newton raphson method research paper

Newton-Raphson Method

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• Jean-Pierre Dedieu 2  

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Introduction

The Newton-Raphson method, named after Isaac Newton (1671) and Joseph Raphson (1690), is a method for finding successively better approximations to the roots of a real-valued function. But both Newton and Raphson viewed this method purely as an algebraic method and restricted its use to polynomials. In 1740, Thomas Simpson described it as an iterative method for solving general nonlinear equations using fluxional calculus (i.e., derivatives), essentially giving the modern description of the method. Historical facts are given by T. Ypma [ 40 ], H. Goldstine [ 21 ], and J. Ezquerro et al. [ 17 ]. Recent developments of this method include alpha-theory, underdetermined or overdetermined systems, and equations defined on Lie groups or on Riemannian manifolds.

Let \(f : U \subset E \rightarrow F\) be the equation to be solved where E and F are two real or complex Banach spaces and where U is open in E and f ∈ C 1 ( U ). If x ∈ E is an approximation of a zero of f ,...

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Jean Pierre Dedieu: deceased.

Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization Algorithms on Matrix Manifolds. Princeton University Press, Princeton/Woodstock (2008)

Book   MATH   Google Scholar  

Adler, R., Dedieu, J.-P., Martens, M., Shub, M.: Newton’s method on Riemannian manifolds with an application to a human spine model. IMA J. Numer. Anal. 22 , 1–32 (2002)

Article   MathSciNet   MATH   Google Scholar  

Allgower, E., Georg, K.: Numerical Continuation Methods. Springer, Berlin/New York (1990)

Alvarez, F., Bolte, J., Munier, J.: A unifying local convergence result for Newton’s method in Riemannian manifolds. Found. Comput. Math. 8 , 197–226 (2008)

Argyros, I.: Convergence and Applications of Newton-Type Iterations. Springer, New York/London (2008)

MATH   Google Scholar  

Argyros, I., Gutiérrez, J.: A unified approach for enlarging the radius of convergence for Newton’s method and applications. Nonlinear Funct. Anal. Appl. 10 , 555–563 (2005)

MathSciNet   MATH   Google Scholar  

Ben-Israel, A.: A Newton-Raphson method for the solution of systems of equations. J. Math. Anal. Appl. 15 , 243–252 (1966)

Beyn, W.-J.: On smoothness and invariance properties of the Gauss-Newton method. Numer. Funct. Anal. Optim. 14 , 243–252 (1993)

Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and Real Computation. Springer, New York (1997)

Dedieu, J.-P.: Points Fixes, Zéros et la Méthode de Newton. Springer, Berlin/New York (2006)

Google Scholar  

Dedieu, J.-P., Kim, M.-H.: Newton’s Method for Analytic Systems of Equations with Constant Rank Derivatives. J. Complex. 18 , 187–209 (2002)

Dedieu, J.-P., Shub, M.: Multihomogeneous Newton’s method. Math. Comput. 69 , 1071–1098 (2000)

Dedieu, J.-P., Shub, M.: Newton’s method for overdetermined systems of equations. Math. Comput. 69 , 1099–1115 (2000)

Dedieu, J.-P., Priouret, P., Malajovich, G.: Newton’s method on Riemannian manifolds: covariant alpha theory. IMA J. Numer. Anal. 23 , 395–419 (2003)

Dennis, J., Schnabel, R.: Numerical Methods for Unconstrained Optimization and Nonlinear Equation. Prentice Hall, Englewood Cliffs (1983)

Edelman, A., Arias, T., Smith, S.: The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 , 303–353 (1998)

Ezquerro, J., Gutiérrez, J., Hernandez, M., Romero, N., Rubio, M.-J.: El metodo de Newton: de Newton a Kantorovich. La Gaceta de la RSME 13 , 53–76 (2010)

Ferreira, O.P.: Local convergence of Newton’s method in Banach space from the viewpoint of the majorant principle. IMA J. Numer. Anal. 29 , 746–759 (2009)

