Simplified Criterion of Steady-State Stability of Electric Power Systems

In the paper the simplified criterion of a steady-state stability of electric power systems (EPS) is justified on the basis of Lyapunov functions in a quadratic form ensuring necessary and sufficient conditions of its performance. Upon that, the use of the node-voltage equations allows reducing study of a steady-state stability of complex EPS to study of the generator-bus system. The obtained results facilitate studies of a steady-state stability of the complex systems and have practical importance.

Stabilityanalysis of tactical missile autopilots based on vector margin

A novel stability computation approach for tactical missile autopilots is detailed. The limi- tations of traditional stability margins are exhibited. Then the vector margin is introduced and com- pared with sensitivity function to show their essential relationship. The longitudinal three-loop auto- pilot for tactical missiles is presented and used as the baseline for all the available linear autopilots. Ten linear autopilot topologies using all the measurable feedback components are given with the iden- tical closed-loop characteristic equation and time-domain step response. However, the stability of the ten autopilots differs when considering the actuator dynamics, which limits their application. Then vector margin method is adopted to compute and evaluate the stability of all available autopi- lots. The analysis and computation results show that the vector margin method could better evaluate autopilot stability.

Parameterized Analysis of Aeroservoelastic Stability for Closed-Loop Aircraft

The closed-loop flight control system of fly by wire is generally adopted in modern air-craft.Based on the frequency-domain stability analysis,the aeroservoelastic model of closedloop aircraft is established,and aeroservoelastic stability parameterized calculation of design improvement is conducted after the preliminary analysis.The design variables are mounted location of integrated sensors and damping coefficientsζ_(1),ζ_(2) of notch filter,with stability margin of the system as design objective.Results indicate that aeroservoelastic margin of the aircraft in certain states is insufficient.While the mounted location of integrated sensors is adjusted,the system stability can be improved to certain extent.It’s more appropriate to mount the integrated sensors in the overlapping field between the nodal lines of vertical and lateral bending for the fuselage.The system stability is also significantly improved by adding notch filter,both gain margin and phase margin increase when the real number pairζ_(1)-ζ_(2) is located in the zone above the 45°diagonal ofζ_(1),ζ_(2) con-struction plane,and the farther theζ_(1)-ζ_(2) is from the 45°diagonal,the stronger the system stability.Also the decrease in the gain peak of frequency response and the enhancement of relative stability of the system are achieved by the appropriateζ_(1)-ζ_(2) of notch filter.

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.

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 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.

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.

STABILITY MARGIN OF SYSTEMS WITH MIXED UNCERTAINTIES UNDER THE IQC DESCRIPTIONS

Stability perturbation bounds problem for systems with mixed uncertainties is discussed. It is supposed that the linear part in the forward loop is of parametric uncertainties described by interval perturbation mode, and that the nonlinear part in the feedback loop is characterized by an integral quadratic constraint (IQC). The definition of stability margin under the interval perturbation mode is given by using the Minkowski functional. The infinite stability checking problem of the mixed uncertain system can be converted to finite or one dimensional stability checking for different structures of the IQC multipliers based on the concepts of biconvex and convex-concave junctions and their properties. The result is illustrated to be efficient through an example.

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.

NOVEL SIMPLIFIED APPROACH TO COMPUTE VOLTAGE STABILITY MARGIN

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A CMOS Fully Integrated Frequency Synthesizer with Stability Compensation

A complete closed-loop third order s-domain model is analyzed for a frequency synthesizer. Based on the model and root-locus technique, the procedure for parameters design is described, and the relationship between the process,voltage,and temperature variation of parameters and the loop stability is quantitatively analyzed. A variation margin is proposed for stability compensation. Furthermore,a simple adjustable current cell in the charge pump is proposed for additional stability compensation and a novel VCO with linear gain is adopted to limit the total variation. A fully integrated frequency synthesizer from 1 to 1.05GHz with 250kHz channel resolution is implemented to verify the methods.

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.

