In smart distribution networks, with the high penetration of the renewable energy systems and electric transportation systems, and the proliferation and the increasing usage of the power electronic devices and motor loadings into all kinds of energy processing systems, the power quality (PQ) problems such as: reactive power and harmonics pollution becomes more serious. The PQ problems distort the source voltage, lower the efficiency, and may cause system instability; thus it makes negative impacts on the performance and reliability of distribution network. The incidents caused by PQ issues include additional electricity cost, equipment overheating, processing error, and transformer failure, etc. Based on the Asia Power Quality Initiative 2017 Report, there were 15 to 24 billion US dollars loss per year in United States due to PQ problems, while there were about 150 billion Euros loss per year for European Union countries. In this regard, power filters for PQ compensation are of high interests and demands. Hybrid active power filters (HAPF), which is a combination of active power filter (APF) and passive power filter (PPF) is considered as a cost-effective PQ solution. HAPF obtains the advantages of good dynamic and steady-state compensating performances with lower initial and operational costs, in comparison with the APF. As the current controller is the heart of the HAPF, its design plays an important role for enhancing the HAPF compensation performances. Among the HAPFs, (LC-coupling hybrid active power filter (LC-HAPF) for the low-to medium-voltage and limited load range application and the thyristor-controlled LC-coupling hybrid active power filter (TCLC-HAPF) for the medium-voltage and wide load range application), obtain the advantages of good dynamic and steady-state compensating performances with lower initial and operational costs, in comparison with the APF. Different from the APF, the LC- and TCLC-HAPF only requires a single-level structure in MV application, which largely saves the cost and simplifies the control. Besides, when multiple HAPFs are installed into the smart distribution networks, their coordination strategy for better system performance and reliability are also important to be explored. In this thesis, the main research objectives focus on designing advanced current controllers and coordination strategy for multiple HAPFs to better address the PQ issues in smart distribution networks. However, based on the state-of-the-art research works of the HAPF controllers, the following points have not been investigated and discussed: 1. The existing current controllers for the HAPFs suffer from one or more drawbacks among high steady-state error, slow dynamic response, and varying switching frequency. 2. The controller robustness for the HAPFs under distorted grid voltage, grid frequency variation, and system parameters variation has not been investigated. 3. The existing equivalent circuit model of the TCLC-HAPF does not overcome its TCLC part nonlinearity issue and is still inaccurate, which makes the controller difficult to design and also affects the system compensating performances. 4. The existing coordination strategies of multiple HAPFs in a smart distribution networks cannot address the voltage regulation, harmonic voltage suppression, and DC-link voltage reduction of the HAPFs simultaneously and also suffer from one or more drawbacks among low accuracy, high communication cost, low reliability, and poor resiliency. In this thesis, under a low-to medium-voltage and limited load range application, a second-order sliding mode controller (SOSMC) for the LC-HAPF is proposed. And the parameter design of the SOSMC under distorted grid voltage, grid frequency variation, and system parameters variation are investigated. To further reduce the required DC-link operating voltage, a vector proportional-integral controller (VPIC)for the LC-HAPF with low steady-state error, fast transient response, fixed switching frequency, and good robustness is proposed, which can obtain good compensation performances even under a minimum DC-link voltage. A detailed robustness analysis of the VPIC including the system parameter variation, distorted grid voltage and grid frequency variation conditions is also studied and discussed. To overcome the nonlinearity of TCLC part of the TCLC-HAPF for medium voltage and wide load range application, a harmonic state-space (HSS) model of TCLC-HAPF that ensures linearity and high accuracy is proposed. The HSS enables the linear matrix inequality(LMI) based H∞ optimal controller (HOC) design, which achieves high steady-state accuracy, fast transient response, and fixed switching frequency simultaneously. To further improve the robustness and disturbance rejection capability of the TCLC-HAPF, an observer-based SOSMC that ensures superior control performance and good system robustness under different grid conditions and system parameter variations is proposed. The TCLC-HAPF based on the observer-based SOSMC achieves the state-of-the-art steady-state and dynamic compensation performances compared with the existing current controllers. Finally, an optimal coordination strategy named distributed voltage quality control (DVQC) for multiple HAPFs operating in a smart distribution networks is proposed. The DVQC provides the network-wide power quality improvement with low DC-link voltage, low communication costs, high reliability, and good resiliency.