Ferreira, O.P.: Local convergence of Newton’s method under majorant condition. J. Comput. Appl. Math. 235 , 1515–1522 (2011)

Ferreira, O.P., Svaiter, B.F.: Kantorovich’s theorem on Newton’s method on Riemannian manifolds. J. Complex. 18 , 304–329 (2002)

Goldstine, H.: A History of Numerical Analysis from the 16th Through the 19th Century. Springer, New York (1977)

Hirsch, M., Pugh, C., Shub, M.: Invariant Manifolds. Lecture Notes in Mathematics, vol. 583. Springer, Berlin/New York (1977)

Kantorovich, L.: Sur la méthode de Newton. Travaux de l’Institut des Mathématiques Steklov XXVIII , 104–144 (1949)

Li, C., Wang, J.H.: Newton’s method on Riemannian manifolds: Smale’s point estimate theory under the r-condition. IMA Numer. Anal. 26 , 228–251 (2006)

Article   MATH   Google Scholar  

Li, C., Wang, J.H.: Newton’s method for sections on Riemannian manifolds: generalized covariant alpha-theory. J. Complex. 24 , 423–451 (2008)

Malajovich, G.: On generalized Newton’s methods. Theor. Comput. Sci. 133 , 65–84 (1994)

Ortega, J., Rheinboldt, V.: Numerical Solutions of Nonlinear Problems. SIAM, Philadelphia (1968)

Ostrowski, A.: Solutions of Equations in Euclidean and Banach Spaces. Academic, New York (1976)

Owren, B., Welfert, B.: The Newton iteration on Lie groups. BIT 40 , 121–145 (2000)

Shub, M.: Some remarks on dynamical systems and numerical analysis. In: Lara-Carrero, L., Lewowicz, J. (eds.) Dynamical Systems and Partial Differential Equations, Proceedings of VII ELAM. Equinoccio, Universidad Simon Bolivar, Caracas (1986)

Shub, M.: Some remarks on Bézout’s theorem and complexity. In: Hirsch, M.V., Marsden, J.E., Shub, M. (eds.) Proceedings of the Smalefest, pp. 443–455. Springer, New York (1993)

Shub, M., Smale, S.: Complexity of Bézout’s theorem I: geometric aspects. J. Am. Math. Soc. 6 , 459–501 (1993)

Shub, M., Smale, S.: Complexity of Bézout’s theorem IV: probability of success, extensions. SIAM J. Numer. Anal. 33 , 128–148 (1996)

Smale, S.: Newton’s method estimates from data at one point. In: Ewing, R., Gross, K., Martin, C. (eds.) The Merging of Disciplines: New Directions in Pure, Applied and Computational Mathematics. Springer, New York (1986)

Smith, S.: Optimization Techniques on Riemannian Manifolds. Fields Institute Communications, vol. 3, pp. 113–146. AMS, Providence (1994)

Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, New York (2002)

Udrişte, C.: Convex Functions and Optimization Methods on Riemannian Manifolds. Kluwer, Dordrecht/Boston (1994)

Wang, X.H.: Convergence of Newton’s method and uniqueness of the solution of equations in Banach spaces. IMA J. Numer. Anal. 20 , 123–134 (2000)

Wang, X.H., Han, D.F.: On the dominating sequence method in the point estimates and Smale’s theorem. Sci. Sin. Ser. A 33 , 135–144 (1990)

Ypma, T.: Historical development of the Newton-Raphson method. SIAM Rev. 37 , 531–551 (1995)

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Dedieu, JP. (2015). Newton-Raphson Method. In: Engquist, B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_374

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Newton Raphson Method

• Saba Akram , Q. Ann
• Published 2015
• Engineering

10 References

Comparative study of bisection, newton-raphson and secant methods of root- finding problems, the analysis of the convergence of newton-raphson method based on the current injection in distribution network case, variable dimension newton-raphson method, a distributed method for solving nonlinear equations applying the power load flow calculation, iterative methods improving newton's method by the decomposition method, newton-raphson method to determine the intrinsic permittivity of xlpe cable, related papers.

