Improved 2-D Stability Margin Test for 2-D Discrete Systems

An improved 2 D stability margin test and its algorithm for 2 D discrete systems are proposed.The stability margin test procedure can be slmplified by using the inner term polynomials of B(z 1,z 2) to construct a margin test table.Different from other well known 2 D stability margin test algorithms,the new approach can directly obtain the stability margin.

The stability margin on EAST tokamak

The experimental advanced superconducting tokamak （EAST） is the first full superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. Its poloidal coils are relatively far from the plasma due to the necessary thermal isolation from the superconducting magnets, which leads to relatively weaker coupling between plasma and poloidal field. This may cause more difficulties in controlling the vertical instability by using the poloidal coils. The measured growth rates of vertical stability are compared with theoretical calculations, based on a rigid plasma model. Poloidal beta and internal inductance are varied to investigate their effects on the stability margin by changing the values of parameters αn and γn（Howl et al 1992 Phys. Fluids B 4 1724）, with plasma shape fixed to be a configuration with k = 1.9 and 5 = 0.5. A number of ways of studying the stability margin are investigated. Among them, changing the values of parameters κ and li is shown to be the most effective way to increase the stability margin. Finally, a guideline of stability margin Ms（ki, li, A） to a new discharge scenario showing whether plasmas can be stabilized is also presented in this paper.

Stability margin of the quadruped bionic robot with spinning gait

Spinning gait is valuable for quadruped robot,which can be used to avoid obstacles quickly for robot walking in unstructured environment. A kind of bionic flexible body is presented for quadruped robot to perform the spinning gait. The spinning gait can be achieved by coordinated movement of body laterally bending and legs swing,which can improve the mobility of robot walking in the unstructured environments. The coordinated movement relationship between the body and the leg mechanism is presented. The stability of quadruped robot with spinning gait is analyzed based on the center of gravity( COG) projection method. The effect of different body bending angle on the stability of quadruped robot with spinning gait is mainly studied. For the quadruped robot walking with spinning gait,during one spinning gait cycle,the supporting polygon and the trajectory of COG projection point under different body bending angle are calculated. Finally,the stability margin of quadruped robot with spinning gait under different body bending angle is determined,which can be used to evaluate reasonableness of spinning gait parameters.

Geothermal investigation of the thickness of gas hydrate stability zone in the north continental margin of the South China Sea

The exploration of unconventional and/or new energy resources has become the focus of energy research worldwide,given the shortage of fossil fuels.As a potential energy resource,gas hydrate exists only in the environment of high pressure and low temperature,mainly distributing in the sediments of the seafloor in the continental margins and the permafrost zones in land.The accurate determination of the thickness of gas hydrate stability zone is essential yet challenging in the assessment of the exploitation potential.The majority of previous studies obtain this thickness by detecting the bottom simulating reflectors（BSRs） layer on the seismic profiles.The phase equilibrium between gas hydrate stable state with its temperature and pressure provides an opportunity to derive the thickness with the geothermal method.Based on the latest geothermal dataset,we calculated the thickness of the gas hydrate stability zone（GHSZ） in the north continental margin of the South China Sea.Our results indicate that the thicknesses of gas hydrate stability zone vary greatly in different areas of the northern margin of the South China Sea.The thickness mainly concentrates on 200–300 m and distributes in the southwestern and eastern areas with belt-like shape.We further confirmed a certain relationship between the GHSZ thickness and factors such as heat flow and water depth.The thickness of gas hydrate stability zone is found to be large where the heat flow is relatively low.The GHSZ thickness increases with the increase of the water depth,but it tends to stay steady when the water depth deeper than 3 000 m.The findings would improve the assessment of gas hydrate resource potential in the South China Sea.

Stability margin of uncertain control systems

Achieving stability is the essential issue in the control system design. In this paper, four approaches that can be used to calculate the stability margin of the interval plant family are summarized and compared. The μ approach gives the bounds of the stability margin, and good estimation can be obtained with the numerical method. The eigenvalue approach yields accurate value, and the MATLAB＇s function robuststab sometimes provides wrong results. Since the eigenvalue approach is both accurate and computationally efficient, it is recommended for the calculation of the stability margin, while utilization of the function robuststab should be avoided due to the unreliable results it gives.

Examine the Stability Margin of Cascade Circuits

This paper proposes an engineering approach to examine the stability margin of cascade circuits. The proposed measurement injects an external perturbation current into the cascade interface and measures the load-side response current. The system stability margin can be figured out by comparing the magnitudes of the perturbation current and the response current. The proposed measurement is strictly derived in theory, implemented with details, and demonstrated by experiment.

