Research on Equivalent Modeling Method of AC-DC Power Networks Integrating with Renewable Energy Generation

Along with the increasing integration of renewable energy generation in AC-DC power networks,investigating the dynamic behaviors of this complex system with a proper equivalent model is significant.This paper presents an equivalent modeling method for the AC-DC power networks with doubly-fed induction generator(DFIG)based wind farms to decrease the simulation scale and computational burden.For the AC-DC power networks,the equivalent modeling strategy in accordance with the physical structure simplification is stated.Regarding the DFIG-based wind farms,the equivalent modeling based on the sequential identification of multi-machine parameters using the improved chaotic cuckoo search algorithm(ICCSA)is conducted.In light of the MATLAB simulation platform,a two-zone four-DC interconnected power grid with wind farms is built to check the efficacy of the proposed equivalentmodelingmethod.Fromthe simulation analyses and comparative validation in different algorithms and cases,the proposed method can precisely reflect the steady and dynamic performance of the demonstrated system under N-1 and N-2 fault scenarios,and it can efficiently achieve the parameter identification of the wind farms and fulfill the equivalent modeling.Consequently,the proposed approach’s effectiveness and suitability are confirmed.

Multi-layer Quasi Three-dimensional Equivalent Model of Axial-Flux Permanent Magnet Synchronous Machine

Axial-flux permanent magnet synchronous machine(AFPMSM)enjoys the merits of high torque density and high efficiency,which make it one good candidate in the direct-drive application.The AFPMSM is usually analyzed based on the three-dimensional finite element method(3D FEM)due to its three-dimensional magnetic field distribution.However,the 3D FEM suffers large amount of calculation,time-consuming and is not suitable for the optimization of AFPMSM.Addressing this issue,a multi-layer quasi three-dimensional equivalent model of the AFPMSM is investigated in this paper,which could take the end leakage into consideration.Firstly,the multi-layer quasi three-dimensional equivalent model of the AFPMSM with single stator and single rotor is derived in details,including the equivalent processes and conversions of structure dimensions,motion conditions and electromagnetic parameters.Then,to consider the influence of end leakage on the performance,a correction factor is introduced in the multi-layer quasi three-dimensional equivalent model.Finally,the proposed multi-layer quasi three-dimensional equivalent model is verified by the 3D FEM based on an AFPMSM under different structure parameters.It demonstrates that the errors of flux linkage and average torque obtained by the multi-layer quasi three-dimensional equivalent model and 3D FEM are only around 2%although the structure parameters of the AFPMSM are varied.Besides,the computation time of one case based on the multi-layer quasi three-dimensional equivalent model is only 6 min,which is much less than that of the 3D FEM,1.8 h,under the same conditions.Thus,the proposed multi-layer quasi three-dimensional equivalent model could be used to optimize the AFPMSM and much time could be saved by this method compared with the 3D FEM.

An equivalent model of discharge instability in the discharge chamber of Kaufman ion thruster

The industrial application of the Kaufman ion thruster in its arc stage is limited owing to the instability of the discharge pulse.Presently,a complete prediction model that can predict the discharge pulse in the high-current stage does not exist.In this study,a complete prediction model for the pulse in the ion thruster is established using the zero-dimensional plasma discharge model and equivalent circuit model.The zero-dimensional plasma discharge model is used to obtain the corresponding plasma parameters by calculating the beam current,discharge current,voltage,and gas flow under actual working conditions.The input parameters of the equivalent circuit model are calculated using empirical formulae to acquire the estimated discharge waveforms.The pulse waveforms obtained using the model are found to be consistent with the experimental results.The model is used to evaluate the process of rapid changes in plasma density.Additionally,this model is employed to predict changes in the pulse waveforms when the volume of the discharge chamber and grid plate transmittance are changed.

