Finite difference calculation of traveltime on non-orthogonal grid

Finite difference methods have been widely employed in solving the eikonal equation so as to calculate traveltime of seismic phase. Most previous studies used regular orthogonal grid. However, much denser grid is required to sample the interfaces that are undulating in depth direction, such as the Moho and the 660 km discontinuity.Here we propose a new finite difference algorithm to solve the eikonal equation on non-orthogonal grid（irregular grid）.To demonstrate its efficiency and accuracy, a test was conducted with a two-layer model. The test result suggests that the similar accuracy of a regular grid with ten times grids could achieve with our new algorithm, but the time cost is only about 0.1 times. A spherical earth model with an undulant660 km discontinuity was constructed to demonstrate the potential application of our new method. In that case, the traveltime curve fluctuation corresponds to topography. Our new algorithm is efficient in solving the first arrival times of waves associated with undulant interfaces.

Performance of Geometric Multigrid Method for Two-Dimensional Burgers’Equations with Non-Orthogonal,Structured Curvilinear Grids

This paper seeks to develop an efficient multigrid algorithm for solving the Burgers problem with the use of non-orthogonal structured curvilinear grids in L-shaped geometry.For this,the differential equations were discretized by Finite Volume Method(FVM)with second-order approximation scheme and deferred correction.Moreover,the algebraic method and the differential method were used to generate the non-orthogonal structured curvilinear grids.Furthermore,the influence of some parameters of geometric multigrid method,as well as lexicographical Gauss–Seidel(Lex-GS),η-line Gauss–Seidel(η-line-GS),Modified Strongly Implicit(MSI)and modified incomplete LU decomposition(MILU)solvers on the Central Processing Unit(CPU)time was investigated.Therefore,several parameters of multigrid method and solvers were tested for the problem,with the use of nonorthogonal structured curvilinear grids and multigrid method,resulting in an algorithm with the combination that achieved the best results and CPU time.The geometric multigrid method with Full Approximation Scheme(FAS),V-cycle and standard coarsening ratio for this problem were utilized.This article shows how to calculate the coordinates transformation metrics in the coarser grids.Results show that the MSI and MILU solvers are the most efficient.Moreover,theMSI solver is faster thanMILU for both grids generators;and the solutions are more accurate for the Burgers problem with grids generated using elliptic equations.

PET image reconstruction with rotationally symmetric polygonal pixel grid based highly compressible system matrix

To achieve a maximum compression of system matrix in positron emission tomography (PET) image reconstruction, we proposed a polygonal image pixel division strategy in accordance with rotationally symmetric PET geometry. Geometrical definition and indexing rule for polygonal pixels were established. Image conversion from polygonal pixel structure to conventional rectangular pixel structure was implemented using a conversion matrix. A set of test images were analytically defined in polygonal pixel structure, converted to conventional rectangular pixel based images, and correctly displayed which verified the correctness of the image definition, conversion description and conversion of polygonal pixel structure. A compressed system matrix for PET image recon was generated by tap model and tested by forward-projecting three different distributions of radioactive sources to the sinogram domain and comparing them with theoretical predictions. On a practical small animal PET scanner, a compress ratio of 12.6:1 of the system matrix size was achieved with the polygonal pixel structure, comparing with the conventional rectangular pixel based tap-mode one. OS-EM iterative image reconstruction algorithms with the polygonal and conventional Cartesian pixel grid were developed. A hot rod phantom was detected and reconstructed based on these two grids with reasonable time cost. Image resolution of reconstructed images was both 1.35 mm. We conclude that it is feasible to reconstruct and display images in a polygonal image pixel structure based on a compressed system matrix in PET image reconstruction.

