Stability Analysis Method Research Articles

A Static Security Region Analysis of New Power Systems Based on Improved Stochastic–Batch Gradient Pile Descent

The uncertainty in the new power system has increased, leading to limitations in traditional stability analysis methods. Therefore, considering the perspective of the three-dimensional static security region (SSR), we propose a novel approach for system static stability analysis. To address the slow training speed of traditional deep learning algorithms using batch gradient descent (BGD), we introduce an improved stochastic–batch gradient descent (S-BGD) search method that combines the advantages of stochastic gradient descent (SGD) in fast training. This method ensures both speed and precision in parameter training. Moreover, to tackle the problem of getting trapped in local optima and saddle points during parameter training, we draw inspiration from kinematic theory and propose a gradient pile (GP) training method. By utilizing accumulated gradients as parameter corrections, this method effectively avoids getting stuck in local optima and saddle points, thereby enhancing precision. Finally, we apply the proposed methods to construct the static security region for the IEEE-118 new power system using its data as samples, demonstrating the effectiveness of our approach.

Stability Analysis of Seismic Slope Based on Relative Residual Displacement Increment Method

The seismic stability analysis of a slope is a complex process influenced by earthquake action characteristics and soil mechanical properties. This paper presents a novel seismic slope stability analysis method using the relative residual displacement increment method in combination with the strength reduction method (SRM) and the actual deformation characteristics of the slope. By calculating the relative displacement of the key point inside the landslide mass and the reference point outside the landslide mass after each reduction, the safety factor of the slope is determined by the strength reduction factor (SRF) corresponding to the maximum absolute value of the relative residual displacement increment that appears after a continuous plastic penetration zone. The method eliminates interference caused by significant displacement fluctuations of key points under earthquake action and reduces the subjective error that can occur when manually identifying displacement mutation points. The proposed method is validated by dynamic calculations of homogeneous and layered soil slopes and compared with three other criteria: applicability, accuracy, and stability.

A novel stability analysis method of single-layer ribbed reticulated shells with roof plates

The steel dome of liquefied natural gas (LNG) storage tanks comprises a curved roof plate welded onto a single-layer ribbed reticulated shell (SLRR shell). However, the roof plate may cause diaphragm effects, which may resulting in instability of the steel dome at a relatively low load level. In this paper, an innovative equivalent single-layer ribbed reticulated shell (ESLRR shell) was proposed to investigate the impact of the diaphragm effect. Specifically, the roof plate and H-shaped radial beam were equated as radial irregular beams based on the principle of plate-shell composite action. Next, we performed a systematic analysis of the instability mechanisms in the ESLRR shell, revealing the interaction between the beam buckling and the overall structural instability. Finally, through parametric study, we explored the effects of roof plate thickness and rise-to-span ratio on the ESLRR shell, and obtained the optimal structural parameters. The results show that the proposed method effectively solves the challenges associated with the presence of roof plates in LNG storage tanks steel dome stability analysis; Under the combination of weak boundary stiffness and high bending moment, radial irregular beams are more prone to buckling; Increasing roof plate thickness or rise-to-span ratio can reinforce the stability of the ESLRR shell. Overall, this research work provides theoretical guidance for the future design and optimization of LNG storage tank domes.

Evaluation of Efficiency of Weighted Average of Stability and Mean Performance Estimated by Linear Mixed Models for Identifying High‐Yielding Lentil Genotypes Adapted to Rainfed Regions

ABSTRACTA combination of the two methods of stability analysis, the additive main effect and multiplicative interaction (AMMI) and the best linear unbiased prediction (BLUP), based on weighted average of stability (WAASB) estimated by the linear mixed models (LMM) index identified the improved genotypes. In this study, 17 advanced genotypes of lentil were studied at two locations, Zanjan and Maragheh, during the two seasons. To examine the genotype × environment interaction, the AMMI and BLUP methods using the WAASB and weighted average of mean performance (WAASBY) index were combined to evaluate the performance stability of genotypes according to different experimental plots. Considering the significant genotype × environment interaction based on likelihood ratio test (LRT), data were analyzed by the BLUP method. The highest grain yield was detected for genotype 13, followed by genotypes 7, 11, 20, 5, 12, and 19 with higher productivity than the grand mean. To select genotypes according to yield and stability, the WAASBY index was defined by combining mean grain yield and stability. Considering 50:50 contributions for the two components, the grain yield and stability of the 13 genotypes were higher than the grand mean. The highest WAASBY was observed for genotypes 7, 20, and 12, which were determined as the best genotypes of lentil under agroecological conditions encountered in the current study regions.

