Inertial Entropy and External Validation of Clusterings

Axiomatization of Shannon entropy is a subject that has received lots of attention in the information theory literature.While Shannon entropy is defined on probability distribution,we define a new type of entropy on the set of partitions of finite subsets of metric spaces,which has a rich algebraic structure as a partially ordered set.We propose an axiomatization of an entropy-like measure of partitions of sets of objects located in metric spaces,and we derive an analytic expression of this new type of entropy referred to as inertial entropy.This approach starts with the notion of inertia of a partition and includes a study of the behavior of the sum of square errors of a partition.In this context,we characterize the chain of partitions produced by the Ward hierarchical clustering method.Starting from inertial entropies of partitions,we introduce conditional entropies which,in turn,generate metrics on partitions of finite sets.These metrics are used as external validation tools for clusterings of labeled data sets.The metric generated by inertial entropy can be used to validate data clustering for labeled data sets.This type of validation aims to determine to what extend labeling of the data coincides with the clustering obtained algorithmically,and we obtain a high degree of consistency of the data labeling with the results of several hierarchical clusterings.

The Nature of Inertia Explained Using the Field Theory

Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.

Moments of inertia of triaxial nuclei in covariant density functional theory

The covariant density functional theory(CDFT)and five-dimensional collective Hamiltonian(5DCH)are used to analyze the experimental deformation parameters and moments of inertia(MoIs)of 12 triaxial nuclei as extracted by Allmond and Wood[J.M.Allmond and J.L.Wood,Phys.Lett.B 767,226(2017)].We find that the CDFT MoIs are generally smaller than the experimental values but exhibit qualitative consistency with the irrotational flow and experimental data for the relative MoIs,indicating that the intermediate axis exhibites the largest MoI.Additionally,it is found that the pairing interaction collapse could result in nuclei behaving as a rigid-body flow,as exhibited in the^(186-192)Os case.Furthermore,by incorporating enhanced CDFT MoIs(factor of f≈1.55)into the 5DCH,the experimental low-lying energy spectra and deformation parameters are reproduced successfully.Compared with both CDFT and the triaxial rotor model,the 5DCH demonstrates superior agreement with the experimental deformation parameters and low-lying energy spectra,respectively,emphasizing the importance of considering shape fluctuations.

Determining the moment of inertia of triaxial Mars with updated global gravity models

The principal moments of inertia(PMIs)with the principal axes are usually taken as the dynamic figure parameters of Mars;they can be deduced from satellite-observed degree-two gravitational potentials in recent global gravity models and from the dynamic ellipticities resulting from precession observations.These PMIs are natural and significant for the geodetic,geophysical,and geodynamic problems of Mars,which are functions of internal density distributions.In this study,a closed and concise formula for determining the PMIs of the entire planet and its core was developed based on the second invariants of gravity and a multipole expansion.We deduced the polar oblateness J^(2)and the equatorial ellipticity J_(22)of Mars to be 1.9566×10^(−3)and 6.3106×10^(−5),respectively.The preferred principal moments of inertia of Mars are A=2.66589×1036 kg·m^(2),B=2.66775×10^(36)kg·m^(2),and C=2.68125×10^(36)kg·m^(2).These values indicate that Mar is slightly triaxial.The equatorial principal moment of inertia of the Martian core is 1.46008×10^(35)kg·m^(2),accounting for~5.47%of the planet’s PMI;this result is critical for investigating the density and size of the core of Mars,and the planet’s free core nutation.

