Stability Analysis Method Research Articles

Mapping submarine landslides susceptibility in continental slopes with rich gas hydrates

Gas production from oceanic hydrates could trigger large submarine landslides. To screen out the sites susceptible to perturbation, this paper proposes a physically-based model for assessing the susceptibility of submarine landslides in continental slopes where gas hydrates are widespread. The model does not require an inventory of historical submarine landslides that are often incomplete or unavailable. Instead, the model is derived within the framework of the limit equilibrium method of slope stability analysis, and accounts for pressure buildup and decreasing cohesion in the slope due to hydrate dissociation. The proposed model is then employed to map the landslide susceptibility of a study area conditioned to a hypothetical scenario of seafloor warming that triggers hydrate dissociation. The susceptible zones are found in the regions with shallow water and high geothermal temperature. Unlike the terrestrial landslides, the slope angle plays a secondary role in affecting the susceptibility of submarine landslides triggered by hydrate dissociation, while the hydrothermal conditions are important factors that control the susceptibility.

Advanced stability analysis method for the tunnel face in jointed rock mass based on DFN-DEM

An advanced stability analysis of surrounding rock can assure safe construction in tunnels. However, in traditional analysis methods, geometric information on the rock mass discontinuities is obtained by a geological compass and treated as an infinitely expanded plane in a numerical simulation, which is inaccurate in both geometric and numerical models. To solve this problem, this paper studied a control network and an image stitch method to assess the accuracy of a geometric model and proposed a more accurate method to obtain the geometric information of rock mass discontinuities based on digital photogrammetry. Based on discrete fracture network and discrete element method (DFN-DEM), this paper treated the rock mass discontinuities obtained by digital photogrammetry as finite disk planes and simulated the excavation process of the Qianyu tunnel. According to the simulation results, this paper determined the specific location of the collapse disaster on the tunnel face, which is of great significance to tunnel support design. Comparing the deformation of the surrounding rock mass on the tunnel face in the simulation results with the actual situation, this paper verified the feasible accuracy of this method in analysing the stability of the surrounding rock mass on a tunnel face in advance.

A perturbation method for upper bound analysis of stability of slopes based on rigid translational/rotational moving elements

Collapse mechanisms consisting of translational or rotational rigid blocks are widely used as the basis for computing the upper bound on the factor of safety in slope stability problems. Constructing admissible velocities for these blocks mechanism often relies on experience, and optimizing these blocks can be cumbersome work, especially for layered slopes containing both hard and soft layers. In this paper, we present a numerical technique for evaluating and optimizing mechanisms composed of an arbitrary number of spline rigid translational/rotational moving elements, assuming plane strain material obeys the Mohr-Coulomb yield condition. In the proposed method, coordinates defining the nodes of the blocks are treated as unknowns, and the optimal geometry is found by successively perturbing node coordinates and block velocities, starting initially from a user-specified structured mesh. Two different definitions of the factor of safety are considered and the corresponding analysis procedures are introduced. The proposed method is applied to four examples related to slope stability analysis, and these examples illustrate that the proposed method is an efficient and reasonable way to analyze the stability of slopes.

Linear programming based lower bounds on average dwell-time via multiple Lyapunov functions

With the objective of developing computational methods for stability analysis of switched systems, we consider the problem of finding the minimal lower bounds on average dwell-time that guarantee global asymptotic stability of the origin. Analytical results in the literature quantifying such lower bounds assume existence of multiple Lyapunov functions that satisfy some inequalities. For our purposes, we formulate an optimization problem that searches for the optimal value of the parameters in those inequalities and includes the computation of the associated Lyapunov functions. In its generality, the problem is nonconvex and difficult to solve numerically, so we fix some parameters which results in a linear program (LP). For linear vector fields described by Hurwitz matrices, we prove that such programs are feasible and the resulting solution provides a lower bound on the average dwell-time for exponential stability. Through some experiments, we compare our results with the bounds obtained from other methods in the literature and we report some improvements in the results obtained using our method.

