Comprehensive Stability Analysis Research Articles

Generalization Guarantees of Gradient Descent for Shallow Neural Networks

Abstract Significant progress has been made recently in understanding the generalization of neural networks (NNs) trained by gradient descent (GD) using the algorithmic stability approach. However, most of the existing research has focused on one-hidden-layer NNs and has not addressed the impact of different network scaling. Here, network scaling corresponds to the normalization of the layers. In this article, we greatly extend the previous work (Lei et al., 2022; Richards & Kuzborskij, 2021) by conducting a comprehensive stability and generalization analysis of GD for two-layer and three-layer NNs. For two-layer NNs, our results are established under general network scaling, relaxing previous conditions. In the case of three-layer NNs, our technical contribution lies in demonstrating its nearly co-coercive property by utilizing a novel induction strategy that thoroughly explores the effects of overparameterization. As a direct application of our general findings, we derive the excess risk rate of O(1/n) for GD in both two-layer and three-layer NNs. This sheds light on sufficient or necessary conditions for underparameterized and overparameterized NNs trained by GD to attain the desired risk rate of O(1/n). Moreover, we demonstrate that as the scaling factor increases or the network complexity decreases, less overparameterization is required for GD to achieve the desired error rates. Additionally, under a low-noise condition, we obtain a fast risk rate of O(1/n) for GD in both two-layer and three-layer NNs.

Robust reference gene selection in Norway spruce: essential for real-time quantitative PCR across different tissue, stress and developmental conditions

Accurate gene expression analysis in Norway spruce (Picea abies) under diverse stress conditions requires the identification of stable reference genes for normalization. Notably, the literature lacks reports on suitable reference genes in Norway spruce. Here, we aimed to address this gap by identifying suitable reference genes for quantitative real-time PCR in Norway spruce across various stress conditions (drought, heat, pathogen infection) in seedlings, tissues (needle, phloem, root), and developmental stages (seedlings, mature trees). We evaluated the stability of 15 candidate reference genes and assessed their expression stability using five statistical algorithms (ΔCt, geNorm, NormFinder, BestKeeper, and RefFinder). Our results highlight ubiquitin-protein ligase (SP1), conserved oligomeric Golgi complex (COG7), and tubby-like F-box protein (TULP6) as the most stable reference genes, while succinate dehydrogenase (SDH5) and heat shock protein 90 (HSP90) were the least stable under various experimental conditions. COG7 and TULP6 are novel candidate reference genes reported for the first time. The expression stability of the identified reference genes was further validated using dehydrin-like protein 5 (PaDhn5) under drought conditions in Norway spruce. Pairwise variation analysis suggests that two reference genes were sufficient to normalize gene expression across all sample sets. This study provides a comprehensive analysis of reference gene stability under different experimental conditions and a catalog of genes for each condition, facilitating future functional genomic research in Norway spruce and related conifers.

New Comprehensive Stability and Sensitivity Analysis on Graphene Nanoribbon Interconnects Parameters

Based on the transmission line modeling for multilayer graphene nanoribbon (MGNR) interconnects, system stability was studied on intrinsic parameters. In addition to width,length and height variation, dielectric constant, permeability and Fermi velocity path change in multilayer graphene nanoribbon (MGNR) interconnects are analyzed. In thispaper, the obtained results show with increasing dielectric constant and decreasing permeability, Fermi velocity system becomes more stable. Nyquist diagram and stepresponse method results confirm these and are matched with physical parameter variation like resistance, capacitance and inductance in the following sensitivity analysis results where it shows with increasing width and length, sensitivity will decrease and increase respectively. Impulse response diagram results show with increasing 50% width, sensitivity will be zero but with increasing 50% length, amplitude will decrease and the time of setting will increase. On the other hand, from the step response of the transfer function, both width and length increase cause more stability for a system but the width parameter will be a better choice for manipulating the dimension of MGNR to reach a stable system.