Disjointed Equivalence of Gravitational and Inertial Mass

Problem—Contemporary physics offers no underlying reason for the equivalence of inertial and gravitational mass. Approach—The equivalence is examined from the new physics provided by the cordus theory, being a non-local hidden-variable (NLHV) theory. Mathematical formalisms are derived for masses and observers in different fabric densities. Findings—A disjointed equivalence is predicted, whereby inertial and gravitational masses are equivalent in any one situation, but a different equivalence holds when the fabric densities change. Consequently this theory predicts that the gravitational constant G varies with fabric density, and hence would be different across the universe and across time. Not only is the gravitational constant non-constant, but the formulation of gravitation changes with fabric density. Specifically, the theory predicts gravity is stronger at genesis (and the end of the universe) such that orbit velocity vB ∝ (where rB is orbit radius), compared to weaker gravitation at middle life epochs with rB ∝ . The current Earth location and epoch correspond to the latter case, i.e. Newtonian gravitation is recovered. The findings disfavour the existence of both dark energy and dark matter, and instead attribute these effects to differences in the fabric density. Originality—The work makes the contribution of deriving a mass equivalence relationship that includes fabric density, identifying a disjointed mass equivalence, and showing that the gravitation formulation itself changes with relative fabric densities.

能量视角下的电力系统惯量

同步机主导的电力系统中,机械旋转惯量是决定频率动态的主导因素,被代指为系统惯量。随着新能源占比升高,机械旋转惯量不断下降,其主导作用被削弱,现有对电力系统惯量的认知不再适用。文中首先回顾惯量作为阻碍物体状态变化能力度量的物理本质,把电力系统建模为包含不同尺度下多种能量形式和元件的能量供应链,将惯量广义化为机械旋转惯量、电惯量、热惯量、流体惯量。能量供应链中,同一尺度上存储惯量和通道惯量组成的“惯量对”决定了该尺度的动态;总的尺度上,不同尺度的多个“惯量对”决定了时域的序贯动态和频域的级联滤波特性。然后,进一步揭示了惯量需求的根源是能量需求,存储单元需要有足够的瞬时可释放能量来应对传输通道引起的能量补充滞后,整个能量供应链需要存储足够的本地能量支撑分散控制。能量视角下的电力系统惯量认知有助于评估新型电力系统的惯量需求,为新型电力系统有功控制的方法设计提供理论指导。

含高比例新能源的电力系统频率稳定研究综述

作为“双碳”战略目标的关键载体,含高比例新能源的电力系统具有惯量水平低、调频能力差、抗扰性能弱等特征,对频率稳定带来了全新挑战,迫切需要深入认识能源转型背景下的频率稳定形态。该文按照“建模分析—稳定评估—调频控制”的路线,归纳近年来国内外关于频率稳定的研究及其应用进展。首先,梳理现有频率稳定定义的特点,将其引申为考虑暂态频率安全的广义频率稳定概念,分析含高比例新能源电力系统的频率响应过程;按照系统全局频率和网络节点频率两个视角分析现有特性建模与分析方法,分别总结频率稳定性、频率安全性的评估方法与评估指标,初步建立考虑频率时空分布特性的节点频率安全性指标;列举并归类源网荷储多主体参与系统调频的控制策略,分析相关频率调控措施的特点;最后,结合现有研究进展,对含高比例新能源的电力系统在频率响应特性建模、频率稳定机理评估以及频率稳定协调控制方面的未来发展方向和研究趋势进行展望。

基于功率微分项的双VSG有功功率振荡抑制策略

针对虚拟同步发电机(VSG)双机并联运行时产生的有功功率振荡问题,通过建立双VSG系统的小信号模型,分析了有功功率振荡产生的机理,提出一种基于改进虚拟阻抗的瞬态功率均分策略和一种基于功率微分项的自适应惯量和阻尼的功率振荡抑制策略,将有功功率微分项与角加速度结合起来实现惯量的自适应调节,同时将有功功率微分项引入阻尼控制环节以替代传统的阻尼项,实现阻尼的自适应调节。所提出的策略可以使动态时VSG之间的角频率差更快速地趋近于零,从而减小有功功率振荡的超调,改善频率动态响应性能。搭建了VSG并联的仿真模型,仿真结果表明:所提改进控制策略可以使瞬态时实现有功均分,使动态时的有功功率振荡超调减小41%,振荡过程减小了1秒。

