This thesis investigates Modular Multilevel Converters (MMCs) with partially integrated Battery Energy Storage Systems (BESS), where only a subset of sub-modules (SMs) are equipped with battery energy storage via bidirectional boost converters. The primary goal of incorporating BESS is to provide inertial and frequency support to the grid. These converters are typically studied using Electromagnetic Transient (EMT) simulations. A continuous-time model of the MMC-BESS is developed based on the state-space equations of the converter. The proposed model enhances computational efficiency in two key ways: (i) it significantly reduces the number of nodes in the conventional switching model, thereby shrinking the size of its admittance matrix, and (ii) it avoids computationally expensive re-triangularization of the admittance matrix during normal operation, restricting it to rare instances of converter blocking. This method results in substantial reductions in the simulation time of MMC circuits, making it particularly useful for studies requiring repetitive simulations. The computational efficiency and accuracy of the proposed model are validated by comparing its implementation in the PSCAD/EMTDC simulator against conventional detailed switching models and experimental measurements from a single-phase scaled-down laboratory setup. The Peak Current Mode (PCM) control strategy is used to manage the DC-DC converters integrating the batteries with the MMC. PCM provides a protective layer that limits the current through the battery and DC-DC converters' switches. An Averaged Value Model (AVM) of the MMC-BESS, along with its per-unit representation, is also derived. The AVM is beneficial for low-frequency studies, such as upstream control design and SM capacitor sizing. Finally, the proposed topology and its model are used to explore replacing Manitoba's outdated Bipole I HVDC system with a VSC-HVDC system featuring MMC and MMC-BESS at the rectifier and inverter terminals, respectively. The study aims to stabilize and maintain system frequency while eliminating synchronous condensers and AC line filters.