In　power　system　transient　stability　assessment　(TSA),　the　misclassification　cost　of　unstable　samples　is　much　more　serious　than　that　of　stable　ones.　Besides,　for　both　unstable　samples　and　stable　samples,　the　impacts　of　critical　samples　on　the　assessment　rules　are　more　important　than　those　of　non-critical　ones.　Thus,　an　improved　cost-sensitive　assignment　(ICSA)　method　based　on　the　fault　severity　is　proposed.　Larger　cost　coefficients　are　assigned　to　critical　samples　compared　with　non-critical　samples.　Furthermore,　sufficiently　learning　the　information　of　misclassified　samples　is　helpful　to　modify　the　assessment　rules　quickly　and　accurately.　Meanwhile,　the　assessment　rules　may　be　greatly　disturbed　due　to　the　existence　of　abnormal　samples　among　training　samples.　Therefore,　on　basis　of　the　ICSA　method,　an　adaptive　cost-sensitive　assignment　(ACSA)　method　is　presented　in　this　paper.　In　the　process　of　model　training,　the　cost　coefficients　of　misclassified　training　samples　are　adaptively　adjusted　to　improve　the　assessment　rules.　Then,　the　impacts　of　the　abnormal　samples　on　the　assessment　rules　are　eliminated　by　assigning　their　cost　coefficients　to　0.　Finally,　simulation　experiments　are　carried　out　in　the　IEEE　39-bus　system　and　a　realistic　system.　It　can　be　shown　that　the　proposed　ACSA　method　has　high　classification　accuracy　and　excellent　generalization　ability.　©　2021　Elsevier　Ltd