ABSTRACT: The load flow study in a power system constitutes a study of paramount importance. The study reveals the electrical performance and power flows (real and reactive) for specified condition when the system is operating under steady state. This paper gives an overview of different techniques used for load flow analysis results by using **Newton** **Raphson** **Method**.

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The structure of the paper is as follows. Section 2 presents a brief account of Tanzanian power network status (generation and high voltage transmission). Section 3 presents material and **method** that include system component modelling procedures and developed models for load flow analysis is given. Section 4 presents overall system network modelling. Formulation of load flow problem using **Newton**- **Raphson** **method** and its solution algorithm is given in section 5. Section 6 presents input data, algorithm, simulation procedures and results. Section 7 discusses the obtained results, and section 8 concludes the paper.

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Abstract-- In this paper we consider numerical evaluation of nonlinear Hamiltonian symmetric matrix of Rank 1 in an inverse eigenvalue problem via **Newton**-**Raphson** **method**. The approach employed **Newton**-Raphson’s **method** for solving the inverse eigenvalue problem in a class of Hamiltonian matrices in the neighborhood of a related nonsingular matrix of rank 1. A few numerical examples are presented to illustrate the result.

Abstract––In this paper deals with steady state analysis of self-excited slip ring induction generator (SESRIG) is performed using **Newton**- **Raphson** **method**. By varying effective rotor resistance of a self excited slip ring induction generator, the magnitude and frequency of the output voltage can be controlled over a wide speed range. A steady state analysis based on normalized equivalent circuit enables the control characteristics to be deduced. In the wind driven SESRIG system the rotor speed is varied along with wind speed. For a given stator load, both frequency and voltage can be maintained constant as speed is varied by changing rotor resistance, with constant excitation capacitance. The proposed scheme may be used in low cost variable speed wind energy system for providing good quality electric power to remote regions.

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The calculations for STEP 2 and STEP 3 are straightforward by applying Eq. 15, 18, 37, and 38. Th results from these 2 steps will be used in STEP 4 to solve for the overall concentrations explicitly. Then, algebraic manipulations of the restriction relations (Eq. 31-34) can help to solve the rest of the variables. In the next section, we shall see how the adaptive **Newton**-**Raphson** **method** can be used in order to conduct STEP 5 with several defined constraints.

systems can be made more flexible by the use of recent developments in power electronic and computing control technology. The Unified Power Flow Controller (UPFC) provides a promising means to control power flow in modern power systems. Essentially, the performance depends on proper control setting achievable through a power flow analysis program. This paper aims to present a reliable **method** to meet the requirements by developing a **Newton**-**Raphson** based load flow calculation program through which control setting of UPFC can be determined directly. A MATLAB program has been developed to calculate the control setting parameters of the UPFC after the load flow is converged. Case studies have been performed on IEEE 5-bus system to show that the proposed **method** is effective. These studies indicate that the **method** maintains the basic NRLF properties such as fast computational speed, high degree of accuracy and good convergence rate.

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Parameter estimates from the Gamma model can easily be obtained by the **method** of Maximum Likelihood Estimation jointly numerical approach (**Newton** **Raphson** **method**) with the help of computer. The result of the study shows that Maximum Likelihood Estimation (MLE) jointly with **Newton** **Raphson** **method** is more efficient for estimating parameters of the Gamma model on real life data than simulation study. Comparing Tables 4 and 5 it can be concluded that the estimate values of α that maximizes Gamma model and proﬁle likelihood Gamma function are close to one another. Similarly, Comparing Tables 6 and 7 it can be concluded that the estimate values of α that maximizes gamma probability distribution and proﬁle likelihood gamma are also not significantly different. It was observed that as the sizes of the sample increases the standard error reduces which obey the law of large numbers.

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The **Newton**-**Raphson** **method** requires an initial value for each parameter be estimated. Initial value specification is one of the most difficult problems encountered in estimating parameters of nonlinear model [1]. If the initial values are too far away from the actual value then the **Newton**-**Raphson** **method** may not converge or we need a large number of iterations [11]. The **method** A to **method** D may be useful for estimating the starting values for the parameter estimates. In this paper, the initial values are provided by any one of these four methods of estimation.

