Melody preservation is crucial in singing voice conversion (SVC). However, in many scenarios, audio is often accompanied with background music (BGM), which can cause audio distortion and interfere with the extraction of melody and other key features, significantly degrading SVC performance. Previous methods have attempted to address this by using more robust neural network-based melody extractors, but their performance drops sharply in the presence of complex accompaniment. Other approaches involve performing source separation before conversion, but this often introduces noticeable artifacts, leading to a significant drop in conversion quality and increasing the user's operational costs. To address these issues, we introduce a novel SVC method that uses self-supervised representation-based melody features to improve melody modeling accuracy in the presence of BGM. In our experiments, we compare the effectiveness of different self-supervised learning (SSL) models for melody extraction and explore for the first time how SSL benefits the task of melody extraction. The experimental results demonstrate that our proposed SVC model significantly outperforms existing baseline methods in terms of melody accuracy and shows higher similarity and naturalness in both subjective and objective evaluations across noisy and clean audio environments.