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.

Harmonic State-Space Based AC-Side Impedance Model of MMC and High Frequency Oscillation Characteristics Analysis

Recently,high-frequency oscillation of themodularmultilevel converter(MMC)based high-voltage direct current(HVDC)projects has attracted great attentions.In order to analyze the small-signal stability,this paper uses the harmonic state-space(HSS)method to establish a detailed frequency domain impedance model of the AC-side of the HVDC transmission system,which considers the internal dynamic characteristics.In addition,the suggested model is also used to assess the system’s high-frequency oscillationmechanism,and the effects of the MMC current inner loop control,feedforward voltage links,and control delay on the high-frequency impedance characteristics and the effect of higher harmonic components.Finally,three oscillation suppression schemes are analyzed for the oscillation problems occurring in actual engineering,and a simplified impedance model considering only the highfrequency impedance characteristics is established to compare the suppression effect with the detailed impedance model to prove its reliability.

Stress wave analysis of high-voltage pulse discharge rock fragmentation based on plasma channel impedance model

High-voltage pulse discharge(HVPD)rock fragmentation controls a plasma channel forming inside the rock by adjusting the electrical parameters,electrode type,etc.In this work,an HVPD rock fragmentation test platform was built and the test waveforms were measured.Considering the effects of temperature,channel expansion and electromagnetic radiation,the impedance model of the plasma channel in the rock was established.The parameters and initial values of the model were determined by an iterative computational process.The model calculation results can reasonably characterize the development of the plasma channel in the rock and estimate the shock wave characteristics.Based on the plasma channel impedance model,the temporal and spatial distribution characteristics of the radial stress and tangential stress in the rock were calculated,and the rock fragmentation effect of the HVPD was analyzed.

Decouple charge transfer reactions in the Li-ion battery

In the development of Li-ion batteries(LIBs)with high energy/power density,long cycle-life,fast charging,and high safety,an insight into charge transfer reactions is required.Although electrochemical impedance spectroscopy(EIS)is regarded as a powerful diagnosis tool,it is not a direct but an indirect measurement.With respect to this,some critical questions need to be answered:(i)why EIS can reflect the kinetics of charge transfer reactions;(ii)what the inherent logical relationship between impedance models under different physical scenes is;(iii)how charge transfer reactions compete with each other at multiple scales.This work aims at answering these questions via developing a theory framework so as to mitigate the blindness and uncertainty in unveiling charge transfer reactions in LIBs.To systematically answer the above questions,this article is organized into a three-in-one(review,tutorial,and research)type and the following contributions are made:(i)a brief review is given for impedance model development of the LIBs over the past half century;(ii)an open source code toolbox is developed based on the unified impedance model;(iii)the competive mechanisms of charge transfer reactions are unveiled based on the developed EIS-Toolbox@LIB.This work not only clarifies theoretical fundamentals,but also provides an easy-to-use open source code for EIS-Toolbox@LIB to optimize fast charge/discharge,mitigate cycle aging,and improve energy/power density.

T-Y TUBE MODEL OF HUMAN ASCENDINGAORTIC INPUT IMPEDANCE

This paper proposed a T- Y tube model to simulate foe input impedance of arterial system. It improves and extends the asymmetric T-tube model which was firstproposed by O' Rourke[1] and developed laier by Liu et al.[2]. Based on foe asymmetricT-tube model. a T-Y tube model was proposed by adding branching tubes whichrepresem the iliac arteries.All the tubes are considered to be uniform,viscoelasticlongitudinally tethered cylindrical tubes.The upper tube terminates with a windkesselmodel, while the terminal arterioles of the lowr tube are expressed as a resistance.After proper eraluation of the parameters.the impedance of the arterial system iscalculated under normal physiological and hypertensive condition.The model canpredict impedance in good agreement with the experimentally obtained data no matterin normal physiological condition or in pathological condition In comparison with theasymmeric T-tube model,T- Y tube model is closer to anatomy structure of the human arlerial system and at the sametime much simpler than the extremely complex multiplebranching tube model Therefore it will be a valuable model in studying the influencesof various parameters on aorta impedance and ventricular-vascular coupling.

Analysis of Sub-Synchronous Oscillation of Virtual Synchronous Generator and Research on Suppression Strategy in Weak Grid

At present,the direct drive permanent magnet synchronous generator(DD-PMSG)grid connected system based on virtual synchronous generator(VSG)control will experience power oscillation at sub synchronous frequencies.The mechanism and characteristics of this new type of sub-synchronous interaction(SSI)are not yet clear,and the system cannot recover to steady state solely based on the characteristics of VSG itself.Especially when connected to a weak current network,oscillations are more pronounced,affecting the stability of the system.In severe cases,the systemmay trigger shutdown protection and be disconnected from the network.Existing research has only analyzed the oscillation mechanism under this phenomenon and has not proposed corresponding control strategies.This article proposes aVSM control strategy based on the VSG control algorithm,which balances the dq axis component of voltage and current,and improves the voltage and current loop of VSG control to reduce the impact of sub-synchronous oscillation(SSO)on the power grid.In MATLAB/Simulink,a simulation model of the proposed control strategy was built to verify its correctness and effectiveness.

