Three-phase　AC　distribution　networks　are　required　to　operate　as　symmetrically　as　possible　for　optimal　performance,　but　the　three-phase-to-ground　parameters　are　asymmetric　in　the　field　due　to　network　construction　deviation,　resulting　in　the　three-phase　voltage　unbalance　and　the　neutral　point　displacement　overvoltage.　The　neutral　point　displacement　overvoltage　would　endanger　the　distribution　networks　and　even　damage　critical　power　equipment.　Therefore,　the　flexible　asymmetry　suppression　device　(FASD)　with　the　topology　of　a　cascaded　H-bridge　(CHB)　inverter　and　the　backstepping　control　(BSC)　method　is　proposed　for　limiting　the　neutral　point　displacement　overvoltage　in　this　paper.　The　FASD　outputs　the　current　to　the　grid　for　compensating　the　unbalanced　distribution　networks　caused　by　the　asymmetry　of　three-phase-to-ground　parameters　and　realizing　the　suppression　of　the　neutral　point　displacement　overvoltage.　A　current-based　BSC　method　is　designed　to　improve　the　stability　and　reliability　of　the　CHB　inverter,　and　the　effectiveness　of　neutral　point　displacement　overvoltage　suppression　based　on　the　BSC　method　is　verified　by　experimental　results,　and　the　advantage　of　the　proposed　method　is　shown　by　comparing　with　proportional-integral　control　(PIC)　method,　sliding　mode　control　(SMC),　and　proportional　resonant　control　(PRC)　methods.　©　2023　Elsevier　Ltd