风电虚拟惯量延时的影响机理模型解析及替代性研究

风电机组采用虚拟惯量参与电网调频时,其本质是带延时的快速功率响应,但虚拟惯量延时对频率控制的非线性影响尚不清晰。同时,虚拟惯量存在测频精度要求高、延时大、频率微分环节放大量测误差等固有缺陷。为此,提出了风电机组虚拟惯量延时的影响机理模型解析及替代性研究的思路。首先,通过将风电机组虚拟惯量和下垂控制的延时特性近似等效为一阶惯性环节,建立风电调频使用虚拟惯量和下垂控制的系统频率响应模型;其次,基于劳斯近似法对高阶模型进行降阶解析,求得系统频率最低点的解析表达式;然后,解析求解风电调频仅使用下垂控制的系统频率响应模型,并在频率最低点指标下给出与虚拟惯量和下垂控制相同调频效果的下垂控制系数设定方法。进一步,在设定下垂控制参数下,对比两种控制方式下的最大频率变化率、稳态频率等关键指标关系,得出结论:适当改变下垂系数可替代带延时虚拟惯量,并能取得比虚拟惯量和下垂控制更佳的调频效果。最后,建立仿真模型,并从系统频率响应动态、调频能量需求、风电机组响应功率等方面验证了分析的正确性。

附加频率控制下并网换流器的动态惯量及其量化评估

新能源大规模并网显著降低了交流系统惯量,并网换流器参与频率控制成为提升频率稳定性的重要手段。基于传递函数模型推导了附加频率控制下并网换流器的动态惯量,发现其受惯量设计参数和其他控制环节的共同影响,呈现时变特性,但是将其简化为与同步发电机旋转惯量类似的常数会导致分析误差。为此,面向定直流电压控制和定功率控制这两类主流的并网换流器控制方式,提出了附加频率控制下并网换流器动态惯量的量化评估方法,分析了控制参数、运行工况和系统特性等不同因素对惯量的影响机制,得到了有功控制外环会显著改变原有设计惯量的结论,需重点关注其控制参数导致的惯量偏差。最后,基于在Simulink中搭建的时域仿真模型,验证了所提传递函数模型及惯量量化评估方法的正确性和有效性。

Moments of Inertia, Magnetic Dipole Moments, and Electric Quadrupole Moments of the Lithium Isotopes

The single-particle Schrödinger fluid model is designed mainly to calculate the moments of inertia of the axially symmetric deformed nuclei by assuming that each nucleon in the nucleus is moving in a single-particle potential which is deformed with time t, through its parametric dependence on a classical shape variable α(t). Also, the Nilsson model is designed for the calculations of the single-particle energy levels, the magnetic dipole moments, and the electric quadrupole moments of axially symmetric deformed nuclei by assuming that all the nucleons are moving in the field of an anisotropic oscillator potential. On the other hand, the nuclear superfluidity model is designed for the calculations of the nuclear moments of inertia and the electric quadrupole moments of deformed nuclei which have no axes of symmetry by assuming that the nucleons are moving in a quadruple deformed potential. Furthermore, the cranked Nilsson model is designed for the calculations of the total nuclear energy and the quadrupole moments of deformed nuclei which have no axes of symmetry by modifying the Nilsson potential to include second and fourth order oscillations. Accordingly, to investigate whether the six p-shell isotopes 6Li, 7Li, 8Li, 9Li, 10Li, and 11Li have axes of symmetry or not, we applied the four mentioned models to each nucleus by calculating their moments of inertia, their magnetic dipole moments, and their electric quadrupole moments by varying the deformation parameter β and the non-axiality parameter γ in wide ranges of values for this reason. Hence for the assumption that these isotopes are deformed and have axes of symmetry, we applied the single-particle Schrödinger fluid model and the Nilsson model. On the other hand, for the assumption that these isotopes are deformed and have no axes of symmetry, we applied the cranked Nilsson model and the nuclear super fluidity model. As a result of our calculations, we can conclude that the nucleus 6Li may be assumed to be deformed and has an axis of symmetry.

