Data Center Power System Stability-Part II: System Modeling and Analysis

This is the second part of a two-part paper on stability study of data center power systems by impedance-based methods.As the basis for this application,Part I[1]developed new impedance models for power supplies that are the most dominant loads in data centers.This second part presents system modeling and analysis methods that can support practical data center power system design to ensure stability.The proposed methods comprise:1)building distribution network modeling by impedance scaling;2)system modeling and model reduction based on equivalent source impedance;3)system stability analysis in the sequence domain to include zero-sequence dynamics;and 4)expansion of system models and analyses to account for network asymmetry and uneven loading.These methods are used to characterize practical resonance problems observed in data centers,explain their root causes,and develop solutions.For systems using Y-connected power supply units(PSUs),the zero sequence is identified as the weakest link and the first to become unstable.The expanded system model and analysis reveal a new,differential-mode instability that is responsible for high frequency resonances.To guarantee system stability,new impedance-based product and system design specifications are developed based on sufficient conditions derived from the Nyquist stability criterion.Laboratory and field measurements are presented to substantiate the proposed methods and conclusions.

Data Center Power System Stability-Part I: Power Supply Impedance Modeling

This two-part paper presents methods to predict,characterize and ensure the stability of data center power systems based on impedance analysis.The work was motivated by recent power system resonance incidents in new data centers.Part I presents new input impedance models for single-phase power supply units(PSUs)to enable this application.Existing impedance models of single-phase PSU cannot meet the requirements of this application because they exclude DC voltage control that affects system stability at low frequency,or are in a dq reference frame that cannot handle the complexity of data center power systems.The developed new models include DC bus dynamics and are directly in the phase domain to simplify system stability analysis,avoiding the need for multiple-input-multiple-output(MIMO)system models and the generalized Nyquist criterion that are difficult to apply but necessary with dq-frame models.Both the converter and system level models also include the coupled current response that is characteristic of AC-DC converters and important for system stability at low frequency.The simple form of the models and system stability analysis directly in the phase domain also make it possible to develop new PSU design methods and performance specifications that together will ensure the stability of new data center power systems.The developed models are validated by laboratory measurements and are used in Part II of the work to study data center power system stability.

Exponential Stability of Interval Time-Varying Dynamical System with Multidelay

This paper studies the exponential stability of interval time-varying dynamical system with multidelay. By the matrix measure and delay differential inequality, some sufficient conditions for exponential stability of interval time-varying dynamical system with multidelay are established. These conditions are an improvement and extension of the results achieved in earlier papers. Finally, a numerical example is given to demonstrate our result.

A New Criterion for Stability of Large-Scale Systems with Delay

A simple criterion for delay-independent stability of large-scale linear time-varying systems is deduced by employing a type of Lyapunov function. The notable features of the results in this paper are its simplicity and efficiency in testing the stability large-scale linear time-varying systems. Some illustrative examples are given to demonstrate the advantages of the obtained results over those in literature.

Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems

In this paper, Lyapunov function method is used to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.

NECESSARY AND SUFFICIENT CRITERIA FOR ABSOLUTE STABILITY OF THE DIRECT CONTROL SYSTEM

Some necessary and sufficient conditions for absolute stability of several classes of direct control system were given, and two simplified forms of the control systems obtained twice were discussed. The results improve those of previous works.

EXPLICIT CRITERIA OF ABSOLUTE STABILITY FOR THE REAL SECOND CANONICAL FORM OF CONTROL SYSTEM

Some explicit criteria of absolute stability for the trivial solution of the real second canonical form of nonlinear control system were given, which include and improve the criteria given in Qiu's paper. By applying the said criteria to the well-known equation of the longitudinal motion of aircraft, some useful results could be obtained, which include and improve the corresponding results in many authors' works. Besides, all of the criteria in this paper are easy to use because they are only related to the system parameters.