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An enhanced continuation power flow method using hybrid parameterization.

1. Introduction

• A simple modification to the basic parameterization method allows convenient adaptation to CPF applications.
• The proposed method reduces the processing time by 32.76% from the well-known arc-length parameterization method while maintaining accuracy.
• The paper proposes a quantitative evaluation method for the accuracy of load margin assessment, which has not previously existed for CPF studies.
• The enhanced computational efficiency of the proposed method enables fast assessment of numerous scenarios to ensure power system stability under a complex and uncertain renewable-integrated grid.

2. Proposed Method

2.1. p-v curve and loadability factor, 2.2. process of continuation power flow, 2.2.1. predictor, 2.2.2. corrector, 2.2.3. parameterization, 2.3. hybrid parameterization, 3. case study, 3.1. power grid test case, 3.2. dg scenarios, 3.3. parameterization comparison, 3.3.1. metrics, 3.3.2. performance, 3.4. performance over different step sizes, 3.5. other parameterization combinations for the hybrid method, 3.6. performace comparation on different grid scales, 4. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

• Kundur, P.; Paserba, J.; Ajjarapu, V.; Andersson, G.; Bose, A.; Canizares, C.; Hatziargyriou, N.; Hill, D.; Stankovic, A.; Taylor, C.; et al. Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions. IEEE Trans. Power Syst. 2004 , 19 , 1387–1401. [ Google Scholar ] [ CrossRef ]
• Canizares, C.; Alvarado, F. Point of collapse and continuation methods for large AC/DC systems. IEEE Trans. Power Syst. 1993 , 8 , 1–8. [ Google Scholar ] [ CrossRef ]
• Woo, H.; Son, Y.; Cho, J.; Choi, S. Stochastic Second-Order Conic Programming for Optimal Sizing of Distributed Generator Units and Electric Vehicle Charging Stations. Sustainability 2022 , 14 , 4964. [ Google Scholar ] [ CrossRef ]
• Wang, D.; Zhang, C.; Li, J.; Zhu, L.; Zhou, B.; Zhou, Q.; Cheng, L.; Shuai, Z. A Novel Interval Power Flow Method Based on Hybrid Box-Ellipsoid Uncertain Sets. IEEE Trans. Power Syst. 2024 , 39 , 6111–6114. [ Google Scholar ] [ CrossRef ]
• Lee, M.; Yoon, M.; Cho, J.; Choi, S. Probabilistic Stability Evaluation Based on Confidence Interval in Distribution Systems with Inverter-Based Distributed Generations. Sustainability 2022 , 14 , 3806. [ Google Scholar ] [ CrossRef ]
• Jaramillo, M.D.; Carrión, D.F.; Muñoz, J.P. A Novel Methodology for Strengthening Stability in Electrical Power Systems by Considering Fast Voltage Stability Index under N − 1 Scenarios. Energies 2023 , 16 , 3396. [ Google Scholar ] [ CrossRef ]
• Jaramillo, M.; Carrión, D.; Muñoz, J. A Deep Neural Network as a Strategy for Optimal Sizing and Location of Reactive Compensation Considering Power Consumption Uncertainties. Energies 2022 , 15 , 9367. [ Google Scholar ] [ CrossRef ]
• Iba, K.; Suzuki, H.; Egawa, M.; Watanabe, T. Calculation of critical loading condition with nose curve using homotopy continuation method. IEEE Trans. Power Syst. 1991 , 6 , 584–593. [ Google Scholar ] [ CrossRef ]
• Ajjarapu, V.; Christy, C. The continuation power flow: A tool for steady state voltage stability analysis. IEEE Trans. Power Syst. 1992 , 7 , 416–423. [ Google Scholar ] [ CrossRef ]
• Farid, K.; Shahriar, A.; Reza Shabani, H. The Continuation Power Flow (CPF) Methods. In Voltage Stability in Electrical Power Systems ; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2022; Chapter 5; pp. 97–118. [ Google Scholar ] [ CrossRef ]
• Chiang, H.D.; Flueck, A.J.; Shah, K.S.; Balu, N. CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations. IEEE Trans. Power Syst. 1995 , 10 , 623–634. [ Google Scholar ] [ CrossRef ]
• Flueck, A.; Dondeti, J. A new continuation power flow tool for investigating the nonlinear effects of transmission branch parameter variations. IEEE Trans. Power Syst. 2000 , 15 , 223–227. [ Google Scholar ] [ CrossRef ]