考虑SOC的混合储能功率分配与自适应虚拟惯性控制

电力电子化的直流配电网存在低惯性问题,不利于系统稳定运行。混合储能设备可向电网提供虚拟惯性,但不同类型的储能之间存在功率协调问题,并且储能的荷电状态(state of charge, SOC)对虚拟惯性的调节也有约束作用。针对上述问题,提出了一种自适应时间常数的分频控制策略,时间常数根据混合储能系统(hybridenergy storage system, HESS)的SOC而动态调整以改变功率分配。首先,通过分析储能SOC与虚拟惯性的关系,并考虑储能充放电极限问题,研究兼顾SOC、电压变化率以及电压幅值的自适应虚拟惯性控制策略,提高系统惯性。然后,建立控制系统的小信号模型,分析虚拟惯性系数对系统的影响。最后,基于Matlab/Simulink搭建直流配电网仿真模型,验证了所提控制策略能合理分配HESS功率,提高超级电容器利用率,改善直流电压与功率稳定性。

新型电力系统主动构网机理与技术路径

随着新一代“双高”电力系统的发展,新能源并网变换系统逐渐由随网型向构网型演变,当新能源机组集群运行时,并网情况将更加复杂。变换器的构网能力需亟待研究,同时也是电力能源转型需承担的重要使命。该文立足并网系统内外形态的全局性和传统并网变换系统性能分析的局限性,对并网变换器的主动构网支撑机理进行再揭示。首先,对虚拟同步技术与构网机理进行简要评述;其次,就集群并网系统的建模问题、多机集群并网运行时的耦合交互问题、支撑构网能力的储能配置和运行边界等3个关键技术问题,进行深入研究;最后,针对上述3个关键技术问题,进行技术路径探索和研判。该文的思路为形成适用于未来新能源集群并网运行的系统化理论和实用化方法奠定一定基础。

基于小扰动频率量测数据的电网节点惯量分布评估方法

惯量在电力系统抵抗扰动中起到关键作用。随着新能源渗透率的提升,电力系统中低惯量与惯量时空分布不均的特征日益凸显,准确评估电网节点惯量分布具有重要意义。为此,文中提出一种基于小扰动频率量测数据的节点惯量分布评估方法。首先,分析了频率与惯量的数学耦合机理,揭示了新型电力系统惯量分布特征。然后,根据单次小扰动下的频率量测数据与系统电源参数,分别提出了考虑各节点频率相较于系统中心频率变化水平偏差的节点等效惯量定义方法,以及基于自适应阶数多项式拟合的节点频率变化率计算方法,两层方法相结合即可计算出单次小扰动下的节点等效惯量。进一步,鉴于单次小扰动下求出的节点等效惯量具有一定的随机误差,提出考虑多次扰动事件评估结果的动态聚合策略,形成适用于新型电力系统的节点等效惯量分布评估方法。最后,分别以IEEE 39节点系统、中国某省级电网为例验证了所提方法的有效性。结果表明,所提方法所需数据量少,仅需各节点同步相量测量单元采集的频率量测数据即可实现对电网惯量分布的有效评估,评估结果准确性高且时效性强。

可再生能源高渗透下时滞孤岛微电网的负荷频率控制

针对孤岛微电网系统中大规模接入可再生能源导致的低惯性和开放通信网络中通信延迟对系统稳定运行造成的不可忽略的影响,该文研究变时滞影响下低惯性孤岛微电网系统的负荷频率控制问题。首先,提出一种引入虚拟惯性控制的时滞微电网分层频率控制模型;然后构造一个新的Lyapunov-Krasovskii泛函,它包括时滞乘积项和增广的s-dependent积分项。进而,选取复合松弛积分不等式、二次函数不等式和凸组合等方法与所构造泛函有效配合,得到保守性更低的稳定性判据。最后,通过不同场景的仿真分析验证所提方法在提高孤岛微电网时滞稳定裕度和系统动态性能方面具有更好的效果,并分析了时滞稳定裕度与控制器参数、非线性负载扰动之间的关系。

