针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityreg...针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityregion,SVSR)临界点,然后基于该临界点处空间切向量的空间角与最大空间角阈值的关系,对SVSRB进行初始分段近似,以SVSR临界点到初始近似边界的距离与最大距离误差阈值的关系为依据,对初始近似边界进行二次近似,计及SVSRB曲率的变化,得到更为精确的SVSR分段超平面近似边界,实现SVSRB近似解析表达式的构建,该方法可有效提高SVSRB近似精度,增强电力系统电压稳定的态势感知能力。最后,将所提方法应用于WECC3机9节点测试系统和欧洲电网13659节点测试系统,结果表明,所提方法可有效实现SVSRB精确近似解析表达和准确构建。展开更多
电力系统静态电压稳定边界(static voltage stability boundary,SVSB)对于判断电压稳定性、评估电压稳定裕度具有重要的指示作用,因此,快速准确地计算SVSB对于电网安全稳定运行具有重要意义。电力系统作为一个超高维多变量的复杂非线性...电力系统静态电压稳定边界(static voltage stability boundary,SVSB)对于判断电压稳定性、评估电压稳定裕度具有重要的指示作用,因此,快速准确地计算SVSB对于电网安全稳定运行具有重要意义。电力系统作为一个超高维多变量的复杂非线性系统,其电压稳定边界本质上是某一拓扑结构下所能维持电源和负荷功率平衡的极限电压所构成的非线性高维边界。因此,将SVSB考虑为高维场景下的电压稳定超曲面,提出计算电压稳定边界的新方法。首先,利用多维全纯嵌入法(multidimensional holomorphic embedding method,MDHEM)求得节点电压的多变量幂级数(multivariate power series,MPS)表达式;然后,基于柯西-阿达马定理,推导并证明电压稳定边界与节点电压幂级数前后项系数之间的解析关系,并通过理论证明将所提出的方法从单维推广到高维场景;接着,基于推导的SVSB解析表达式,提出高维电压稳定边界计算与电压稳定性快速评估方法;最后,在IEEE 14节点、新英格兰39节点和IEEE 118节点系统中验证所提方法的有效性。展开更多
To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introdu...To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions： w （x） , U（x） and O（x） are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.展开更多
This work deals with the analysis of soil-structure interaction modeling of pipeline problems in static behavior using the coupling between FEM （finite element method） and BEM （boundary element method）. The repres...This work deals with the analysis of soil-structure interaction modeling of pipeline problems in static behavior using the coupling between FEM （finite element method） and BEM （boundary element method）. The representation of the pipe is made by MEF using one fmite element in the cylindrical panel formulated from the theory of equivalent discrete layers （Layerwise theory）, proposed by J. N. Reddy. The soil is represented by elastic continum infimite or semi-infinite and modeled using boundary elements with special curved surface, associated with cylindrical panel used to represent the soil-structure interaction within the soil, especially at the contact surface with the pipe.展开更多
The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explic...The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H2- exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C norm are derived.展开更多
文摘针对电力系统静态电压稳定域边界(staticvoltage stability region boundary,SVSRB)近似解析表达式的构建问题,该文提出一种SVSRB近似的空间切向量法。首先采用SVSRB搜索的预测–校正算法搜索静态电压稳定域(static voltagestabilityregion,SVSR)临界点,然后基于该临界点处空间切向量的空间角与最大空间角阈值的关系,对SVSRB进行初始分段近似,以SVSR临界点到初始近似边界的距离与最大距离误差阈值的关系为依据,对初始近似边界进行二次近似,计及SVSRB曲率的变化,得到更为精确的SVSR分段超平面近似边界,实现SVSRB近似解析表达式的构建,该方法可有效提高SVSRB近似精度,增强电力系统电压稳定的态势感知能力。最后,将所提方法应用于WECC3机9节点测试系统和欧洲电网13659节点测试系统,结果表明,所提方法可有效实现SVSRB精确近似解析表达和准确构建。
基金Sponsored by the National Natural Science Foundation of China(Grant No.50578054)
文摘To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions： w （x） , U（x） and O（x） are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.
文摘This work deals with the analysis of soil-structure interaction modeling of pipeline problems in static behavior using the coupling between FEM （finite element method） and BEM （boundary element method）. The representation of the pipe is made by MEF using one fmite element in the cylindrical panel formulated from the theory of equivalent discrete layers （Layerwise theory）, proposed by J. N. Reddy. The soil is represented by elastic continum infimite or semi-infinite and modeled using boundary elements with special curved surface, associated with cylindrical panel used to represent the soil-structure interaction within the soil, especially at the contact surface with the pipe.
基金Project supported by the Initial Training Network "FIRST" of the Seventh Framework Programme of the European Community’s (No. 238702) the DFG-Priority Program 1253: Optimization with PDEs (No. GU 376/7-1)
文摘The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H2- exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C norm are derived.
