its accuracy and efficiency. This method could detect both existing and new breakdowns timely without labeled data, which can reduce the cost and time of maintenance. • Domain knowledge is utilized in feature extraction, problem formulation, and optimization. • A feature (DCV) is developed with voltages measured by same-phase CVTs are the same. • A ratio error estimator with details of breakdowns in a CVT is proposed. • The detection task is formulated into an optimization problem. • A DCV-guided algorithm is developed to accelerate the optimization. [ABSTRACT FROM AUTHOR]