计及工作点偏移的减载风电系统频率响应模型

随着风电并网容量不断升高,利用减载风电机组参与一次调频对保障系统频率稳定性具有重要意义。然而,风机的工作点会随其转速变化而发生偏移,使得风机的实际一次调频贡献小于期望值。为此,文中首先分析了频率故障后风电机组减载功率跟踪控制与综合惯量控制的交互影响,指出了风机工作点偏移导致其调频效果削弱的基本原理。其次,基于风机的转子运动方程推导了风电功频传递函数,建立了计及减载风电机组工作点偏移的系统频率响应模型,并利用最小二乘法对其进行降阶,推导了系统频率最低点的解析式。然后,针对虚拟惯量控制的频率恢复期间引起功率倒流、微分环节放大噪声等缺点,提出利用下垂控制替代综合惯量控制。同时,为使减载风电机组获得期望的调频效果,基于频率最低点和稳态频率指标对风机控制参数进行了修正,提出了两种等效下垂系数的计算方法。最后,在MATLAB/Simulink平台建立了四机两区域模型,验证了所提降阶方法及修正方法的有效性。

新能源场站快速频率支撑能力评估研究现状与技术展望

随着以风电、光伏为代表的新能源发电逐步取代同步机组,系统调频资源不足、抗扰动能力下降,频率安全问题凸显,新能源场站提供快速频率支撑成为构建新型电力系统的必然要求。新能源场站快速频率支撑是其内部多设备、多环节综合作用的结果,受风光资源、控制策略、电网条件等多因素的影响和制约。量化评估新能源场站的快速频率支撑能力是指导场站调频优化控制、分析新型电力系统频率响应特性、实现场站调频资源与电网交互的基础和前提。文中对新能源场站快速频率支撑能力评估问题进行了全面综述。首先,分析场站快速频率支撑的特征,并给出了场站快速频率支撑能力的定义;然后,从状态属性、控制特性、调频效果3个维度梳理了场站快速频率支撑能力的评估指标体系,并对各类评估指标的常用计算方法进行分析评述;最后,提出了值得关注和进一步研究的关键技术问题。

风电集群汇集的共享储能虚拟惯量补偿控制策略

针对大规模风电并网导致系统惯量削弱问题,提出风电集群汇集的共享储能虚拟惯量补偿控制策略。首先,计算风电集群惯量削弱量及共享储能电站的惯量补偿目标;然后,根据惯性响应的基本物理意义,定义储能装置的虚拟惯量;接着,探明其时变特性,求解储能虚拟惯量时域过程,确定储能电站以及各储能单元虚拟惯量补偿目标,提出各储能单元补偿目标动态设置控制参数的控制策略;最后,通过Matlab/Simulink仿真,验证了所提策略在不同储能配置容量、不同风电渗透率下均具有良好控制效果和适应性。

圆环筒贮箱液体绕横轴的有效转动惯量

航天器贮箱内液体绕横轴和纵轴的有效转动惯量参数是飞行控制系统仿真分析的重要基础,本文分析整理了航天器圆环筒形平底贮箱内液体的有效转动惯量计算方法,依据自由液面平底圆环筒贮箱平动和绕质心横向转动激励下的液体晃动力与力矩的解析表达式,推导了激励频率趋于无限大时,液体平动晃动合力作用点所在位置和绕质心的有效转动惯量表达式,并在平底圆筒条件下利用移轴定理,验证了与液体惯性中心所在位置和绕惯性中心有效转动惯量的一致性。分析了贮箱深度和内、外径比对液体转动惯量的影响规律,补充完善了液体转动晃动特性的理论分析成果。

储能虚拟惯量主动支撑与调频状态转移控制

释放储能装置的频率支撑潜力,将是提升风、光高占比系统并网稳定性的关键。该文首先对比分析常规发电机组的固有惯量、风电机组的虚拟惯量及储能的惯性支撑特性。其次,根据系统中的储能容量配置,约束量化储能的虚拟惯量,为系统惯量需求提供评估依据,以保障频率安全。在此基础上,利用储能独特的功率支撑特性,提出恒频控制与调频状态转移控制结合的储能并网频率主动支撑控制策略,突破虚拟惯量及一次调频的传统控制模式。最后,搭建风电高渗透电网仿真系统,验证储能装置在所提控制策略下能够显著提升系统的频率稳定性,改善其对电网的主动支撑性能。