A review of system topologies, key operation and control technologies for offshore wind power transmission based on HVDC

AbstractOffshore wind farm (OWF) is considered as a perfect zero‐carbon energy source for the future power system. However, the growing offshore distance and water depth of OWF make the OWF HVDC transmission technique a more promising solution than HVAC due to higher cost‐efficiency and reliability. In this paper, the current situation of OWF‐HVDC projects is introduced at first. Then, novel converter topologies with the higher power density and cost‐efficiency are presented, including the hybrid modular multilevel converter (MMC), alternative arm converter (AAC), and diode rectifier (DR). Next, several OWF HVDC transmission system topologies are introduced, including terminal‐hybrid, station‐hybrid and all‐DC delivered system. Furthermore, the key technologies for OWF HVDC operation and control are summarized, including grid‐forming control strategy for offshore wind turbines, stability analysis method, corresponding stability enhancement measures and frequency support control strategies. Additionally, the fault ride‐through and protection strategies for different fault locations have been presented. Finally, the main conclusions and prospects for OWF HVDC are summarized.

Analysis and Suppression of High-Frequency Resonance for Offshore Wind Power Grid-Connected Converter Considering Cable Capacitance Effect

Large-scale offshore wind farms have become the development trend in wind power generation. Long submarine cables are used to collect electrical energy in the collection networks of offshore wind farms. However, the distributed capacitance of cables cannot be ignored, which makes the impedance of the collection network complex and changeable. It is common to encounter high-frequency harmonic resonance (HFHR) problems when cables interact with wind turbine generators (WTGs). The HFHR may threaten the safe and stable operation of wind turbines. In order to solve this problem, firstly, the impedance of a collection network was constructed. Furthermore, the wind farm collection network was divided into the equivalent wind turbine subsystem (EWTS) and the remaining equivalent wind farm subsystem (REWFS). Then, the mechanism of HFHR was revealed based on the impedance stability analysis method. The effects of cable parameters, the number of connected WTG, and the grid impedance on the HFHR of the interconnected system were also analyzed. Finally, the hybrid damping control method, combining active damping control (ADC) and passive damping control (PDC), was proposed to suppress the resonance. A simulation and experiment were performed to verify the effectiveness of the analysis results and proposed control method.

A Gray-Box Stability Analysis Method of Grid-Connected Inverter Considering Synchronization Dynamics

The Grid-Connected Inverter (GCI) can be considered a gray box when circuit and controller parameters are missing due to intellectual property rights or parameter variations caused by aging, which poses an impediment to assessing the stability of the system. This paper presents a gray-box stability analysis method based on impedance identification of GCI considering the synchronization dynamics. The impedance frequency responses of GCI are measured by the frequency scanning method on the dq-frame. Meanwhile, the influence of synchronization dynamics and background harmonics is theoretically investigated. A vector fitting (VF) algorithm, co-designed with impedance identification, is then applied to generate polynomial transfer functions. Based on the obtained transfer functions, the stability of the GCI can be judged by the distance relationship between the prohibited area boundary and the center of the gershgorin-circle through the distance formula. Finally, the experiments of both RT-LAB and experimental prototypes are conducted to verify the feasibility of the proposed method.

An Improved Robust Deadbeat Predictive Current Control for the Consequent-Pole Hybrid Excitation Motor

This paper proposes an improved robust deadbeat predictive current control (DPCC) to optimize the current loop control performance of the hybrid excitation motor (HEM) drive system, which is a multi-variable and strongly coupled system. First, the topology and mathematical model of a consequent-pole hybrid excitation machine (CPHEM) are introduced. In order to optimize the current performance of HEM drive system, a DPCC strategy is proposed, followed by a proposed stability analysis method for parameter mismatch. In addition, a robust deadbeat predictive current control (RDPCC) based on extended state observer (ESO) is proposed to suppress the effects of parameter mismatch in DPCC. Furthermore, in the predictive control of HEMs, the divergence of current prediction is caused by certain combinations of controller parameters, which is not resolved by RDPCC. To deal with this issue, the estimation equations of the virtual parameter are introduced into the current prediction of RDPCC. Finally, the effectiveness of proposed control strategy is verified in experiments.

