This thesis investigates modeling of modular multilevel converters (MMCs) using an averaging method known as extended-frequency dynamic phasors. An MMC can be used as an inverter or a rectifier in high voltage direct current (HVDC) system. This research develops a dynamic phasor model for an MMC operated as an inverter. Extended-frequency dynamic phasors are used to model a system with only interested harmonics present. The developed model is capable of capturing both the low and high-frequency dynamic behavior of the converter depending on the requirements of the study to be performed. The selected MMC model has 5 submodules per arm (6-level converter), nearest level control, capacitor voltage balancing, direct control and phase-locked loop (PLL) synchronization. With the above features, the developed dynamic phasor model is validated with electromagnetic transient model is developed using PSCAD simulation software. The results are compared at transient and steady state with disturbances. The main computational advantage of this modeling is achieving less simulation time with inclusion of harmonics of interest. / October 2016

This thesis presents a transient stability method using dynamic phasors. This method can be used to investigate low frequency (<5Hz) and sub-synchronous frequency (5Hz-60Hz) oscillations. It has major advantages as compared to traditional transient stability method and EMT method. It allows modeling of higher-frequency oscillation possible using time domain simulations, which is not achievable with conventional method. It also can be simulated at much larger time step as compared to PSCAD/EMTDC simulation. Comparison of the results with traditional model and detailed EMT model are also present, and they show very accurate results at frequency ranges up to 60Hz.