EFFICIENT STEADY-STATE ANALYSIS METHOD FOR CLOSED-LOOP PWM SWITCHING CONVERTERS

An analysis technique of steady state and stability for closed-loop PWM DC/DC switching converters is presented. Using this method, the closed-loop switching converter is transformed into an open-loop system. By means of the fact that in steady state, the two boundary values are equal in one switching period. The exponential matrix is evaluated by precise time-domain-integration method, and then the related curve between feedback duty cycle and the input one is obtained. Not only can the steady-state duty cycle be found from the curve, but also the stability and stable domain of the system. Compared with other methods, it features with simplicity and less calculation, and fit for numerical simulation and analysis for closed-loop switching converters. The simulation results of examples indicate the correctness of the presented method.

A CONDITION OF THE EXISTENCE OF STABLE POSITIVE STEADY-STATE SOLUTIONS FOR A ONE PREDATOR TWO PREY SYSTEM

One predator two prey system is a research topic which has both the theoretical and practical values. This paper provides a natural condition of the existence of stable positive steady-state solutions for the one predator two prey system. Under this condition we study the existence of the positive steady-state solutions at vicinity of the triple eigenvalue by implicit function theorem, discuss the positive stable solution problem bifurcated from the semi-trivial solutions containing two positive components with the help of bifurcation and perturbation methods.

Study on Impact of Wind Turbines on Static Voltage Stability of Power System

The static voltage stability of the power system integrating wind farms adopting different kinds of wind turbines is analyzed. Through the simulation of one certain local power grid in Xinjiang Uygur Autonomous Region, the PV curves at the point of common coupling (PCC), key buses and important substations are plotted; the variation of voltage as well as the limit and margin of static stability are analyzed. It is resulted from the simulation that the limit of static voltage at weak nodes is lower, and the static voltage of the power system with wind farms adopting doubly-fed induction generators (DFIG) is more stable than that with wind farms adopting common asynchronous generators.

肥胖与普通男性跨越不同高度障碍动态稳定性的差异

背景:肥胖对步行时的动态平衡产生负面影响,而跨越障碍是较为日常的功能活动,对控制身体姿势的稳定性要求更高。目的:探讨肥胖男性与普通男性动态稳定性的差异,采用相对更具挑战性的跨越障碍对肥胖男性的平衡能力进行评估。方法:招募24名男性青年,肥胖组与普通组(非肥胖组)各12名,分别以随机顺序完成平地行走和不同高度(4,11,15 cm)障碍物的跨越测试。使用Qualisys运动捕捉系统与Kistler测力台采集运动学与动力学数据。采用双因素(2组别*4动作类型)重复测量方差分析,对各指标进行统计分析。结果与结论:①肥胖组比普通组步速更低(P<0.05),跨越11 cm与15 cm障碍时第一单支撑期占比减小,第二双支撑期占比增加(P<0.05);②在平地行走时,普通组的内外方向动态稳度大于肥胖组(P<0.05);③在跨越4 cm障碍时,肥胖组前后方向动态稳度低于普通组(P<0.05);④在跨越11 cm障碍时,两组前后方向动态稳度无显著性差异(P>0.05),而内外方向差异有显著性意义(P<0.05);⑤在跨越15 cm障碍时,肥胖组动态稳度低于普通组(P<0.05);⑥提示肥胖使人体在跨越障碍过程中对身体的控制能力下降,动态稳定性降低,发生跌倒的风险较普通人群更高;此外,相较于平地行走,跨越障碍时肥胖组稳定性下降较普通人群更为显著。

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.

Impact of Renewable Energy Sources on Steady-state Stability of Weak AC/DC Systems

In recent years,the penetration of renewable resources into AC power systems has increased tremendously,creating a significantly impact on the latter’s operations and stability.In this respect,it is also important to gain a basic analytical understanding of such impact on the steady-state stability of power systems with electrically weak AC/DC interconnections,but such works are not very evident in the literature.Therefore,a classical analytic model of the single and multi-infeed HVDC system which now incorporates renewable resources is proposed.Then the well-established concept of voltage sensitivity of the AC/DC interconnection is applied to analyze the impact of the renewable resources on the steady-state stability of these composite system models,as well as on the influence of system conditions and parameters.This impact is also compared with that arising from other types of shunt devices alternatively connected at the same AC/DC interconnection,therefore their relative beneficial or negative impacts will also be benchmarked.