Event-driven intelligent fault-tolerant containment control for nonlinear multiagent systems with unknown disturbances

This paper investigates the event-driven intelligent fault-tolerant containment control problem for nonlinear multiagent systems affected by unknown disturbances, and conducts a comprehensive analysis of the dynamic stability of the system. Reduced-order modelling is employed for system modelling and identification, while radial basis function neural networks are utilised to estimate the nonlinear functions of the system model. An event-driven control scheme is designed based on the backstepping method and Lyapunov functional approach. In contrast to existing consensus control schemes, the proposed event-driven control schemes are specifically tailored to improve the energy efficiency and endurance of nonlinear multiagent systems operating in complex environments. Under the proposed control law, the output of each follower is converge to the convex hull spanned by the outputs of the leaders. The effectiveness of the proposed method is rigorously validated through numerical simulations. Furthermore, a practical example involving the design of a marine surface vehicle using advanced robotics technology is presented to further substantiate the efficacy of the proposed method.

Robust model-based control and stability analysis of PMSM drive with DC-link voltage and parameter variations

To ensure a stable operation of Permanent Magnet Synchronous Motor (PMSM) drive under both DC link voltage and parameter variations, a robust control technique based on a new dynamic model that includes both drive’s and motor’s specifications is proposed in this paper. In the proposed controller, the first component of the drive’s control law consists of the d-component error of the stator current, and the second one is shaped based on the error in the square value of q-component of the stator current. To further deal with the dynamic alterations of the drive system, compensators are designed to reduce the adverse effects of rotor angular frequency variations and the difference between electrical and load torque errors. Another compensator based on the drive’s output power error is also placed at the q-component of the proposed control law. Moreover, a general operation curve (GOC) for the stator current is introduced to further assess the operation of the PMSM. In the next step, a comprehensive stability analysis verifying the stable operation of both d- and q-components of the stator current is performed using two closed-loop descriptions of the proposed control strategy. Several simulation results in MATLAB/SIMULINK environment are provided to verify the validity of the proposed control technique under various dynamic scenarios. It is worth mentioning that comparative results show that the proposed control technique compared to conventional PI controller has enabled the PMSM speed and torque to reach its 50% and 95% of their desirable values with respectively 42.9% and 28.6% less time. Also, the PMSM speed and torque responses due to proposed control technique have 75% less undershoot compared to conventional PI controller.

Photodynamic Therapy as a Novel Therapeutic Modality Applying Quinizarin-Loaded Nanocapsules and 3D Bioprinting Skin Permeation for Inflammation Treatment.

Skin inflammation associated with chronic diseases involves a direct role of keratinocytes in its immunopathogenesis, triggering a cascade of immune responses. Despite this, highly targeted treatments remain elusive, highlighting the need for more specific therapeutic strategies. In this study, nanocapsules containing quinizarin (QZ/NC) were developed and evaluated in an in vitro model of keratinocyte-mediated inflammation, incorporating the action of photodynamic therapy (PDT) and analyzing permeation in a 3D skin model. Comprehensive physicochemical, stability, cytotoxicity, and permeation analyses of the nanomaterials were conducted. The nanocapsules demonstrated desirable physicochemical properties, remained stable throughout the analysis period, and exhibited no spectroscopic alterations. Cytotoxicity tests revealed no toxicity at the lowest concentrations of QZ/NC. Permeation and cellular uptake studies confirmed QZ/NC permeation in 3D skin models, along with intracellular incorporation and internalization of the drug, thereby enhancing its efficacy in drug delivery. The developed model for inducing the inflammatory process in vitro yielded promising results, particularly when the synthesized nanomaterial was combined with PDT, showing a reduction in cytokine levels. These findings suggest a potential new therapeutic approach for treating inflammatory skin diseases.

An Analysis of the Slope Stability of Young Rock Cliffs in Sibang, Bali Using GEO5

This study presents a comprehensive analysis of slope stability for young rock cliffs in the Sibang region of Bali, employing advanced geotechnical software GEO5. The investigation is crucial due to the dynamic geological conditions and rapid changes in land use in the area, posing potential risks to infrastructure and environmental stability. The research focuses on young rock cliffs, characterized by recent geological formations, which are inherently susceptible to slope instability. This slope stability analysis is carried out using the GEO5 auxiliary program which will produce a Safety Factor value which is used as the basis for building a construction which interprets whether the slope is safe or not. The safety factor value used as the minimum value is 1.5, so the slope must have a SF value ≥ SF min = 1.5. This analysis was carried out on 4 cross sections with 2 method which name is Morgenstern-Price and Bishop Method because the analysis carried out was complex in terms of force and moment. The Safety Factor of cross section on BH-03 to BH-01 is not safe because the value is 1,16 and 1,15 which is < 1,5 (the minimum safety factor). Therefore, the slope must modelled with terraced slopes and also retaining wall reinforcement for each modelled terrace height.

