arXiv subjects

Timothy C. Green

Publications and source records attributed to Timothy C. Green.

11 recordsLinked to original sources

arXiv2026

An Admittance-Based Inverter Connection Screening Tool for Small-Signal System Strength

The increasing occurrence of small-signal instability, particularly sub-synchronous oscillations (SSOs), in power systems with a high penetration of inverter-based resources (IBRs) has made the planning of new IBR connections increasingly important and challenging. The impact of such connections on small-signal stability is not always straightforward, as it strongly depends on the connection location, inverter operating mode, control configuration, parametrisation, and operating conditions. This paper proposes an inverter connection screening tool (ICST) that enables efficient and accurate assessment of the impact of prospective inverter configurations on small-signal system strength. It can identify, among the candidates considered, the most suitable inverter configuration for a given connection location that avoids degrading small-signal system strength and can also enhance it. As a result, higher IBR penetration can be supported while maintaining small-signal stability. The ICST evaluates candidate inverter configurations using their admittances at critical modal frequencies, along with the system's admittance spectrum, thereby avoiding the need for analytical models. The ICST-based planning procedure, which can support system operators, asset owners, and IBR developers in decision-making across different stages of planning studies, is demonstrated using a modified IEEE 57-bus system. Comparisons with model-based studies demonstrate the accuracy of the ICST in predicting the modal impact of inverter connections and its effectiveness in selecting suitable inverter control configurations.

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arXiv2026

Consideration of Control-Loop Interaction in Transient Stability of Grid-Following Inverters using Bandwidth Separation Method

Grid-following inverters have been widely adopted as a grid interface for renewable energy, and ensuring their small-signal and large-signal stability is critical to modern power systems. Their large-signal, or transient, stability is a significant challenge to analyze because of the interaction of the phase-locked loop (PLL), which must maintain synchronism with various outer-loop controllers. Simple analysis in which outer-loop controllers are idealized is insufficient, and the interactions between the nonlinear dynamics of the PLL and the dynamics of the DC-link voltage control (DVC), as well as the AC terminal voltage control (TVC) when present, must be considered. An asymptotic analysis approach, termed the bandwidth separation method, is proposed. This method enables simplification and order reduction of the original differential equations when sufficient bandwidth separation exists. Through this method, the interaction between the DVC and PLL is explicitly characterized, revealing that such interaction degrades system stability and shrinks the stability region. The analysis also indicates that voltage instability, rather than PLL loss of synchronization alone, is often the root cause of transient instability. Optimal bandwidth configurations for the PLL and DVC are identified under various grid fault conditions: a larger PLL bandwidth improves resilience to phase-jump faults, while a larger DVC bandwidth enhances tolerance to power fluctuations. In addition, the influence of the TVC loop is analyzed, showing that a high TVC bandwidth can mitigate the destabilizing effects of PLL-DVC interaction and further improve transient stability. All analytical findings are validated through hardware-in-the-loop (HIL) experiments.

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arXiv2025

Large-Signal Stability of Power Systems with Mixtures of GFL, GFM and GSP Inverters

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators, and convenient concepts such as the equal-area criterion and global energy function do not apply in the same way. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates the interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine the stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This paper establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to accurately determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used based on multiscale analysis. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, which is called the stability radius (SR). Using the proposed framework, the analysis reults of two-inverter system show that both GFM and GSP inverters significantly enhance the large-signal stability of a two-inverter system where the other inverter is GFL, with GFM providing slightly superior performance. This improvement is attributed to the voltage support effects and is maximized when the GFM or GSP inverter is located at the midpoint of the transmission line, where the voltage is lowest. All findings in this paper are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.

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arXiv2024

Reserve Provision from Electric Vehicles: Aggregate Boundaries and Stochastic Model Predictive Control

Controlled charging of electric vehicles, EVs, is a major potential source of flexibility to facilitate the integration of variable renewable energy and reduce the need for stationary energy storage. To offer system services from EVs, fleet aggregators must address the uncertainty of individual driving and charging behaviour. This paper introduces a means of forecasting the service volume available from EVs by considering several EV batteries as one conceptual battery with aggregate power and energy boundaries. Aggregation avoids the difficult prediction of individual driving behaviour. The predictability of the boundaries is demonstrated using a multiple linear regression model which achieves a normalised root mean square error of 20% - 40% for a fleet of 1,000 EVs. A two-stage stochastic model predictive control algorithm is used to schedule reserve services on a day-ahead basis addressing risk trade-offs by including Conditional Value-at-Risk in the objective function. A case study with 1.2 million domestic EV charge records from Great Britain illustrates that increasing fleet size improves prediction accuracy, thereby increasing reserve revenues and decreasing an aggregator's operational costs. For fleet sizes of 400 or above, cost reductions plateau at 60% compared to uncontrolled charging, with an average of 1.8kW of reserve provided per vehicle.

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arXiv2023

The Intrinsic Communication in Power Systems: A New Perspective to Understand Synchronization Stability

Synchronization is an essential element in three-phase ac electric power systems. The large-scale integration of converter-interfaced resources leads to the power grid transformation from voltage-source-dominated to voltage-current-source-composite, which also raises new challenges to model and analyze the system synchronization. In this article, we present the intrinsic analogy of a power system to a communication system, which is here called power-communication isomorphism. Based on this isomorphism, we revisit power system synchronization stability from a communication perspective and thereby establish a theory that unifies the synchronization dynamics of heterogeneous power apparatuses. In particular, the proposed theory is used to interpret and analyze, for example, the different power control speeds of power apparatuses; the role of network line dynamics in synchronization analysis; and the synchronization capability of current-source-dominated (e.g., grid-following-converter-dominated) grids. The findings are verified on the IEEE 68-bus test system.