基于对称控制的三相并网变流器单输入单输出阻抗建模与分析

三相并网变流器的不对称控制结构会导致频率耦合效应,降低其接入弱电网的稳定裕度,增加了阻抗分析的复杂度。首先,该文提出一种三相并网变流器的对称控制策略,以消除由锁相环和直流电压环引起的频率耦合效应。该控制策略通过在控制环路中引入直流电压环q轴补偿,以形成对称的直流电压闭环结构,同时引入对称锁相环,消除传统锁相环的非对称动态特性。因此,三相并网变流器可建模为单输入单输出的阻抗复矢量形式,进而可采用标准奈奎斯特准则进行阻抗稳定性分析,能够直观地说明控制器对系统阻抗特性的主导作用。然后,对并网变流器的阻抗特性进行分析,得出弱电网中对称锁相环的带宽对系统稳定性有着至关重要的影响,并且,不同运行工况也会改变并网变流器的阻抗特性,进而影响系统的稳定性。最后,仿真和实验结果验证了所提控制策略对频率耦合效应抑制的有效性以及阻抗特性分析的准确性。

含跟网和构网型新能源发电单元的混联电力系统暂态同步稳定分析

在新能源发电单元与同步发电机共同接入的混联电力系统中,不同同步方式新能源间,新能源与同步发电机间耦合复杂,深刻影响系统的暂态同步稳定性。为揭示电网对称短路故障下不同发电单元间的动态耦合机理及其对系统暂态同步稳定性的作用机制,该文首先建立故障条件下混联系统的暂态稳定分析数学模型。随后,利用空间矢量图示法与相平面法分析跟网型新能源发电单元注入电流、锁相环参数以及构网型新能源发电单元有功控制环参数等因素对混联系统内各发电单元暂态同步稳定性的影响规律,并据此给出系统控制器参数的设计原则。最后,通过不同工况下的仿真验证理论分析的正确性。

一种改进的基于电网幅值跌落的SWISS整流器协调优化控制方法

SWISS整流器因其优越的性能被广泛应用于充电桩、分布式直流电源等场合。其首要的控制目标是维持稳定的直流侧输出电压、正弦且对称的交流侧三相电流以及网侧单位功率因数。然而,当电网出现幅值跌落时,基于传统的控制方法很难同时实现上述3个控制目标。因此,该文分别提出适用于电网幅值跌落的输出电压恒定控制(constant output voltage control,COVC)方法和电流正弦对称控制(sinusoidal and symmetrical current control,SSCC)方法。前者可实现直流侧输出电压恒定无波动,但无法实现网侧电流的正弦且对称。后者可实现网侧电流正弦且对称,但无法实现直流侧电压输出恒定无波动。在此基础上,该文结合这2种控制方法的优势进一步提出一种改进的协调优化控制(improved coordination and optimization control,ICOC)方法,可实现网侧处于单位功率因数的同时,在直流侧输出电压恒定无波动和网侧电流正弦且对称之间进行协调优化,实验结果证明ICOC方法相较于COVC和SSCC具有显著的优势,与该文的理论分析一致。

不平衡电网下AC-DC矩阵变换器的新型模型预测控制

为降低AC-DC矩阵变换器在输入不平衡条件下网侧有功功率波动,以及离散型模型预测控制中开关频率不固定的问题,提出一种新型模型预测控制方法。通过根据电网电流相位角选择有效矢量,避免了传统模型预测控制评估价值函数计算的负担。提出了一种二阶扩展复数卡尔曼滤波器,计算精度可以达到泰勒级数展开的二阶项,新型模型预测控制能够在不平衡电网系统中应用。仿真结果表明:所提控制策略在输入电压不平衡工况下,能够有效抑制网侧电流谐波,稳定系统输出的有功功率,并且表现出良好的性能。

FINITE ELEMENT APPROXIMATIONS OF SYMMETRIC TENSORS ON SIMPLICIAL GRIDS IN R^n： THE HIGHER ORDER CASE

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of H（div,Ω;S）-Pk＋1 tensors whose divergence is a Pk-1 polynomial on each triangle for k ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of H（div, Ω; S）-Pk＋2 tensors, whose divergence is a Pk-1 polynomial on each tetrahedron for k ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in R^n for any space dimension. On the contrary, the discrete stress space here is the space of H（div,Ω; S）-Pk tensors, and the discrete displacement space here is the space of L^2（Ω; R^n）-Pk＋1 vectors for k ≥ n＋ 1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.