• Li, S.H.; Chiang, H.D. Nonlinear predictors and hybrid corrector for fast continuation power flow. IET Gener. Transm. Distrib. 2008 , 2 , 341–354. [ Google Scholar ] [ CrossRef ]
• Mori, H.; Yamada, S. Continuation power flow with the nonlinear predictor of the Lagrange’s polynomial interpolation formula. In Proceedings of the IEEE/PES Transmission and Distribution Conference and Exhibition, Yokohama, Japan, 6–10 October 2002; Volume 2, pp. 1133–1138. [ Google Scholar ] [ CrossRef ]
• Kim, H.T.; Lee, J.; Yoon, M.; Lee, M.J.; Cho, N.; Choi, S. Continuation power flow based distributed energy resource hosting capacity estimation considering renewable energy uncertainty and stability in distribution systems. Energies 2020 , 13 , 4367. [ Google Scholar ] [ CrossRef ]
• Alves, D.; da Silva, L.; Castro, C.; da Costa, V. Continuation fast decoupled power flow with secant predictor. IEEE Trans. Power Syst. 2003 , 18 , 1078–1085. [ Google Scholar ] [ CrossRef ]
• Dong, X.; Wang, C.; Yun, Z.; Han, X.; Liang, J.; Wang, Y.; Zhao, P. Calculation of optimal load margin based on improved continuation power flow model. Int. J. Electr. Power Energy Syst. 2018 , 94 , 225–233. [ Google Scholar ] [ CrossRef ]
• Liang, H.; Zhao, J. A New Method of Continuous Power Flow for Voltage Stability Analysis. In Proceedings of the 2021 IEEE Asia-Pacific Conference on Image Processing, Electronics and Computers (IPEC), Dalian, China, 14–16 April 2021; pp. 337–340. [ Google Scholar ] [ CrossRef ]
• Neto, A.B.; Filho, L.R.A.G.; Alves, D.A. Continuation Power Flow: A Parameterization Technique and Adaptive Step Size Control. In Proceedings of the 2021 IEEE URUCON, Montevideo, Uruguay, 24–26 November 2021; pp. 75–79. [ Google Scholar ] [ CrossRef ]
• Pourbagher, R.; Derakhshandeh, S.Y.; Hamedani Golshan, M.E. An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems. Int. J. Electr. Power Energy Syst. 2022 , 134 , 107425. [ Google Scholar ] [ CrossRef ]
• Alves, D.A.; da Silva, L.C.; Castro, C.A.; da Costa, V.F. Alternative parameters for the continuation power flow method. Electr. Power Syst. Res. 2003 , 66 , 105–113. [ Google Scholar ] [ CrossRef ]
• Ju, Y.; Wu, W.; Zhang, B.; Sun, H. Continuation power flow based on a novel local geometric parameterisation approach. IET Gener. Transm. Distrib. 2014 , 8 , 811–818. [ Google Scholar ] [ CrossRef ]
• Ruan, C.; Wang, X.; Wang, X.; Gao, F.; Li, Y. Improved Continuation Power Flow Calculation Method Based on Coordinated Combination of Parameterization. In Proceedings of the 2018 IEEE 2nd International Electrical and Energy Conference (CIEEC), Beijing, China, 4–6 November 2018; pp. 207–211. [ Google Scholar ] [ CrossRef ]
• Gao, H.; Wang, L.; Yang, D.; Cai, G. Mechanism Enhanced Data-Driven Method for Reliability Improvement of Load Margin Estimation. IEEE Trans. Power Syst. 2024 , 39 , 3715–3724. [ Google Scholar ] [ CrossRef ]
• Bento, M.E.C. Physics-Guided Neural Network for Load Margin Assessment of Power Systems. IEEE Trans. Power Syst. 2024 , 39 , 564–575. [ Google Scholar ] [ CrossRef ]
• Lee, B.; Song, H.; Kwon, S.H.; Jang, G.; Kim, J.H.; Ajjarapu, V. A study on determination of interface flow limits in the KEPCO system using modified continuation power flow (MCPF). IEEE Trans. Power Syst. 2002 , 17 , 557–564. [ Google Scholar ] [ CrossRef ]
• de Araujo, L.R.; Penido, D.R.R.; de Souza, B.C.; de Alcântara Vieira, F. Discontinuities and unstable solutions beyond the maximum load point of nonlinear unbalanced distribution systems. Electr. Power Syst. Res. 2023 , 214 , 108865. [ Google Scholar ] [ CrossRef ]
• Zhang, X.P.; Ju, P.; Handschin, E. Continuation three-phase power flow: A tool for voltage stability analysis of unbalanced three-phase power systems. IEEE Trans. Power Syst. 2005 , 20 , 1320–1329. [ Google Scholar ] [ CrossRef ]