Stability analysis of grid-connected inverter under full operating conditions based on small-signal stability region

Impedance analysis is a practical approach for assessing the small-signal stability of renewable energy power systems. However, existing research predominantly focuses on specific operating conditions, neglecting the fundamental principles governing stability evolution under time-varying operating conditions. This paper presents a methodology to develop the small-signal stability region (SSSR) for grid-connected inverters using the impedance method. A comprehensive stability analysis for grid-connected inverter systems is performed based on the stability region. Firstly, the multi-parameter SSSR of the grid-connected inverter is defined according to both the aggregated impedance criterion and the generalized Nyquist criterion. Furthermore, a polynomial approximation expression for the SSSR boundary is derived. Secondly, the sensitivity analysis of operating points and control parameters is performed under full operating conditions to investigate their impact on stability based on the quantified boundary. The analyses reveal that the stability of the grid-connected inverter system near the SSSR boundary decreases with increasing active power and decreasing reactive power but exhibits an initial increase followed by a decrease with a larger PLL bandwidth. Finally, the accuracy of the stability region and the influence of key parameters are verified through case studies and experiments. The study in this paper can be used for quantitative analysis of stability margins and decision guidance of control optimization for grid-connected inverters.

Antisaturation fixed-time backstepping fuzzy integral sliding mode control for automatic landing of fixed-wing unmanned aerial vehicles

This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.

Stability control and analysis of hydrogen production using a multi-terminal DC EV charging system with PV

In the shift towards sustainable energy, DC microgrids have emerged as efficient and reliable alternatives to traditional AC systems, particularly suited for low-voltage applications. The adoption of electric vehicles (EVs) in multi-terminal DC (MTDC) systems introduces challenges in maintaining voltage stability, particularly during master station failures. Our research introduces a decentralized control strategy with multi-mode switching to ensure stability under such conditions. We conduct a comprehensive stability analysis of MTDC systems heavily integrated with EVs, identifying the instability risks and proposing mitigation strategies. The effectiveness of our control approach is validated through simulation studies and a detailed state-space model. Additionally, we explore the integration of renewable energy sources and hydrogen production into MTDC systems for EV charging, which minimizes the need for a new power infrastructure and enhances renewable energy use. This integration optimally reduces renewable energy discard rates, thereby improving energy efficiency without compromising system performance. Our study provides practical insights and theoretical support for renewable energy-driven hydrogen production within DC microgrids. The proposed scheme's performance is validated through simulation studies using a state-space model.

Comprehensive analysis of chemical and enantiomeric stability of terpenes in Cannabis sativa L. flowers.

Cannabis sativa L. is renowned for its medicinal and recreational uses. With the increasing global legalization of C.sativa L.-based products for medicinal purposes, there is a growing need for well-characterized products. While the stability of cannabinoids such as tetrahydrocannabinol and cannabidiol is well understood, information on the chemical and enantiomeric stability of terpenes remains scarce. This is despite the fact that terpenes are also thought to have pharmacological activity and may contribute to the overall effect of C.sativa L. To address these challenges, four analytical methods based on chiral, polar, and apolar gas chromatographic separation combined with either MS or FID detection were developed and validated. These methods successfully separated and quantified a total of 29 terpenes, including 13 enantiomers and 5 diastereomers specific to C.sativa L. Furthermore, terpenes and authentic C.sativa L. flowers and extracts were subjected to UV and heat treatments to observe potential degradation reactions over time. Each terpene generates a unique pattern of degradation products resulting in a diverse array of oxidation and cyclization products. P-cymene was identified as a major product of terpene aging. Notably, no enantiomeric conversion was detected, suggesting that the formation of (-)-α-pinene in cannabis extracts, for example, originates from other terpenes. Terpenes have different degradation rates, even though they are structurally similar. In addition, cultivar- and growth-condition-specific enantiomeric ratios were observed in C.sativa L., confirming that enantiomer production is species-specific and has to be considered for therapeutical applications.