Observer-based control for large-scale interconnected systems with parameter uncertainty and application to wireless power transfer systems

In the work, the observer-based control is designed and analyzed for a class of large-scale interconnected systems subject to parameter uncertainty. In the beginning, we build a large-scale interconnected system with parameter uncertainty and apply this model to a multi-level wireless power transfer system. By using this modeling method, the order of multi-level wireless power transfer system is greatly deduced. In addition, the multi-level wireless power transfer system include coupling terms and uncertain parameters considered in the observer-based control law design. We earn sufficient conditions of this model stability for multi-level wireless power transfer systems under this control law through the Lyapunov stability theorem and Young’s inequality. The stability analysis method suggested in the work could also be adopted in other practical plants. At last, the correctness and availability of this suggested approach are verified through simulation results.

Effect of surface radiation on the stability of hypersonic flat plate boundary layer

Transition of hypersonic boundary layer flow is an important problem in aerodynamic research. To obtain the natural transition position using the flow stability analysis method, it is necessary to analysis the neutral curve and the perturbation growth rule. Accurate calculation of the basic flow is the basis and prerequisite for stability analysis. This paper proposes that surface radiation should be considered in the analysis of hypersonic boundary layer flow stability due to the high temperatures at the vehicle surface caused by aerodynamic heating. In order to obtain the influence of surface radiation on the flow stability, we assume that the surface satisfies the energy balance and the gas satisfies calorimetrically perfect gas properties. To simplify the analysis, gas radiation has been neglected. The boundary layer analysis of a hypersonic flat plate with and without radiation has been performed by a combination of flow stability theory and direct numerical simulation. It is found that high temperature radiation on the surface causes energy to transfer outwards. The results showed that surface temperature decreases along the streamwise direction and is no longer an adiabatic surface temperature. Instability interval decreases and the maximum growth rate increases. The range of the instability region expressed in dimensionless frequency values moves to lower frequency as the Mach number increases. Maximum growth rate shows a tendency to increase and then decrease as the Mach number increases.

Seismic Reliability Analysis of an Excavation Slope Based on Direct Probability Integral Method

China, situated in the circum-Pacific seismic belt, experiences frequent seismic activity and faces diverse geological conditions, making structural stability of paramount importance, especially under seismic conditions. The majority of current earthquake generation methods do not consider the nonstationary nature of earthquakes. This paper introduces a spectral representation-random function model for generating nonstationary earthquakes, effectively simulating stochastic seismic ground motion. Furthermore, traditional slope stability analysis methods are deterministic and incapable of providing probabilistic assessments of slope instability. Therefore, this paper proposes a unified framework for static and dynamic structural reliability analysis based on the direct probability integration method, quantifying the impact of stochastic seismic ground motion on the dynamic reliability of slope stability. Finally, the proposed methods are applied to an excavation slope in Nanjing, using sliding displacement and safety factors as evaluation criteria to study the reliability of the slope under the influence of stochastic seismic events.