Stability Analysis of Phase Locked Loops for AC Microgrids With Hybrid Power Sources

Synchronous instability of the multiple distributed generations has been an important issue for microgrids. Therein, the phase locked loop (PLL) instability is one of the significant reason for synchronous instability of multi-inverter microgrids. Although this instability issue has been widely studied, it is ignored for microgrids with numerous inverters controlled through different controllers. To full this gap, this paper proposes a multi-inverter parallel microgrid stability analysis method based on PLL. Firstly, this paper establishes a PLL small signal model based on the droop control strategy and the P&Q control strategy. Furthermore, the whole PLL small signal analysis model of multi-inverter parallel microgrid is proposed by signal flow graph and Mason Gain Theorem, which is more convenient for power engineers. Eventually, the closed-loop transfer function of PLL is obtained. The proposed integrated small signal model can predict the synchronous stability regarding the PLL of the multi-inverter under grid-connected mode and the island mode. Finally, the simulation and experimental results can well validate the feasibility and effectiveness of the proposed stability analysis strategy based on PLL in the multi-inverter parallel microgrid. Therein, the simulation and experimental results illustrate that the proposed stability identification approach can provide an effective stability control parameter selection method.

A novel linear stability analysis method for plane Couette flow considering rarefaction effects

Following the stability analysis method in classic fluid dynamics, a linear stability equation (LSE) suitable for rarefied flows is derived based on the Bhatnagar–Gross–Krook (BGK) equation. The global method and singular value decomposition method are used for modal and non-modal analysis, respectively. This approach is validated by results obtained from Navier–Stokes (NS) equations. The modal analysis shows that LSEs based on NS equations (NS-LSEs) begin to fail when the Knudsen number ($Kn$) increases past$\sim$0.01, regardless of whether a slip model is used. When$Kn\geq 0.01$, the growth rate of the least stable mode is generally underestimated by the NS-LSEs. Under a fixed wavenumber, the pattern (travelling or standing wave) of the least stable mode changes with$Kn$; when the mode presents the same pattern, the growth rate decreases almost linearly with increasing$Kn$; otherwise, rarefaction effects may not stabilize the flow. The characteristic lengths of the different modes are different, and the single-scale classic stability analysis method cannot predict multiple modes accurately, even when combined with a slip model and even for continuum flow. However, non-modal analysis shows that this error does not affect the transient growth because modes with small growth rates offer little contribution to the transient growth. In rarefied flow, as long as the Mach number ($Ma$) is large enough, transient growth will occur in some wavenumber ranges. The rarefaction effect plays a stabilizing role in transient growth. The NS-LSEs-based method always overestimates the maximum transient growth.

A combined method for stability analysis of linear time invariant control systems based on Hermite‐Fujiwara matrix and Cholesky decomposition

AbstractIn this paper, we have developed an integrative method for checking the stability of linear time‐invariant (LTI) systems as well as nonlinear continuous‐time ones. In our method, we first apply the iterative Faddeev–Leverrier algorithm to obtain the characteristic polynomial of the LTI system. Subsequently, the associated Hermite‐Fujiwara matrix will be evaluated by a particularly efficient technique for the calculation of the Bézoutian matrices. The positive‐definiteness of the Hermite‐Fujiwara form, as the stability criterion, is next tested by performing the Cholesky decomposition. Our method is extended to assess the local stability of nonlinear continuous‐time systems with the help of the Jacobian matrix concept. The proposed method is demonstrated to approximately be 2.2 times faster than the classical Hurwitz algorithm in average, at least for matrices with dimensions less than 40, according to a performed central processing unit (CPU) time analysis. For the sake of illustration, four numerical examples are given, including dynamical models for a real‐world hydrolysis reactor and a well‐mixed bioreactor.