Dynamic Equivalent Modeling for Black-box Microgrids Under Multi-operating-point by Using LSTM

Since the high penetration of distributed energy sources complicates the dynamics of electrical power systems,accurate dynamic models are indispensable for study on the transient behavior of the microgrid(MG).In some practices,the lack of full detailed information results in failure of dif-ferential equation based dynamic modeling,which leads to a demand for a black-box MG modeling method.It is a critical challenge to maintain the effectiveness of the black-box model under a wide operating range and various fault conditions.In this paper,inspired by the mathematical equivalence between the recurrent neural network(RNN)and differential-algebraic equations(DAEs),a dynamic equivalent modeling method,using long short-term memory(LSTM),is presented to tackle this challenge.At first,the modeling equivalence and advantages of our basic idea are explained.Then,modeling procedures,including data preparation and design guidelines,are presented.Finally,the proposed method is applied to a multi-microgrid testing system for performance evaluation.The results,under various scenarios,reveal that the proposed modeling method has an adequate capability for representing the dynamic behaviors of a black-box MG under grid fault and operating point changing conditions.Index Terms-Deep learning,dynamic behavior,dynamic equivalent model,microgrid,neural network.

Integrated Equivalent Model of Permanent Magnet Synchronous Generator Based Wind Turbine for Large-scale Offshore Wind Farm Simulation

The high-speed simulation of large-scale offshore wind farms(OWFs) preserving the internal machine information has become a huge challenge due to the large wind turbine(WT) count and microsecond-range time step. Hence, it is undoable to investigate the internal node information of the OWF in the electro-magnetic transient(EMT) programs. To fill this gap,this paper presents an equivalent modeling method for largescale OWF, whose accuracy and efficiency are guaranteed by integrating the individual devices of permanent magnet synchronous generator(PMSG) based WT. The node-elimination algorithm is used while the internal machine information is recursively updated. Unlike the existing aggregation methods, the developed EMT model can reflect the characteristics of each WT under different wind speeds and WT parameters without modifying the codes. The access to each WT controller is preserved so that the time-varying dynamics of all the WTs could be simulated. Comparisons of the proposed model with the detailed model in PSCAD/EMTDC have shown very high precision and high efficiency. The proposed modeling procedures can be used as reference for other types of WTs once the structures and parameters are given.

Time-varying gravity field model of Sichuan-Yunnan region based on the equivalent mass source model

High-precision time-varying gravity field is an effective way to study the internal mass movement and understanding the spatio-temporal evolution process of the geodynamic system.Compared to the satellite gravity measurement,the repeated terrestrial gravity observation can provide a more high-order signal related to the shallow crust and subsurface.However,the suitable and unified method for gravity model estimation is a key problem for further applications.In this study,we introduce the spherical hexahedron element to simulate the field source mass and forward model the change of gravity field located at the Sichuan-Yunnan region(99—104°E,23—29°N)in the four epochs from 2015 to 2017.Compared to the experimental results based on Slepian or spherical harmonics frequency domain method,this alternative approach is suitable for constructing the equivalent mass source model of regional-scale gravity data,by introducing the first-order smooth prior condition of gravity time-varying signal to suppress the high-frequency component of the signal.The results can provide a higher spatial resolution reference for regional gravity field modeling in the Sichuan-Yunnan region.

Simplified equivalent models of large-scale wind power and their application on small-signal stability

With the rapid growth of grid-connected wind power penetration level,it is necessary to study the impacts of wind power on power system stability.The small-signal stability of power systems with large-scale wind power is explored using the eigenvalue analysis method.A prototype sample system,the two-synchronous-generator system with a wind farm,is proposed for theoretical analysis.Then,simplified models of wind turbines(WTs)and the corresponding equivalent models of wind farms are analyzed.Three kinds of typical WT models,i.e.,squirrel cage induction generator,doubly-fed induction generator,and permanent magnet synchronous generator are used.Furthermore,based on the simplified equivalent models,effects of large-scale wind farms on the electromechanical oscillation modes(EOMs)of synchronous systems are discussed.Simulation results indicate that wind farms of the three kinds of WTs have positive effects on EOMs.However,long transmission lines connecting wind farmto the systemmay produce negative effects on the small-signal stability of the system.

