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This study deals with the evaluation of the longitudinal and transverse coupling impedance of a charge travelling in a drift tube with a perfectly electric conductive angular strip. The problem is formulated in the particle frame as dual series equations, and efficiently solved through the representation of the unknown in terms of Neumann series. Then, the electric parameters are obtained in the pipe frame through the Lorentz transforms. The presented solution can be adopted as the general methodology in case of angular discontinuities in particle accelerators. [ABSTRACT FROM AUTHOR]

This study introduces a modified tensor‐based power flow method designed using complex voltages represented in their rectangular form. Tensor‐based methods employ the second‐order Taylor series expansion of the power flow equations to estimate a correction vector to be added to the iterative increments of the Newton–Raphson method. In the proposed approach, the estimation of the correction vector is improved by taking advantage of a relation between the Jacobian and tensor arrays and symmetries between matrix–vector products involving Jacobian matrices. Result analysis highlights the efficiency and robustness of the proposed method in comparison with the original tensor‐based approach using test systems and an actual system. [ABSTRACT FROM AUTHOR]

A detailed analysis is presented for the inductance calculations of rectangular coils with parallel end faces, with the coils of parallel sides as the special case. Integral solutions are given by the theory of second‐order scalar potential. The authors further provide the series solutions for the inductance, which are based on the truncated region eigenfunction expansion method. These series are quite concise and accurate, and with higher computational efficiency by comparison with the integrals. The integral and series solutions are also obtained for the planar rectangular coils. The numerical results of both methods are compared with those of the experimental data, and the proposed methods prove to be accurate and efficient enough for practical applications. [ABSTRACT FROM AUTHOR]

This study presents a new fault location algorithm for multiple‐circuit shared tower transmission lines with different voltages utilising synchronised measurements. The formulation of the proposed algorithm is based on overhead transmission lines theory and Taylor series expansion of distributed‐parameter line model. The untransposition of the lines and the mutual coupling between the parallel lines are considered to achieve precise fault location. Kirchhoff's current law and fault location equation are used to identify the faulty section and obtain the location of all normal shunt faults and inter‐circuit faults. The power system is simulated with DIgSILENT Power Factory software and all calculations are performed by MATLAB. Numerous fault cases are conducted to demonstrate the efficacy of the proposed algorithm considering different values of fault resistances, different fault locations and all fault types. In addition, the effects of synchrophasors errors, measurement errors and the soil resistivity variations are investigated. The results of simulation prove the efficacy of the proposed algorithm for all fault cases. [ABSTRACT FROM AUTHOR]

Taylor product theorem is applied to the evaluation of a class of integrals that arise in high-frequency wave scattering problems. We expand a term 1/(t^2+1) under the integral into exponentiated powers of $t$ that are suitable for term-by-term integrations. We utilize the expansion in an example and make accuracy and speed analysis. [ABSTRACT FROM PUBLISHER]

The integral equation technique, in combination with the method of moments, is widely used for treating the electromagnetic scattering from periodic rough surfaces. This method, however, requires the computation of a kernel (a periodic Green's function) that consists of a slowly converging infinite series of conventional Green's functions. To accelerate the convergence of this series, different methods have been proposed in literature. In this paper, we use a complex image (CI) technique to find a closed-form expression for the periodic Green's function, which is then used to analyze the electromagnetic scattering from arbitrary periodic rough surfaces. The resulting CI Green's function consists of a finite number of terms corresponding to real and complex sources. Moreover, the CI Green's function in the Hankel form (evanescent waves) is used if the observation and source points are close. In the far-field region, the series in the plane-wave form (propagating Floquet modes) caused by the extraction of poles are sufficient and necessary. The results indicate that the presented CI Green's function leads to numerical efficiency yet having a rather high level of accuracy. [ABSTRACT FROM PUBLISHER]

The staircase waveform produced by digital‐to‐analogue conversion is applied widely in electricity metrology, based on the known properties. However, a continuous investigation of new properties is still very important for its further applications. An infinite series is presented through analysis of the producing process of the staircase waveform. Based on the model of 'digital‐to‐analogue converter (DAC) aliasing effect', when the parameters of the series are extended from an integral to a real number, new properties are discussed. The concepts of 'asynchronous sampling', 'sub‐' and 'inter‐harmonic' and 'under‐Nyquist sampling' are derived into DAC. The more interesting phenomena are detailed. The results of simulations and experiments are reported. [ABSTRACT FROM AUTHOR]

