This paper presents analytical expressions for the multiple-input multiple-output （MIMO） channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the ergodic capac...This paper presents analytical expressions for the multiple-input multiple-output （MIMO） channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the ergodic capacity for single-input multiple-output （SIMO） channels. The analysis shows that the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive approximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumulative distribution function （CCDF） of the MIMO channel capacity （outage capacity）. Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. Moreover, these analytical expressions are relatively simple which makes them very useful for practical computations.展开更多
From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart'...From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk,but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore,the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.展开更多
Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we de...Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.展开更多
Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using corresponde...Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.展开更多
Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this pape...Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.展开更多
The tide-induced net advective salt flux in well-mixed estuaries consists of five terms according to the method from Kjerfve.The term resulted from the vertical variation in salinity can be negligible in well-mixed es...The tide-induced net advective salt flux in well-mixed estuaries consists of five terms according to the method from Kjerfve.The term resulted from the vertical variation in salinity can be negligible in well-mixed estuaries with four tide-induced salt flux terms,known as F1−F4.To explore the effects of wind on these salt fluxes,the current-salinity analytical model combined with the perturbation analysis is extended by including wind.Analytical expressions for the four salt fluxes are derived separately in the present model.Under the assumption that only the M_(2) tidal component is accounted for and the salt flux generated by diffusion is not studied,the tide-induced net advective salt flux Q_(sx) is in the seaward direction without the wind effect.By applying the Western Scheldt estuary case,the wind influence on the tidal advection salt flux(TASF)distribution in the F4 term was investigated.The phase difference between zero-order velocity and first-order salinity(Δφ)at the surface layer of the estuary is larger than 90°and smaller than 90°at the bottom layer,which leads to landward TASF in the surface layer and seaward TASF in the bottom layer.The distribution ofΔφis not uniform in the horizontal direction with wind included,which differs from the result without wind.In the case of seaward wind with the speed of 18 m/s,the decrease in the zeroth-order velocity phase(φu)at the surface layer is larger than that of the first-order salinity phase(φs)downstream,which leads to an abnormal seaward TASF in this region.Owing to the surface stress caused by wind,the Stokes compensation flow in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is opposite.Thus,the first-order velocity in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is also opposite.The first-order salinity also increases/decreases with the increase of landward/seaward wind,while the upstream salinity tends to zero.Therefore,the tide-induced net advective salt flux Q_(sx) increases/decreases with the increase of the landward/seaward wind,which is contrary to the usual recognition.展开更多
Generated by an ideal sinusoidal motion of the vertical plate, the simplest linear solution in time domain for two-dimensional regular waves is derived. The solution describes the propagation process of the plane prog...Generated by an ideal sinusoidal motion of the vertical plate, the simplest linear solution in time domain for two-dimensional regular waves is derived. The solution describes the propagation process of the plane progressive wave with a front, and will approach the linear steady- state solution as the oscillation time of the plate approaches infinity. The solution presented in this paper can be used to provide an incident wave model with analytical expression for solving the problems of diffraction and response of floating bodies in time domain.展开更多
Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first ti...Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first time, which is suitable for the subwavelength aperture and the near-field region. The transverse properties of intensity distributions and their evolutions with the propagating distance, and the power transmission functions for diffracted fields containing the whole field, the evanescent field and the propagating field are investigated in detail, which is helpful for understanding the relationship between evanescent and propagating components in the near-field region and can be applied to apertured near-field scanning optical microscopy.展开更多
On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for t...On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.展开更多
Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the ...Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.展开更多
The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered...The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered half-space model by a point current source within the surface layer or the bottom layer.Finally,the electrical potential by a source electrode in any layer of a layered half-space model is presented.展开更多
Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximM classicM correlations are obtained via numerical computations, while i...Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximM classicM correlations are obtained via numerical computations, while in the second approach they are analytically derived. Quantum correlations captured with both approaches completely coincide, as is in accord with the conclusion of Cen et al. [Phys. Rev. A 83 （2011） 054101]. The symmetry reduction of the concerned states concerning quantum correlations is accomplished. The captured discords are amply analyzed so that some inherent distinct properties are revealed.展开更多
Based on the Smit-Suhl formula,we propose a universal approach for solving the magnon-magnon coupling problem in bilayer coupled systems(e.g.,antiferromagnets).This method requires only the energy expression,enabling ...Based on the Smit-Suhl formula,we propose a universal approach for solving the magnon-magnon coupling problem in bilayer coupled systems(e.g.,antiferromagnets).This method requires only the energy expression,enabling the automatic derivation of analytical expressions for the eigenmatrix elements via symbolic computation,eliminating the need for tedious manual calculations.Using this approach,we investigate the impact of magnetic hysteresis on magnon-magnon coupling in a system with interlayer Dzyaloshinskii-Moriya interaction(DMI).The magnetic hysteresis leads to an asymmetric magnetic field dependence of the resonance frequency and alters the number of degeneracy points between the pure optical and acoustic modes.Moreover,it can result in the coupling strength at the gap of the f–H phase diagram being nearly vanishing,contrary to the conventionally expected maximum.These results deepen the understanding of the effect of interlayer DMI on magnon–magnon coupling and the proposed universal method significantly streamlines the solving process of magnon–magnon coupling problems.展开更多
N−1 security is an important criterion for the development and planning of distribution networks.The existing N−1 contingency analysis methods of distribution networks are primarily based on the unit of components,and...N−1 security is an important criterion for the development and planning of distribution networks.The existing N−1 contingency analysis methods of distribution networks are primarily based on the unit of components,and the faults of each component are analyzed and verified one by one.The calculation process of these methods is complicated,and the positioning effect of the weak links needed for distribution network planning is insufficient.For this reason,this paper proposes a method of N−1 contingency parallel analysis for main transformers based on the incidence matrix.First,the main transformer incidence matrix is established,and the load transfer process is classified into three types,according to different transfer modes,and the contact matrices are then established respectively.Second,considering the capacity constraint of main transformers and tie-lines,the corresponding capacity matrices are established.The maximum transfer capability(MTC)of the distribution network in the case of each main transformer fault is calculated by contact matrices and capacity matrices,and the N−1 contingency analysis result is obtained by comparing MTC with the load that needs transferring.Meanwhile,the transfer margin of the main transformers and tie-lines after transferring can be obtained in the process of N−1 contingency analysis,so as to find any weak links.An example is given to verify the correctness and effectiveness of the proposed method.In this paper,the N−1 contingency analysis results of all main transformers in the distribution network are expressed analytically through matrices operations,and the weak links can then be intuitively identified.The cumbersome operation of checking each component is avoided,and the computational efficiency is improved.展开更多
The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically.In this paper,a constellation design ...The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically.In this paper,a constellation design method is proposed,considering satellite imaging width,formation flying of subgroup satellites,and global uniform coverage by payloads.Firstly,a configuration of satellites with the same subsatellite trajectory is proposed,and its orbital analytical expression under J2 perturbation is provided.Then,the relative motion feature points are extracted near the orbit of each satellite,and a group of uniform natural accompanying satellites are set to corresponding points.Afterwards,the orbit parameters of satellite and its companions are set as initial values,and the precise orbits under the High Precision Orbit Propagator model are solved in the neighborhood by using the Nondominated Sort Particle Swarm Optimization algorithm.Finally,the correctness of the configuration design method is verified by numerical simulation.展开更多
文摘This paper presents analytical expressions for the multiple-input multiple-output （MIMO） channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the ergodic capacity for single-input multiple-output （SIMO） channels. The analysis shows that the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive approximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumulative distribution function （CCDF） of the MIMO channel capacity （outage capacity）. Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. Moreover, these analytical expressions are relatively simple which makes them very useful for practical computations.
文摘From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk,but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore,the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.
基金supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(Grant Nos.12371132,12075159,12171044,12071179,and 12405006)the specific research fund of the Innovation Platform for Academicians of Hainan Province.
文摘Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.
基金Chinese Joint Seismological Science Foundation (101105)
文摘Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.
文摘Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.
