Model　predictive　current　control　(MPCC)　uses　the　discrete-time　model　of　a　system　to　predict　the　future　behaviour　of　the　current　for　all　voltage　vectors　(VVs)　generated　by　a　power　converter.　In　multilevel　inverters,　the　large　number　of　VVs　imposes　a　long　computation　time　for　the　prediction　and　selection　of　the　optimal　state　to　be　applied　to　the　converter,　which　increases　the　sampling　time　and　decreases　the　closed-loop　performance.　An　MPCC　is　proposed　based　on　the　idea　of　generalised　adjacent　voltage　vectors　(GAVVs)　for　multilevel　cascaded　H-bridge　inverters　with　a　DC-link　voltage　fed　by　photovoltaic　(PV)　cells.　This　method　deals　with　the　voltage　drop　and　often　small　inter-bridge　voltage　imbalance　and　irradiance　issues　that　occur　in　PV　power　plants.　The　proposed　GAVV　method　is　analytically　formulated　to　provide　three　types　of　subsets　for　a　given　number　of　inverter　levels.　The　use　of　the　newly　added　subsets　of　four　and　five　VVs　contributes　to　boosting　the　converter　output　voltage　and　achieving　acceptably　balanced　current　and　line-to-line　voltage　under　low　irradiance　compared　with　the　classical　approach.　Simulation　and　experimental　results　show　good　current　response　and　reduced　switching　frequency　even　under　a　high　current　reference　with　DC-link　voltage　drop.