Outlier Reconstruction Based Distribution System State Estimation Using Equivalent Model of Long Short-term Memory and Metropolis-Hastings Sampling

The accuracy of distribution system state estimation(DDSE)is reduced when phasor measurement unit(PMU)measurements contain outliers because of cyber attacks or global positioning system spoofing attacks.Therefore,to enhance the robustness of DDSE to measurement outliers,approximate the target distribution of Metropolis-Hastings(MH)sampling,and judge the prediction of the long short-term memory(LSTM)network,this paper proposes an outlier reconstruction based state estimation method using the equivalent model of the LSTM network and MH sampling(E-LM model),motivated by the characteristics of the chronological correlations of PMU measurements.First,the target distribution of outlier reconstruction is derived using a kernel density estimation function.Subsequently,the reasons and advantages of the E-LM model are explained and analyzed from a mathematical point of view.The proposed LSTM-based MH sampling can approximate the target distribution of MH sampling to decrease the number of the futile iterations.Moreover,the proposed MH-based forecasting of the LSTM can judge each LSTM prediction,which is independent of its true value.Finally,simulations are conducted to evaluate the performance of the E-LM model by integrating the LSTM network and the MH sampling into the outlier reconstruction based DDSE.

Probabilistic equivalent model of DFIG-based wind farms and its application in stability analysis

A probabilistic equivalent method for doubly fed induction generator (DFIG) based wind farms is proposed in this paper.First,the wind farm equivalent model is assumed to be composed of three types of equivalent DFIGs with different dynamic characteristics.The structure of equivalent model remains constant,whereas the parameters change with the migration of different scenarios in the wind farm.Then,historical meteorological data are utilized to investigate the probability distribution of key equivalent parameters,such as capacity,wind speed and electrical impedance to the point of common coupling.Each type of equivalent DFIG is further clustered into several groups according to their active power output.Combinations are created to generate representative scenarios.The probabilistic equivalent model of wind farm is finally achieved after removing invalid combinations.Most matched representative scenarios can be predicted according to the real-time measurement.The equivalentmodel is applied to the probabilistic power flow calculation and the stability analysis of test systems.

Equivalent model of multi-type distributed generators under faults with fast-iterative calculation method based on improved PSO algorithm

There are various types of distributed generators (DGs) with different grid integration strategies. The transient characteristics of the fault currents provided by the DGs are different to those of conventional synchronous generators. In this paper, a distribution network with multi-type DGs is investigated, including consideration of DG low-voltage ride through (LVRT). The fault current characteristics of two typical DGs, i.e. an inverter-interfaced distributed generator (IIDG) and a doubly-fed induction generator (DFIG), are analyzed, considering the specific operation modes. Based on analysis of the fault characteristics, an equivalent model of the multi-type DGs under symmetrical/asymmetrical fault conditions is established. A fast-iterative fault calculation method for enhancing the calculation efficiency while avoiding local convergence is then proposed using an improved particle swarm optimization (PSO) algorithm. A simulation system of the distribution network with multi-type DGs is established in PSCAD/EMTDC. The simulation results validate the high accuracy and calculation efficiency of the proposed calculation method of the fault components. This can assist in the settings of the protection threshold.

Mass‑Spring‑Damping Theory Based Equivalent Mechanical Model for Cylindrical Lithium‑ion Batteries under Mechanical Abuse

An equivalent mechanical model with the equivalent physical meaning of mass-spring-damping is proposed for cylindrical lithium-ion batteries through experiments and theory.The equivalent mechanical model of a cylindrical lithium-ion battery consists of a spring-damping parallel unit.Therefore,a spring-damping parallel unit connecting a damping unit in series is selected to construct the constitutive characteristics of the battery under mechanical abuse.Comparison results show that the equivalent mechanical model can more effectively describe the mechanical properties of the batteries than most cubic fitting models,of which the average relative error of the equivalent mechanical model under different states-of-charge is less than 6.75%.Combined with the proposed equivalent mechanical model,the failure process of the batteries was simulated and analyzed using LS-Dyna and HyperWorks.Under rigid rod tests,failure occurred at the core and bottom of the batteries;under hemispherical punch tests,failure occurred at the core and top,consistent with the experimental results.The average prediction error for the failure displacement under different abuse conditions is less than 4%in the simulations.The equivalent mechanical model requires only a few parameters and can be recognized easily.In the future,the model can be used in safety warning devices based on mechanical penetration.

