State-of-charge　(SOC)　balancing　is　a　critical　issue　for　the　development　of　battery　management　systems　for　electric　vehicles.　In　the　series　of　two　papers,　an　adaptive　estimation-based　hierarchical　model　predictive　control　(MPC)　balancing　methodology　is　proposed　to　explore　different　equalization　topologies.　In　the　first　paper,　the　superior　control　for　optimal　SOC　balancing　in　typical　topologies,　i.e.,　dissipative,　unidirectional　adjacent,　bidirectional　adjacent,　and　bus-based,　is　developed　by　formulating　the　proposed　MPC.　SOC　balancing　problems　of　different　topologies　are　modeled　by　describing　the　behavior　of　energy　transferring　during　the　charge/discharge　process　considering　practical　loss.　The　MPC　balancing　strategy　is　proposed　to　solve　the　constrained　quadratic　optimization　by　minimizing　the　balancing　time　and　energy　loss.　A　rule-based　fuzzy　logic　control　(FLC)　balancing　is　compared,　and　in　the　5-series　cells　simulation,　the　result　indicates　that　the　balancing　time　of　MPC　and　FLC　are　292　s　and　654　s,　respectively.　To　verify　the　real-time　feasibility　of　the　proposed　MPC　balancing　strategy,　a　controller　hardware-in-the-loop　(HIL)　test　is　further　implemented.　Finally,　the　influences　of　bidirectional　adjacent　and　bus-based　topologies　on　equalization　performance　are　discussed,　demonstrating　a　strong　correlation　between　the　number　of　series-connected　cells　and　adopted　topology.　The　proposed　MPC-based　superior　control　can　be　integrated　with　the　later　designed　low-level　adaptive　estimation　laws　driven　individual　cell　equalizer　(ICE)　controller　to　comprehensively　tackle　SOC　optimal　balancing　problems.　©　2021　Elsevier　Ltd