Quantitative Stability Conditions for Grid-Forming Converters With Complex Droop Control

In this paper, we study analytically the transient stability of grid-connected distributed generation systems with grid-forming (GFM) complex droop control, also known as dispatchable virtual oscillator control (dVOC). We prove theoretically that complex droop control, as a state-of-the-art GFM control, always possesses steady-state equilibria whereas classical droop control does not. We provide quantitative conditions for complex droop control maintaining transient stability (global asymptotic stability) under grid disturbances, which is beyond the well-established local (non-global) stability for classical droop control. For the transient instability of complex droop control, we reveal that the unstable trajectories are bounded, manifesting as limit cycle oscillations. Moreover, we extend our stability results from second-order GFM control dynamics to full-order system dynamics that additionally encompass both circuit electromagnetic transients and inner-loop dynamics. Our theoretical results contribute an insightful understanding of the transient stability and instability of complex droop control and offer practical guidelines for parameter tuning and stability guarantees

Dynamic Ancillary Services: From Grid Codes to Transfer Function-Based Converter Control

Conventional grid-code specifications for dynamic ancillary services provision such as fast frequency and voltage regulation are typically defined by means of piece-wise linear step-response capability curves in the time domain. However, although the specification of such time-domain curves is straightforward, their practical implementation in a converter-based generation system is not immediate, and no customary methods have been developed yet. In this paper, we thus propose a systematic approach for the practical implementation of piece-wise linear time-domain curves to provide dynamic ancillary services by converter-based generation systems, while ensuring grid-code and device-level requirements to be reliably satisfied. Namely, we translate the piece-wise linear time-domain curves for active and reactive power provision in response to a frequency and voltage step change into a desired rational parametric transfer function in the frequency domain, which defines a dynamic response behavior to be realized by the converter. The obtained transfer function can be easily implemented e.g. via a PI-based matching control in the power loop of standard converter control architectures. We demonstrate the performance of our method in numerical grid-code compliance tests, and reveal its superiority over classical droop and virtual inertia schemes which may not satisfy the grid codes due to their structural limitations.Comment: 7 pages, 9 figure

Joint Oscillation Damping and Inertia Provision Service for Converter-Interfaced Generation

As renewable generation becomes more prevalent, traditional power systems dominated by synchronous generators are transitioning to systems dominated by converter-interfaced generation. These devices, with their weaker damping capabilities and lower inertia, compromise the system's ability to withstand disturbances, pose a threat to system stability, and lead to oscillations and poor frequency response performance. While some new converter-interfaced generations are capable of providing superior damping and fast frequency control, there is a lack of effective measures to incentivize manufacturers to adopt them. To address this gap, this paper defines the joint oscillation damping and inertia provision services at the system level, seeking to encourage converter-interfaced generation to provide enhanced damping and fast frequency response capabilities. Our approach is anchored in a novel convex parametric formulation that combines oscillation mode and frequency stability constraints. These constraints ensure a sufficient damping ratio for all oscillation modes and maintain transient frequency trajectories within acceptable limits. They are designed to integrate smoothly into various operational and planning optimization frameworks. Using this formulation, we introduce a joint service for oscillation damping and inertia provision based on a cost-minimization problem. This facilitates the optimal allocation of damping and virtual inertia to converters, achieving both small-signal stability and frequency stability. Furthermore, we investigate the economic effects of introducing this service into a new ancillary service market, assessing its impact on system operations and cost-efficiency. Numerical tests highlight the service's efficacy in ensuring both small-signal stability and frequency stability, and offer insights into potential economic benefits.Comment: Submitted for IEEE PES journal for possible publication

MIMO Grid Impedance Identification of Three-Phase Power Systems: Parametric vs. Nonparametric Approaches

A fast and accurate grid impedance measurement of three-phase power systems is crucial for online assessment of power system stability and adaptive control of grid-connected converters. Existing grid impedance measurement approaches typically rely on pointwise sinusoidal injections or sequential wideband perturbations to identify a nonparametric grid impedance curve via fast Fourier computations in the frequency domain. This is not only time-consuming, but also inaccurate during time-varying grid conditions, while on top of that, the identified nonparametric model cannot be immediately used for stability analysis or control design. To tackle these problems, we propose to use parametric system identification techniques (e.g., prediction error or subspace methods) to obtain a parametric impedance model directly from time-domain current and voltage data. Our approach relies on injecting wideband excitation signals in the converter's controller and allows to accurately identify the grid impedance in closed loop within one injection and measurement cycle. Even though the underlying parametric system identification techniques are well-studied in general, their utilization in a grid impedance identification setup poses specific challenges, is vastly underexplored, and has not gained adequate attention in urgent and timely power systems applications. To this end, we demonstrate in numerical experiments how the proposed parametric approach can accomplish a significant improvement compared to prevalent nonparametric methods.Comment: 7 pages, 7 figure

