Voltage Stability Margin in DC Grids With CPLs: A Recursive Newton–Raphson Approximation

This brief explores the formulation of the power flow problem in DC grids with a classical incidence matrix through a graph-based formulation. This corresponds to a compact representation of the conventional backward/forward sweep methods, which is applicable to radial and mesh networks with a unique voltage controlled source. To guarantee the existence and uniqueness of the power flow solution in the DC network under well-defined operative conditions, the Banach fixed-point theorem is employed. Simulation results confirm that the solution of the proposed method is numerically comparable with classical approaches, such as Gauss-Seidel, Newton-Raphson, successive approximations and Taylor-based methods. All the simulations are conducted in MATLAB software.

In this study, Newton–Raphson Based (NRB) scalar speed control (SSC) is recommended to control the speed of Induction Motors (IM). As is known, the Newton–Raphson method, which is often used in numerical analysis, is one of the methods that provide a rapid convergence of the desired value. In this study, the frequency value required for the desired speed value is calculated by Newton–Raphson method. Three different models including Newton–Raphson Based + Scalar Speed Control (NRB_SSC), Difference Speed + NRB_SSC (DS_NRB_SSC), DS + NRB_SSC + Difference Frequency (DS_NRB_SSC_DF) were used for optimization tests. Simulation of the work was done in Matlab/Simulink programme. According to obtained test results DS_NRB_SSC_DF has produced better results.

The tendency to gain the benefits of both ac and dc grids pushed the power industries to introduce the ac-dc hybrid system as the future of distribution systems. Although these grids bring substantial advantages for the power system, such as stability, reliability, resiliency, they add more complexities to power network studies, such as load flow, short circuit, dynamic, stability analyses. These complexities arise due to the presence of ac-dc converters. In a hybrid grid, ac and dc system equations should be solved either simultaneously or sequentially. Despite the sequential method that was in a center of attention, the simultaneous approaches have not been deeply researched due to some technical barriers. This paper aims to explore the ac equivalent circuits of dc grids so that the ac-dc hybrid grid can be considered and analyzed as one ac grid. Accordingly, dealing with separate sets of equations for ac and dc networks is avoided. Therefore, all of the classical power system studies, such as the Newton Raphson (NR) based load flow algorithm, stability and dynamic analyses, and short circuit study, can be applied to the ac-dc network with a small modification that substantially saves time and effort.

It is difficult to accurately simulate supercurrent in high-temperature superconducting bulk even by adopting the finite-element method. The equivalent electrical conductivity of high-temperature superconducting bulk, which has a strong nonlinearity according to the E-J power law, is introduced for the supercurrent analysis. However, the strong nonlinearity results in bad convergency of the nonlinear equation solvers, i.e., the Newton-Raphson (NR) method. Consequently, the unsuitable and/or undulating supercurrent is observed. Therefore, in this paper, the accuracy of the supercurrent analysis in the high-temperature superconducting bulk is discussed and a new method is proposed for the accurate high-temperature superconducting bulk simulation. Then, the method combined a line search with the NR method is adopted as a nonlinear equation solver, and the improvement of convergency and computation time are investigated.

This study introduces a novel unified power flow algorithm for hybrid AC/DC power grids. For hybrid AC/DC power grids that incorporate voltage source converters (VSCs), the proposed algorithm uses the voltage amplitude and the phase angle of the AC bus and the voltage of the DC bus as the minimum set of state variables. The power equation of the converter is deduced by these state variables. Then, the bus-power-equilibrium (BPE) equations can be deduced based on the DC node classification and VSC converter station control modes. The Newton–Raphson method can be used to solve these BPE equations with good convergence behavior. In addition, the DC grid and converter station modeling impose no restriction on the hybrid grid topology. As a result, the Jacobian matrix in the modified equations can accurately reflect the coupling relationship between AC and DC grids and simultaneously maintain the sparse feature. The proposed unified algorithm uses the sparse technology and can solve the power flow problem for a large hybrid power grid. A simulation is implemented to illustrate the effectiveness of the proposed algorithm.