Optimization of Wind Farm Collection Line Structure under Symmetrical Grid Fault

A power-transmission collection line is connected to each wind turbine of a wind farm and then connected to the incoming switchgear at the low-voltage side of the booster station at a certain distance.Therefore,the grouping of the wind turbines in the wind farm determines the layout of the lines and affects the line impedance.The line structure and composition of the wind farm are analyzed,and the relationship between the impedance of the collection line and reactive power generated by the wind turbine at low-voltage ride through is derived.We conclude that the smaller the equivalent impedance of the wind farm collection line structure is,the greater the reactive power at the wind farm collection line point is.In addition,the economic aspect of the collection line needs to be considered in the design.The economic aspect and impedance values have contrasting characteristics.Therefore,according to the condition of minimum impedance and optimized economic aspect,an optimization model of a wind-farm collector-circuit structure is proposed.The optimal structure of the wind farm collector circuit is calculated using the Monte Carlo method,and the theoretical analysis is verified by simulation.

Fault Current and Voltage Estimation Method in Symmetrical Monopolar MMC-based DC Grids

Symmetrical monopolar configuration is the prevailing scheme configuration for modular multilevel converter based high-voltage direct current(MMC-HVDC) links, in which severe DC overvoltage or overcurrent can be caused by the DC faults. To deal with the possible asymmetry in the DC faults and the coupling effects of the DC lines, this paper analyzes the DC fault characteristics based on the phase-mode transformation. First, the DC grid is decomposed into the common-mode and the differential-mode networks. The equivalent models of the MMCs and DC lines in the two networks are derived, respectively. Then, based on the state matrices, a unified numerical calculation method for the fault voltages and currents at the DC side is proposed. Compared with the time-domain simulations performed on PSCAD/EMTDC, the accuracy of the proposed method is validated. Last, the system parameter analysis shows that the grounding parameters play an important role in reducing the severity of the pole-to-ground faults, whereas the coupling effects of the DC lines should be considered when calculating the DC fault currents associated with the pole-to-pole faults.

电网对称故障下虚拟同步发电机建模与改进控制

虚拟同步发电机(virtual synchronous generator,VSG)是近些年新发展的电力电子装备,可为电网提供惯性和动态频率支撑。直接电压式虚拟同步发电机直接通过脉宽调制(pulse width modulation,PWM)产生内电势,无内电流和交流电压控制环,具有更好的动态支撑能力及稳定性;但当电网发生对称短路故障时,直接电压式虚拟同步机无法抑制故障电流,这将危及VSG的安全并限制了直接电压式虚拟同步控制的发展与应用前景。该文将虚拟电阻与相量限流方法相结合,在保证VSG正常运行频率、电压动态支撑的前提下,提出适用于直接电压式VSG的故障电流限制方法。仿真和实验结果证明了所提出的故障电流限制方法的可行性与有效性。

电网对称故障下含DFIG和PMSG的混合风电场群的协同控制策略

针对含双馈异步发电机和永磁直驱同步发电机的混合风电场群的低电压穿越技术进行详细研究。在推导双馈发电机和永磁直驱发电机的无功电流极限表达式的基础上,详细分析电压跌落程度和风速变化对其无功电流极限的影响规律,并获得满足风电场低电压穿越导则要求下双馈风电场和永磁直驱风电场的可控运行区域及其电流分配原则,进而提出无互联通信条件下混合风电场群的协同控制策略,该控制策略通过在电网故障过程中使风电场群输出最大无功电流以提高电网的暂态电压水平,并减少电网故障前后风电场群输出有功功率的变化以避免机群超速运行,使得该混合风电场群在全工况下的低电压穿越性能得到显著提高。通过仿真计算验证了所提控制策略的可靠性和有效性。

双dq变换软件锁相环的数学模型研究

对于三相并网型PWM变换器,要求锁相环能够准确、快速地检测出电网在不对称、畸变等情况下的基波频率与相位等信息,为控制系统及时提供准确的相关信息。本文根据双dq变换软件锁相环(SPLL)的基本原理,分析、推导了三相电源基波正、负序分量与锁相角和实际电压相位之间的数学关系,建立了基于该数学关系的双dq变换SPLL模型。仿真和实验均表明该模型适用性强,能够快速有效地提取三相电源在三相不对称、三相畸变、三相不对称且畸变等情况下的基波频率、正负序分量的大小与相位。

