Abstarct: The AC and DC microgrids are connected together by a bi-directional AC-DC interfacing converter to form the hybrid AC-DC microgrid. The grid may have voltage power quality problems such as voltage sag/swell/harmonic. So, the grid-connected hybrid AC-DC microgrid is faced with same power quality problems in the AC bus voltage and voltage level variations in the DC bus. With the presence of nonlinear loads in the AC bus, the grid current also has unwanted distortions and harmonics. The conventional structure of the grid-connected hybrid AC-DC microgrid has not sufficient ability to control the AC bus voltage and improve its power quality. In this thesis, to solve the problem, the conventional structure of the hybrid AC-DC microgrid is changed by adding a series converter between the DC bus and the main grid. This converter is responsible for compensating the power quality problems of the grid voltage and creating a sinusoidal voltage with the desired amplitude and frequency in the AC bus. Also, the interfacing converter, in addition to bi-directional transferring power between main AC and DC buses, is responsible for compensating reactive power and distortion active power of the non-linear AC load. Hence, the grid current is sinusoidal with unity power factor. Control systems for the interfacing and series converters are proposed using instantaneous reactive power theory and current prediction control. In this way, the power quality problems of the microgrid and the grid are not transmitted to each other. By performing the required simulations on the typical microgrid, the performance of the proposed method is confirmed. In order to improve the reliability, instead of using an interfacing converter with large rating to increase the power exchange capacity between AC and DC buses, smaller parallel interfacing converters are used. In the second part of this thesis, a method is proposed to find the optimal number of paralleling interfacing converters in terms of reducing the annual investment cost and increasing the reliability. Values of transferring apparent, active and non-active powers between AC and DC busses are determined by considering the microgrid power flow and improving the power quality. baxsed on them, the reliability indices of the expected apparent power shortage and the expected energy shortage are proposed. The reliability cost is obtained by multiplying the reliability indices by the price of power. The annual investment cost of parallel converters is also calculated. Sum of these two terms is considered as an objective function of the decision-making process. baxsed on the number of parallel interfacing (Exhaustive Enumeration method), the values of the objective function are calculated and by comparing them, the optimal number of parallel converters is determined. The simulations are performed on the typical microgrid with experimental data and the optimal number of parallel interfacing converters is determined.