High voltage direct current (HVDC) system used for bulk power transfer over longer distance offers numerous advantages compared to high voltage alternating current (HVAC) transmission system, such as inter-connect networks operating at different frequencies, comparatively low line losses because of constant current and absence of reactance. Power converters are needed (AC-to-DC-to-AC) to embed DC links into power transmission systems. Among the power converters, the modular multilevel converter (MMC) based on voltage-source converters (VSCs) is emerging as a potential candidate for HVDC transmission systems. It offers several advantages, such as the absence of large power supplies at each module, lower harmonics, less switching losses, modular structure, and scalable output voltage. However, for a large DC-network (HVDC system), MMC requires large number of sub-modules (SMs) and switches, which makes its modeling very challenging and computationally intensive using electromagnetic transient (EMT) type programs like PSCAD/EMTDC. Average Value Model (AVM) offers a better option to model MMCs by combining SMs to make an arm equivalent circuit. Each arm of an MMC can be modeled as a controllable voltage source due to cascaded connection of identical SMs, which in turn results in scalable output voltage for MMC. Circulating current and voltage fluctuations of SMs capacitors are important issues to consider during the operation and stability of MMCs. Circulating currents contribute to power loss in MMCs as root mean square (RMS) value of the arm current increases. Circulating current also increases the amplitude of voltage fluctuations of SMs capacitors, DC side current oscillations that affects the stability of MMC. The traditional method for inserting SMs in each arm is based on direct modulation, which utilizes two reference waveforms for controlling arm voltages in MMC. It does not compensate the arm voltage oscillations, and generates circulating current in each leg of a three-phase MMC systems. Existing circulating current control methods can be divided in two groups: (1) elimination of higher order harmonics reduces the RMS value of arm currents at expense of increase in capacitor voltage ripple; and (2) injecting higher order harmonics in circulating currents, which reduces the capacitor voltage ripple at expense of increase in the RMS value of the arm current. In this research work, a new method is proposed and simulated to minimize capacitor energy variations by injecting even order harmonics to the upper and lower arm currents based on direct modulation method. This injection will restrict excessive negative currents in each arm of the MMC, leading to the presence of DC current components, which results in the reduction of circulating currents and RMS values of the arm current inside each leg of 3-phase MMC. Furthermore, with this technique voltage fluctuations of SMs capacitors and oscillations in DC link current also reduce. A two terminal symmetrical monopole MMC-HVDC test system based on time variant AVM model is designed and simulated in PSCAD/EMTDC to validate the effectiveness of proposed method. This symmetrical monopole MMC-HVDC system use vector current control that needs grid voltage for synchronization and to accurately extract phase angle and frequency at the point of common coupling (PCC) for the control system. Conventionally Phase-locked loop (PLL) is implemented to synchronize MMC output voltage to grid voltage while estimating, grid voltage phase angle and frequency in order to generate voltage and current references for the grid side converter control system. However, presence of the DC-offset at input voltage of a PLLresults in fundamental frequency oscillations, that introduces phase angle error leading to instability of the MMC-HVDC system as the current references tracked by controllers with erroneous values. Therefore, a 3-phase double integration method (DIM) is proposed and implemented for grid synchronization of a 3-phase MMC in HVDC system, that removes DC offset at input voltage and enables a smooth start during normal start-up of a grid or after disturbance improves the stability of HVDC system. Finally, this research work also highlights the challenges and issues related to the integration of electric power produced by wind energy into the AC Grid. It is concluded that HVDC system provides better option for the possible future expansion of existing AC transmission lines in order to integrate electrical power generated by wind energy sources.