If a disturbance rocks a low-inertia power system, the frequency decline may be too rapid to arrest before it triggers undesirable responses from generators and loads. In the worst case, this instability could lead to blackout and major equipment damage. Electric utilities, to combat this, study inertia adequacy in systems that are particularly vulnerable. This process, involving detailed transient simulations, usually leads to a notion of a system-wide inertia floor. Ongoing questions in this analysis are in how to set the inertial floor and to what extent the location of frequency control resources matters. This paper proposes a new analysis technique that quantifies theoretical locational rate of change of frequency (ROCOF) as a computationally efficient screening algorithm scalable to large systems. An additional challenge in moving this area forward is the lack of high-quality, public benchmark dynamics cases. This paper presents a synthetic case for such purposes and a methodology for validation, to ensure that it is well suited to inertia adequacy studies to improve electric grid performance.
This study examines the transient stability of low-inertia power systems with inverter-based generation (IBG) and proposes a sufficient stability criterion. In low-inertia grids, transient interactions are induced between the electromagnetic dynamics of the IBG and the electromechanical dynamics of the synchronous generator (SG) under a fault. For this, a hybrid IBG-SG system is established and a delta-power-frequency model is developed. Based on this model, new mechanisms of transient instability different from those of conventional power systems from the energy perspective are discovered. Fi…
Coupled nonlinear oscillators, e.g., Kuramoto models, are commonly used to analyze electrical power systems. The cage model from statistical mechanics has also been used to describe the dynamics of synchronously connected generation stations. Whereas the Kuramoto model is good for describing high inertia grid systems, the cage one allows both high and low inertia grids to be modelled. This is illustrated by comparing both the synchronization time and relaxation towards synchronization of each model by treating their equations of motion in a common framework rooted in the dynamics of many coupl…
The virtual synchronous generator technology analogs the characteristics of the synchronous generator via the controller design. It improved the stability of the grid systems which include the new energy. At the same time, according to the adjustable characteristics of the virtual synchronous generator parameters, the parameter adaptive adjustment is used to improve the dynamic performance of the system. However, the traditional virtual synchronous generator adaptive control technology still has two drawbacks: on the one hand, the large-scale adjustment of the damping droop coefficient and the…
The grid-following and grid-forming controls in voltage-source converters are considered as different operation modes and the synchronization mechanism of them are studied separately. In this article, the intrinsic relationships between gridfollowing and grid-forming controlled converters are established as follows: 1) the proportional gain of PLL is in inverse proportion to damping; 2) the integral gain of PLL is similar to integral droop; 3) PLL has no practical inertia but acts like grid-forming control in zero inertia cases. Further, a general stability-enhanced method combining damping an…
The absolute requirement to increase the amount of energy generation from renewable sources e.g. predominantly asynchronously connected wind turbines and photovoltaic installations, may in practice during transient events (where frequency changes are examined) excite oscillatory response of the power output of large grid connected synchronous-generators. The response of such generators must be controlled either by varying the applied torque of a turbine or by altering the electromagnetic torque in the airgap. Choosing the latter, the adequacy of a voltage regulator, particularly that of the em…
Transient frequency dips that follow sudden power imbalances --frequency Nadir-- represent a big challenge for frequency stability of low-inertia power systems. Since low inertia is identified as one of the causes for deep frequency Nadir, virtual inertia, which is provided by energy storage units, is said to be one of the solutions to the problem. In the present paper, we propose a new method for frequency control with energy storage systems (ESS), called dynamic droop control (iDroop), that can completely eliminate frequency Nadir during transients. Nadir elimination allows us to perform fre…
This paper investigates the transient stability of power systems co-dominated by different types of grid-forming (GFM) devices. Synchronous generators (SGs and VSGs) and droop-controlled inverters are typical GFM devices in modern power systems. SGs/VSGs are able to provide inertia while droop-controlled inverters are generally inertialess. The transient stability of power systems dominated by homogeneous GFM devices has been extensively studied. Regarding the hybrid system jointly dominated by heterogeneous GFM devices, the transient stability is rarely reported. This paper aims to fill this …
The integration of converter-interfaced generation (CIG) from renewable energy sources poses challenges to the stability and transient behavior of electric power systems. Understanding the dynamic behavior of low-inertia power systems is critical to addressing these stability questions. However, there is a limited availability of open source tools explicitly geared towards low-inertia systems modeling. In this paper, we develop an open source simulation toolbox to study transient responses under high penetration scenarios. LITS.jl is implemented in the Julia computing language and features mul…
Virtual inertia is an effective control approach to attenuate sudden voltage changes during transient events in low-inertia DC grids. While methods have been proposed to implement virtual inertia, its impact on DC grid stability in the presence of constant power loads (CPLs) remains unclear. In this paper, we perform a rigorous stability analysis for DC grids with CPLs powered by virtual-inertia-enhanced converters. We derive a closed-form stability criterion that can be used to evaluate the impact of virtual inertia on the system stability, and demonstrate that, given a set of system paramete…