Apoptosis pattern and alterations of expression of apoptosis-related factors of supporting cells in Kölliker’s organ in vivo in early stage after birth in rats

Kölliker’s organ is a temporary but indispensable structure in the development of the cochlea. Supporting cells (SCs) within it release adenosine 5’-triphosphate (ATP), which may play a crucial role in cochlear development before the onset of hearing. To reveal the apoptosis of Kölliker’s organ in new-born rats, we studied the morphological changes and expression of apoptosis-related factors during early postnatal development. We found SCs in Kölliker’s organ decreased in number and changed in appearance along the cochlea apex-to-base gradient, and the expression of caspase-3, caspase-8, caspase-9 and bcl-2 in Kölliker’s organ of the cochlea fluctuated along the course of postnatal development, with an expression peak at postnatal day 3. This study demonstrates a time-dependent degeneration of Kölliker’s organ during postnatal cochlea development, which might be triggered by endogenous factors. </p

Sichuan Rainfall Prediction Using an Analog Ensemble

This study aimed to address the significant bias in 0–44-day precipitation forecasts under numerical weather conditions. To achieve this, we utilized observational data obtained from 156 surface stations in the Sichuan region and reanalysis grid data from the National Centers for Environmental Prediction Climate Forecast System Model version 2. Statistical analysis of the spatiotemporal characteristics of precipitation in Sichuan was conducted, followed by a correction experiment based on the Analog Ensemble algorithm for 0–44-day precipitation forecasts for different seasons in the Sichuan region. The results show that, in terms of spatial distribution, the precipitation amounts and precipitation days in Sichuan Province gradually decreased from east to west. Temporally, the highest number of precipitation days occurred in autumn, while the maximum precipitation amount was observed in summer. The Analog Ensemble algorithm effectively reduced the error in the model forecast results for different seasons in the Sichuan region. However, the correction effectiveness varied seasonally, primarily because of the differing performance of the AnEn method in relation to precipitation events of various magnitudes. Notably, the correction effect was the poorest for heavy-rain forecasts. In addition, the degree of improvement of the Analog Ensemble algorithm varied for different initial forecast times and forecast lead times. As the forecast lead time increased, the correction effect gradually weakened

Association between platelet count and hepatocellular carcinoma overall survival: a large retrospective cohort study

Objectives To explore the non-linear relationship between platelet count (PLT) and hepatocellular carcinoma (HCC) overall survival (OS).Setting The study was done in Sun Yat-sen University Cancer Center (SYSUCC) from January 2007 to May 2012, a total of 5005 consecutive participants at SYSUCC were retrospectively reviewed, and 979 patients with Barcelona clinic liver cancer (BCLC) stage B were selected for the final analysis.Participants A total of 979 newly diagnosed patients with HCC with BCLC stage B were identified for the secondary analysis. Eight cases were excluded for missing data of PLT.Main outcome measures Cox proportional hazard regression models were used to calculate multivariable-adjusted HRs and 95% CIs for HCC. The non-linear relationship was estimated through a restricted cubic spline regression, and a two-piecewise Cox proportional hazards model was further performed to calculate the threshold effect. We used multiple imputation to deal with the missing data.Results In the multivariate analysis, Log PLT was associated with a 91% risk increase in death (HR 1.91; 1.28 to 2.85) with adjustment for gender, Child-Pugh class, age × diameter of main tumour, both lobe with lesions × number of the intrahepatic lesions, alpha-fetoprotein (&lt;25, ≥25) and lactic dehydrogenase (&lt;245, ≥245). We also found a U-shape relationship between PLT and HCC OS at the inflexion point of 67.6×109/L. The HR was 0.12 (95% CI 0.03 to 0.52) for Log PLT≤10.83 and 3.07 (CI 1.91 to 4.92) for Log PLT&gt;10.83 after adjusting for potential confounders. The core results were consistent with those from the sensitivity analysis. Besides, a significantly higher hazard risk was found in the patients with age &lt;55, both lobes with lesions, tumour diameter &gt;50, haemoglobin ≥120 and C reactive protein &gt;10.Conclusion PLT was nonlinearly associated with HCC OS