This　paper　addresses　the　issue　of　power　system　transient　stability　assessment　and　control　(TSA&C)　based　on　phase　plane　representation　of　the　power　angle　and　rotor　speed.　First,　the　relationship　between　transient　stability–instability　and　concavity–convexity　of　the　phase-plane　trajectory　is　found　and　proved　based　on　the　single　machine　infinite　bus　(SMIB)　system,　and　a　transient　instability　criterion　is　derived　for　real-time　instability　detection.　Second,　with　the　aim　that　the　phase-plane　trajectory　swings　back　before　the　unstable　equilibrium　point　(UEP)　once　instability　is　detected,　near-optimal　control　size　of　generator　tripping　to　stabilize　the　system　is　determined　based　on　the　relationship　between　unbalanced　power　and　the　slope　of　the　phase-plane　trajectory.　Finally,　the　instability　detection　and　control　technique　is　extended　to　a　multimachine　power　system　based　on　SMIB　equivalent　transform.　The　proposed　method　is　independent　of　the　network　structure　and　operation　mode,　which　can　be　applied　for　real-time　emergency　control　based　on　wide　area　measurement　system　(WAMS).　The　simulations　in　the　Institute　of　Electrical　and　Electronics　Engineers　(IEEE)　39-bus　system　and　the　Sanhua　Power　Grid　(in　China)　validate　the　accuracy　and　efficiency　of　the　proposed　method.　©　2019　Institute　of　Electrical　Engineers　of　Japan.　Published　by　John　Wiley　&　Sons,　Inc.　©　2019　Institute　of　Electrical　Engineers　of　Japan.　Published　by　John　Wiley　&　Sons,　Inc.