Stability boundary analysis in single-phase grid-connected inverters with PLL by LTP theory

Stability analysis of power converters in AC net¬works is complex due to the non-linear nature of the conversion systems. Whereas interactions of converters in DC networks can be studied by linearising about the operating point, the extension of the same approach to AC systems poses serious challenges, especially for single-phase or unbalanced three-phase systems. A general method for stability analysis of power converters suitable for single-phase or unbalanced AC networks is presented in this paper, based on Linear Time Periodic (LTP) theory. A single-phase grid-connected inverter with PLL is considered as case study. It is demonstrated that the stability boundaries can be precisely evaluated by the proposed method, despite the non-linearity introduced by the PLL. Simulation and experimental results from a 10kW laboratory prototype are provided to confirm the effectiveness of the proposed analysis

Self-Organized Dynamics of Power Grids: Smart Grids, Fluctuations and Cascades

Climate change is one of the most pressing issues of our time and mitigating it requires a reduction of CO2 emissions. A big step towards achieving this goal is increasing the share of renewable energy sources, as the energy sector currently contributes 35% to all greenhouse gas emissions. However, integrating these renewable energy sources challenges the current power system in two major ways. Firstly, renewable generation consists of more spatially distributed and smaller power plants than conventional generation by nuclear or coal plants, questioning the established hierarchical structures and demanding a new grid design. Restructuring becomes necessary because wind and solar plants have to be placed at favorable sites, e.g., close to coasts in the case of wind. Secondly, renewables do not provide a deterministic and controllable power output but introduce power fluctuations that have to be controlled adequately. Many solutions to these challenges are build on the concept of smart grids, which require an extensive information technology (IT) infrastructure communicating between consumers and generators to coordinate efficient actions. However, an intertwined power and IT system raises great privacy and security concerns. Is it possible to forgo a large IT infrastructure in future power grids and instead operate them purely based on local information? How would such a decentrally organized system work? What is the impact of fluctuation on short time scales on the dynamical stability? Which grid topologies are robust against random failures or targeted attacks? This thesis aims to establish a framework of such a self-organized dynamics of a power grid, analyzing its benefits and limitations with respect to fluctuations and discrete events. Instead of a centrally monitored and controlled smart grid, we propose the concept of Decentral Smart Grid Control, translating local power grid frequency information into actions to stabilize the grid. This is not limited to power generators but applies equally to consumers, naturally introducing a demand response. We analyze the dynamical stability properties of this framework using linear stability methods as well as applying numerical simulations to determine the size of the basin of attraction. To do so, we investigate general stability effects and sample network motifs to find that this self-organized grid dynamics is stable for large parameter regimes. However, when the actors of the power grid react to a frequency signal, this reaction has to be sufficiently fast since reaction delays are shown to destabilize the grid. We derive expressions for a maximum delay, which always desynchronizes the system based on a rebound effect, and for destabilizing delays based on resonance effects. These resonance instabilities are cured when the frequency signal is averaged over a few seconds (low-pass filter). Overall, we propose an alternative smart grid model without any IT infrastructure and analyze its stable operating space. Furthermore, we analyze the impact of fluctuations on the power grid. First, we determine the escape time of the grid, i.e., the time until the grid desynchronizes when subject to stochastic perturbations. We simulate these events and derive an analytical expression using Kramer's method, obtaining the scaling of the escape time as a function of the grid inertia, transmitted power, damping etc. Thereby, we identify weak links in networks, which have to be enhanced to guarantee a stable operation. Second, we collect power grid frequency measurements from different regions across the world and evaluate their statistical properties. Distributions are found to be heavy-tailed so that large disturbances are more common than predicted by Gaussian statistics. We model the grid dynamics using a stochastic differential equation to derive the scaling of the fluctuations based on power grid parameters, identifying effective damping as essential in reducing fluctuation risks. This damping may be provided by increased demand control as proposed by Decentral Smart Grid Control. Finally, we investigate discrete events, in particular the failure of a single transmission line, as a complementary form of disturbances. An initial failure of a transmission line leads to additional load on other lines, potentially overloading them and thereby causing secondary outages. Hence, a cascade of failures is induced that propagated through the network, resulting in a large-scale blackout. We investigate these cascades in a combined dynamical and event-driven framework, which includes transient dynamics, in contrast to the often used steady state analysis that only solves static flows in the grid while neglecting any dynamics. Concluding, we identify critical lines, prone to cause cascades when failing, and observe a nearly constant speed of the propagation of the cascade in an appropriate metric. Overall, we investigate the self-organized dynamics of power grids, demonstrating its benefits and limitations. We provide tools to improve current grid operation and outline a smart grid solution that is not reliant on IT. Thereby, we support establishing a 100% renewable energy system

Addressing Instability Issues in Microgrids Caused By Constant Power Loads Using Energy Storage Systems

Renewable energy sources, the most reasonable fuel-shift taken over the naturally limited conventional fuels, necessarily deal with the self-functional microgrid system rather than the traditional grid distribution system. The study shows that the microgrid system, a comparatively low-powered system, experiences the challenge of instability due to the constant power load (CPL) from many electronic devices such as inverter-based systems. In this dissertation, as a methodical approach to mitigate the instability complication, AC microgrid stability is thoroughly investigated for each and every considerable parameter of the system. Furthermore, a specific loading limit is depicted by evaluating the stability margin from the small signal analysis of the microgrid scheme. After demonstrating all cases regarding the instability problem, the storage-based virtual impedance power compensation method is introduced to restore the system stability and literally extend the loading limit of the microgrid system. Here, a PID controller is implemented to maintain the constant terminal voltage of CPL via current injection method from storage. Since the system is highly nonlinear by nature, advanced nonlinear control techniques, such as Sliding Mode Control and Lyapunov Redesign Control technique, are implemented to control the entire nonlinear system. Robustness, noise rejection, and frequency variation are scrutinized rigorously in a virtual platform such as Matlab/Simulink with appreciable aftermaths. After that, a comparative analysis is presented between SMC and LRC controller robustness by varying CPL power. From this analysis, it is evident that Lyapunov redesign controller performs better than the previous one in retaining microgrid stability for dense CPL-loaded conditions. Finally, to ensure a robust storage system, Hybrid Energy Storage System is introduced and its advantages are discussed as extended research work