Hybrid active power filter (HAPF) has become a more and more important power quality compensator in the past two decades. Due to the development of power electronic devices and equipments in distribution system, power quality issues such as harmonic currents and reactive power produced by nonlinear loads are increasing. They pollute the power system and induce a lot of electricity safety problems, thus creating a desperate need for power compensators to solve these power quality problems. Actually, hybrid active power filter is a combined system of active power filter (APF) and passive filter (PF), both of which are able to eliminate harmonic currents and reactive power. However, their inherent limitations bring about their shortcomings, whereas hybrid active power filter is a way to overcome these disadvantages as it has the capability of anti-resonance and a low power rating. Soft-Switching Technique is employed to solve the switching transition problems of power devices, as high voltage and current stress cause high switching loss, high system loss and low system efficiency. As a result, soft-switching circuits can not only reduce switching loss but also release voltage and current stress; moreover, they can also reduce the changing rate of voltage and current of power switches, i.e., dv/dt and di/dt, which is the cause of electromagnetic interference (EMI). Quasi-Resonant DC-Link (QRDCL) Inverter is a useful topology of soft-switching circuit integrated into the inverter to achieve soft-switching operation. This topology has been already applied in two-level and three-level inverters for ten years due to its obvious advantages: less auxiliary switches, lower voltage rating and a simple control method. Therefore, with the quasi-resonant dc-link circuit, the converter has the ability to reduce switching loss and improve system efficiency. The proposed topology is a three-level hybrid active power filter combined with quasi-resonant dc-link circuits in three-phase four-wire system. As is discussed above, this three-level quasi-resonant dc-link hybrid active power filter can achieve both advantages of hybrid active power filter and quasi-resonant dc-link technique: to compensate for harmonic currents and reactive power with a low dc voltage, and reduce switching loss and release voltage and current stress. Meanwhile, the multilevel inverter can reduce voltage stress across switches in high voltage application, and provide more available vector for selecting appropriate switching vectors to reduce output harmonic components. In this thesis, the mathematical models are presented of quasi-resonant dc-link circuits, three-level active power filter and three-level quasi-resonant dc-link hybrid active power filter. Furthermore, a comparison is made between the three-level active power filter, the three-level quasiresonant dc-link active power filter and the proposed three-level quasi-resonant dclink hybrid active power filter. Then, the proposed topology is studied and analyzed in terms of the operational principle, the control system and the design of system parameters. The well-known instantaneous reactive power theory, which has been applied in many power compensators, is employed in the control system of the proposed topology. Three dimensional direct pulse width modulation is applied since it is easy to manipulate and requires low computation. The zero voltage switching controller is used to coordinate with PWM inverter. Along with the operation of quasi-resonant dc-link circuits by a fixed delay time, they achieve zero voltage switching for the main devices of the inverter. At the same time, the effect of zero voltage switching is taken into consideration, as they will affect pulse width of the inverter so that its compensating performance will be degraded. Finally, simulation results are given to verify the validity of the proposed topology. It’s proved that the proposed three-level hybrid active power filter with quasi-resonant dc-link circuits can reduce switching loss and improve system efficiency, and the compensating results are also accepted. Then, simulation comparison between active power filter, hybrid active power filter and soft-switching hybrid active power filter is made. A discussion of the proposed quasi-resonant dc-link hybrid active power filter is conducted as to its different ratios including the resonant period and the switching period, and its performance with varied loads.