• Zhou, Y.; Zhang, J.; Gao, W. Fast Calculation Method for Continuous Power Flow of Microgrid Based on Levenberg-Marquardt Algorithm. IEEE Access 2023 , 11 , 49578–49586. [ Google Scholar ] [ CrossRef ]
• Colombari, L.F.S.; Kuiava, R.; Peric, V.; Ramos, R.A. Continuation Load Flow Considering Discontinuous Behaviors of Distribution Grids. IEEE Trans. Power Syst. 2019 , 34 , 3476–3483. [ Google Scholar ] [ CrossRef ]
• Nirbhavane, P.S.; Corson, L.; Rizvi, S.M.H.; Srivastava, A.K. TPCPF: Three-Phase Continuation Power Flow Tool for Voltage Stability Assessment of Distribution Networks with Distributed Energy Resources. IEEE Trans. Ind. Appl. 2021 , 57 , 5425–5436. [ Google Scholar ] [ CrossRef ]
• Zeng, L.; Chiang, H.D.; Neves, L.S.; Alberto, L.F.C. On the accuracy of power flow and load margin calculation caused by incorrect logical PV/PQ switching: Analytics and improved methods. Int. J. Electr. Power Energy Syst. 2023 , 147 , 108905. [ Google Scholar ] [ CrossRef ]
• Wang, T.; Wang, S.; Ma, S.; Guo, J.; Zhou, X. An Extended Continuation Power Flow Method for Static Voltage Stability Assessment of Renewable Power Generation-Penetrated Power Systems. IEEE Trans. Circuits Syst. II Express Briefs 2022 , 71 , 1. [ Google Scholar ] [ CrossRef ]
• Zhang, X.; Shin, D.; Son, Y.; Woo, H.; Kim, S.Y.; Choi, S. Three-Stage Flexibility Provision Framework for Radial Distribution Systems Considering Uncertainties. IEEE Trans. Sustain. Energy 2023 , 14 , 948–961. [ Google Scholar ] [ CrossRef ]
• Zhang, C.; Liu, Q.; Zhou, B.; Chung, C.Y.; Li, J.; Zhu, L.; Shuai, Z. A Central Limit Theorem-Based Method for DC and AC Power Flow Analysis Under Interval Uncertainty of Renewable Power Generation. IEEE Trans. Sustain. Energy 2023 , 14 , 563–575. [ Google Scholar ] [ CrossRef ]
• Yoon, M.; Cho, N.; Choi, S. Analysis of temporary overvoltage due to inverter-based distributed generation in networked distribution systems. Appl. Energy 2023 , 341 , 121059. [ Google Scholar ] [ CrossRef ]
• Cho, J.; Kim, H.; Ryu, H.; Son, Y.; Choi, S. Analysis of distributed power generation forecasting model for power distribution planning. Trans. Korean Inst. Electr. Eng. 2021 , 70 , 1248–1262. [ Google Scholar ] [ CrossRef ]
• Zhang, X.; Woo, H.; Choi, S. An interval power flow method for radial distribution systems based on hybrid second-order cone and linear programming. Sustain. Energy Grids Netw. 2023 , 36 , 101158. [ Google Scholar ] [ CrossRef ]
• Li, X.; Zhao, J.; Liang, H.; Xu, J. Application of an Improved Continuous Power Flow Method in Voltage Stability Analysis. In Proceedings of the 2019 6th International Conference on Systems and Informatics (ICSAI), Shanghai, China, 2–4 November 2019; pp. 244–248. [ Google Scholar ] [ CrossRef ]
• Kuroda, E.; Watanabe, M.; Kato, D.; Saito, N.; Yatsu, M. Fast computation method of static voltage stability using geometric parameter adjustment for the continuation power flow. Electr. Eng. Jpn. 2021 , 214 , e23296. [ Google Scholar ] [ CrossRef ]
• Baran, M.; Wu, F. Network reconfiguration in distribution systems for loss reduction and load balancing. IEEE Trans. Power Deliv. 1989 , 4 , 1401–1407. [ Google Scholar ] [ CrossRef ]
• Das, D. Optimal placement of capacitors in radial distribution system using a Fuzzy-GA method. Int. J. Electr. Power Energy Syst. 2008 , 30 , 361–367. [ Google Scholar ] [ CrossRef ]
• Das, D.; Kothari, D.; Kalam, A. Simple and efficient method for load flow solution of radial distribution networks. Int. J. Electr. Power Energy Syst. 1995 , 17 , 335–346. [ Google Scholar ] [ CrossRef ]
• Khodr, H.; Olsina, F.; Jesus, P.D.O.D.; Yusta, J. Maximum savings approach for location and sizing of capacitors in distribution systems. Electr. Power Syst. Res. 2008 , 78 , 1192–1203. [ Google Scholar ] [ CrossRef ]
• Birchfield, A.B.; Xu, T.; Gegner, K.M.; Shetye, K.S.; Overbye, T.J. Grid Structural Characteristics as Validation Criteria for Synthetic Networks. IEEE Trans. Power Syst. 2017 , 32 , 3258–3265. [ Google Scholar ] [ CrossRef ]

