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In recent years the interest in environmental protection and energy sustainability has steadily increased; this fact has promoted research activities, and projects focused on non-conventional renewable energy (NCRE) sources as a replacement for fossil fuels. In this context, NCRE-based technologies offer a solution for integrating distributed energy resources where the Microgrid (MG) concept has been introduced to facilitate the integration of a large number of micro-generators, energy storage units and loads. This integration is enabled by power electronic converters, and therefore there is an increase in the number of these devices in the modern electrical power systems. The proliferation of power electronic-based systems will inevitably affect both the power quality and the stability of electrical systems which have power electronic interfaces. In this context, two key issues that need to be addressed are the following: (i) the imbalances and harmonics inherently present in MG due to the random nature of loads and (ii) since MGs are weak systems, the stability between the power electronic-interface and the Point of Common Coupling (PCC). These two critical issues in MGs are studied in this thesis. The former is analysed considering 4-leg systems while the latter is studied considering a 3-leg system. The 3-wire system is used for developing a methodology to study the effects of the weak nature of MGs on a simple system. As future work, this methodology can be modified to analyse specific control schemes proposed in this thesis to manage imbalances and harmonic in MGs. To manage imbalance and harmonic issues in 4-leg MGs, two approaches are proposed. First, a novel methodology based on the application of a 4-leg shunt Active Power Filter (APF) is proposed. The control for the compensator is based on the Conservative Power Theory (CPT) augmented by resonant controllers. Experimental validation of the APF will be performed with a focus on the transient behaviour and on its performance when frequency variations occur. In the second approach, a cooperative control scheme based on the CPT is proposed for sharing imbalances and harmonics in three-phase four-wire droop-controlled systems. With this approach, it is demonstrated that the CPT can be an effective tool to develop imbalance sharing algorithms in isolated MGs. The behaviour of proposed control schemes is demonstrated using experimental prototypes deployed in a laboratory scale 4-leg MG, and using unbalanced and distorted conditions of a real isolated MG located in Canada. To study how the weak nature of MGs affect the stability of the interface between a converter and the PCC, a stability analysis focused on the phase-locked loop (PLL) has been undertaken based on a simple dq model proposed in this thesis. The aim of this proposal is to understand the effect of the weak nature of the MG (measured with the short circuit ratio) and the PLL bandwidth on the stability of the system. The system studied corresponds to a 3-leg converter connected to a balanced three-phase weak grid. The performance of this method is validated through simulation using Plexim PLECS software, and experimental validation using a laboratory-scale system is performed. The main contributions of this thesis can be summarised as follows: • In microgrids, relatively large variations in the electrical frequency may occur. The sensitivity to grid frequency variations is a known limitation of the CPT, and this work proposes and validates an implementation approach that shows the limited impact of frequency variation on the APF performance. • The CPT is applied to 4-wire systems considering full control of the 4 legs in the APF, to regulate the positive, negative and zero sequence voltages synthesised by the power converter. This includes the operation of the CPT compensator with single-phase non-linear loads. • The proposed sharing algorithm uses a novel approach based on the CPT methodology that can be used to implement a simple identification of the balanced, unbalanced and non-linear components of the currents and powers. Separation of the sequence components is not required. This produces a more robust imbalance sharing algorithm, particularly because most of the sequence separation algorithms are strongly affected by noise, harmonic distortion, small variations in the sampling time, etc. • A very simple method to share harmonic distortion between the generation sources is realised considering the application of the CPT transform. In this thesis, this methodology is discussed and experimentally validated. • A control algorithm is proposed based on the CPT which is very robust to issues such as distortion, noise, changes in the sampling time etc. As is demonstrated in this work, it is very simple to extend the proposed methodology to include harmonic distortion. • A systematic PLL design process is proposed to be used in weak grids to ensure system stability. This design process is based on a proposed low-complexity small signal model of the system in the dq reference frame. Based on this proposal, it could be possible (in future work), analyse the effects of the weak nature of MGs on the performance of the CPT-based controllers proposed in this thesis.