This paper presents a new digital background calibration method to correct MDAC errors. The novelty of this research is to use Newton–Raphson algorithm in order to reduce the number of divisions as well as power in digital domain. This is achieved by combining the conventional slope mismatch averaging and linear approximation technique to compute the correction coefficient in fast iterative method. To validate the accuracy of the proposed method, the digital part of the calibration scheme is implemented on FPGA. The superiorities of the proposed method are fast convergence time, less power consumption, and less digital complexity in compared to previous studies. These benefits are due to using split structure along with Newton–Raphson method. Several simulations of a 12-bit 100MS/s pipelined ADC indicate that SNDR/SFDR is improved from 30/33 dB to 70/79 dB after calibration. Calibration process is achieved in approximately 2000 clock cycles. The proposed ADC achieves a FoM of 0.03-pJ/conversion-step and consumes an analog power of 6.7 mW.

At the core of every system for the efficient control of the network steady-state operation is the AC-power-flow problem solver. For local distribution networks to continue to operate effectively, it is necessary to use the most powerful and numerically stable AC-power-flow problem solvers within the software that controls the power flows in these networks. This communication presents the results of analyses of the computational performance and stability of three methods for solving the AC-power-flow problem. Specifically, this communication compares the robustness and speed of execution of the Gauss–Seidel (G–S), Newton–Raphson (N–R), and Newton–Raphson method with Iwamoto multipliers (N–R–I), which were tested in open-source pandapower software using a meshed electrical network model of various topologies. The test results show that the pandapower implementations of the N–R method and the N–R–I method are significantly more robust and faster than the G–S method, regardless of the network topology. In addition, a generalized Python interface between the pandapower and the SciPy package was implemented and tested, and results show that the hybrid Powell, Levenberg–Marquardt, and Krylov methods, a quasilinearization algorithm, and the continuous Newton method can sometimes achieve better results than the classical N–R method.

PurposeThe paper aims to improve convergence characteristics of the Newton–Raphson (NR) method applied to time-periodic finite element method using various line searches, as time-periodic finite element method causes deterioration of convergence characteristic of nonlinear analysis based on NR method. The study also aims to accelerate and improve accuracy of electromagnetic field analysis for improvement of the performance of electrical machine.Design/methodology/approachThe paper proposes new type line searches that set approximate step size for NR method. The line search evaluated step size using higher-order interpolation of functional derivative. In addition, two criteria for applying these line search were proposed. First method set one scalar value for every NR iteration that is named constant step size. Second method define different step size in each time step of time-periodic finite element method to update solution vector that is named different step size.FindingsThe paper provides efficient line searches to improve convergence characteristics for NR method. Nonlinear magnetic field analysis of two transformer models is demonstrated. The proposed methods achieve the following results: higher-order functional NR is efficient in improving convergence characteristics, and the proposed methods succeeded about twice faster in both models.Originality/valueThe paper fulfills improvement of convergence characteristics of the NR method applied to time-periodic finite element method using proposed line searches and accelerate electromagnetic field analysis.

In this paper, a simple waveguide measurement technique is presented to determine the complex permittivity of a dielectric material. The dielectric sample is loaded in a short-circuited rectangular waveguide. The reflection coefficient of the waveguide is measured by Network analyser and calculated as a function of the complex permittivity using theory of transmissions lines. The Newton Raphson method is then used to determine de complex permittivity by matching the calculated value with the measured value. The results obtained using Newton Raphson are in good agreement with the results obtained by the Nicholson-Ross technique.

In this paper, a novel algorithm is proposed for balancing water looped network in steady state through a fully automated general framework of hydraulic networks regardless of their topological complexity. The model is developed by combining the following two steps, firstly a set of independent loops are identified based on a graph theoretical analysis in a looped network. Further the second step is devoted to the equilibrium process by determining the flow rate distribution within the network ducts and the pressure in the delivery nodes. The above such equilibrium process gives rise to a system of non linear algebraic equations which are solved numerically using both Hardy Cross (HC) and Newton Raphson (NR) methods. In HC method, the flow correction term is modified and a generalized expression is given to consider various possibilities of independent loops selection. Some real networks topologies that were commonly used as benchmarks, for testing various independent loops selection algorithms, are taken as case studies to apply the general automatic framework for hydraulic network analysis. Such network analysis enhances proving the applicability as well as the effectiveness of the proposed approach. Also, during the equilibrium procedure, it is proved that NR method is capable of producing accurate results and it converges more rapidly comparing to the widely used HC method. Moreover, it is demonstrated that NR’s iterative process, contrary to HC’s one, converges to reliable results even with a choice of random initial flow rates which makes a NR algorithm quite simple to implement without affecting the accuracy of the results.