SPEED CONTROL OF PERMANENT MAGNET SYNCHRONOUS MOTOR IN SLIDING MODE

The paper examines a series of speed control algorithms for a synchronous permanent magnet motor in sliding mode, providing asymptotic stability of the first, second, and third order. In the sliding mode, the control system exhibits properties that are unattainable with classical continuous control algorithms. The control algorithms are developed based on the inverse dynamics method combined with the minimization of local instantaneous energy functionals. The key idea of the method lies in the reversibility of the direct Lyapunov method for stability analysis. The closed-loop control system has a predefined Lyapunov function, represented by the instantaneous energy. Notably, the control algorithms do not require knowledge of the object's parameters or differentiation operations, which facilitates their practical implementation. The regulator parameters consist solely of coefficients used to specify the desired duration and shape of current and motor speed transient processes. The vector speed control system comprises two controllers for the stator current components and the motor speed controller. All regulators operate in sliding mode. The output signals of the stator current component controllers and speed vary discontinuously from maximum to minimum values. Simulation results demonstrate the effectiveness and high-quality performance of the control algorithms. To determine the control performance indicators for the three synthesized speed controllers, the motor startup trajectory is formed from characteristic segments of constant, linearly increasing, and parabolic signals. The speed control algorithm with a first-order asymptote ensures zero tracking error only for a constant reference signal. With a linearly increasing reference signal, the steady-state relative tracking error is 2,5 %, while for a parabolic reference signal, the error varies between zero and 2,5 %. The second-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant and linearly increasing reference signals, and for a parabolic reference signal, the steady-state relative tracking error is 0,125 %. The third-order asymptotic speed control algorithm ensures zero steady-state tracking error for constant, linearly increasing, and parabolic reference signals, with a maximum dynamic relative tracking error of 0,05 %.

Dynamic stability analysis method of anchored rocky slope considering seismic deterioration effect

The seismic deterioration effects of anchor cables and slope structural planes are often neglected in the dynamic stability analysis of anchored rocky slopes to the extent that the stability of slopes is overestimated. In this paper, a dynamic calculation method for anchored rocky slopes considering the seismic deterioration effect is established, and a stability evaluation method for anchored rocky slopes based on the Gaussian mixture model is proposed. The seismic deterioration effect on the stability of anchored rocky slopes is quantitatively analyzed with an engineering example, and the relationship between seismic intensity and the failure probability of slopes is clarified. The results show that compared with the calculation method without considering the seismic deterioration effect, the minimum safety factor and post-earthquake safety factor obtained by the proposed method in this paper are smaller. The number of seismic deteriorations of the slope is used as the number of components of the Gaussian mixture model to construct the failure probability model of the slope, which can accurately predict the failure probability of anchored rocky slopes. The research results significantly improve the accuracy of the stability calculation of anchored rocky slopes, which can be used to guide the seismic design and safety assessment of anchored rocky slopes.

Stability Analysis of Milling Based on the Barycentric Rational Interpolation Differential Quadrature Method

Chatter causes great damage to the machining process, and the selection of appropriate process parameters through chatter stability analysis is of great significance for achieving chatter-free machining. This article proposes a milling stability analysis method based on the barycentric rational interpolation differential quadrature method (DQM). The dynamics of the milling process considering the regeneration effect is first modelled as a time-delay differential equation (DDE). When adjacent pitch angles of the milling cutter are symmetric, the milling dynamic equation contains a single time delay. Otherwise, when adjacent pitch angles are asymmetric, the dynamic equation contains multiple time delays. The barycentric rational interpolation DQM is then used to approximate the differential and delay terms of the milling dynamics equation, and to construct a state transition matrix between adjacent milling periods. Finally, the chatter stability lobe diagram (SLD) is obtained based on the Floquet theory. According to the SLD, the appropriate spindle speed can be selected to obtain the maximum stable axial depth of cutting, thereby effectively improving the material removal rate. The accuracy and efficiency of the proposed method have been validated by two widely used milling models, and the results show that the proposed method has good accuracy and computational efficiency.

Quasi-3D slope stability analysis of waste dump based on double wedge failure

The double wedges sliding along the weak layer of the foundation can be observed on the slope of the waste dump and the sliding body is divided into the active wedge and passive wedge by the weak foundation and the failure surfaces of the waste dump. Because the conventional limit equilibrium slice method cannot reflect the polygonal slip surface of the slope of the waste dump with weak foundation, this study proposed a double wedge calculation method for the slope of the waste dump with weak foundation. The limit equilibrium analysis is performed on double wedges by considering the direction and values of the interaction force between double wedges to obtain the safety factor of the slope of the waste dump. Meanwhile, the quasi-3D double wedges stability analysis method of the waste dump slope with weak foundation is proposed by considering the influence of the geometry and sliding direction of the slope surface on the slope stability. The safety factor of the inverted dump slope is 0.82, the volume of the sliding body is 6.43 million m3, and the main sliding direction is 20° south by east. The shear strain rate cloud diagram of the section is ‘y’ type distribution, and the sliding body is divided into two independent blocks. The safety factor of the sliding body section obtained by the double wedge method is between 0.76 and 0.92, and the closer to the boundary of the sliding body, the greater the safety factor of the section. The quasi-three-dimensional safety factor obtained by theoretical analysis is 0.817. The results show that the calculation results of quasi-3D double wedge are basically consistent with the calculation results of strength reduction method, while the proposed method is simpler. It can be used as a quick method to evaluate slope stability in engineering practice.