Comprehensive analysis of secretome and transcriptome stability of Wharton jelly mesenchymal stromal cells during good manufacturing practice-compliant production

BackgroundMesenchymal stromal cells (MSCs) hold promise for cell-based therapies due to their ability to stimulate tissue repair and modulate immune responses. Umbilical cord-derived MSCs from Wharton jelly (WJ) offer advantages such as low immunogenicity and potent immune modulatory effects. However, ensuring consistent quality and safety throughout their manufacturing process remains critical. RNA sequencing (RNA-seq) emerges as a crucial tool for assessing genetic stability and expression dynamics in cell-based therapeutic products. MethodsWe examined the secretome and transcriptome of WJ-MSC signatures throughout Good Manufacturing Practice (GMP) production, focusing on the performance of total RNA or Massive Analysis of cDNA Ends (MACE) sequencing. ResultsThrough extensive transcriptomic analysis, we demonstrated consistent stability of WJ-MSC expression signatures across different manufacturing stages. Notably, MACE-seq showed improved identification of key expression patterns related to senescence and immunomodulation. ConclusionsThese findings highlight the potential of MACE-seq as a quality assessment tool for WJ-MSC-based therapies, ensuring their efficacy and safety in clinical applications. Importantly, MACE-seq demonstrated its value in characterizing WJ-MSC-derived products, offering insights that traditional assays cannot provide.

Assessment of Genetic Stability in Chickpea Varieties Through GGE and AMMI Analyses

Background: Chickpea is grown in diverse agro-climatic conditions and various varieties respond differently to these environments. Stability analysis identifies adaptable varieties that yield consistently across regions. Our study focuses on identifying high-yield, reliable chickpea varieties through extensive multi-environment trials Methods: To accomplish our research goal, we conducted a comprehensive stability analysis during 2020-21 and 2021-22 using 12 different methods which include parametric, non-parametric and PCA-based AMMI, GGE biplot analysis. This extensive analysis was applied to six distinct Chickpea varieties cultivated in three diverse environments. Result: CSJ515 consistently demonstrated stability in all 10 analyses, while GNG2144 and RSG959 showed stability in 7 analyses. GNG1958 exhibited stability in four analyses and GNG2171 and RSG974 were stable in 3 and 2 analyses, respectively. These results suggest that CSJ515, GNG2144 and RSG959 have broad and stable adaptability across diverse environments.

Stability Analysis of Gravity Dam using Matlab Programming

Gravity dams are critical structures in civil engineering, designed to withstand the immense forces exerted by water pressure and gravity. Ensuring their stability is paramount to prevent catastrophic failures that could result in significant economic and environmental consequences. This study presents a comprehensive stability analysis of a gravity dam using MATLAB programming. The analysis focuses on evaluating the structural integrity and safety factors of the dam under various loading conditions, including hydrostatic pressure and seismic forces. MATLAB's computational capabilities are utilized to perform rigorous numerical simulations, incorporating finite element analysis (FEA) and stability criteria assessments. Key aspects of the stability analysis include the determination of critical failure modes such as sliding, overturning, and base pressure distribution. Through MATLAB programming, the study explores different dam geometries and material properties to assess their influence on overall stability. Furthermore, sensitivity analyses are conducted to investigate the impact of uncertainties in input parameters on the dam's stability margins. This provides insights into potential weak points and allows for optimization of design parameters to enhance dam safety.

Elucidating the Influence of Coating Materials in the Microencapsulation Process of Hempseed Oil Via Spray Drying: A Comprehensive Analysis of Physicochemical Attributes, Oxidation Stability, and Thermal Properties

In this study, it was aimed to investigate the effect of different coating materials on the microencapsulation of hempseed oil by spray drying. For this purpose, hempseed oil emulsions were prepared with skimmed milk powder (SMP), maltodextrin (MD), and whey protein concentrate (WPC). The properties of these emulsions including rheological, zeta potential, and physicochemical properties were analyzed. Then, hempseed oil microcapsules were produced using spray drying. The effect of the different coating materials on spray-dried hempseed oil capsules was evaluated in terms of microencapsulation yield, surface oil, microencapsulation efficiency, oxidation stability, and physicochemical properties. The combinations of SMP (50.58%) or WPC (56.21%) with MD significantly enhanced the microencapsulation yield. The highest microencapsulation efficiency (92.16%) was obtained in the microcapsule with SMP: MD. This microcapsule with SMP: MD also showed higher oxidative stability compared to other microcapsules. Besides, this combination (SMP: MD) effectively protected the hempseed oil against oxidation during the Schaal oven test. Additionally, spray-dried hempseed oil microcapsules were characterized using FT-IR, TGA, and SEM. It was determined that using MD as a coating material improved the thermal stability of the microcapsules. As a result, it was concluded that the SMP: MD as a coating material was suitable for the microencapsulation of hempseed oil.