The program FANTOM (fast Newton–Raphson torsion angle energy minimizer) performs minimizations of the ECEPP/2 energy function for proteins with the Newton–Raphson method. It is implemented for use with conventional computer hardware. The torsion angles are chosen as independent variables. The first and second derivatives are calculated with a previously described rapid algorithm. For the matrix inversion a modified Cholesky factorization is used. A line search adjusts the step length and nonbonded interactions can be calculated with a cutoff. The following tests of the program are described: All local minima of the ECEPP/2 energy function for the amino acids glycine and alanine were determined. An exhaustive search by more than 16,000 independent energy minimizations was used to identify low‐energy structures of Met‐enkephalin, which were then compared with previously published structures of this pentapeptide. To investigate the use of FANTOM with disulfide bonds, it was applied with conotoxin. As an illustration of the intended primary use of the program, an energy refinement of the structure of the basic pancreatic trypsin inhibitor determined by nmr spectroscopy in solution is described.

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command “while”.

DNA microarray technology has become a prospective tool for cancer classification. However, DNA microarray datasets typically have very large number of genes (usually more than tens of thousands) and less number of samples (often less than one hundred). This raises the issue of getting the most relevant genes prior to cancer classification. In this paper, we have proposed a two-phase feature selection method for cancer classification. This method selects a low-dimensional set of genes to classify biological samples of binary and multi-class cancers by integrating ReliefF with recursive binary gravitational search algorithm (RBGSA). The proposed RBGSA refines the gene space from a very coarse level to a fine-grained one at each recursive step of the algorithm without degrading the accuracy. We evaluate our method by comparing it with state-of-the-art methods on 11 benchmark microarray datasets of different cancer types. Comparison results show that our method selects only a small number of genes while yielding substantial improvements in accuracy over other methods. In particular, it achieved up to 100% classification accuracy for 7 out of 11 datasets with a very small size of gene subset (up to < 1.5%) for all 11 datasets.

This study focuses on estimating the nine parameters of the three-diode model (3DM) for photovoltaic (PV) cells by integrating the Atan-Sinc Optimization Algorithm (ASOA) with the Newton–Raphson (NR) method. The ASOA, a population-based metaheuristic approach inspired by the behaviors of the Sech and Tanh functions, systematically generates candidate solutions for the complete set of parameters in the 3DM. For each of these solutions, the NR method is employed to solve the transcendental equation governing the solar cell model, facilitating a precise evaluation of the associated objective function. To guide the parameter estimation process, experimental current-voltage (I-V) and voltage-power (V-P) curves are utilized. The robustness of the proposed methodology is validated through studies on both monocrystalline and polycrystalline solar cells. Computational results reveal that the ASOA effectively navigates the parameter space, while the NR method provides accurate evaluations, resulting in reliable and precise parameter estimations. All numerical validations were conducted using MATLAB software, version 2024b.

This study aims to compare analytical methods and numerical methods in determining the roots of equations of a complex function. The numerical method used in this research is the Newton Raphson method. In this study two examples of complex functions were given, after which the roots of the equation were searched using the analytical method and the Newton Raphson method, then the results were compared. In this study, two examples are given, namely and . In example one, three different roots were obtained analytically, while numerical calculations using the Newton Raphson method obtained a value that converged to one of the roots that had been obtained analytically. In example two, four different roots were obtained analytically, while numerically using the Newton Raphson method similarly if done using the Newton Raphson method, a value that converged to one of the roots that had been obtained analytically was obtained.