Modular Multilevel Converter (MMC) secured its place in applications where high reliability, efficiency and effortless voltage/power scalability are of paramount importance. Without compromising these benefits, this paper proposes a novel control and appropriate design approach for Hybrid-MMC topology, comprising a mix of Full-Bridge and Half-Bridge submodules in converter branches, as a grid-side stage of a back-to-back MMC, enabling operation at variable DC link voltage and arbitrary power factor. In the midst of transition to Renewable Energy Sources-dominated power systems, variable DC link voltage operation opens door to the use of Hybrid-MMC in retrofit of large Pumped Hydro Storage Plants to variable speed operation, where existing machines would not tolerate high common-mode voltage stress imposed by fixed-DC-link-voltage operated machine-side MMC stage. In this way, highly flexible grid-scale energy storage use of existing hydro capacities is enabled. Converter design approach and additional control layers have been developed and verified through a set of test scenarios. Sizing and operation at typical operating points are compared to equally-rated Full-Bridge-based MMC. Improvements over the existing Hybrid-MMC solutions include unity-power-factor operation at the entire attainable DC link voltage range and equal loading of upper and lower phase-leg branches regardless of the operating point.