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Register a new userFrequency stability assessment of modern power systems: models definition and parameters identification
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One of the fundamental concerns in the operation of modern power systems is the assessment of their frequency stability in case of inertia-reduction induced by the large share of power electronic interfaced resources. Within this context, the paper proposes a framework that, by making use of linear models of the frequency response of different types of power plants, including also grid--forming and grid-following converters, is capable to infer a numerically tractable dynamical model to be used in frequency stability assessment. Furthermore, the proposed framework makes use of models defined in a way such that their parameters can be inferred from real-time measurements feeding a classical least squares estimator. The paper validates the proposed framework using a full-replica of the dynamical model of the IEEE 39 bus system simulated in a real-time platform.
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Stability of power grids with synchronous generators (SGs) and renewable generation interfaced with grid-forming converters (GFCs) under dc-side current limitation is studied. To that end, we first consider a simple 2-bus test system and reduced-order models to highlight the fundamental difference between two classes of GFC controls -- (A) droop, dispatchable virtual oscillator control (dVOC) and virtual synchronous machine (VSM), and (B) matching control. Next, we study Lyapunov stability and input-output stability of the dc voltage dynamics of class-A GFCs for the simple system and extend it to a generic system. Next, we provide a sufficiency condition for input-to-state stability of the 2-bus system with a class-B GFC and extend it for a generic system. Finally, time-domain simulations from a reduced-order averaged model of the simple test system and a detailed switched model of the GFC validate the proposed conditions.
This paper introduces the notion of quantitative resilience of a control system. Following prior work, we study systems enduring a loss of control authority over some of their actuators. Such a malfunction results in actuators producing possibly undesirable inputs over which the controller has real-time readings but no control. By definition, a system is resilient if it can still reach a target after a loss of control authority. However, after a malfunction a resilient system might be significantly slower to reach a target compared to its initial capabilities. We quantify this loss of performance through the new concept of quantitative resilience. We define this metric as the maximal ratio of the minimal times required to reach any target for the initial and malfunctioning systems. Naive computation of quantitative resilience directly from the definition is a time-consuming task as it requires solving four nested, possibly nonlinear, optimization problems. The main technical contribution of this work is to provide an efficient method to compute quantitative resilience. Relying on control theory and on three novel geometric results we reduce the computation of quantitative resilience to a single linear optimization problem. We illustrate our method on two numerical examples: an opinion dynamics scenario and a trajectory controller for low-thrust spacecrafts.
In this paper, we develop a compositional scheme for the construction of continuous approximations for interconnections of infinitely many discrete-time switched systems. An approximation (also known as abstraction) is itself a continuous-space system, which can be used as a replacement of the original (also known as concrete) system in a controller design process. Having designed a controller for the abstract system, it is refined to a more detailed one for the concrete system. We use the notion of so-called simulation functions to quantify the mismatch between the original system and its approximation. In particular, each subsystem in the concrete network and its corresponding one in the abstract network are related through a notion of local simulation functions. We show that if the local simulation functions satisfy certain small-gain type conditions developed for a network containing infinitely many subsystems, then the aggregation of the individual simulation functions provides an overall simulation function quantifying the error between the overall abstraction network and the concrete one. In addition, we show that our methodology results in a scale-free compositional approach for any finite-but-arbitrarily large networks obtained from truncation of an infinite network. We provide a systematic approach to construct local abstractions and simulation functions for networks of linear switched systems. The required conditions are expressed in terms of linear matrix inequalities that can be efficiently computed. We illustrate the effectiveness of our approach through an application to AC islanded microgirds.
The transient stability of power systems and synchronization of non-uniform Kuramoto oscillators are closely related problems. In this paper, we develop a novel regional stability analysis framework based on the proposed region-parametrized Lyapunov function to solve the problems. Also, a new synchronization definition is introduced and characterized by frequency boundedness and angle cohesiveness, the latter of which requires angles of any two connected nodes rather than any two arbitrary nodes to stay cohesive. It allows to take power fluctuations into explicit account as disturbances and can lead to less conservative stability condition. Applying the analysis framework, we derive two algebraic stability conditions for power systems that relate the underlying network topology and system parameters to the stability. Finally, to authors best knowledge, we first explicitly give the estimation of region of attraction for power systems. The analysis is verified via numerical simulation showing that two stability conditions can complement each other for predicting the stability.
As one important means of ensuring secure operation in a power system, the contingency selection and ranking methods need to be more rapid and accurate. A novel method-based least absolute shrinkage and selection operator (Lasso) algorithm is proposed in this paper to apply to online static security assessment (OSSA). The assessment is based on a security index, which is applied to select and screen contingencies. Firstly, the multi-step adaptive Lasso (MSA-Lasso) regression algorithm is introduced based on the regression algorithm, whose predictive performance has an advantage. Then, an OSSA module is proposed to evaluate and select contingencies in different load conditions. In addition, the Lasso algorithm is employed to predict the security index of each power system operation state with the consideration of bus voltages and power flows, according to Newton-Raphson load flow (NRLF) analysis in post-contingency states. Finally, the numerical results of applying the proposed approach to the IEEE 14-bus, 118-bus, and 300-bus test systems demonstrate the accuracy and rapidity of OSSA.
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