Evaluating rural sustainable land use from a system perspective based on the ecosystem service value

Rural sustainable land use(RSLU) is important to China’s implementation of the UN 2030 Agenda for Sustainable Development Goals and the goals of rural revitalization strategy in China. Research on RSLU is key to understanding the impact of human activities on rural sustainability. This paper explored the evaluation method of RSLU from a system perspective based on the ecosystem service value(ESV). Three systems were proposed for consideration when conducting this evaluation method. One was the sustainability of the land system, the other was the sustainability of the ecoeconomic system, and the rest was the sustainability of the land-eco-economy system. Indicators including(1) land use intensity and land system stability,(2) gross domestic production(GDP), ESV, and the eco-economic harmony degree(EEHD), and(3) coupling degree and coupling coordination degree were used to analyze the sustainability of the land, eco-economic, and landeco-economic systems, respectively. An empirical research on Yanhe ecovillage was conducted and the study period extended from 2008 to 2020. The results showed that forest land had always accounted for more than 81.20% of the total area in Yanhe eco-village from 2008 to 2020, which greatly influenced land system stability and restricted economic development. This feature contrasted with RSLU. The total ESV of Yanhe eco-village declined by 1.60×106CNY during 2008–2020 because of land use changes. The EEHD was –0.01, which presented that there was a very slight unharmonious between ecology and economy. The coupling degree and coupling coordination degree showed that the development between the land and ecoeconomic systems exhibited a coupling coordination relationship. The results indicated that ecology and economy in Yanhe eco-village will change significantly in response to land use changes in rural areas, which further revealed the dynamic linkage between human beings and nature. Moreover, opposite variation tendencies in land system stability and ESV revealed that the contradiction between the high stability of the land system and well development of the eco-economic system. The results of this study implied that it is necessary and useful to integrate ESV into land management to achieve RSLU.

Stability Analysis of DC Microgrid Clusters Based on Step-by-step System Matrix Building Algorithm

DC microgrids(DCMGs)are made up of a network of sources and loads that are connected by a number of power electronic converters(PECs).The increase in the number of these PECs instigates major concerns in system stability.While interconnecting the microgrids to form a cluster,the system stability must be ensured.This paper proposes a novel stepby-step system matrix building(SMB)algorithm to update the system matrix of an existing DCMG cluster when a new microgrid is added to the cluster through a distribution line.The stability of the individual DCMGs and the DCMG cluster is analyzed using the eigenvalue method.Further,the particle swarm optimization(PSO)algorithm is used to retune the controller gains if the newly formed cluster is not stable.The simulation of the DCMG cluster is carried out in MATLAB/Simulink environment to test the proposed algorithm.The results are also validated using the OP4510 real-time simulator(RTS).

An Advanced FMRL Controller for FACTS Devices to Enhance Dynamic Performance of Power Systems

The parameters of power system slowly change with time due to environmental effects or may change rapidly due to faults. It is preferable that the control technique in this system possesses robustness for various fault conditions and disturbances. The used flexible alternating current transmission system （FACTS） in this paper is an advanced super-conducting magnetic energy storage （ASMES）. Many control techniques that use ASMES to improve power system stability have been proposed. While fuzzy controller has proven its value in some applications, the researches applying fuzzy controller with ASMES have been actively reported. However, it is sometimes very difficult to specify the rule base for some plants, when the parameters change. To solve this problem, a fuzzy model reference learning controller （FMRLC） is proposed in this paper, which investigates multi-input multi-output FMRLC for time-variant nonlinear system. This control method provides the motivation for adaptive fuzzy control, where the focus is on the automatic online synthesis and tuning of fuzzy controller parameters （i.e., using online data to continually learn the fuzzy controller that will ensure that the performance objectives are met）. Simulation results show that the proposed robust controller is able to work with nonlinear and nonstationary power system （i.e., single machine-infinite bus （SMIB） system）, under various fault conditions and disturbances.

Computation Method for the Real-Time Control Problems in Differential-Algebraic Systems

In this paper, a real-time computation method for the control problems in differential-algebraic systems is presented. The errors of the method are estimated, and the relation between the sampling stepsize and the controlled errors is analyzed. The stability analysis is done for a model problem, and the stability region is ploted which gives the range of the sampling stepsizes with which the stability of control process is guaranteed.

