arXiv subjects

Xi Ru

Publications and source records attributed to Xi Ru.

8 recordsLinked to original sources

arXiv2026

Relative-Degree Wall Restricts Passivity-Based Stability Analysis in Inverter-Dominant Grids

This letter reveals a fundamental limitation of passivity-based distributed stability analysis in power systems. Under the standard formulation, passivity certification inherently imposes a relative-degree compatibility constraint that excludes many high-fidelity inverter dynamic models (e.g., those that include electromagnetic transients). Potential extensions of passivity frameworks are discussed to break this limitation.

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arXiv2026

When Can Phasor-Domain Device Models Be Trusted for Electromechanical Stability Analysis of Grid-Forming Converter-Dominated Microgrids?

Grid-forming (GFM) converter-dominated microgrids are often analyzed using reduced-order phasor-domain electromechanical GFM models, but the validity of these models is often taken for granted. Assuming ideal inner-loop tracking (IILT) of terminal-voltage references, these models neglect the inner-loop and filter dynamics at the electromagnetic-transient (EMT) timescale to simplify stability analysis. This paper argues that such neglected dynamics can destabilize the system, invalidating the stability conclusions drawn from the IILT model. To address this cross-timescale stability issue, we formulate the validity of the IILT stability conclusion as a robust-stability certification problem. The EMT-induced model mismatch between the reduced-order converter model and the actual converter model is represented as a structured uncertainty embedded around the IILT feedback loop. This yields a frequency-resolved interaction index and a structured singular-value sufficient certificate for determining when the stability conclusion of the IILT model can be certified with respect to a prescribed EMT uncertainty weight. The uncertainty weight can be obtained from detailed EMT models or terminal reference-response measurements. Case studies confirm that the proposed certificate correctly certifies model validity and identifies the loss of trustworthiness. We also demonstrate that the measurement-based uncertainty weights closely match the model-based ones, which enables deployment without accessing inner-loop models.

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arXiv2026

Equilibrium-Free Contraction Stability Analysis for Grid-Forming Converter-Based Microgrids

Renewable-driven microgrids dominated by grid-forming (GFM) converters are subject to persistent power fluctuations, making equilibrium-known stability assessments restrictive. This paper develops an equilibrium-free contraction stability method based on semi-contraction theory. By formulating the system in a symmetry-aware projected state space, the intrinsic rotational mode induced by uniform angle shifts is removed. A blockwise Jacobian decomposition is introduced to characterize the coupled active and reactive power dynamics, yielding a computable regional contraction condition. This condition is then converted into forward-invariant stability certificates that provide trajectory-level performance guarantees. For autonomous operation without disturbances, the method provides an equilibrium-free nonlinear stability characterization together with an estimation of the region of attraction (ROA). For non-autonomous operation under disturbances, it derives explicit bounds for quasi-steady tracking under slowly varying injections and for robustness under fast or composite disturbances. Case studies on a 9-bus system validate the proposed method.

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arXiv2026

Toward less conservative distributed stability analysis of power systems via matrix-valued differential passivity indices

Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can introduce excessive conservatism and compromise analysis accuracy. To overcome these limitations, this paper extends the differential passivity index to a matrix-valued formulation that captures both channel-wise passivity properties and inter-channel coupling effects in MIMO subsystems. On this basis, semi-distributed and fully distributed stability criteria are developed for power systems with heterogeneous nonlinear devices. It is shown that system stability is guaranteed when the aggregate passivity excess of devices compensates for the passivity shortage imposed by the network. Furthermore, analytical passivity matrix expressions for typical power system components are derived, facilitating compositional stability analysis. Case studies on a three-bus system and a modified IEEE 118-bus system validate the effectiveness of the proposed framework.

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arXiv2026

Positive Damping Region: A Graphic Tool for Passivization Analysis with Passivity Index

This paper presents a geometric framework for analyzing output-feedback and input-feedforward passivization of linear time-invariant systems. We reveal that a system is passivizable with a given passivity index when the Nyquist plot for SISO systems or the Rayleigh quotient of the transfer function for MIMO systems lies within a specific, index-dependent region in the complex plane, termed the positive damping region. The criteria enable a convenient graphic tool for analyzing the passivization, the associated frequency bands, the maximum achievable passivity index, and the waterbed effect between them. Additionally, the tool can be encoded into classical tools such as the Nyquist plot, the Nichols plot, and the generalized KYP lemma to aid control design. Finally, we demonstrate its application in passivity-based power system stability analysis and discuss its implications for electrical engineers regarding device controller design trade-offs.

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arXiv2026

Matrix-Valued Passivity Indices: Foundations, Properties, and Stability Implications

The passivity index, a quantitative measure of a system's passivity deficiency or excess, has been widely used in stability analysis and control. Existing studies mostly rely on scalar forms of indices, which are restrictive for multi-input, multi-output (MIMO) systems. This paper extends the classical scalar indices to a systematic matrix-valued framework, referred to as passivity matrices. A broad range of classical results in passivity theory can be naturally generalized in this framework. We first show that, under the matrix representation, passivity indices essentially correspond to the curvature of the dissipativity functional under a second-variation interpretation. This result reveals that the intrinsic geometric structure of passivity consists of its directions and intensities, which a scalar index cannot fully capture. For linear time-invariant (LTI) systems, we examine the structural properties of passivity matrices with respect to the Loewner partial order and propose two principled criteria for selecting representative matrices. Compared with conventional scalar indices, the matrix-valued indices capture the passivity coupling among different input-output channels in MIMO systems and provide a more comprehensive description of system passivity. This richer information leads to lower passivation effort and less conservative stability assessment.

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arXiv2025

Controlled Evolution-Based Day-Ahead Robust Dispatch Considering Frequency Security with Frequency Regulation Loads and Curtailable Loads

With the extensive integration of volatile and uncertain renewable energy, power systems face significant challenges in primary frequency regulation due to instantaneous power fluctuations. However, the maximum frequency deviation constraint is inherently non-convex, and commonly used two-stage dispatch methods overlook causality, potentially resulting in infeasible day-ahead decisions. This paper presents a controlled evolution-based day-ahead robust dispatch method to address these issues. First, we suggest the convex relaxation technique to transform the maximum frequency deviation constraint to facilitate optimization. Then, an evolution-based robust dispatch framework is introduced to align day-ahead decisions with intraday strategies, ensuring both frequency security and power supply reliability. Additionally, a novel controlled evolution-based algorithm is developed to solve this framework efficiently. Case studies on a modified IEEE 14-bus system demonstrate the superiority of the proposed method in enhancing frequency security and system reliability.

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arXiv2025

Compositional and Equilibrium-Free Conditions for Power System Stability -- Part I: Theory

Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove that using equilibrium-free local conditions we can certificate system-wide stability of power systems with heterogeneous nonlinear devices and structure-preserving lossy networks. This is built on a recently developed notion of delta dissipativity, which yields local stability conditions without knowing the system-wide equilibrium. As a consequence, our proposed theory can certificate stability of equilibria set rather than single equilibrium. In Part I, we verify our theory and demonstrate promising implications by the single machine single load benchmark, which helps to better explain the compositional and equilibrium-set-oriented stability analysis. Part II of this paper will provide methods for applying our theory to complex power grids, together with case studies across a wide range of system scales. Our results enable a more scalable and adaptable approach to stability analysis. It also sheds light on how to regulate grid-connected devices to guarantee system-wide stability.

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