基金supported by the National Key R&D Program of China(Grant No.2017YFC0405401)the Open Research Foundation of Key Laboratory of the Pearl River Estuarine Dynamics and Associated Process Regulation,Ministry of Water Resources(Grant No.[2018]KJ07)+1 种基金the Open Research Foundation of Key Laboratory of Coastal Disaster and Defence,Ministry of Education(Grant No.201706)the Six Talent Peaks Project in Jiangsu Province(Grant No.HYGC-0040).
文摘The tide-induced net advective salt flux in well-mixed estuaries consists of five terms according to the method from Kjerfve.The term resulted from the vertical variation in salinity can be negligible in well-mixed estuaries with four tide-induced salt flux terms,known as F1−F4.To explore the effects of wind on these salt fluxes,the current-salinity analytical model combined with the perturbation analysis is extended by including wind.Analytical expressions for the four salt fluxes are derived separately in the present model.Under the assumption that only the M_(2) tidal component is accounted for and the salt flux generated by diffusion is not studied,the tide-induced net advective salt flux Q_(sx) is in the seaward direction without the wind effect.By applying the Western Scheldt estuary case,the wind influence on the tidal advection salt flux(TASF)distribution in the F4 term was investigated.The phase difference between zero-order velocity and first-order salinity(Δφ)at the surface layer of the estuary is larger than 90°and smaller than 90°at the bottom layer,which leads to landward TASF in the surface layer and seaward TASF in the bottom layer.The distribution ofΔφis not uniform in the horizontal direction with wind included,which differs from the result without wind.In the case of seaward wind with the speed of 18 m/s,the decrease in the zeroth-order velocity phase(φu)at the surface layer is larger than that of the first-order salinity phase(φs)downstream,which leads to an abnormal seaward TASF in this region.Owing to the surface stress caused by wind,the Stokes compensation flow in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is opposite.Thus,the first-order velocity in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is also opposite.The first-order salinity also increases/decreases with the increase of landward/seaward wind,while the upstream salinity tends to zero.Therefore,the tide-induced net advective salt flux Q_(sx) increases/decreases with the increase of the landward/seaward wind,which is contrary to the usual recognition.
基金This study is financially supported by the National Natural Science Foundation of China
文摘Generated by an ideal sinusoidal motion of the vertical plate, the simplest linear solution in time domain for two-dimensional regular waves is derived. The solution describes the propagation process of the plane progressive wave with a front, and will approach the linear steady- state solution as the oscillation time of the plate approaches infinity. The solution presented in this paper can be used to provide an incident wave model with analytical expression for solving the problems of diffraction and response of floating bodies in time domain.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50975128)the National Key Basic Research Program of China (Grant No. 2011CB013004)+2 种基金the Natural Science Foundation of Jiangsu Province,China (Grant No. BK2011462)the National Science Foundation for Postdoctoral Scientists of China (Grant No. 20100481093)Jiangsu Provincial Planned Projects for Postdoctoral Research Funds,China (Grant No. 0902028C)
文摘Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first time, which is suitable for the subwavelength aperture and the near-field region. The transverse properties of intensity distributions and their evolutions with the propagating distance, and the power transmission functions for diffracted fields containing the whole field, the evanescent field and the propagating field are investigated in detail, which is helpful for understanding the relationship between evanescent and propagating components in the near-field region and can be applied to apertured near-field scanning optical microscopy.
基金Joint Seismological Science Foundation of China (101105) and National Natural Science Foundation of China (10232050).
文摘On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.
文摘Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.
基金funded under the key project,Study on Techniques of Medium and Short-term Earthquake Prediction for Tianjin and Its Nearby Areas(07ZCGYSF03100),of the Science & Technology Pillar Program of Tianjin Municipality
文摘The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered half-space model by a point current source within the surface layer or the bottom layer.Finally,the electrical potential by a source electrode in any layer of a layered half-space model is presented.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20103401110007,20123401110008the National Natural Science Foundation of China under Grant Nos.10975001,11375011,51072002,and 51272003+1 种基金the Program for Excellent Talents at the University of Guangdong Province(Guangdong Teacher Letter[1010]No.79)the 211 Project of Anhui University
文摘Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximM classicM correlations are obtained via numerical computations, while in the second approach they are analytically derived. Quantum correlations captured with both approaches completely coincide, as is in accord with the conclusion of Cen et al. [Phys. Rev. A 83 （2011） 054101]. The symmetry reduction of the concerned states concerning quantum correlations is accomplished. The captured discords are amply analyzed so that some inherent distinct properties are revealed.