Generalization of integral inequalities and (c_1,c_1) stability of neutral differential equations with time-varying delays

A uniform stability analysis is developed for a type of neutral delays differential equations which depend on more general nonlinear integral inequalities. Many original investigations and results are obtained. Firstly, generations of two integral nonlinear inequalities are presented, which are very effective in dealing with the complicated integro-differential inequalities whose variable exponents are greater than zero. Compared with existed integral inequalities, those proposed here can be applied to more complicated differential equations, such as time-varying delay neutral differential equations. Secondly, the notions of (ω, Ω) uniform stable and (ω, Ω) uniform asymptotically stable, especially (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable, are presented. Sufficient conditions on about (c1, c1) uniform stable and (c1, c1) uniform asymptotically stable of time-varying delay neutral differential equations are established by the proposed integral inequalities. Finally, a complex numerical example is presented to illustrate the main results effectively. The above work allows to provide further applications on the proposed stability analysis and control system design for different nonlinear systems. © 2017 Beijing Institute of Aerospace Information.

Robust H_∞ Stabilization of Uncertain Linear Time-Delay System with Delayed/Undelayed State Feedback Controllers

This paper focuses on the H∞ controller design for linear systems with time-varying delays and norm-bounded parameter perturbations in the system state and control/disturbance. On the existence of delayed/undelayed full state feedback controllers, we present a sufficient condition and give a design method in the form of Riccati equation. The controller can not only stabilize the time-delay system, but also make the H∞ norm of the closed-loop system be less than a given bound. This result practically generalizes the related results in current literature.

An Improved Immune Clone Selection Algorithm for Parameters Optimization of Marine Electric Power System Stabilizer

In themarine electric power system,the marine generators will be disturbed by the large change of loads or the fault of the power system.The marine generators usually installed power system stabilizers to damp power system oscillations through the excitation control.This paper proposes a novel method to obtain optimal parameter values for Power System Stabilizer(PSS)to suppress low-frequency oscillations in the marine electric power system.In this paper,a newly developed immune clone selection algorithm was improved from the three aspects of the adaptive incentive degree,vaccination,and adaptive mutation strategies.Firstly,the typical PSS implementation type of leader-lag structure was adopted and the objective function was set in the optimization process.The performance of PSS tuned by improved immune clone selection algorithm was compared with PSS tuned by basic immune clone selection algorithm(ICSA)under various operating conditions and disturbances.Then,an improved immune clone selection algorithm(IICSA)optimization technique was implemented on two test systems for test purposes.Based on the simulations,it is found that an improved immune clone selection algorithm demonstrates superiority over the basic immune clone selection algorithm in getting a smaller number of iterations and fast convergence rates to achieve the optimal parameters of the power system stabilizers.Moreover,the proposed approach improves the stability and dynamic performance under various loads conditions and disturbances of the marine electric power system.

Stability Study of a 23 MVA Turbine Generator

Power system stability is a very important issue in power system engineering because a decrease in the stability margins can cause unacceptable operating conditions, which leads to frequent failures. In this paper, SKM POWER TOOLS PTW-32 Version 4.5.2.0 was used to study different Stability recovery tests after a medium voltage short circuit fault on a turbine generator in the power system. The analysis focused on the generator electrical and mechanical powers stability recovery test, generator speed stability recovery test, excitation voltage stability recovery test, bus voltage and bus frequency stability recovery test. In our study, when the introduced fault was cleared after 0.5 s, it reveals that the recovery rate of electrical power was much faster than that of mechanical power. Also, the results reveal that it took about 10 seconds for the turbine speed to stabilize while it took fewer seconds for the frequency to stabilize.

Stability of water yield in watersheds

The hydrological system of a watershed is intricately influenced by both underlying characteristics and climate conditions.Understanding the variability in water yield is essential for effective water resources management and water security in the context of changing environments.In this study,we adopted the Budyko framework and leveraged simulations from the CMIP6 model to investigate the compensation effects of climate and underlying characteristics on watershed water yield.Based on Taylor expansion and Budyko framework,we estimated the sensitivity of watershed water yield to climate and underlying characteristics(the first-and second-order partial derivatives).By combining external watershed characteristics(e.g.,water yield ratios and underlying characteristics)with internal sensitivity coefficients,this study further used vine copula and principal component analysis to quantify the stability of watershed water yield.Our findings show:(1)Water-yield changes related to underlying characteristics could be offset by climate-related water-yield changes across all climate zones,maintaining the water yield ratio steady(i.e.,the compensation effects).(2)However,global watersheds will turn more sensitive to underlying characteristics and less sensitive to climate variation in the future.Both climate-and underlying-related sensitivities increase in watersheds with arid climates.(3)The stability of watershed water yield will gradually diminish in the future.From 1901–1950to 2051–2100,the global stability of 280 watersheds drops from 0.054 to 0.021(i.e.,stability index identified by the joint probability).Particularly,the largest change in stability of water yield reaches-0.347±0.18 in arid regions.In semi-arid,semihumid,and humid regions,the changes are-0.039±0.010,-0.028±0.005,and-0.005±0.002,respectively.The findings provide a reference for the future sustainable water resources development under climate change,highlighting the vulnerability of the water resources in arid and semi-arid watersheds.