Event-triggered tracking control of uncertain [formula omitted]-normal nonlinear systems with full-state constraints

This paper investigates the tracking control problem of uncertain p-normal nonlinear systems with full-state constraints via event-triggered mechanism. By skillful constructing an adaptive dynamic gain and a time-varying event-triggered strategy, a state-feedback controller is proposed to achieve practical tracking. The adaptive dynamic gain is incorporated to deal with the system uncertainties and eliminate the bad effect of the sampling error. A rigorous Lyapunov stability analysis method is put forward to verify that all the closed-loop signals are uniformly bounded and the tracking error converges into a prescribed arbitrary accuracy, and full-state constraints are not violated. Compared with the existing event-triggered strategies, the proposed time-varying event-triggered strategy is low-complexity without designing the hyperbolic tangent function.

Observer-based quantised control of networked systems with round-robin protocol and transmission delay

This paper addresses the ultimate boundedness control problem for a class of networked nonlinear systems with the round-robin (RR) protocol and uniform quantisation. The communication between sensor nodes and the controller is implemented via a constrained communication channel. The quantised output of the system is transmitted to the remote controller through a communication channel subject to a transmission delay. For the purpose of alleviating possible data collision, the well-known RR communication protocol is deployed to schedule the data transmissions. On the other hand, the uniform quantisation effects of the network are characterised by a round function (i.e. the nearest integer function). The purpose of the addressed problem is to design an observer-based controller for the networked nonlinear systems such that, in the presence of RR protocol and uniform quantisation effects, the closed-loop system is ultimately bounded. The controller is designed based on mean square stability analysis and Lyapunov-like method. A set of sufficient conditions for the ultimate boundedness of the closed-loop system are established and, on the basis of which, the desired controller gains are obtained by solving a set of linear matrix inequalities. The effectiveness of the proposed method is verified by numerical examples.

One simplified method for seismic stability analysis of an unsaturated slope considering seismic amplification effect

Seismic amplification effect in soil slope is not considered by traditional Newmark method; therefore, there will be some deviation in soil slope seismic stability analysis. In order to determine the effect of seismic amplification effect, a simplified method for unsaturated slope stability evaluation is proposed by coupling the Sweden slice method and Newmark method. Research results show that the seismic amplification effect has a great influence on yield acceleration of the slope while it exerts a little influence on critical slip surface shape; if the seismic amplification effect is not considered, permanent displacement of the slope will be underestimated, and there is potential danger in seismic design of slope engineering. Finally, an unsaturated slope model with 1:20 scale is designed through derivation of similarity law, and progressive failure process of the slope under seismic action is simulated. The results of our proposed method are in good agreement with experimental results, which proves the feasibility of our proposed method. This study can provide a simple and reliable method for evaluating the seismic stability of an unsaturated slope.

Slope stability assessment of some waste rock dumps at a typical gold mine in Ghana

Mining results in both economic and uneconomic materials being generated. The uneconomic materials (wastes) are stacked in a convenient place for further use or stored permanently as a slope or embankment. In Ghana, a typical gold mine set up dumping sites to accommodate the waste generated from its operations. Samples were collected from three waste dumps and tested in the laboratory, and the parameters obtained were used as input for 2D model development. The Factor of Safety (FS) of the three waste dumps were determined using the Janbu Generalised slope stability analysis method. Path and slope surface (circular and non-circular) search methods were used for the three cases. The FS for the waste dumps were determined and ranged from 1.61-2.74, 1.49- 2.50 and 1.32-2.10 under dry, static and pseudo-static loading conditions, respectively. These values exceed the minimum requirements of 1.1-1.5 for stability conditions. The geometry of the waste dumps, Suraw Waste Dump (SWD), is within the standard and hence, does not require reshaping, while the slope angles for the remaining waste dumps, Tano Waste Dump (TWD) and Akoti Waste Dump (AWD) need to be reshaped to achieve the proposed slope angle of 3H:1V (18.40 degrees) as stipulated in the mine’s Environmental Impact Statement (EIS).