High-frequency Resonance Analysis and Impedance Reshaping Control of MMC-HVDC System Based on Frequency Coupling Impedance Model

In recent years, high-frequency resonance (HFR) events occurred in several modular multilevel converter based high-voltage direct current (MMC-HVDC) projects. The time delay of an MMC-HVDC system is the critical factor that induces HFR. The frequency coupling affects the impedance characteristics of an MMC and further deteriorates system stability. Therefore, in this paper, a multi-input multi-output admittance model of an MMC-HVDC system is developed to analyze its frequency characteristics. The effects of current loop, power loop, phase-locked loop, and operating point on the MMC frequency coupling degree are analyzed in detail. Meanwhile, to further suppress HFR in the MMC-HVDC system, an enhanced impedance reshaping control strategy based on the equivalent single-input single-output impedance model is proposed. Finally, the accuracy of the enhanced impedance model and the effectiveness of the impedance reshaping control are verified by electromagnetic transient simulations in PSCAD.

Stability Investigation and Improvement for DC Cascade Systems with Simplified Impedance-based Stability Criterion

In DC distributed power systems(DPSs),the complex impedance interactions possibly lead to DC bus voltage oscillation or collapse.In previous research,the stability analysis of DPSs is implemented based on mathematical analysis in control theory.The specific mechanisms of the instability of the cascade system have not been intuitively clarified.In this paper,the stability analysis of DPSs based on the traditional Nyquist criterion is simplified to the resonance analysis of the seriesconnected port impedance(Z=R+jX)of source and load converters.It reveals that the essential reason for impedance instability of a DC cascade system is that the negative damping characteristic(R<0)of the port the overall impedance amplifies the internal resonance source at reactance zero-crossing frequency.The simplified stability criterion for DC cascade systems can be concluded as:in the negative damping frequency ranges(R<0),there exists no zero-crossing point of the reactance component(i.e.,X=0).According to the proposed stability criterion,the oscillation modes of cascade systems are classified.A typical one is the internal impedance instability excited by the negative damping,and the other one is that the external disturbance amplified by negativity in a low stability margin.Thus,the impedance reshaping method for stability improvement of the system can be further specified.The validity of the simplified criterion is verified theoretically and experimentally by a positive damping reshaping method.

Study of Mode Coupling on Coaxial Resonators

A study of mode coupling phenomenon of coaxial resonators has been conducted with theories. Through establishing the source-free transmission line equation, boundary conditions of the coaxial resonators with a corrugated inner conductor are analyzed. In the end, calculations are performed in a wide range of corrugation parameters for the resonator of the Karlsruhe Institute of Technology （KIT） relevant coaxial gyrotron.

Impedance learning adaptive super-twisting control of a robotic exoskeleton for physical human-robot interaction

This study addresses two issues about the interaction of the upper limb rehabilitation robot with individuals who have disabilities.The first step is to estimate the human's target position(also known as TPH).The second step is to develop a robust adaptive impedance control mechanism.A novel Non-singular Terminal Sliding Mode Control combined with an adaptive super-twisting controller is being developed to achieve this goal.This combination's purpose is to provide high reliability,continuous performance tracking of the system's trajectories.The proposed adaptive control strategy reduces matched dynamic uncertainty while also lowering chattering,which is the sliding mode's most glaring issue.The proposed TPH is coupled with adaptive impedance control with the use of a Radial Basis Function Neural Network,which allows a robotic exoskeleton to simply track the desired impedance model.To validate the approach in real-time,an exoskeleton robot was deployed in controlled experimental circumstances.A comparison study has been set up to show how the adaptive impedance approach proposed is better than other traditional controllers.

An Impedance-based Parameter Design Method for Active Damping of Load Converter Station in MTDC Distribution System

To achieve the efficient application of impedance analysis in the stability assessment and enhancement of multiterminal DC distribution systems, this paper proposes the DCside reduced-order impedance models with power control and AC voltage control, respectively, by taking the load converter station as the object. By using the DC-side current as the feedforward state, the active compensator applied to the load converter station with two control modes is also derived as well as the corresponding reduced-order impedance models. Combined with the reduced-order impedance models, a method based on damping factor sensitivity is further proposed to design the parameters of the derived active compensators. The verification results in the frequency domain and time domain demonstrate the accuracy of the reduced-order impedance and the effectiveness of the proposed compensator parameter design method.

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.