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Abstract: The important implication of complex-variable **Newton**-**Raphson** load flow analysis is that reduction in memory access is achieved by the complex-variable **Newton**- **Raphson** **method**. This significant reduction in memory access achieved will lead to the advantage of substantial reduction in computing time which will increase the efficiency. In addition complex-variables offer a flexible and direct approach for modelling of UPFC. This paper develops a **Newton**-**Raphson** load flow analysis formulation which includes UPFC. A brief analysis on load flow calculation methods and UPFC is presented. Proposed system is simulated for IEEE 30 BUS system using Mi-Power software.

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In Deregulation Electricity Market, the optimal location of Independent power producer (IPP) is found by using Locational Marginal Pricing (LMP) with **Newton**-**Raphson** **Method**. LMP is the most trendy congestion management technique and used to find out the congestion charge at particular nodes based on the marginal generation cost. The aim of this paper is to maximize the social welfare and to obtain the optimal site of IPP using an LMP and managing the transmission lines overflow while rewarding security constraints of transmission lines in the competitive power marketplace. The LMP ranking **method** is used to find out the location of IPP. This paper explains how LMP calculation is performed at each bus at which location the transmission lines overflow occurs and how the overflow is alleviated by connecting the IPP at the congested spot in order to maximize the social welfare. The proposed **method** illustrated by case studies on the IEEE 30 bus and Indian utility 69 bus system.

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The goal of this thesis is to develop a new, fast, adaptive load flow algorithm that “automatically alternates” numerical methods including **Newton**-**Raphson** **method**, Gauss-Seidel **method** and Gauss **method** for a load flow run to achieve less run time. Unlike the proposed **method**, the traditional load flow analysis uses only one numerical **method** at a time. This adaptive algorithm performs all the computation for finding the bus voltage angles and magnitudes, real and reactive powers for the given generation and load values, while keeping track of the proximity to convergence of a solution. This work focuses on finding the algorithm that uses multiple numerical techniques, rather than investigating programming techniques and programming languages. The convergence time is compared with those from using each of the numerical techniques. The proposed **method** is implemented on the IEEE 39-bus system with different contingencies and the solutions obtained are verified with PowerWorld Simulator, a commercial software for load flow analysis.

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Pulse width modulation technique is extensively used to eliminate harmful low-order harmonics in inverters. In PWM control the inverter switches are turned ON and OFF during each half cycle and inverter output voltage is controlled by varying the pulse width. Duty cycle for each pulse is decided to control the width of each pulse. In this **method** of selective harmonics elimination the switching angles are calculated and used to control the output voltage waveform. The harmonics equations are obtained by performing the Fourier analysis [7]. The derived nonlinear equations are then solved by different available solving tools and methods. Solving tools such as Mathcad, Mathematica [9], Maple etc are used to solve these nonlinear equations. The harmonics equations in this paper are solved by using **Newton** **Raphson** **method**. In order to control the fundamental output voltage and eliminate ‘n’ harmonics, ‘n+1’ equations are needed. The **method** of elimination will be presented for 9-level inverter such that the solution of four angles is achieved. The switching angles can be found by solving the following equations.

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106 The principle information obtained from power flow study is magnitude and phase angle of voltage at each bus and real and reactive power flowing in each transmission lines. In this work, the increase in voltage profile is done through the insertion of Static Synchronous Compensator (STATCOM), a shunt connected FACTS controller which is capable of generating or absorbing reactive power in order to control the voltage magnitude of the bus where they are connected. The following objectives are hopefully to be achieved in this work: The technical literatures contributed by esteemed authors and scientists have been reviewed for this work. To develop the mathematical model of STATCOM. To develop the **Newton**-**Raphson** **method** of load flow in electrical power system. To use the NRLF technique for optimal location of STATCOM in electrical power system. To use the NRLF technique for optimal size of STATCOM in electrical power system. To compare the results of voltage profile obtain from **Newton**-**Raphson** **method**. To compare the power loss with and without STATCOM in electrical in power system.