Analysis of the Sending-Side System Instability Caused by Multiple HVDC Commutation Failure

As high-voltage direct current(HVDC)lines with large capacity are being commissioned with higher frequency,the characteristics of“strong”DC and“weak”AC transmission in the power grid are topics of interest.In particular,the coupling and interaction between the sending-side and receivingside AC systems interconnected by large-scale DC links is gaining importance.In this paper,the impact of the multiple HVDC commutation failure on the stability of the sending system under different power flow directions is analyzed based on the threearea AC/DC equivalent model.The main influencing factors and the counter-measures are discussed,and the single HVDC line blocking is taken as a comparison.Finally,the results are verified using the North China-Central China-East China power grid case system.The study provides a basis and reference to ensure security and stability of the ultra-high-voltage(UHV)AC/DC hybrid power grid.

STUDY ON GAIN-SCHEDULING PROBLEM IN FLIGHT CONTROL

Gain-scheduling has got its wide applications in modern flight control, in which control gains are scheduled with variables such as dynamic pressure and Mach number, to meet dynamic response requirements in different flight conditions. Classical gain-scheduling approaches may result in some problems, which can not guarantee global robustness and stability in transitions of different flight conditions. Gain-scheduling problem is systematically investigated from robustness point of view in the paper. Detailed procedures for gain-scheduled controller to achieve both robustness and stability performance are given and applied to a typical flight control system. For switching stability problems of different flight conditions in flight control systems, a new approach is proposed, in which different flight conditions are reduced into a parameter varying plant using interpolation firstly, and then parameter-varying controller design goes next. Though interpolation errors may exist, the robust parameter varying controller design can compensate for those uncertainties and errors, and finally achieve good performance of robustness and switching stability during transitions. Illustrative simulation at last shows satisfactory results.

Linearization threshold condition and stability analysis of a stochastic dynamic model of one-machine infinite-bus (OMIB) power systems

With the increase in the proportion of multiple renewable energy sources, power electronics equipment and new loads, power systems are gradually evolving towards the integration of multi-energy, multi-network and multi-subject affected by more stochastic excitation with greater intensity. There is a problem of establishing an effective stochastic dynamic model and algorithm under different stochastic excitation intensities. A Milstein-Euler predictor-corrector method for a nonlinear and linearized stochastic dynamic model of a power system is constructed to numerically discretize the models. The optimal threshold model of stochastic excitation intensity for linearizing the nonlinear stochastic dynamic model is proposed to obtain the corresponding linearization threshold condition. The simulation results of one-machine infinite-bus (OMIB) systems show the correctness and rationality of the predictor-corrector method and the linearization threshold condition for the power system stochastic dynamic model. This study provides a reference for stochastic modelling and efficient simulation of power systems with multiple stochastic excitations and has important application value for stability judgment and security evaluation.

STUDY ON ACTIVE CONTROL FOR A FLEXIBLE BEAM UNDER THE CONDITION OF ZERO GRAVITY

The system of coupling structure with controlling is a kind of dynamic feedback system in which the mechanical load and the actuator/controller interact. The mechanical system and the control system can be considered integrally as a close system, and the driving forces actuating the mechanical load can be taken as inner forces in the coupling structure system with controlling. Therefore, one can use the method for dealing with conservative systems to simplify greatly modeling and analyses. The relative equilibrium state of motion of the flexible beam under the condition of zero gravity is studied by using the energy method, in which the characteristics of structure and controlling are considered synthetically. And further, the stability conditions for the relative equilibrium state of the system have been found. If the stability conditions are used as controlling parameters of motion of the system, the kinetic energy of the flexible beam can be converted advantageously into the electromagnetic energy of the motor and controller as well as the vibration of the flexible structure can be reduced rapidly. The results in the research provide a kind of very simple and effective real-time control method reducing the vibration of the flexible beam. The method has been verified in many kinds of experimental systems of flexible beams.