Modules with series and parallel connectivity add new features and operation modes to modular multilevel converters (MMCs). Compared to full- and half-bridges, the series/parallel modules allow sensorless module balancing and reduce conduction loss with the same semiconductor area. However, in high-voltage applications with limited switching rates, the sensorless operation of the series/parallel modules suffers from large charge-balancing currents. This paper introduces a series/parallel module variant with a small port inductor. The port inductor suppresses the charge-balancing current despite low switching rates. We also propose a carrier-based modulation framework and show the importance of the carrier assignment in terms of efficiency and balancing. The proposed module and the modulation method are verified on a lab setup with module switching rates down to 200 Hz. The module voltages are kept within a narrow band with the charge-balancing currents below 5% of the arm current. The experimental results show practicality and advantages of the new series/parallel modules in high-voltage MMC applications.