Bug tracking systems store many bug reports, some of which are related to security. Identifying those security bug reports (SBRs) may help us predict some security-related bugs and solve security issues promptly so that the project can avoid threats and attacks. However, in the real world, the ratio of security bug reports is severely low; thus, directly training a prediction model with raw data may result in inaccurate results. Faced with the massive challenge of data imbalance, many researchers in the past have attempted to use text filtering or clustering methods to minimize the proportion of non-security bug reports (NSBRs) or apply oversampling methods to synthesize SBRs to make the dataset as balanced as possible. Nevertheless, there are still two challenges to those methods: 1) They ignore long-distance contextual information. 2) They fail to generate an utterly balanced dataset. To tackle these two challenges, we propose SEDAC, a new SBR identification method that generates similar bug report vectors to solve data imbalance problems and accurately detect security bug reports. Unlike previous studies, it first converts bug reports into individual bug report vectors with distilBERT, which are based on word2vec. Then, it trains a generative model through conditional variational auto-encoder (CVAE) to generate similar vectors with security labels, which makes the number of SBRs equal to NSBRs'. Finally, balanced data are used to train a security bug report classifier. To evaluate the effectiveness of our framework, we conduct it on 45,940 bug reports from Chromium and four Apache projects. The experimental results show that SEDAC outperforms all the baselines in g-measure with improvements of around 14.24%-50.10%.