Simulation study of a magnetocardiogram based on a virtual heart model:effect of a cardiac equivalent source and a volume conductor

In this paper, we present a magnetocardiogram （MCG） simulation study using the boundary element method （BEM） and based on the virtual heart model and the realistic human volume conductor model. The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated. The single dipole source model, the multiple dipoles source model and the equivalent double layer （EDL） source model are analysed and compared with the cardiac equivalent source models. Meanwhile, the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated. The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken, while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source. Therefore, the EDL source is suitable for the study of MCG forward and inverse problems, and more attention should be paid to it in future MCG studies.

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.

Extrinsic equivalent circuit modeling of InP HEMTs based on full-wave electromagnetic simulation

With the widespread utilization of indium-phosphide-based high-electron-mobility transistors(InP HEMTs)in the millimeter-wave(mmW)band,the distributed and high-frequency parasitic coupling behavior of the device is particularly prominent.We present an InP HEMT extrinsic parasitic equivalent circuit,in which the conductance between the device electrodes and a new gate-drain mutual inductance term L_(mgd)are taken into account for the high-frequency magnetic field coupling between device electrodes.Based on the suggested parasitic equivalent circuit,through HFSS and advanced design system(ADS)co-simulation,the equivalent circuit parameters are directly extracted in the multi-step system.The HFSS simulation prediction,measurement data,and modeled frequency response are compared with each other to verify the feasibility of the extraction method and the accuracy of the equivalent circuit.The proposed model demonstrates the distributed and radio-frequency behavior of the device and solves the problem that the equivalent circuit parameters of the conventional InP HEMTs device are limited by the device model and inaccurate at high frequencies when being extracted.

Ferroelectric effect and equivalent polarization charge model of PbZr_(0.2)Ti_(0.8)O_(3)on AlGaN/GaN MIS-HEMT

PbZr_(0.2)Ti_(0.8)O_(3)(PZT)gate insulator with the thickness of 30 nm is grown by pulsed laser deposition(PLD)in AlGaN/GaN metal-insulator-semiconductor high electron mobility transistors(MIS-HEMTs).The ferroelectric effect of PZT AlGaN/GaN MIS-HEMT is demonstrated.The polarization charge in PZT varies with different gate voltages.The equivalent polarization charge model(EPCM)is proposed for calculating the polarization charge and the concentration of two-dimensional electron gas(2DEG).The threshold voltage(V_(th))and output current density(I_(DS))can also be obtained by the EPCM.The theoretical values are in good agreement with the experimental results and the model can provide a guide for the design of the PZT MIS-HEMT.The polarization charges of PZT can be modulated by different gate-voltage stresses and the V_(th)has a regulation range of 4.0 V.The polarization charge changes after the stress of gate voltage for several seconds.When the gate voltage is stable or changes at high frequency,the output characteristics and the current collapse of the device remain stable.

An equivalent circuit model for terahertz quantum cascade lasers:Modeling and experiments

Terahertz quantum cascade lasers（THz QCLs） emitted at 4.4 THz are fabricated and characterized. An equivalent circuit model is established based on the five-level rate equations to describe their characteristics. In order to illustrate the capability of the model, the steady and dynamic performances of the fabricated THz QCLs are simulated by the model.Compared to the sophisticated numerical methods, the presented model has advantages of fast calculation and good compatibility with circuit simulation for system-level designs and optimizations. The validity of the model is verified by the experimental and numerical results.