This paper presents a trajectory tracking control strategy that modulates the active power injected by geographically distributed inverter-based resources to support transient stability. Each resource is independently controlled, and its response drives the local bus voltage angle toward a trajectory that tracks the angle of the center of inertia. The center-of-inertia angle is estimated in real time from wide-area measurements. The main objectives are to stabilize transient disturbances and increase the amount of power that can be safely transferred over key transmission paths without loss of…
Unlike conventional generators, inverter-based generation do not possess any rotational inertia. While grid-forming inverters can synthesize small (virtual) inertia via advanced feedback control loops, additional control mechanisms are needed to ensure safety and security of the power grid during transients. In this paper, we propose novel real-time safety-constrained feedback controllers ("safety filters") for droop-based (grid-forming) inverters to ensure transient security of the grid. The safety filter acts as a buffer between the network operational layer and the inverter-control layer, a…
The infusion of renewable energy sources into the conventional synchronous generation system decreases the overall system inertia and negatively impacts the stability of its primary frequency response. The lowered inertia is due to the absence of inertia in some of the renewable energy-based systems. To maintain the stability of the system, we need to keep the frequency in the permissible limits and maintain low rotational inertia. Some authors in the literature have used the virtual synchronous generators (VSG) as a solution to this problem. Although the VSG based distributed recourses (DER) …
Time-domain simulations are a critical tool for power system operators. Depending on the instability mechanism under consideration and the system characteristics, such as the time constants of controllers, either phasor or Electro-Magnetic Transient (EMT) models should be employed. On the one hand, EMT models provide a detailed-modeling of the system dynamics, thus increase the reliability of stability analysis; on the other end, using these models increase the computational times of simulations, slowing down the security assessment process. To decrease computational time, system operators cou…
Grid-forming voltage source converter (GF-VSC) has been identified as the key technology for the operation of future converter-dominated power systems. Among many other issues, transient stability of this type of power systems remains an open topic of research because it is still a key limiting factor for stressed power systems. Previous studies have proposed control strategies for GF-VSC to improve transient stability of this type of systems by suitable current-limitation algorithms and/or control of active-power injections. As an alternative, this paper proposes two fast voltage boosters to …
The growing penetration of distributed energy resources (DERs) has increased the complexity of the power system due to their intermittent characteristics and lower inertial response, such as photovoltaic (PV) systems and wind turbines. This restructuring of the power system has a considerable effect on the transient response of the system resulting in inter-area oscillations, less synchronized coupling and power swings. Furthermore, the concept of being distributed itself and generating electricity from multiple locations in the power system makes the transient impact of DERs even worse by rai…
Research on Adaptive Inertial Control in Synchronization Systems: Based on Variational Optimization Methods and Their Applications in the Stability of Complex Networks
Department of Automation, School of Robotics, Wuhan University（武汉大学机器人学院自动化系）
Transient stability of power systems is becoming increasingly important because of the growing integration of renewable resources. These resources lead to a reduction in mechanical inertia but also provide increased flexibility in frequency responses. Namely, their power electronic interfaces can implement almost arbitrary control laws. To design these controllers, reinforcement learning (RL) has emerged as a powerful method in searching for optimal non-linear control policy parameterized by neural networks. A key challenge is to enforce that a learned controller must be stabilizing. This pape…
Nodal Braess's Paradox and Inertia Destabilization with Dynamic Node and Line Failures in Power Grids
Potsdam Institute for Climate Impact Research (PIK)（波茨坦气候影响研究所）；Reiner Lemoine Institut gGmbH（莱纳·莱莫因研究所）；Technische Universität Berlin（柏林工业大学）；Humboldt-Universität zu Berlin（柏林洪堡大学）；Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG（弗劳恩霍夫能源基础设施和岩土技术研究院）
As the share of renewable sources is increasing the need for multiple storage units appropriately sized and located is essential to achieve better inertial response. This work focuses on the question of "how to distribute constant number of storage units in the gird under transient events such that the inertial response of the maximum frequency deviation is minimized?". To answer this question, we provide a comprehensive modeling framework for energy storage units placement and size for frequency stability under spatial effects. The distributed storage units are modeled as grid supporting inve…
A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the grid's stiffness. In this paper, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverter-based frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies --droop control (DC) and virtual inertia (VI)-- on several performance metrics induced by $\mathcal L_2$ and…
Inverter-connected resources can improve transient stability in low-inertia grids by injecting active power to minimize system frequency deviations following disturbances. In practice, most generation and load disturbances are step changes and the engineering figure-of-merit is often the peak overshoot in frequency resulting from these step disturbances. In addition, the inverter-connected resources tend to saturate much more easily than conventional synchronous machines. However, despite these challenges, standard controller designs must deal with averaged quantities through $H_2$ or $H_\inft…