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Kim, H.; Woo, H.; Yoon, Y.; Kim, H.-T.; Kim, Y.J.; Kang, M.; Zhang, X.; Choi, S. An Enhanced Continuation Power Flow Method Using Hybrid Parameterization. Sustainability 2024 , 16 , 7595. https://doi.org/10.3390/su16177595

Kim H, Woo H, Yoon Y, Kim H-T, Kim YJ, Kang M, Zhang X, Choi S. An Enhanced Continuation Power Flow Method Using Hybrid Parameterization. Sustainability . 2024; 16(17):7595. https://doi.org/10.3390/su16177595

Kim, Haelee, Hyeon Woo, Yeunggurl Yoon, Hyun-Tae Kim, Yong Jung Kim, Moonho Kang, Xuehan Zhang, and Sungyun Choi. 2024. "An Enhanced Continuation Power Flow Method Using Hybrid Parameterization" Sustainability 16, no. 17: 7595. https://doi.org/10.3390/su16177595

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Newton Raphson Method

The paper is about Newton Raphson Method which is all-inclusive to solve the non-square and non-linear problems. The study also aims to comparing the rate of performance, rate of convergence of Bisection method, root findings of the Newton meted and Secant method. It also represents a new approach of calculation using nonlinear equation and this will be similar to Newton Raphson simple method and inverse Jacobian matrix will be used for the iteration process and this will be further used for distributed power load flow calculation and will also be helpful in some of the applications. The paper also discusses the difference between the use of built in derivative function and self-derivative function in solving non-linear equation in scientific calculator. The derivation Newton Raphson formula, algorithm, use and drawbacks of Newton Raphson Method have also been discussed.