Adaptive PI Control Based Stability Margin Configuration of Aircraft Control Systems with Unknown System Parameters and Time Delay

The stability margin is a vital indicator for assessing the safety level of aircraft control systems.It should maintain sufficient stability margin to ensure safety during flight,especially in the process of large maneuver operations.The stability margin is generally quantified by the Bode diagram,which strictly depends on the system parameters and the open-loop transfer function.However,due to the uncertain flight environments,transmission delays of sensors and mode switchings,etc.,there exist large parameter and structure uncertainties in the aircraft control systems,which make it difficult to precisely configure the stability margin to the desired value by the usual control methods.To address this problem,an indirect adaptive control strategy is proposed in this paper,where an adaptive PI control law with the capability of self-configuration of stability margin is developed.The developed control law not only achieves stable time-varying command tracking in the time domain,but also is able to automatically configure the phase margin and gain margin in the frequency domain.Finally,the simulation of the one-degree-of-freedom roll rate control model of the air vehicle verifies the validity of the proposed control method.

Identification of the Worst-case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

Calculation of static voltage stability margin(SVSM)of AC/DC power systems with lots of renewable energy sources(RESs)integration requires consideration of uncertain load growth and renewable energy generation output.This paper presents a bi-level optimal power flow(BLOPF)model to identify the worst-case SVSM of an AC/DC power system with line commutation converter-based HVDC and multi-terminal voltage sourced converter-based HVDC transmission lines.Constraints of uncertain load growth’s hypercone model and control mode switching of DC converter stations are considered in the BLOPF model.Moreover,uncertain RES output fluctuations are described as intervals,and two three-level optimal power flow(TLOPF)models are established to identify interval bounds of the system worst-case SVSM.The two TLOPF models are both transformed into max–min bi-level optimization models according to independent characteristics of different uncertain variables.Then,transforming the inner level model into its dual form,max–min BLOPF models are simplified to single-level optimization models for direct solution.Calculation results on the modified IEEE-39 bus AC/DC case and an actual large-scale AC/DC case in China indicate correctness and efficiency of the proposed identification method.

Chaos quantum particle swarm optimization for reactive power optimization considering voltage stability

The reactive power optimization considering voltage stability is an effective method to improve voltage stablity margin and decrease network losses,but it is a complex combinatorial optimization problem involving nonlinear functions having multiple local minima and nonlinear and discontinuous constraints. To deal with the problem,quantum particle swarm optimization (QPSO) is firstly introduced in this paper,and according to QPSO,chaotic quantum particle swarm optimization (CQPSO) is presented,which makes use of the randomness,regularity and ergodicity of chaotic variables to improve the quantum particle swarm optimization algorithm. When the swarm is trapped in local minima,a smaller searching space chaos optimization is used to guide the swarm jumping out the local minima. So it can avoid the premature phenomenon and to trap in a local minima of QPSO. The feasibility and efficiency of the proposed algorithm are verified by the results of calculation and simulation for IEEE 14-buses and IEEE 30-buses systems.

QUANTITATIVE METHODOLOGY FOR STABILITY ANALYSIS OF NONLINEAR ROTOR SYSTEMS

Rotor-bearings systems applied widely in industry are nonlinear dynamic systems of multi-degree-of-freedom. Modem concepts on design and maintenance call for quantitative stability analysis. Using trajectory based stability-preserving and dimensional-reduction, a quantitative stability analysis method for rotor systems is presented. At first, an n-dimensional nonlinear non-autonomous rotor system is decoupled into n subsystems after numerical integration. Each of them has only onedegree-of-freedom and contains time-varying parameters to represent all other state variables. In this way, n-dimensional trajectory is mapped into a set of one-dimensional trajectories. Dynamic central point （DCP） of a subsystem is then defined on the extended phase plane, namely, force-position plane. Characteristics of curves on the extended phase plane and the DCP＇s kinetic energy difference sequence for general motion in rotor systems are studied. The corresponding stability margins of trajectory are evaluated quantitatively. By means of the margin and its sensitivity analysis, the critical parameters of the period doubling bifurcation and the Hopf bifurcation in a flexible rotor supported by two short journal bearings with nonlinear suspensionare are determined.

