Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified beyond limits of international standards by the interactions of individual CIDERs through the grid. To this end, appropriate analysis tools are required in order to model and quantify harmonic levels as well as to assess the associated harmonic stability, identify causes of instability, and develop robust controllers. Frequency-domain analysis has been identified to be a computationally efficient approach for the study of harmonics. However, many of the existing frequency-domain models are only valid for specific devices, or neglect the coupling between harmonics.In order to overcome these limitations, a modular and generic modelling framework for power grids with a high share of CIDERs is proposed in this thesis. The framework models a power system as a composition of a grid and a number of resources (including, but not limited to, CIDERs). The grid components are characterized by compound electrical parameters, which allow to represent both transposed or non-transposed lines. The CIDERs are represented by a generic structure that allows to treat both grid-forming and grid-following CIDERs. In particular, this structure is fully modular w.r.t. different reference frames (e.g., between the electrical components and the control of a CIDER) as well as circuit configurations (e.g., between grid and resources). All components of the system model are represented by Linear Time-Periodic (LTP) models or functions, that are transformed to frequency domain by means of Fourier transform and Toeplitz theory.Building on this modelling framework, a Harmonic Power-Flow (HPF) method is proposed. The HPF problem is formulated through the mismatch equations of the nodal quantities between the hybrid parameters of the grid and the closed-loop responses of the CIDERs. The system of equations is solved numerically using a Newton-Raphson algorithm. The results are validated against time-domain simulations in Simulink. The HPF method has been shown to accurately capture the propagation of harmonics between AC and DC components of CIDERs, and through entire hybrid AC/DC power systems. For the purpose of stability assessment, the system model is derived in harmonic domain as the closed-loop model between the grid and the resources. On the obtained system model, an eigenvalue analysis is performed using LTP system theory. The Harmonic Stability Assessment (HSA) is shown to be applicable to individual CIDER models as well as to an entire power system. Furthermore, it can be used for sensitivity analysis of the eigenvalue loci w.r.t. control parameter variations. Additionally, the HSA is confirmed to be effective in identifying a harmonic instability in a small yet realistic example system operating under standard conditions.