Preliminarily modeling of creep effect in electro-dynamic loudspeaker suspensions

The creep effect of suspensions in electro-dynamic loudspeakers was modeled based on fractional order derivatives.The fractional standard linear solid（FSLS） model was presented by substituting the Abel dashpot for Newton dashpot in Standard Linear Solid（SLS） model.The electrical impedance as well as the transfer function between diaphragm displacement and input voltage of the two tested midrange loudspeakers was measured by Klippel laser analyzer system,and the model parameters were identified by the least-mean-square method.By comparing the fitting results of FSLS model with the other two classical models- 4 Parameter Logarithmic model and SLS model,the results show that the FSLS model can rightly predict the frequency dependent compliance loss factor and yield higher accuracy for modeling the creep effect in loudspeaker suspensions.

Research and Modeling on the Characteristic Changes of EMI Filter Passive Components under the Influence of Aging

At present,the power density of power electronic devices in data centers and electric vehicles is constantly increasing,and numerous electronic components are concentrated in a tight,high-temperature environment,which aggravates the performance degradation of electronic components.Consequently,X and Y capacitors,common-mode inductors,and differential-mode inductors used for electromagnetic interference(EMI)suppression suffer from aging effects,and their performance continues to decline.However,the electromagnetic compatibility test is often conducted immediately after the power electronic equipment leaves the factory.The electromagnetic compatibility of power electronic equipment is affected by aging,which is not assessed in current industrial testing.This study conducts aging experiments on passive electronic components in EMI filters and measures the impedance in the frequency range from 150 kHz to 30 MHz.Subsequently,a multi-element aging model based on electromagnetic field analysis is established.The proposed model is suitable for electromagnetic compatibility analysis considering aging.Finally,the aging performance of a commercial two-stage EMI filter is predicted to verify the model proposed in the study.The proposed model explains the degeneration of the EMI filter with aging in the frequency range of 150 kHz to 1 MHz,with a maximum amplitude error of 0.58 dB and phase error of 1.0°.

Compensation Control and Parameters Design for High Frequency Resonance Suppression of MMC-HVDC System

Large time delay is one of the inherent features of a modular multilevel converter(MMC)-based high voltage direct current(HVDC)system and is the main factor leading to the unfavorable’negative resistance and inductance’characteristic of MMC impedance.Research indicates that this characteristic interacting with the capacitive characteristics of an AC system is the cause of high frequency resonance(HFR)in the Yu-E HVDC project.As the current controller is one of the main factors that affects the MMC impedance,a compensation control to imitate the paralleled impedance at the point of common coupling(PCC)is proposed.Therefore,the structure and parameter design of the compensation controller are core to realizing HFR suppression.There are two potentially risky frequency ranges of HFRs(around 700 Hz and 1.8 kHz)in the studied AC system within 2.0 kHz.The core concept of HFR suppression is to make the phase angle of MMC impedance smaller than 90◦in the two risky frequency ranges according to impedance stability theory.Hence,the design parameters aim to coordinate the phase angle of MMC impedance in the two risky frequency ranges.In this paper,three types of compensation controller are studied to suppress HFRs,namely,first-order low pass filter(LPF),second-order LPF,and third-order band pass filter.The results of parameter design show that the first-order LPF cannot suppress both HFRs simultaneously.The second-order LPF can suppress both HFRs,however,it introduces a DC component into the current control loop.Therefore,a high pass filter is added to form the recommended third-order controller.All parameter ranges of the compensation controller are derived using analytical expressions.Finally,the correctness of the parameter design is proofed using time-domain simulations.

AVA Simultaneous Inversion of Prestack Seismic Data Using Particle Swarm Optimization

A new prestack AVA simultaneous inversion using particle swarm optimization algorithm is proposed, which can obtain the elastic parameters such as P-wave and S-wave impedance from P-wave reflection data simultaneously. Compared with the conventional AVA inversion based on generalized linear technique, this method does not depend on the initial model and can reach the global minimum. In order to increase the stability of the inversion, low-frequency trends of P-wave and S-wave impedances are built into the inversion. This method has been successfully applied to synthetic and field data. The estimated P-wave and S-wave impedances can be combined to derive other elastic parameters, which are sensitive for lithology identification and fluid prediction.

Low-Frequency Stability Analysis of Power Electronic Traction Transformer Based Train-Network System

Power electronic traction transformers(PETTs)will be increasingly applied to locomotives in the future for their small volume and light weight.However,similar to conventional trains,PETTs behave as constant power loads and may cause low-frequency oscillation(LFO)to the train-network system.To solve this issue,a mathematical model of the PETT is firstly proposed and verified based on the extended describing function(EDF)method in this paper.In the proposed model,the LLC converter is simplified to an equivalent circuit consisting of a capacitor and a resistor in parallel.It is further demonstrated that the model can apply to various LLC converters with different topologies and controls.Particularly,when the parameter differences between cells are not obvious,the PETT can be simplified to a single-phase rectifier(i.e.,conventional train)by equivalent transformation.Based on the model of PETT,the system low-frequency stability and influential factors are analyzed by using the generalized Nyquist criterion.Lastly,the correctness and accuracy of theoretical analyses are validated by off-line and hardware-in-the-loop simulation results.