The recent introduction of a new converter topology, the modular multilevel converter (MMC) is a major step forward in voltage sourced converter (VSC) technology for high voltage, high power applications. To obtain a multilevel ac output waveform, a large number of semiconductor switches has to be used in the converter. The number of switches in the MMC for HVDC transmission is typically two orders of magnitudes larger than that in a two or three level VSC used in earlier generation. This large device count creates a computational challenge for electromagnetic transients (EMT) simulation programs, as it significantly increases the simulation time. The purpose of this research is to investigate whether the simulation can be speeded up. This research develops an efficient, time-varying Thévenin's equivalent model for the MMC converter based on partitioning the system’s admittance matrix. EMT simulation results show that the proposed equivalent model can drastically reduce the computational time without loss of accuracy. The use of the proposed equivalent method is demonstrated by simulating a point to point MMC based HVDC transmission system successfully with more than 100 levels. This approach enables what was hitherto not practical; the modeling of large MMC based HVDC systems on personal computers. With the assumption of ideal switch operation and using an equivalent average capacitor value based approach, an average valued model of MMC is also proposed in this thesis. The average model can be accurately used in most of the system level studies. The control algorithms and other modeling aspects of MMC applications are also presented in this thesis. One of the advantages of multilevel converters is the low operating losses as the smaller switching frequency of each individual power electronics switch and the low voltage step change during each switching. Using a recently developed, time domain simulation approach, the operating losses of the MMC converter are estimated in this thesis. When comparing the MMC operating losses against the losses of two-level VSC, the power loss for the two-level VSC is found to be significantly higher than the power loss of the MMC.