基金supported by the National Key Research and Development Program of China (MOST)(Grant No.2022YFA1402800)the Chinese Academy of Sciences (CAS) Presidents International Fellowship Initiative (PIFI)(Grant No.2025PG0006)+3 种基金the National Natural Science Foundation of China (NSFC)(Grant Nos.51831012,12274437,and 52161160334)the CAS Project for Young Scientists in Basic Research (Grant No.YSBR-084)the CAS Youth Interdisciplinary Teamthe China Postdoctoral Science Foundation (Grant No.2025M773402)。
文摘Based on the Smit-Suhl formula,we propose a universal approach for solving the magnon-magnon coupling problem in bilayer coupled systems(e.g.,antiferromagnets).This method requires only the energy expression,enabling the automatic derivation of analytical expressions for the eigenmatrix elements via symbolic computation,eliminating the need for tedious manual calculations.Using this approach,we investigate the impact of magnetic hysteresis on magnon-magnon coupling in a system with interlayer Dzyaloshinskii-Moriya interaction(DMI).The magnetic hysteresis leads to an asymmetric magnetic field dependence of the resonance frequency and alters the number of degeneracy points between the pure optical and acoustic modes.Moreover,it can result in the coupling strength at the gap of the f–H phase diagram being nearly vanishing,contrary to the conventionally expected maximum.These results deepen the understanding of the effect of interlayer DMI on magnon–magnon coupling and the proposed universal method significantly streamlines the solving process of magnon–magnon coupling problems.
基金supported in part by National Key Research and Development Program of China under Grant 2020YFB0906000in part by National Natural Science Foundation of China under Grant 51977140,Grant U1866207 and Grant 51207101in part by Natural Science Foundation of Tianjin under Grant 19JCYBJC21300。
文摘N−1 security is an important criterion for the development and planning of distribution networks.The existing N−1 contingency analysis methods of distribution networks are primarily based on the unit of components,and the faults of each component are analyzed and verified one by one.The calculation process of these methods is complicated,and the positioning effect of the weak links needed for distribution network planning is insufficient.For this reason,this paper proposes a method of N−1 contingency parallel analysis for main transformers based on the incidence matrix.First,the main transformer incidence matrix is established,and the load transfer process is classified into three types,according to different transfer modes,and the contact matrices are then established respectively.Second,considering the capacity constraint of main transformers and tie-lines,the corresponding capacity matrices are established.The maximum transfer capability(MTC)of the distribution network in the case of each main transformer fault is calculated by contact matrices and capacity matrices,and the N−1 contingency analysis result is obtained by comparing MTC with the load that needs transferring.Meanwhile,the transfer margin of the main transformers and tie-lines after transferring can be obtained in the process of N−1 contingency analysis,so as to find any weak links.An example is given to verify the correctness and effectiveness of the proposed method.In this paper,the N−1 contingency analysis results of all main transformers in the distribution network are expressed analytically through matrices operations,and the weak links can then be intuitively identified.The cumbersome operation of checking each component is avoided,and the computational efficiency is improved.
基金supported in part by the Fundamental Research Funds for the Central Universities(No.3072022JC0202).
文摘The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically.In this paper,a constellation design method is proposed,considering satellite imaging width,formation flying of subgroup satellites,and global uniform coverage by payloads.Firstly,a configuration of satellites with the same subsatellite trajectory is proposed,and its orbital analytical expression under J2 perturbation is provided.Then,the relative motion feature points are extracted near the orbit of each satellite,and a group of uniform natural accompanying satellites are set to corresponding points.Afterwards,the orbit parameters of satellite and its companions are set as initial values,and the precise orbits under the High Precision Orbit Propagator model are solved in the neighborhood by using the Nondominated Sort Particle Swarm Optimization algorithm.Finally,the correctness of the configuration design method is verified by numerical simulation.