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International Journal for Research in Applied Science and Engineering Technology -IJRASET

IJRASET Publication

The paper is about Newton Raphson Method which is all inclusive to solve the non-square and non-linear problems. The study also aims to comparing the rate of performance, rate of convergence of bisection method, root finding of the Newton meted and Secant method. It also represents a new approach of calculation using nonlinear equation and this will be similar to Newton Raphson Method and inverse Jacobian matrix will be used for the iteration process and this will be further used for distributed power load flow calculation and will also be useful in some of the applications. The paper also difference the use of built in derivative function and self-derivative function in solving non-linear equation in scientific calculator. And paper also discuss about single variable and multi variable Newton-Raphson techniques

The Newton's Raphson method is also known as Newton method. It is named after Isaac Newton and Joseph Raphson. This method is easy way to find an approximate to the roots of real value and also to solve the non-square and nonlinear problems. It also aims to represents a new approach of calculation of non-linear equation which is very similar to Newton Raphson method simple method and inverse Jacobian matrix will be used for further calculation and will also in some application. Self-derivative function in solving non-linear equation in scientific calculator, derivative Newton Raphson formula algorithm, uses and limitations of Newton Raphson method is been discussed below.

International Journal of Engineering Research and Technology (IJERT)

IJERT Journal

https://www.ijert.org/load-flow-solution-u-sing-simplified-newton-raphson-method https://www.ijert.org/research/load-flow-solution-u-sing-simplified-newton-raphson-method-IJERTV2IS121281.pdf The power flow analysis is of great importance in planning and designing for the future expansion of power systems as well as in determining the best operation of existing systems. There exist two widely-used numerical methods (the Gauss-Seidel: GS and the Newton-Raphson: NR) to solve this problem and therefore referred to as the GS and the NR power-flow solution methods, respectively. Although the standard Newton-Raphson (NR) method is the most powerful algorithm for the power flow analysis in electric power systems, the calculation of Jacobian matrix derivatives involves high computational time. The proposed method presents a simplified Newton-Raphson power flow solution method to simplify overall equation complexity and computation time. The simplified Newton-Raphson method employs nonlinear current mismatch equations instead of the commonly used power mismatch equations. Numerical results are presented with 5-bus test system and IEEE 30-bus test system and compared with standards NR method.

Prof. Dr. Ali Eltamaly

Iee Proceedings-generation Transmission and Distribution

Walid Hubbi

Electrical and Electronic Engineering

RUBEN ABIUD VILLAFUERTE

Zubair Ahmed

Abstract:This paper used the Newton-type Methodfor estimating a single root of nonlinear equations. This method is iterative method and also known as one of the open methods. Open method are fast converging method as compared to closed method but the convergence is not guaranteed. Since open methods are fast convergence methods that is why they are widely used in Applied Mathematics. The proposed numerical technique is second order of convergence, and which is based on Newton Raphson method. The developed algorithm is compared with the well-known Newton Raphson Method and results show that our developed method is much better than the well-known method. Furthermore, examples are also give in order to give more detailed about the present work and reader will come to know that why developed method is much better as compare to well-known method.

2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century

Innocent Kamwa

International Journal of Energy and Power Engineering

Mashauri Kusekwa

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Mathematics > Numerical Analysis

Title: sketched newton-raphson.

Abstract: We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p \rightarrow \mathbb{R}^m$. We then show how to design several stochastic second order optimization methods by re-writing the optimization problem of interest as a system of nonlinear equations and applying SNR. For instance, by applying SNR to find a stationary point of a generalized linear model (GLM), we derive completely new and scalable stochastic second order methods. We show that the resulting method is very competitive as compared to state-of-the-art variance reduced methods. Furthermore, using a variable splitting trick, we also show that the Stochastic Newton method (SNM) is a special case of SNR, and use this connection to establish the first global convergence theory of SNM. We establish the global convergence of SNR by showing that it is a variant of the stochastic gradient descent (SGD) method, and then leveraging proof techniques of SGD. As a special case, our theory also provides a new global convergence theory for the original Newton-Raphson method under strictly weaker assumptions as compared to the classic monotone convergence theory.

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