A Mathematical Model for Differentiated Thyroid Cancer with Combination Therapy

Objectives: Differentiated thyroid cancer (DTC) is usually treated with surgery and radioactive iodine therapy. However, in advanced stages, molecular changes can lead to a progressive loss of sensitivity to iodine, making the cancer resistant to radioactive iodine treatment (known as radioactive iodine-refractory, or RAIR). For cases of RAIR-DTC, alternative treatments such as tyrosine kinase inhibitors and immunotherapy are explored. To better understand the dynamics of these alternative treatments, a new mathematical model has been developed. In this model, Sorafenib represents the tyrosine kinase inhibitor, while Pembrolizumab is the immunotherapy agent under investigation. Methods: Two mathematical models were developed based on systems of ordinary differential equations to study differentiated thyroid cancer treated with (1) Sorafenib alone and (2) a combination of a Sorafenib and Pembrolizumab. The first model included three variables: drug concentration of Sorafenib, number of cancer cells, and number of immune cells with fourteen parameters. The second model additionally incorporated the concentration of the Pembrolizumab. Parameter values were estimated through simulations utilizing the fmincon optimization technique in MATLAB. Local asymptotic stability analysis was performed to investigate the models' behavior around equilibrium points. Moreover, the Lyapunov method was employed to establish global asymptotic stability of the models. Findings: The findings revealed insights into the dynamics of treating RAIR-DTC patients with tyrosine kinase inhibitors and immunotherapy. The stability analysis contributed to the understanding of the system's behavior under different conditions, offering valuable information for clinical application. Numerical simulations were then performed using Simbiology in MATLAB to simulate the treatment dynamics over time. Novelty: This research contributes to the field by presenting a novel mathematical model that integrates tyrosine kinase inhibitors and immunotherapy for the treatment of RAIR-DTC. The comprehensive analysis of equation stability enhances the reliability of the model, while the numerical simulations provide a practical and visual tool for assessing the potential outcomes of the proposed therapeutic strategy. This study offers a valuable framework for further exploration and refinement of treatment approaches for patients with challenging DTC cases. Keywords: Mathematical modeling, Routh Hurwitz Criteria, Jacobian, Differentiated thyroid Cancer, Stability Analysis

Attosecond two-color x-ray free-electron lasers with dual chirp-taper configuration and bunching inheritance

Attosecond x-ray pulses play a crucial role in the study of ultrafast phenomena occurring within inner and valence electrons. To achieve attosecond time-resolution studies and gain control over electronic wave functions, it is crucial to develop techniques capable of generating and synchronizing two-color x-ray pulses at the attosecond scale. In this paper, we present a novel approach for generating attosecond pulse pairs using a dual chirp-taper free-electron laser with bunching inheritance. An electron beam with a sinusoidal energy chirp, introduced by the external laser, passes through the main undulator and afterburner, both with tapers. Two-color x-ray pulses are generated from the main undulator and the afterburner, respectively, with temporal separations of several femtoseconds and energy separations of tens of electron volts. Notably, the afterburner is much shorter than the main undulator due to the bunching inheritance, which reduces the distance between two source points and alleviates the beamline focusing requirements of the two-color pulses. A comprehensive stability analysis is conducted in this paper, considering the individual effects of shot noise from self-amplified spontaneous emission and carrier-envelope phase jitter of the few-cycle laser. The results show that the radiation from the afterburner exhibits excellent stability in the proposed scheme, which is beneficial for x-ray pump-probe experiments. The proposed scheme opens up new possibilities for attosecond science enabled by x-ray attosecond pump-probe techniques and coherent control of ultrafast electronic wave packets in quantum systems. Published by the American Physical Society 2024

Dynamical System for Tuberculosis Outbreak with Vaccination Treatment and Different Interventions on the Burden of Drug Resistance