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arXiv2023

Descriptor State Space Modeling of Power Systems

State space is widely used for modeling power systems and analyzing their dynamics but it is limited to representing causal and proper systems in which the number of zeros does not exceed the number of poles. In other words, the system input, output, and state can not be freely selected. This limits how flexibly models are constructed, and in some circumstances, can introduce errors because of the addition of virtual elements in order to connect the mismatched ports of subsystem models. An extension known as descriptor state space can model both proper and improper systems and is a promising candidate for solving the noted problems. It facilitates a modular construction of power system models with flexible choice of ports of subsystems. Algorithms for mathematical manipulation of descriptor state space models are derived such as preforming inverse, connection, and transform. Corresponding physical interpretations are also given. Importantly, the proposed algorithms preserve the subsystem states in the whole system model, which therefore enables the analysis of root causes of instability and mode participation. Theoretical advances are validated by example power systems of varied scales including a single-inductor or -capacitor system, two-inductor or -capacitor system, and a modified IEEE 14-bus generator-inverter-composite system.

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arXiv2022

Impedance-based Root-cause Analysis: Comparative Study of Impedance Models and Calculation of Eigenvalue Sensitivity

Impedance models of power systems are useful when state-space models of apparatus such as inverter-based resources (IBRs) have not been made available and instead only black-box impedance models are available. For tracing the root causes of poor damping and tuning modes of the system, the sensitivity of the modes to components and parameters are needed. The so-called critical admittance-eigenvalue sensitivity based on nodal admittance model has provided a partial solution but omits meaningful directional information. The alternative whole-system impedance model yields participation factors of shunt-connected apparatus with directional information that allows separate tuning for damping and frequency, yet do not cover series-connected components. This paper formalises the relationships between the two forms of impedance models and between the two forms of root-cause analysis. The calculation of system eigenvalue sensitivity in impedance models is further developed, which fills the gaps of previous research and establishes a complete theory of impedance-based root-cause analysis. The theoretical relationships and the tuning of parameters have been illustrated with a three-node passive network, a modified IEEE 14-bus network and a modified NETS-NYPS 68-bus network, showing that tools can be developed for tuning of IBR-rich power systems where only black-box impedance models are available.

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arXiv2022

Revisiting Grid-Forming and Grid-Following Inverters: A Duality Theory

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 grid-following inverters are duals of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability in both small-signal and transient/large-signal. The theoretical analysis and simulation results are used to illustrate cases for simple single-inverter-infinite-bus systems and a multi-inverter power network.

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arXiv2021

Participation Analysis in Impedance Models: The Grey-Box Approach for Power System Stability

This paper develops a grey-box approach to small-signal stability analysis of complex power systems that facilitates root-cause tracing without requiring disclosure of the full details of the internal control structure of apparatus connected to the system. The grey-box enables participation analysis in impedance models, which is popular in power electronics and increasingly accepted in power systems for stability analysis. The Impedance participation factor is proposed and defined in terms of the residue of the whole-system admittance matrix. It is proved that, the so defined impedance participation factor equals the sensitivity of the whole-system eigenvalue with respect to apparatus impedance. The classic state participation factor is related to the impedance participation factor via a chain-rule. Based on the chain-rule, a three-layer grey-box approach, with three degrees of transparency, is proposed for root-cause tracing to different depths, i.e. apparatus, states, and parameters, according to the available information. The association of impedance participation factor with eigenvalue sensitivity points to the re-tuning that would stabilize the system. The impedance participation factor can be measured in the field or calculated from the black-box impedance spectra with little prior knowledge required.

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arXiv2021

Mapping of Dynamics between Mechanical and Electrical Ports in SG-IBR Composite Grids

Power grids are traditionally dominated by synchronous generators (SGs) but are currently undergoing a major transformation through the increasing integration of inverter-based resources (IBRs). The SG-dominated grid is traditionally analyzed in a mechanical-centric view which ignores fast electrical dynamics and focuses on the torque-speed dynamics. By contrast, analysis of the emergent IBR-dominated grid usually takes the electrical-centric view which focuses on the voltage-current interaction. In this article, a port-mapping method is proposed to fill the gap between these approaches and combine them in a unified model. Specifically, the mechanical dynamics are mapped to the electrical impedance seen at the electrical port; and the electrical dynamics are also mapped to the torque coefficient seen at the mechanical port. The bidirectional mapping gives additional flexibility and insights to analyze the sub-system interactions in whole-system dynamics and guide the tuning of parameter. Application of the proposed method is illustrated in three cases with increasing scales, namely a single-SG-infinite-bus system, a single-IBR-weak-grid system, and a modified IEEE 14-bus SG-IBR composite system.

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arXiv2019

Interpreting Frame Transformations as Diagonalization of Harmonic Transfer Functions

Analysis of ac electrical systems can be performed via frame transformations in the time-domain or via harmonic transfer functions (HTFs) in the frequency-domain. The two approaches each have unique advantages but are hard to reconcile because the coupling effect in the frequency-domain leads to infinite dimensional HTF matrices that need to be truncated. This paper explores the relation between the two representations and shows that applying a similarity transformation to an HTF matrix creates a direct equivalence to a frame transformation on the input-output signals. Under certain conditions, such similarity transformations have a diagonalizing effect which, essentially, reduces the HTF matrix order from infinity to two or one, making the matrix tractable mathematically without truncation or approximation. This theory is applied to a droop-controlled voltage source inverter as an illustrative example. A stability criterion is derived in the frequency-domain which agrees with the conventional state-space model but offers greater insights into the mechanism of instability in terms of the negative damping (non-passivity) under droop control. The paper not only establishes a unified view in theory but also offers an effective practical tool for stability assessment.

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