Critical　situations　are　difficult　to　predict　reliably　by　the　machine　learning-based　transient　stability　assessment　(TSA)　methods.　Therefore,　the　practicality　of　the　data-driven　TSA　is　limited.　A　parallel　TSA　framework　constructed　by　two　basic　predictors　and　a　comprehensive　decider　(CD)　is　proposed　to　achieve　fast　and　reliable　real-time　transient　stability　assessment　(RTSA).　A　cost-sensitive　method　is　utilized　for　stacked　sparse　auto-encoders　to　establish　two　basic　predictors　with　opposite　evaluation　biases.　Then,　the　outputs　of　the　two　basic　predictors　are　sent　to　the　CD.　Finally,　the　stability　of　the　non-critical　cases　can　be　judged　directly,　and　the　critical　cases　are　suggested　to　be　analyzed　by　other　methods.　Besides,　in　order　to　enhance　the　reliability　of　the　parallel　predictor,　a　simple　data　augmentation　approach　with　Gaussian　white　noise　is　employed　to　expand　the　classification　boundaries.　A　fault　severity　factor　is　introduced　to　filter　basic　critical　samples　for　data　augmentation　to　improve　the　performance　of　the　proposed　framework.　The　effect　of　the　proposed　strategy　is　verified　on　the　IEEE-39　bus　system　and　a　realistic　regional　system.　©　2021　John　Wiley　&　Sons　Ltd.