Analysis of Permanent Magnet-assisted Synchronous Reluctance Motor Based on Equivalent Reluctance Network Model

In this paper,the equivalent reluctance network model(ERNM)is used to calculate the magnetic circuit of a permanent magnet-assisted synchronous reluctance motor(PMASynRM)and calculate no-load air-gap magnetic field and electromagnetic torque.Iteration method is used to solve the relative permeability of iron core.A novel reluctance network model based on actual distribution of the magnetic flux inside the motor is established.The magnetomotive force(MMF)generated by armature winding affects the relative permeability of iron core,which is considered in the calculation of ERNM to improve the accuracy when the motor is under load.ERNM can be used to measure air-gap flux density,no-load back electromotive force(EMF),the average value of motor torque,the armature winding voltage under load,and power factor.The method of calculating the motor performance is proposed.The results of calculation are consistent with finite element method(FEM)and the computational complexity is much less than that of the FEM.The results of ERNM has been verified,which will provide a simple method for motor design and analysis.

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model(ECM).The traditional recursive least squares(RLS)method is easily biased with the noise disturbances from sensors,which degrades the modeling accuracy in practice.Meanwhile,the recursive total least squares(RTLS)method can deal with the noise interferences,but the parameter slowly converges to the reference with initial value uncertainty.To alleviate the above issues,this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM.RLS converges quickly by updating the parameters along the gradient of the cost function.RTLS is applied to attenuate the noise effect once the parameters have converged.Both simulation and experimental results prove that the proposed method has good accuracy,a fast convergence rate,and also robustness against noise corruption.

The initial stages of Li_(2)O_(2) formation during oxygen reduction reaction in Li-O_(2) batteries:The significance of Li_(2)O_(2) in charge-transfer reactions within devices

Lithium-oxygen batteries are a promising technology because they can greatly surpass the energy density of lithium-ion batteries.However,this theoretical characteristic has not yet been converted into a real device with high cyclability.Problems with air contamination,metallic lithium reactivity,and complex discharge and charge reactions are the main issues for this technology.A fast and reversible oxygen reduction reaction(ORR)is crucial for good performance of secondary batteries',but the partial knowledge of its mechanisms,especially when devices are concerned,hinders further development.From this perspective,the present work uses operando Raman experiments and electrochemical impedance spectroscopy(EIS)to assess the first stages of the discharge processes in porous carbon electrodes,following their changes cycle by cycle at initial operation.A growth kinetic formation of the discharge product signal(Li_(2)O_(2))was observed with operando Raman,indicating a first-order reaction and enabling an analysis by a microkinetic model.The solution mechanism in the evaluated system was ascribed for an equivalent circuit with three time constants.While the time constant for the anode interface reveals to remain relatively constant after the first discharge,its surface seemed to be more non-uniform.The model indicated that the reaction occurs at the Li_(2)O_(2) surface,decreasing the associated resistance during the initial discharge phase.Furthermore,the growth of Li_(2)O_(2) forms a hetero-phase between Li_(2)O_(2)/electrolyte,while creating a more compact and homogeneous on the Li_(2)O_(2)/cathode surface.The methodology here described thus offers a way of directly probing changes in surface chemistry evolution during cycling from a device through EIS analysis.

Development of wind-energy modeling technology and standards

To ensure the stable operation of power systems with large proportions of wind power,China has published a series of national,industry,and enterprise standards for wind power.The increase in the number of standards and the expansion of their application scope have given rise to a situation where multiple standards overlap and conflict with regard to the establishment of models and their applicability,resulting in unclear standard application scenarios.Therefore,it is imperative to analyze the development of wind-turbine and wind-farm modeling,along with the relevant standards.This paper presents the methods for wind-turbine modeling,the equivalent model of wind farms based on the general model of wind turbines,and the technical provisions and application scenarios involved in the relevant domestic and international standards.The adaptability of the relevant standards is examined.The results of this study are helpful for advancing wind power generation in China and ensuring the safe and stable operation of large-scale wind power systems.