The　synchronization　stability　of　the　system　that　one　single　VSC　is　connected　to　an　infinite　source　via　the　line　is　studied　in　this　letter.　Based　on　Bendixson　criterion,　closed　orbit　(limit　cycle)　does　not　exist　in　the　derived　stable　region,　while　may　exist　in　the　region　between　the　conservative　stable　boundary　and　the　unstable　equilibrium　point　(UEP).　Nonlinear　damping　effect　on　the　system　stability　is　analytically　defined,　and　an　unstable　limit　cycle　appears　when　the　positive　and　negative　damping　effect　of　the　system　over　one　period　is　mutually　balanced.　Numerical　results　verify　the　existence　of　limit　cycle　and　nonlinear　damping　property　of　VSC.