Non-linear stability of inverter-dominated power grids

对现有电力系统脱碳的持续推动与其中可再生能源的增加安装直接相关。这些可再生能源需要电力电子逆变器，以便将其连接到现有的电网。电力电子逆变器由控制算法主导，尽管与传统的同步发电机相比，它们可以在网络的操作和控制中提供更大的灵活性，但它们也为网络引入了新的和前所未有的动态，威胁着电力系统的稳定性。能否保证电网的稳定运行，避免对公众服务的中断，对未来电网的平稳运行至关重要。我的博士研究重点是研究电力电子高度渗透下的电网稳定性。更具体地说，它集中于研究和分析它们的暂态稳定性，这是大的干扰，如短路故障，线路断开和相位跳变，发生在它的系统的稳定性。所使用的电力电子逆变器分为两个主要类型的逆变器取决于他们的方法与电网的同步和他们的操作。这两种类型是电网跟随逆变器和电网形成逆变器，电网跟随逆变器通过形成电流并跟随电网电压向电网注入功率，电网形成逆变器形成可以从中汲取功率的电压源。这些类型的逆变器利用不同的同步控制器来维持它们与网络的同步，因此它们在来自电网的不同干扰下与网络的交互不同。我的研究旨在深入了解网络中发生干扰后的个体行为，并推导出关于如何在网络中配置和使用它们以尽可能减少系统潜在不稳定性的有价值的结论。该方法包括微分方程的分析推导，描述在不同情况下的逆变器的行为，并在一系列的网络配置。这些配置将包括连接到几个示例电网的不同数量的逆变器，覆盖不同强度和结构的电网，旨在覆盖大范围的可能场景，并得出这些逆变器如何影响系统稳定性的综合结果。导出的分析方程将用于执行系统的相平面分析，并获得对其行为的直观见解，以及采用用于研究非线性系统稳定性的其他技术和方法。这种分析之后将在仿真软件中对所研究的系统进行时域仿真，以验证所获得的理论结果。预计该分析将有助于电网系统运营商选择如何规划和配置他们的电网。

The continuous drive towards the decarbonisation of existing power systems is directly connected with the increasing installation of renewable energy resources in them. These renewable resources require power electronic inverters in order to interface them to the existing power networks. The power electronic inverters are dominated by control algorithms and despite the fact that they can offer increased flexibility in operation and control of the network compared to the traditional synchronous generators, they also introduce new and unprecedented dynamics to the network that are threatening the stability of the power systems. It is of vital importance for the smooth operation of future power networks to be able to guarantee the stability of the networks and avoid in this way interruption of services to the public. My PhD research focuses on investigating the stability of the power networks under high penetration of power electronics. More specifically it concentrates on studying and analysing their transient stability, which is the stability of the system after large disturbances, such as short circuit faults, line disconnections and phase jumps, take place in it. The power electronic inverters that are used are distinguished into two main types of inverter depending on their method of synchronisation with the grid and their operation. These two types are the Grid-Following inverters, which inject power to the grid by forming the current and following the grid's voltage and the Grid-Forming inverters which form a voltage source from which power can be drawn. These types of inverters utilize different synchronisation controllers to sustain their synchronisation with the network and therefore their interaction with the network under different disturbances from the grid differs. My research aims to provide insights into their individual behaviours after disturbances take place in the network and deduce valuable conclusions on how they should be configured and used in the network to reduce as much as possible potential instabilities to the system. The approach includes analytical derivations of differential equations describing the behaviour of the inverters under different circumstances and in a range of network configurations. These configurations will include different number of inverters connected to several example grids, covering grids of different strengths and structures aiming to cover a large range of possible scenarios and derive comprehensive results on how these inverters affect the system's stability. The derived analytical equations will be used to perform Phase Plane analysis of the systems and gain visual insights on their behaviours as well as employ other techniques and methods that are used for investigating the stability of non-linear systems. This analysis will be followed by time-domain simulations of the examined systems in simulation software for validation of theoretical results obtained. It is anticipated that the analysis will be useful to grid system operators in choosing how to plan and configure their power grids.