Tuberculosis, a highly contagious and lethal infectious disease, remains a global health concern with challenging treatment options. To combat its widespread impact, prevention strategies, such as vaccination, are imperative. This research focuses on developing a mathematical model with the addition of a vaccination compartment to understand the dynamics of tuberculosis transmission with vaccination. Subsequently, the study proceeds to identify the equilibrium points and calculate the basic reproduction number (ℜ0). Following this, a comprehensive stability analysis is conducted, and a numerical simulation is executed to observe the population dynamics. Furthermore, parameter sensitivity analysis is undertaken to assess the extent to which these parameters impact ℜ0. Preliminary analysis shows that the modified model has a solution that remains in the non-negative and bounded region. Furthermore, model analysis reveals two equilibrium points, namely the disease-free equilibrium and the endemic equilibrium. It is established that the disease-free equilibrium exhibits local asymptotic stability when ℜ0 1. Remarkably, the numerical simulation aligns with the analytical findings, reinforcing the robustness of the results. Analysis of the sensitivity of the parameter to ℜ0 shows that the parameter of the proportion of susceptible population entering the vaccination class has a significant effect on the value of ℜ0. The parameter of proportion of susceptible population entering the vaccination class has a negative effect on the number of populations with infection.

A comprehensive analysis of cermet design and thermal cyclic stability via elasto-viscoplastic crystal plasticity modeling

Ceramic-metal composites, or cermets, exhibit beneficial properties resulting in their use in many industrial applications. One challenge with cermets is mismatches in the coefficient of thermal expansion (CTE) values between the ceramic and metal phases that lead to residual stresses after processing, plasticity in the metal phase, internal stresses, and instability after thermal cycling. In order to make predictions of these properties to inform the design of cermets, we employ an incremental elasto-viscoplastic, self-consistent formulation to calculate the thermal, elastic, and plastic strains in two-phase polycrystalline cermet materials. This framework is extended to include temperature dependent properties, which are called implicitly within the temperature-dependent, incremental elasto-viscoplastic, self-consistent (TE-VPSC) model. Temperature-induced cooling and thermal cycling simulations are conducted using the TE-VPSC framework to study the residual stresses and plastic strains in the metal phases. Two materials are discussed in detail exhibiting stark differences based on the CTE between their ceramic and metal phases, WC/57-vol% Cu (exhibiting a pronounced CTE mismatch) and Y2O3/27-vol% Nb (exhibiting a negligible CTE mismatch). The model demonstrates high residual stresses in the Cu phase during processing and reverse plasticity leading to recovery of plastic strain during thermal cycling of the WC/Cu cermet. Moreover, the model demonstrates relatively low residual stresses and plasticity in Y2O3/Nb and a thermal stability point of 1251 °C, below which no plasticity develops in the cermet. We employ the TE-VPSC model as a design tool for cermets to systematically investigate the effects of process-induced microstructure variations (volume fraction, grain aspect ratio, and crystallographic texture are investigated) and compositional differences (19 compositions are explored) on the residual stress, degree of plasticity in the metal phase, and thermal stability point. The computational efficiency of the TE-VPSC framework makes it a desktop design tool that can be used to quantify the impact of changing composition, processing, and thermo-mechanical loading on the performance of the cermet, which can help reduce the number of time intensive and costly high temperature experiments.

Stability analysis of hydropower unit operation conditions considering hydro-turbine nonlinearity

Abstract This paper aims to study the law that the stability of hydropower systems changes with the system operating point and clarify the impact of hydro-turbine nonlinearity and hydraulic nonlinearity on the system stability. Firstly, the piecewise linearized model of the hydro-turbine regulation system (HTRS) at various operating points is established. Then, the HTRS stability domain is calculated and analyzed under various working heads and guide vane openings, and the impact of head variation on system stability is researched from the perspectives of discharge and power. Finally, the stability of various operating conditions under ideal hydro-turbine conditions and rated hydraulic parameter conditions are and compared to clarify the role of the water system and turbine nonlinearity on the stability. The results show that hydro-turbine nonlinearity helps to improve the system stability of the overall operating conditions, but the stability of the HTRS is relatively weak during high-load and low-head operations. Moreover, the hydro-turbine nonlinearity plays a dominant role in the process of stability changing with the operating head. This paper provides a comprehensive analysis of the system stability at different operating points, which can help guide the control optimization of hydropower systems.