Newton–Raphson based scalar speed control and optimization of IM

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 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.

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.

Introduction. Scalar control (SC) and field-oriented control (FOC) are widely used in sensorless induction motor (IM) drives for their balance of performance and cost. Among estimation techniques, the voltage-model (VM) based model reference adaptive system (MRAS) is preferred in industry due to its simple structure and low computational load. Problem. Traditional VM-based MRAS schemes are highly sensitive to parameter uncertainties, especially to variations in stator resistance Rs caused by temperature changes. These variations degrade flux estimation accuracy, leading to significant speed-tracking errors, increased transients, and reduced stability in both SC and FOC. Goal. This study quantitatively evaluates how the estimation of stator resistance Rs and the dependent rotor resistance Rr affects the speed-control performance of sensorless SC and FOC under parameter mismatch. Methodology. An improved VM-based MRAS is proposed with parallel Rs estimation and Rr updated via a linear relation to Rs. Estimator stability and convergence are proven using Lyapunov theory. The estimator is integrated into SC and FOC and tested in MATLAB/Simulink under identical conditions, including a sudden 30 % increase in resistance. Speed tracking is quantified using the integral of time-weighted absolute error (ITAE). Results. Parameter estimation markedly enhances the robustness of both strategies. In sensorless SC, ITAE drops by about 66.2 % (5.512 to 1.863), indicating much lower transient oscillations. In sensorless FOC, ITAE falls by about 54 % (0.7075 to 0.323), with speed overshoot nearly eliminated (0.031). Scientific novelty. The study provides a unified quantitative comparison of sensorless SC and FOC using ITAE under identical operating and estimation conditions, revealing different levels of performance recovery with the proposed dual-resistance adaptation. Practical value. The findings guide the design of more reliable industrial IM drives, showing that while FOC retains superior dynamics, SC with estimation becomes a robust, cost-effective option for applications with significant parameter uncertainty. References 31, table 1, figures 13.

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.

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.

This express brief addresses the voltage collapse problem in direct-current (dc) networks by using a recursive heuristic search algorithm based on the Newton–Raphson method. The determinant of the Jacobian matrix in the Newton–Raphson method is used as a sensitivity index to determine the maximum power consumption of the dc network. The recursive solution approach corresponds to a sequential power flow approach by incrementing all values of the power consumptions uniformly. Simulation results validate the efficiency of the proposed method in comparison to the large-scale nonlinear solvers available in the general algebraic modeling system optimization package. The MATLAB programming environment was employed for implementing the proposed recursive Newton–Raphson method.

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”.

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.

Induction motor optimization can be time consuming. One of the parameters central to the design is slip, and the slip at peak torque changes greatly as the field analyst modifies the layout of the machine. Vector controllers allow induction motor manufacturers to operate very close to pull out. The designer has the continued task of predicting performance near peak for all proposed modifications in order to compare the designs equitably. This paper discusses techniques useful for working with the smallest sub-portion of the machine possible during optimization. Second, it discusses the importance of integrating multiple objectives into the optimization index. Special attention is given to a linear induction motor which introduces the added complexity of end effects

Abstract. In this paper, we study a stationary ARCH(q) model with parameters α0,α1,α2,…,αq. It is known that the model requires all parameters αi to be non‐negative, but sometimes the usual algorithm based on Newton–Raphson's method leads us to obtain some negative solutions. So this study proposes a method of computing the maximum likelihood estimator (MLE) of parameters under the non‐negative restriction. A similar method is also proposed for the case where the parameters are restricted by a simple order: α1≥α2≥⋯≥αp. The strong consistency of the above two estimators is discussed. Furthermore, we consider the problem of testing homogeneity of parameters against the simple order restriction. We give the likelihood ratio (LR) test statistic for the testing problem and derive its asymptotic null distribution.

Modelling of Heat Transfer in a Fluidized Bed Reactor Irradiated Indirectly by Concentrated Solar Energy

This research evaluates the efficiency and accuracy of some iterative methods for solving scalar nonlinear equations. The study focuses on four types of iterative methods, such as Newton-Raphson, Bisection, Secant, and Algorithm 1, a novel fourth-order and derivative-free root-finding algorithm exhibiting different convergence orders. The accuracy of these methods is tested numerically on some real-life nonlinear equations such as the fluid permeability problem, the blood rheology model, Van Der Wall’s and Planck’s radiation laws, and lastly, the beam design problem. Numerical experiments are conducted using the Python programming language with a tolerance of 10-14 and 10-15. The results indicate that the Secant method requires fewer iterations and CPU time if compared with Newton-Raphson, Bisection and Algorithm 1 in solving fluid permeability problems, blood rheology models, and Van Der Wall’s problems. The bisection method converges quickly compared with other methods for solving Planck’s radiation law, while Algorithm 1 converges quicker than other methods for solving the beam design problem. In terms of accuracy, the Secant method gives greater accuracy in solving fluid permeability and Van Der Wall’s problems. Meanwhile, for the blood rheology model, Newton Raphson's methods overcome other methods. On the other hand, the Bisection method gives greater accuracy for Planck’s radiation law and beam design problems. Algorithm 1 performance showed effective convergence to the root, but, in many cases, it encounters a division by zero issue. The study suggests extending investigations to Algorithm 1 refinement, comparative studies on various equation types, exploration of hybrid methods, real-world application and validation, and user-friendly implementation.

The energy flow calculation of the integrated electric power and natural gas system (IEGS) is generally tackled by the classical Newton–Raphson (NR) method with second‐order convergence. However, this method may fail to converge or incur oscillating iterations leading to heavy computation burden if the initial point is not selected properly, especially in heterogenous integrated energy systems containing the natural gas system. To handle this problem, a variant of Newton–Raphson method with third‐order convergence is proposed, which needs one function and two derivative evaluations per iteration without increasing the number of derivative evaluations. In order to verify the effectiveness of the proposed method, simulation studies are carried out on several different cases for the energy flow calculation of IEGS. Experiment results reveal that the proposed method is superior to the classical Newton–Raphson method and its other variants in terms of computational efficiency.