The modulation methods for quasi-Z-source cascade multilevel inverters relate to control and signal modulation of quasi-Z-source cascade multilevel inverters, such as those used with photovoltaic power systems. The modulation methods for quasi-Z-source cascade multilevel inverters include a modular multilevel space vector modulation method for a photovoltaic quasi-Z-source cascade multilevel inverter for compensating for unequal voltages of separate photovoltaic modules, a pulse-width-amplitude modulation method for multilevel inverters for use in solar panel arrays attached to a three phase power grid, and a grid-connected control method for quasi-Z-source cascade multilevel inverter-based photovoltaic power generation for extracting maximum power from each Z-source cascade multilevel inverter.