Stability and Synchronization of Delayed Quaternion-Valued Neural Networks under Multi-Disturbances

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory.

A Static Stability Analysis Method for Passively Stabilized Sounding Rockets

Sounding rockets constitute a class of rocket with a generally simple layout, being composed of a cylindrical center-body, a nosecone, a number of fins placed symmetrically around the longitudinal axis (usually three or four), and possibly a boat-tail. This type of flying craft is typically not actively controlled; instead, a passive stabilization effect is obtained through suitable positioning and sizing of the fins. Therefore, in the context of dynamic performance analysis, the margin of static stability is an index of primary interest. However, the classical approach to static stability analysis, which consists in splitting computations in two decoupled domains, namely, around the pitch and yaw axis, provides a very limited insight to the missile performance for this type of vehicle due to the violation of the classical assumptions of planar symmetry and symmetric flight conditions commonly adopted for winged aircraft. To tackle this issue, this paper introduces a method for analyzing static stability through a novel index, capable of more generally assessing the level of static stability for sounding rockets, exploiting the same information on aerodynamic coefficients typically required for more usual (i.e., decoupled) static stability analyses, and suggests a way to assess the validity and shortcoming of the method in each case at hand.

Complex pattern evolution of a two-dimensional space diffusion model of malware spread

In order to investigate the propagation mechanism of malware in cyber-physical systems (CPSs), the cross-diffusion in two-dimensional space is attempted to be introduced into a class of susceptible-infected (SI) malware propagation model depicted by partial differential equations (PDEs). Most of the traditional reaction-diffusion models of malware propagation only take into account the self-diffusion in one-dimensional space, but take less consideration of the cross-diffusion in two-dimensional space. This paper investigates the spatial diffusion behaviour of malware nodes spreading through physical devices. The formations of Turing patterns after homogeneous stationary instability triggered by Turing bifurcation are investigated by linear stability analysis and multiscale analysis methods. The conditions under the occurence of Hopf bifurcation and Turing bifurcation in the malware model are obtained. The amplitude equations are derived in the vicinity of the bifurcation point to explore the conditions for the formation of Turing patterns in two-dimensional space. And the corresponding patterns are obtained by varying the control parameters. It is shown that malicious virus nodes spread in different forms including hexagons, stripes and a mixture of the two. This paper will extend a new direction for the study of system security theory.

Efficient numerical implementation of limit equilibrium method for stability analysis of unsaturated soil slopes using Gaussian integral

Unsaturated soil is widely distributed around the world but less considered in design due to the absence of a convenient analysis method in practice. The Morgenstern–Price (MP) method incorporating the extended Mohr–Coulomb shear strength equation provides a reliable approach to evaluate slope stability in such conditions. However, this method is time-consuming due to the need for a tedious trial-and-error process in determining the scaling factor, which involves complex iterations during each trial. Furthermore, since the relatively complicated nature of unsaturated soil, a dense slice division is necessary to obtain reliable results, making the analysis even more cumbersome. In this paper, an improved MP method for unsaturated soil slope stability analysis is presented, which eliminates the need for a dense slice mesh by employing only a few strategically placed Gauss points along the slip surface. Moreover, the trial-and-error process for determining the scaling factor with the corresponding complex iterations is replaced by an efficient search algorithm with a more concise iteration process, resulting in a more convenient implementation of the proposed method. Extensive examples are provided to validate the effectiveness of the proposed improved MP method, indicating its potential as an accurate and efficient analysis method for unsaturated soil slopes in practical application and relative study involving repetitive analyses.

