Papers by Keyword: Newton-Raphson Method

Abstract: In this work we discussed the modeling of the demixing curve in the liquid state in the Lead – Zinc binary system. We are interested to recalculate the free energies relating on Pb-Zn alloys for several temperatures based on the thermodynamic data collected in the bibliography. This calculation allows us to trace the curve of phase separation from a program after obtaining the mole fractions corresponding to the common tangent to the curve of the free energy with two minima at different temperatures. To do this, we used the Matlab 7.1 as the programming language and the Redlich-Kister polynomial as a mathematical model of development. The results obtained are very satisfactory by comparing them with those of the bibliography.

Abstract: One step inverse analysis is widely used in sheet metal forming process, since its effective prediction in a short time. A non-linear equation about unknown displacements from final part to plane part is deduced in one step inverse analysis, and it is often solved by Newton-Raphson method. The initial value of the displacements is quite essential to convergence of Newton-Raphson method. An adaptive triangle mesh on 3D surface equipped with metric frame using advancing front method is presented in this paper to improve condition number of matrix and enhance the convergence rate. Numerical results are showed that one step inverse analysis has faster convergence when the initial displacement is solved by adaptive triangle mesh compared with the part mesh (more triangles on final part), and one step inverse analysis has a well distribution of thickness when initial displacement is solved by adaptive triangle mesh compared with tool mesh (bad-quality triangles on final part).

Abstract: With the development of the society, the power system flow calculation becomes more important. Another new method for the polar coordinates Newton Raphson power flow calculation was proposed according to the power system operating characteristics. This research eliminated the vacant of the Jacobian matrix completely, reduced the amount of computer memory requirements greatly and also canceled the inversion completely.

Abstract: The Electrical Resistance Tomography (ERT) is a new technology developed in recent years. Because of the characteristics as simple structure, low cost and non-invasive, the ERT has already application in geophysics, physical geography, mineral detection et al.in this paper, the ERT is used to detect the damage of the remote carbon fiber felt with wireless sensing technology. In experiment, the wireless technology is used to avoid the noise and the introduction of the long wires, which realized the remote detection; the Improved Newton -- Raphson algorithm is used to achieve the detective imaging, which had good results.

Abstract: This paper introduces an homotopy algorithm which has convergence stability to solve the alternating current optimal power flow problem. The complicated Alternating Current Power Flow (ACPF) can simplify as simple Direct Current Power Flow (DCPF). The homotopy participation factor is introduced into the linear DCPF to make DCPF convert back into ACPF gradually to realize Alternating Current Power Flow Homotopy method (ACPFH). The homotopy curves are generated to solve a series of nonlinear problems.The traditional method can not solve the unstable points,because the calculate process always turn up Jacobian matrix.But the Homotopy method can calculate all results. It is a superiority for Homotopy,and then can explore power system problem more entirety.This novel algorithm is different from Newton - Raphson method, because it isnt sensitive to the initial point selection and has the global convergence.The homotopy algorithm is applied to IEEE - 3, 9, 14, 30, 36, 57, 118 node testing systems for power flow optional calculation, the simulation results show that the novel algorithm can solve power flow problem better and its calculating speed is much faster than the traditional algorithm, it can calculate the optimal value more direct.

Abstract: Newton-Raphson method is used in global equilibrium for the numerical solution of elasto-plastic problems. It is necessary to determine the fourth-rank constitutive parameters of consistent tangent modulus in each integration point. Euler backward method and implicit stress integration is applied while constitutive model is implemented into ANSYS software. Take Chen, Jiao, and Kim model (2005) as an example, comparison of fourth-rank constitutive parameters and without fourth-rank constitutive parameters of consistent tangent modulus indicates that the convergence is obviously influenced by fourth-rank constitutive parameters of consistent tangent modulus for the larger load case, whereas the influence of plastic modulus is almost neglected.

Abstract: Owing to the given variables are measurable in online power flow calculation, the electrical variables of higher measuring accuracy should be chosen for calculation. Currently the theory of reactive power is deficient and several methods for reactive power measurement are briefly introduced in this paper. The inaccuracy of those methods is pointed out by the relevant references in non-sinusoidal conditions. The measuring accuracy of Active power directly obtained by voltage and current is the same as that of voltage and current. For increasing the accuracy of online power flow calculation, a method substituting voltage magnitude for reactive power is proposed in this paper. The new method eliminates the effects resulted from inaccurate reactive power measurement. The simulation results on software MATPOWER verify the correctness and rationality of the new method.

Abstract: Elastohydrodynamic lubrication is a form of hydrodynamic lubrication involving physical interaction between two contacting surfaces and liquid where elastic deformation of the contacting surfaces due to heavily loading applied will affect the elastohydrodynamic pressure and fluid film thickness significantly. In this paper, a line contact EHL is modeled through the cylinder contact to a flat surface to represent the application of roller bearing. This solution is limited to two dimensional line contact problem only, an infinite length of cylinder was used as physical modeling. The behavior of non-Newtonian fluid also was investigated using power law fluid model. Bearing speed is to be assumed in steady state and temperature is assumed constant. The bearing performance parameters such as pressure and film thickness of lubricated contacts are calculated using Newton-Raphson method.The results show that the peak pressure increases as the parameters such as velocity, load and material parameter were increases and the spike was found to shift to the center of roller. The film was almost flat at contact region and formed a dimple shape near the outlet flow. The value of pressure spike and minimum film thickness were smaller at lower speed and were increased during raising speed then the peak point was found to be shifted to center of roller.

Abstract: A novel power limiter based on Newton-Raphson method is proposed in this paper for the Doubly-fed Induction Generator (DFIG) under the conditions of unbalanced grid voltage drop. Unlike the existing power limiters, which provide an approximate estimation of the maximal reactive power at the cost of introducing a large error in achieving its control target, ours formulates the design of power limiter into an optimization problem which tries to maximize the DFIG’s reactive power towards its two decisive factors: limited rotor current and rotor side converter’s output voltage. Finally the Newton-Raphson method is exploited to find the global maximum of the proposed optimization problem. Consequently, the proposed power limiter could more accurately determine the DFIG’s maximal reactive power without any loss of the accuracy in achieving its control target. Simulation results on a 1.5MW DFIG shows the efficacy of the proposed power limiter for DFIG under the conditions of unbalanced voltage drop.

Abstract: In this paper a small strain elastic element is presented its utility is demonstrated through static displacement problems. Four different methods solve an example, like direct method, Newton-Rapshon method, Modified Newton-Rapshon method and use commercial software Ansys. The MNR method is the fastest method.