In massive multiple‐input–multiple‐output (MIMO) systems, the downlink zero‐forcing (ZF) precoding method needs to compute the pseudoinverse of large matrices, which introduces high computational complexity, especially when the number of antennas is large or infinite. Although, based on Neumann series expansion, several approximation algorithms could reduce the complexity, calculating the optimisation coefficients would cost large amounts of resources and produce large delay. A novel method, also based on Neumann series expansion, is proposed. In this method, the multiplication of full matrices is transformed into multiplication of diagonal matrices by hollow matrices, effectively reducing computational complexity. Meanwhile, consideration of a simple expression of optimisation coefficients so as to avoid large delay is very useful in high‐mobility scenarios. Analysis and simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

It is shown that smooth spatial paths for nonredundant serial robots can always be smoothly reparametrized in the vicinity of kinematic singularities with finite root multiplicity using a Puiseux series. This reparametrization, based on the algebraic structure of the manipulator kinematics, is formed using the /spl nu/th root of the path parameter distance to the singularity, where /spl nu/ is some integer not exceeding the root multiplicity of the singularity. By contrast, self-motion singularities, which have infinite root multiplicity, do not possess such a reparametrization. However, smooth motions directly through such singularities are generally possible because approaching path solutions are unaffected by them. These results help quantify how joint derivatives blow up at singularities, and can readily be used to generate singularity-robust motions along any path, with no spatial error. This is illustrated with an example involving the PUMA manipulator. [ABSTRACT FROM PUBLISHER]

The paper presents a method for the reconstruction of an axisymmetric configuration of magnetic field. The reconstruction procedure is based on a multipolar series expansion of the magnetic field and requires a number of experimental measurements of magnetic field and flux. The accuracy and efficiency of the procedure is analysed and compared with another procedure based on an integral approach. [ABSTRACT FROM AUTHOR]

This paper deals with a hybrid FEM-SERIES formulation and solution for axisymmetrical linear and nonlinear magnetostatic problems with an open region. In the interior region, a conventional FEM is formulated, while a SERIES formulation is proposed in the exterior region. Several examples are given for illustration and the numerical results are compared with those obtained by finite element solutions. [ABSTRACT FROM AUTHOR]

The kinematic differential equations express the paths taken by points, lines, and coordinate frames attached to a rigid body in terms of the instantaneous screw for the motion of that body. Such differential equations are linear but with a time-varying coefficient and hence solvable by power series. A single-loop kinematic chain may be expressed by a system of such differential equations subject to a linear constraint. A single matrix factorization followed by a sequence of substitutions of linear-system right-hand-side terms determines successive orders of the joint rate coefficients in the kinematic solution for this mechanism. The present work extends this procedure to the forward dynamics problem, applying it to a Clemens constant-velocity coupling expressed as a spatial 9R closed kinematic chain. [ABSTRACT FROM AUTHOR]

A novel numerical method based on the differential transformation is proposed for solving nonlinear optimal control problems in this paper. The differential transformation is a linear operator that transforms a function from the original time and/or space domain into another domain in order to simplify the differential calculations. The optimality conditions for the optimal control problems can be represented by algebraic and differential equations. Using the differential transformation, these algebraic and differential equations with their boundary conditions are first converted into a system of nonlinear algebraic equations. Then the numerical optimal solutions are obtained in the form of finite-term Taylor series by solving the system of nonlinear algebraic equations. The differential transformation algorithm is similar to the spectral element methods in that the computational region splits into several subregions but it uses polynomials of high degrees by keeping a small number of subregions. The differential transformation algorithm could solve the finite- (or infinite-) time horizon optimal control problems formulated as either the algebraic and ordinary differential equations using Pontryagin's minimum principle or the Hamilton-Jacobi-Bellman partial differential equation using dynamic programming in one unified framework. In addition, the differential transformation algorithm can efficiently solve optimal control problems with the piecewise continuous dynamics and/or nonsmooth control. The performance is demonstrated through illustrative examples. [ABSTRACT FROM AUTHOR]