Interval analysis of the small‐signal stability of grid‐connected voltage‐source converter system considering multiparameter uncertainty

AbstractGrid‐connected voltage source converters (VSCs) have been broadly applied in modern power system. However, instability issues may be triggered by the integration of grid‐connected VSCs, jeopardising the operation of the power grid. Conventional stability analysis methods can be utilised to derive system stability margins under nominal conditions. Whereas grid‐connected VSCs inevitably operate under multiparameter uncertainty, which may result in overly optimistic or even incorrect estimations of stability margins, thereby posing potential risks to system operation. To address this issue, an interval small‐signal stability analysis approach is proposed to investigate the system stability under multiparameter uncertainty. First, the interval state‐space model of the grid‐connected VSC system is constructed based on interval symbolic linearisation. Furthermore, the interval eigenvalue decomposition is introduced to calculate the interval eigenvalue distribution of the interval state‐space model. Eventually, the upper bounds of the real part of the dominant interval eigenvalues are utilised for deriving interval stable parameter regions. Results of Monte Carlo analysis and time‐domain simulations of the grid‐connected VSC system are utilised to verify the effectiveness of the proposed interval stability analysis method.

An Iteratively-Nested Modeling Method for Stability Analysis of the Multirate Power System

An Iteratively-Nested Modeling Method for Stability Analysis of the Multirate Power System

Injection-Space Security Region for Sub/Super-Synchronous Oscillation in Wind Power Integrated Power Systems

The complex interactions between converter-based wind turbine generators (WTGs) and power grid have brought new sub/super-synchronous oscillation (SSO) issues. The stability of such oscillation is closely related to system operating conditions. Thus it is necessary to identify SSO stability under various possible operating conditions. To achieve this, this paper first proposes the concept of security region (SR) for SSO, which is composed of all operating points in the injection space to ensure the stability of SSO modes. Then an operating condition dependent impedance model-based oscillation stability analysis method is developed to evaluate the SSO stability. Next, the predictor-corrector technique is adopted to build the SR boundary using the correlation among adjacent boundary points. The boundary is further approximated via hyperplane fitting according to its topological property. Finally, the proposed method is applied on a practical wind power system suffering SSO to construct the SR. Its effectiveness as well as advantages over traditional point-wise based method are demonstrated with random experiment and EMT simulation.

A Small-Signal Stability Analysis Method Based on Minimum Characteristic Locus and Its Application in Controller Parameter Tuning

A small-signal stability analysis method based on minimum characteristic locus (MCL) was recently proposed by the authors. The method is found to be particularly useful in analyzing various oscillation modes in a unified way. The present work continues this line of research. After providing a brief review of the basic principle of MCL method, the paper proceeds to show the mathematical relationship between the stability margin obtained using an MCL method, and that obtained by traditional modal analysis method. Next, a sensitivity analysis procedure is proposed to study quantitatively the effects of control parameters on the stability of the system. Third, the properties of the so-called exciter mode are explained in detail, in particular, explicit formulas of exciter mode frequency and power system stabilizer (PSS) critical gain are derived. Finally, taking PSS4B as an example, a controller parameter tuning method is proposed. The effectiveness and practicability of the proposed method are verified by case studies of Kundur's four-machine-two-area system and China's Yunnan power grid.

State estimation-based parameter identification for a class of nonlinear fractional-order systems

Parametric identification is an important part of system theory since knowledge of the parameters allows the analysis and control of the system. The aim of this paper is to propose a novel robust (against measurement noise) parameter identification method for a class of nonlinear fractional-order systems. In order to solve the parametric identification we carry out this problem to a state estimation problem, we introduce a Fractional Algebraic Identifiability (FAI) property which allows to represent the system parameters as a function of the inputs and outputs of the system, this parameter identification method provides an on-line identification process (while the system is operating), we also propose a fractional-order differentiator which allows to reduce the effect of measurement noise as well as to provide the estimation of a fractional-order derivative of the system output. Moreover, we use the Mittag–Leffler boundedness to demonstrate the convergence of this method, a different approach for this stability analysis method is given in this paper. Finally, we illustrate the accuracy and robustness of our proposed method by means of the parametric identification of two nonlinear fractional-order systems: a time-varying nonlinear fractional-order system and a nonlinear fractional-order mathematical model of a simple pendulum.