A Data-driven Method for Transient Stability Margin Prediction Based on Security Region

Transient stability assessment(TSA)based on security region is of great significance to the security of power systems.In this paper,we propose a novel methodology for the assessment of online transient stability margin.Combined with a geographic information system(GIS)and transformation rules,the topology information and pre-fault power flow characteristics can be extracted by 2 D computer-vision-based power flow images(CVPFIs).Then,a convolutional neural network(CNN)-based comprehensive network is constructed to map the relationship between the steady-state power flow and the generator stability indices under the anticipated contingency set.The network consists of two components:the classification network classifies the input samples into the credibly stable/unstable and uncertain categories,and the prediction network is utilized to further predict the generator stability indices of the categorized samples,which improves the network ability to distinguish between the samples with similar characteristics.The proposed methodology can be used to quickly and quantitatively evaluate the transient stability margin of a power system,and the simulation results validate the effectiveness of the method.

Impact of Electric Vehicle Aggregator with Communication Time Delay on Stability Regions and Stability Delay Margins in Load Frequency Control System

This paper investigates the impact of electric vehicle(EV)aggregator with communication time delay on stability regions and stability delay margins of a single-area load frequency control(LFC)system.Primarily,a graphical method characterizing stability boundary locus is implemented.For a given time delay,the method computes all the stabilizing proportional-integral(PI)controller gains,which constitutes a stability region in the parameter space of PI controller.Secondly,in order to complement the stability regions,a frequency-domain exact method is used to calculate stability delay margins for various values of PI controller gains.The qualitative impact of EV aggregator on both stability regions and stability delay margins is thoroughly analyzed and the results are authenticated by time-domain simulations and quasi-polynomial mapping-based root finder(QPmR)algorithm.

A simple approach for stability margin of discrete systems

In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stability is obtained. The method is illustrated with an example and it is compared with other methods proposed in the literature. The results have applications in the filter design.

A stability locomotion-control strategy for quadruped robots with center-of-mass dynamic planning

Locomotion stability is essential for controlling quadruped robots and adapting them to unstructured terrain.We propose a control strategy with center-of-mass(CoM)dynamic planning for the stable locomotion of these robots.The motion trajectories of the swing legs are synchronized with the CoM of the robot.To implement the synchronous control scheme,we adjusted the swing legs to form a support triangle.The strategy is applicable to both static walk gait and dynamic trot gait.In the motion control processes of the robot legs,the distribution of the ground reaction forces is optimized to minimize joint torque and locomotion energy consumption.We also used an improved joint-torque controller with varied controller coefficients in the stance and swing phases.The simulation and experimental results demonstrate that the robot can complete omnidirectional locomotion in both walk and trot gaits.At a given locomotion speed,the stability margins for the robot during walking and trotting were 27.25%and 37.25%higher,respectively,than in the scheme without CoM planning.The control strategy with energy consumption optimization(ECO)reduced the energy consumption of the robot in walk and trot gaits by 11.25%and 13.83%,respectively,from those of the control scheme without ECO.

Effects of Probe Support on the Stall Characteristics of a Low-Speed Axial Compressor

In order to investigate the effects of probe support on the stall characteristics of micro compressors, an experiment was carried out on a large-scale low-speed research compressor according to the principle of geometric similarity. A cylindrical probe support intruding to 50% blade span was mounted at 50% chord upstream from the rotor blade leading edge. The static pressure rise characteristic of the compressor is measured, with and without the probe support respectively. The dynamic compressor behavior from pre-stall to full stall was also measured. The results indicate that the stability margin of the compressor is lowered after installing the probe support. The stall inception is aroused by modal wave disturbances. The disturbances developed into two stall cells smoothly before installing the probe support, while the disturbances first developed into a single stall cell then splitting into two stall cells after installing the probe support. The presence of probe support lowers the initial intensity of the rotating stall of the compressor, while it doesn't alter the intensity of the rotation stall after the compressor enters into full stall.

Loadability Assessment and Enhancement in Unbalanced Distribution Systems

Voltage stability is a major concern in heavily loaded distribution networks.Careful determination of control parameters for loadability enhancement may maximize the utilization of distribution networks.In applicable studies,most of the approaches optimize real/reactive power losses for the current operating conditions of the distribution network.Although,these types of approaches increase the stability margin,such an increase may not be sufficient.The most important factor in loadability enhancement is representation of future load scenarios in addressing the optimization problem.In this paper a look ahead approach is developed for loadability enhancement of an unbalanced distribution system.The determination of the critical loading point is conventionally done using continuation power flow,which is computationally very demanding,and also complex for implementation in unbalanced distribution networks.Therefore,a new,computationally very efficient voltage stability indicator is developed here for determination of the loadability limit.The proposed methodology is demonstrated on IEEE 4 bus and 25 bus unbalanced distribution systems with different transformer connections.