两层土壤中变电站接地网的精确计算

复镜象法是一种模拟计算变电站接地网的新方法 ,该方法适用于多层大地模型中任意结构接地网的模拟。但在分析大型地网时 ,由于接地导体数n较大 ,接地电阻的互导矩阵阶数为n ,数据待求量则为n2 。这是一个很庞大的数据计算量 ,而提出的对称复镜象法则可以大大减少数据输入量 ,并用这种方法分析了几个实际的接地网 。

电网电压对称故障时DFIG转子电流的优化控制策略

为抑制电网电压对称故障时双馈感应风力发电机(DFIG)的转子过电流,本文在电网电压对称故障时DFIG数学模型的基础上,分析了DFIG磁链自由分量引起的转子过电流机理,提出了一种以抑制转子电流自由分量为目标的DFIG优化控制策略。在转子电流基频分量闭环常规控制策略的基础上,加入了转子电流自由分量调节器,以构成DFIG电流优化控制系统,并分析了其对DFIG控制系统稳定性、动态特性的影响,进而给出了转子电流自由分量调节器参数的设计,增强了对转子电流自由分量的阻尼。最后,通过构建实验机组,对控制策略的有效性进行了实验验证。

电网对称故障时双馈感应发电机低电压穿越控制

分析电网对称故障时,双馈感应风力发电机定子磁链变化过程、导致定转子过电流的原因、电网故障发生具体时刻及故障程度对双馈感应发电机定转子的影响,提出一种双馈感应风力发电机转子侧变换器低电压穿越控制策略,改善了双馈感应发电机在电网故障时定、转子过电流的情况,实现了双馈感应发电机在电网对称故障时的低电压穿越。在理论分析基础上,建立双馈感应发电机转子侧变换器低电压穿越控制模型和3 kW双馈感应发电机励磁变换器低电压穿越控制实验系统。实验结果表明,所提出的双馈感应发电机低电压穿越控制策略动态响应快、方法行之有效。

不同电网故障时并网型光伏逆变器的动态特性分析

推导并网型光伏逆变器不同电网故障时在正、反同步旋转坐标系下的数学模型。对比强、弱光照条件下光伏逆变器的动态特性,指出电网发生对称故障时光伏阵列的工作状态由逆变器的功率送出能力决定。对常规控制策略下光伏逆变器的动态特性进行理论分析,指出电网发生不对称故障时常规控制策略中对输出电流的限制并不能限制每个单相的电流,负序分量的存在会造成直流母线电压和直流功率的二倍频波动,这种波动不会干扰最大功率追踪(MPPT)控制,逆变器输出电流中的三次谐波是由传统PI控制器不能对交流量实现无静差跟踪引起的,与直流母线电压波动无关。仿真算例验证了理论分析的正确性。

双馈风力发电系统在电网故障下的动态响应分析

该文在建立电网故障时双馈发电机定子电压空间矢量模型的基础上,对双馈感应发电机以及变换器在电网不对称故障及对称故障时的动态响应特性进行了详细的定量和定性分析,揭示了双馈发电系统暂态故障响应的本质及各电磁量的变化规律。推导出了双馈发电机电网故障电流的最大值及其发生时刻。并在此基础上,提出了实现风电机组故障穿越技术的基本准则。

电网对称故障时双馈感应发电机不脱网运行的系统仿真研究

利用经实验验证的时域仿真模型对一典型的2MW双馈感应风力发电系统在电网对称故障时的控制和响应进行仿真研究。与在电网故障时将转子端部直接短接的保护方案相比较,采用所提出的电网故障励磁控制与正常运行时的风能跟踪控制相结合,可以保证发电机迅速恢复有功输出,从而提高整个电力系统在故障切除后的运行稳定性。针对电网对称故障时发电机不脱网运行的可控范围进行仿真计算的结果表明:典型双馈感应风力发电机可在电网故障引起发电机变压器系统侧电压最低下降到30％额定电压时仍可保持不脱网运行。对影响电网故障励磁控制性能的各种因素,包括发电机故障前初始运行点及电机参数进行了研究,发现适当增加发电机漏感或定予侧电阻有助于进一步提高电网故障时励磁控制的效果。