Modular multilevel converters with embedded storage (MMC-ES) have attracted the attention of researchers as a flexible converter of integrating energy storage to ac and dc networks using a single converter. Conventional EMT simulation methods are highly inefficient in simulating MMC-ES due to the large number of switching elements in the converter. Detailed equivalent model (DEM) have been developed in previous research that could efficiently simulate the MMC-ES, but are ineffective in mathematically analysing the converter. This thesis proposes a novel averaged-value model (AVM) to the MMC-ES multivalve, which simulates the converter based on multivalve averaged quantities. The model is capable of conducting general EMT simulations, and analytically estimating circulating currents and capacitor voltage ripple. The AVM is validated against detailed EMT simulation results, mathematical analysis, and laboratory prototype observations. The thesis also improves the AVM and DEM to simulate converter's blocking state and validates the models against detailed simulation model. A novel MMC-ES HVDC link startup procedure is also developed and verified. Two case studies are conducted to study the use of MMC-ES in providing extensive ancillary services and it is concluded that MMC-ES supported by dedicated measurement communication lines and conventional fast frequency response controllers could greatly improve network frequency response.