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, and only lets those dispatch control signals pass to the inverter droop-controller, which are guaranteed to not violate the safety specifications (frequency, voltage, current limits). Using a distributed barrier certificates method, we construct state-inclusive bounds on the allowable control inputs, which guarantee the satisfaction of transient safety specifications. Sum-of-square programming is used to synthesize the safety filters. Numerical simulation results are provided to illustrate the performance of the proposed filter in inverter-based microgrids.
The fundamental mechanism of transient stability of the conventional power system can be physically understood with the rotor swing dynamics of synchronous generators (SGs). The basic factor affecting the transient stability is the power-angle relationship among the SGs. The integration of a large number of inverter-based generations (IBGs) into the power system inevitably changes the original power-angle relationship, therefore leading to a more complicated transient stability mechanism. In this letter, the impact of IBG on the power system transient stability is analytically investigated. It…
Due to the rise of distributed energy resources, the control of networks of grid-forming inverters is now a pressing issue for power system operation. Droop control is a popular control strategy in the literature for frequency control of these inverters. In this paper, we analyze transient stability in droop-controlled inverter networks that are subject to multiple operating constraints. Using a physically-meaningful Lyapunov-like function, we provide two sets of criteria (one mathematical and one computational) to certify that a post-fault trajectory achieves frequency synchronization while r…
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…
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…
Modern safety-critical energy infrastructures are increasingly operated in a hierarchical and modular control framework which allows for limited data exchange between the modules. In this context, it is important for each module to synthesize and communicate constraints on the values of exchanged information in order to assure system-wide safety. To ensure transient safety in inverter-based microgrids, we develop a set invariance-based distributed safety verification algorithm for each inverter module. Applying Nagumo's invariance condition, we construct a robust polynomial optimization proble…
An islanded microgrid supplied by multiple distributed energy resources (DERs) often employs droop-control mechanisms for power sharing. Because microgrids do not include inertial elements, and low pass filtering of noisy measurements introduces lags in control, droop-like controllers may pose significant stability concerns. This paper aims to understand the effects of droop-control on the small-signal stability and transient response of the microgrid. Towards this goal, we present a compendium of results on the small-signal stability of droop-controlled inverter-based microgrids with heteroge…
This paper developed a novel control approach for the sparse and safe frequency regulation for inverter intensive microgrids (MGs). In the scenario, the inverters and external grids are expected to reach a synchronized desired frequency under regulations. To this end, the active power set-point acting as a control from a high-level controller is designed while considering two important performance metrics "sparsity" and "safety", which are to reduce the information exchange between controllers and ensure that the frequency keeps in safety regions during the whole operation process. Our propose…
Relative-Degree Wall Restricts Passivity-Based Stability Analysis in Inverter-Dominant Grids
Tsinghua University（清华大学）；State Key Laboratory of Power System Operation and Control, Tsinghua University（电力系统运行与控制国家重点实验室，清华大学）；Power Dispatch Control Center, Guangdong Power Grid Corporation（广东电网有限责任公司电力调度控制中心）
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 …
Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on duality is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and g…
Power system restoration is an important part of system planning. Power utilities are required to maintain black start capable generators that can energize the transmission system and provide cranking power to non-blackstart capable generators. Traditionally, hydro and diesel units are used as black start capable generators. With the increased penetration of bulk size solar farms, inverter based generation can play an important role in faster and parallel black start thus ensuring system can be brought back into service without the conventional delays that can be expected with limited black st…
This article proposes the design of H-infinity-based robust current controller for single-phase grid-feeding voltage source inverter with an LCL filter. The main objective of the proposed controller is to have good reference tracking, disturbance rejection and sufficient LCL resonance damping under a large range of variations of grid impedance. Based on the aforementioned performance requirements, frequency dependent weighting functions are designed. Subsequently, the sub-optimal control problem is formulated and solved to determine the stabilizing controller. Computational footprint of the co…
In commercial inverters, an LCL filter is considered an integral part to filter out the switching harmonics and generate a sinusoidal output voltage. The existing literature on the averaged virtual oscillator controller (VOC) dynamics is for current feedback before the output LCL filter that contains the switching harmonics or for inductive filters ignoring the effect of filter capacitance. In this work, a new version of averaged VOC dynamics is presented for islanded inverters with current feedback after the LCL filter thus avoiding the switching harmonics going into the VOC. The embedded dro…
Synchronous generators and inverter-based resources are complex systems with dynamics that cut across multiple intertwined physical domains and control loops. Modeling individual generators and inverters is, in itself, a very involved activity and has attracted dedicated attention from power engineers and control theorists over the years. Control and stability challenges associated with increasing penetration of grid-following inverters have generated tremendous interest in grid-forming inverter technology. The envisioned coexistence of inverter technologies alongside rotating machines call fo…
With increased attention on grid-forming inverters as a power system stabilizing device during periods of high shares of inverter-based resource operations, there is a present need for a transparent and rigorous investigation of the inverted and direct power to frequency control capabilities, and associated impacts, of these devices on hybrid systems. Here, analysis of the frequency dynamics of the droop controlled grid-forming inverter and the synchronous generator illuminates the inverted active power-frequency relationship and the frequency response order reduction, forming the basis for no…
This paper presents a novel control structure and control synthesis method for regulating the output voltage/frequency and power injection of DC-AC inverters. The traditional droop method offers attractive solution to achieve compromise between clashing power and voltage/frequency regulation objectives. However, it relies on use of nonlinear power variables through slow outer control loop. In this paper we formulate the traditional droop method as a feedback control problem based on static power-flow equations and show how neglecting the dynamics of inverter and transmission line restricts the…
