arXiv subjects

Tianwei Xia

Publications and source records attributed to Tianwei Xia.

5 recordsLinked to original sources

arXiv2025

On the Uniqueness of Participation Factors in Nonlinear Dynamical Systems

In the modal analysis and control of nonlinear dynamical systems, the participation factors of state variables with respect to a critical or selected mode serve as a pivotal tool for simplifying stability studies by focusing on a subset of highly influential state variables. For linear systems, the participation factors of state variables regarding a mode are uniquely determined by the mode's composition and shape, defined by the system's left and right eigenvectors, respectively. However, the uniqueness of other types of participation factors necessitates further investigation. This paper establishes a sufficient condition for the uniqueness of nonlinear participation factors and five other variants of participation factors, accounting for uncertain scaling factors in a mode's shape and composition. These scaling factors arise from variations in the selection of physical units or the value ranges of state variables when analyzing and controlling real-world dynamical systems. Understanding the sufficient condition of the uniqueness is therefore crucial for the correct application of participation factors in practical scenarios. Additionally, the paper explores the relationship between perturbation magnitudes in state variables and the selection of optimal scaling factors.

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arXiv2024

Estimation of Participation Factors for Power System Oscillation from Measurements

In a power system, when the participation factors of generators are computed to rank their participations into an oscillatory mode, a model-based approach is conventionally used on the linearized system model by means of the corresponding right and left eigenvectors. This paper proposes a new approach for estimating participation factors directly from measurement data on generator responses under selected disturbances. The approach computes extended participation factors that coincide with accurate model-based participation factors when the measured responses satisfy an ideally symmetric condition. This paper relaxes this symmetric condition with the original measurement space by identifying and utilizing a coordinate transformation to a new space optimally recovering the symmetry. Thus, the optimal estimates of participation factors solely from measurements are achieved, and the accuracy and influencing factors are discussed. The proposed approach is first demonstrated in detail on a two-area system and then tested on an NPCC 48-machine power system. The penetration of inverter-based resources is also considered.

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arXiv2022

Time-variant Nonlinear Participation Factors Considering Resonances in Power Systems

The participation factor (PF), as an important modal property for small-signal stability, evaluates the linkage between a state variable and a mode. Applying the normal form theory, a nonlinear PF can be defined to evaluate the participation of a state variable into modal dynamics following a large disturbance, that gives considerations to resonances and nonlinearities up to a desired order. However, existing nonlinear PFs are inconsistent with the conventional linear PF when nonlinear dynamics following a large disturbance attenuate and linear modal dynamics become dominating. This paper proposes a time-variant nonlinear PF by introducing a time decaying factor and the definition of a nonlinear mode. The new PFs consider modes of resonances and their values naturally transition to a linear PF when the system state becomes close to its equilibrium. The case study on a two-area four-generator system shows that the new PF can correctly rank generators by their participations in natural and resonance modes of nonlinear oscillation subject to a large disturbance.

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arXiv2022

Machine Learning based Optimal Feedback Control for Microgrid Stabilization

Microgrids have more operational flexibilities as well as uncertainties than conventional power grids, especially when renewable energy resources are utilized. An energy storage based feedback controller can compensate undesired dynamics of a microgrid to improve its stability. However, the optimal feedback control of a microgrid subject to a large disturbance needs to solve a Hamilton-Jacobi-Bellman problem. This paper proposes a machine learning-based optimal feedback control scheme. Its training dataset is generated from a linear-quadratic regulator and a brute-force method respectively addressing small and large disturbances. Then, a three-layer neural network is constructed from the data for the purpose of optimal feedback control. A case study is carried out for a microgrid model based on a modified Kundur two-area system to test the real-time performance of the proposed control scheme.

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arXiv2020

Extended Prony Analysis on Power System Oscillation Under a Near-Resonance Condition

Power system oscillations under a large disturbance often exhibit distorted waveforms as captured by increasingly deployed phasor measurement units. One cause is the occurrence of a near-resonance condition among several dominant modes that are influenced by nonlinear transient dynamics of generators. This paper proposes an Extended Prony Analysis method for measurement-based modal analysis. Based on the normal form theory, it compares analyses on transient and post-transient waveforms to distinguish a resonance mode caused by a near-resonance condition from natural modes so that the method can give more accurate modal properties than a traditional Prony Analysis method, especially for large disturbances. The new method is first demonstrated in detail on Kundur's two-area system and then tested on the IEEE 39-bus system to show its performance under a near-resonance condition.

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