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One of the primary objectives of numerical analysis is to decide which algorithms can be implemented to solve mathematical problems on computer [1]. These algorithms accurately approximate the solution of problems which the latter can't be solved exactly and after that a typical techniques for estimating error bounds for the approximation process can be handled [2]. Many researches focused their attention toward using such methods to solve their problems. C. Thinzar and N. Aye made use of the digital image correlation that is based on the sub-pixel accuracy with the aid of **Newton** **Raphson** **method** to detect storm direction for managing and to prevent the possible land's attacked region [3]. D. Biolè, etc. used Secant **method** in addition to other techniques to measure apparent contact angles of non-axisymmetric drops [4]. Md. G. Moazzam, etc. used a robust **method** for solving transcendental equations. The presented **method** by them gave better results rather than the well-known False Position **method** and the Bisection **method** for solving such equations [5]. W. Chu, etc. demonstrated a new registration algorithm based on **Newton** **Raphson** iteration process to align images with rigid body transformation [6]. So, an attempt to detect error propagation

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algorithm of finding UPOs is the **Newton**-**Raphson** **method** with a Poincar´e section, which reduces a continuous dynam- ical system to a discrete system. Another **method** is to de- tect a UPO by stabilizing the periodic orbit in the sense of chaos control (Pyragas, 1992) 1 . Kazantsev (1998) devel- ops a **method** which requires similar techniques to data as- similation, and there is also a variational **method** (Lan and Cvitanovi´c, 2004). However, in this paper, we focus our at- tention to the **Newton**-**Raphson**-Mees **method** (Mees, 1981; Parker and Chua, 1989) with a damping coefficient, where we do not need to have trouble of choosing the appropriate Poincar´e section.

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Abstract: The forward kinematics is the process of finding the position of end effector using joint angles and inverse kinematics is vice-versa of it. The forward kinematics is straight forward and gives a unique solution while inverse kinematics may lead to multiple solutions or sometimes even no solution. Traditional methods such as graphical, analytical and iterative are quite popular to solve the inverse kinematics but due to their computational complexity, alternative methods using neural network and genetic algorithm are being proposed. This paper proposes a hybridization algorithm to solve the inverse kinematics of a UR5 (six degrees of freedom) mechanical manipulator. The hybridization algorithm proposed in this paper uses global optimization of the genetic algorithm and fast local optimization of the **Newton**-**Raphson** **method**. This paper also presents a simulation of the proposed algorithm on a UR5 mechanical manipulator.

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slope of a line through two points on the function. In this case, the Secant **method** results. These methods are discussed in many books on Numerical Analysis and Operations Research. See, for example, Ralston and Rabinowitz [2], Dennis and Schnabel [1], Stoer and Bulirsch [3] and Taha [4]. To avoid computing f'(x) because f'(x) may not always be available or may be costly to compute and to preserve the excellent convergence properties of the **Newton**-**Raphson** **method**, f'(x n ) is replaced by f [ x n , x n − 1 ] in

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KEYWORDS: Global positioning system, Accurate position, Newton Raphson method, Faulty Satellites, Space segment, Control segment, User segment, fault detection and.. i[r]

ABSTRACT: In this research work, the power flow problem, also called as the load flow problem, has been dealt with. The load flow solution gives the complex voltages at all the buses and the complex power flows in the lines. To obtain power flow solution, the most popular **Newton**-**Raphson** **method** is used. The **method** has been used to obtain power flow solutions and is tested on IEEE 57- bus distribution system. In IEEE 57-bus system, , the total power generated were 1278MW whereas the power demand were 1250MW thus a loss of 28 MW and the optimal cost ranges from 42.13$/MVA-hr to 46.83$/MVA-hr.

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The nonlinear equations, often arise from the numerical modeling of problems in many branches of science and engineering [1]. These equations more often are not solved analytically hence resort to numerical solutions. More robust and efficient methods for solving the nonlinear equations are continuously being sought. There are many papers that deal with nonlinear algebraic equations, such as, improving **Newton** **Raphson** **method** for nonlinear equations by modified Adomian decomposition **method** [2], iterative **method** improving Newton’s **method** by the decomposition **method** [3], new family of Iterative methods for nonlinear equations [4], iterative Methods for the solution of Equations

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