A three‐dimensional limit equilibrium method for slope stability analysis integrating machine learning optimized intercolumn force function

A calculation of the safety factor is the basis of slope stability analysis. The three‐dimensional (3D) limit equilibrium method is one of the most effective safety calculation methods, and ignoring the partial shear force between columns is the most common calculation assumption, which will lead to an unreasonable safety factor. By constraining the range of the intercolumn shear function and the position of the action point of the force between columns and integrating machine learning to optimize the net moment of the column, the simulated annealing algorithm is used to obtain the intercolumn shear function under the minimum net moment, and the safety factor is calculated by using boundary conditions. Finally, proving the accuracy of this method by calculating two examples of commonly used slopes. Example A verifies that the result of the proposed method is more conservative than that of other 3D calculation methods and that the coordinates of the action point of the intercolumn forces in the and directions have little influence on safety factor. Example B verifies the applicability of this method to various slope forms. This method fully considers the stress of soil under actual conditions, making the calculation results more reasonable.

Research on an Improved Method for Galloping Stability Analysis Considering Large Angles of Attack

In view of the deficiency of the quasi-steady galloping critical wind speed calculation method based on the classical Den Hartog criterion, this paper proposes a quasi-steady galloping stability analysis method that considers the wind attack angle criterion (dCV/dα) through theoretical analysis. Firstly, the tri-component force coefficients of a square-section model were measured through wind tunnel tests, and the galloping force coefficients calculated with three different galloping criteria (the dCV/dα criterion, Den Hartog criterion, and Xie criterion) were compared and analyzed. Secondly, to further verify the reliability and applicability of the criteria proposed in this study, wind tunnel tests and numerical simulations were conducted on an H-shaped section. The verification results of the H-shaped section showed that under the action of the incoming flow at a large angle of attack of 70°, the maximum error of the classic Den Hartog criterion could reach about 44%. This study used the dCV/dα criterion while considering the large angle of attack of the incoming flow, and its calculation error could be controlled within 10%. At the same time, the numerical simulation showed that there was serious aerodynamic instability in this section under the critical wind speed. A pair of periodic vortex structures were formed in the wake region of the H-shaped section, resulting in constant generation and separation phenomena, which induced structural instability.

A transient stability analysis method for wind power system with thyristor controlled phase shifting transformer based on branch potential energy index

With the growing usage of renewable energy technologies like wind power and photovoltaics, and the increased integration of FACTS (Flexible Alternating Current Transmission System) devices into the power system, the transient characteristics of the evolving power system undergo changes that require appropriate analysis methods. As a new type of FACTS device, TCPST (Thyristor Controlled Phase Shifting Transformer) is introduced to facilitate the superior operation of renewable energy sources by controlling the power flow of access branches. From the perspective of branches, the dynamic characteristics of renewable energy sources and TCPST might be uniformly studied and simply calculated in the transient stability analysis. Therefore, the paper proposes a transient stability analysis method for wind power systems with TCPST based on the branch potential energy index. First, considering the variation characteristics of branch potential energy, this paper employed the stability index to analyze the transient stability of branches and the system by finding vulnerable lines. Then, based on the stability index, the paper investigates the influence of wind turbine removal, the installation and control parameter adjustment of TCPST on the transient stability of wind power systems. The simulation results in PSAT demonstrate that the removal of a proper amount of wind turbine post-fault and the installation of TCPST can improve the transient stability of the wind power system. Furthermore, it can also be improved by reasonably adjusting the TCPST control parameters. All simulation results are verified by the time domain simulation method.

Dynamic Response of a Flexible Multi-Body in Large Wind Turbines: A Review

Dynamic response of flexible multi-body large wind turbines has been quickly growing in recent years. With the new normal economic policy, the economy of China is developing innovatively and stably. New energy development and utilization is an important strategy for people’s lives and economic development around the world. It is feasible to analyze from a broad perspective. In particular, the development and application of wind power is affecting the economic development of industry to a certain extent. Persistent and significant large wind turbines have cast concern over the prospects of wind power technology, and a comprehensive development potential of wind power technology has been analyzed its potential use in the future. The multi-body dynamics method can better analyze and describe the impact of flexible blade elastic deformation on motion characteristics and provides a practical analysis method for the aeroelastic stability analysis and control system design of wind turbines.

Improvement research on the stability of explicit integration algorithms with 3D viscoelastic artificial boundary elements

PurposeWhen explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.Design/methodology/approachA stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.FindingsNumerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.Originality/valueThe stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.