Search results for: Pendulum nonlinear dynamics

Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

Abstract:

In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: J. Fernandez de Canete, S. Gonzalez-Perez, P. del Saz-Orozco, I. Garcia-Moral

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Robust stability and performance are the two most basic features of feedback control systems. The harmonic balance analysis technique enables to analyze the stability of limit cycles arising from a neural network control based system operating over nonlinear plants. In this work a robust stability analysis based on the harmonic balance is presented and applied to a neural based control of a non-linear binary distillation column with unstructured uncertainty. We develop ways to describe uncertainty in the form of neglected nonlinear dynamics and high harmonics for the plant and controller respectively. Finally, conclusions about the performance of the neural control system are discussed using the Nyquist stability margin together with the structured singular values of the uncertainty as a robustness measure.

Keywords: Robust stability, neural network control, unstructured uncertainty, singular values, distillation column.

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Authors: Gholamreza Hojjati, Kourosh Parand

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In this paper we propose a class of second derivative multistep methods for solving some well-known classes of Lane- Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. These methods, which have good stability and accuracy properties, are useful in deal with stiff ODEs. We show superiority of these methods by applying them on the some famous Lane-Emden type equations.

Keywords: Lane-Emden type equations, nonlinear ODE, stiff problems, multistep methods, astrophysics.

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Authors: Barenten Suciu

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In this work, effects of the friction and truncation on the dynamics of a double-cone gravitational motor, self-propelled on a straight V-shaped horizontal rail, are evaluated. Such mechanism has a variable radius of contact, and, on one hand, it is similar to a pulley mechanism that changes the potential energy into the kinetic energy of rotation, but on the other hand, it is similar to a pendulum mechanism that converts the potential energy of the suspended body into the kinetic energy of translation along a circular path. Movies of the self- propelled double-cones, made of S45C carbon steel and wood, along rails made of aluminum alloy, were shot for various opening angles of the rails. Kinematical features of the double-cones were estimated through the slow-motion processing of the recorded movies. Then, a kinematical model is derived under assumption that the distance traveled by the contact points on the rectilinear rails is identical with the distance traveled by the contact points on the truncated conical surface. Additionally, a dynamic model, for this particular contact problem, was proposed and validated against the experimental results. Based on such model, the traction force and the traction torque acting on the double-cone are identified. One proved that the rolling traction force is always smaller than the sliding friction force; i.e., the double-cone is rolling without slipping. Results obtained in this work can be used to achieve the proper design of such gravitational motor.

Keywords: Truncated double-cone, friction, rolling and sliding, dynamic model, gravitational motor.

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Authors: Leila Motamed-Jahromi, Mohsen Hatami, Alireza Keshavarz

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This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As₂S₃ chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion.

Keywords: Nonlinear optics, propagation equation, plasmonic waveguide.

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Authors: M.O. Makhmalbaf, M. GhanooniBagha, M.A. Tutunchian, M. Zabihi Samani

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In this paper first, Two buildings have been modeled and then analyzed using nonlinear static analysis method under two different conditions in Nonlinear SAP 2000 software. In the first condition the interaction of soil adjacent to the walls of basement are ignored while in the second case this interaction have been modeled using Gap elements of nonlinear SAP2000 software. Finally, comparing the results of two models, the effects of soil-structure on period, target point displacement, internal forces, shape deformations and base shears have been studied. According to the results, this interaction has always increased the base shear of buildings, decreased the period of structure and target point displacement, and often decreased the internal forces and displacements.

Keywords: Seismic Rehabilitation, Soil-Structure Interaction, Short Structure, Nonlinear Static Analysis.

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Authors: S. H. Sabzpoushan

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In this research we show that the dynamics of an action potential in a cell can be modeled with a linear combination of the dynamics of the gating state variables. It is shown that the modeling error is negligible. Our findings can be used for simplifying cell models and reduction of computational burden i.e. it is useful for simulating action potential propagation in large scale computations like tissue modeling. We have verified our finding with the use of several cell models.

Keywords: Linear model, Action potential, gating dynamics.

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Authors: Bhawna Tandon, Shiv Narayan, Jagdish Kumar

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This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is performed using a maximum of N-1 steps where N being the dimension of the system.

Keywords: Explicit Algorithm, Feedback Linearization, Nonlinear control, Magnetic Levitation System.

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová

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The article presents two mathematical models of the interaction between a rotating shaft and an incompressible fluid. The mathematical model includes both the journal bearings and the axially traversed hydrodynamic sealing gaps of hydraulic machines. A method is shown for the identification of additional effects of the fluid acting on the rotor of the machine, both for a linear and a nonlinear model. The interaction is expressed by matrices of mass, stiffness and damping.

Keywords: CFD modeling, hydrodynamic gap, matrices of mass, stiffness and damping, nonlinear mathematical model.

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Authors: Qiuling Xie, Shanliang Zhu, Zongdi Sun

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In this paper, we analyzed the correlation relationship among PM2.5 from other five Air Quality Indices (AQIs) based on the grey relational degree, and built a multivariate nonlinear regression equation model of PM2.5 and the five monitoring indexes. For the optimal control problem of PM2.5, we took the partial large Cauchy distribution of membership equation as satisfaction function. We established a nonlinear programming model with the goal of maximum performance to price ratio. And the optimal control scheme is given.

Keywords: Grey relational degree, multiple linear regression, membership function, nonlinear programming.

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Authors: Lianglin Xiong, Xiuyong Ding, Shouming Zhong

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In this paper, the problem of asymptotical stability of neutral systems with nonlinear perturbations is investigated. Based on a class of novel augment Lyapunov functionals which contain freeweighting matrices, some new delay-dependent asymptotical stability criteria are formulated in terms of linear matrix inequalities (LMIs) by using new inequality analysis technique. Numerical examples are given to demonstrate the derived condition are much less conservative than those given in the literature.

Keywords: Asymptotical stability, neutral system, nonlinear perturbation, delay-dependent, linear matrix inequality (LMI).

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Authors: Ke Zhao, Ballarat Colin Richardson, Jerry Courvisanos, John Crawford

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Climate change has profound consequences for the agriculture of south-eastern Australia and its climate-induced water shortage in the Murray-Darling Basin. Post Keynesian Economics (PKE) macro-dynamics, along with Kaleckian investment and growth theory, are used to develop an ecological-economic system dynamics model of this complex nonlinear river basin system. The Murray- Darling Basin Simulation Model (MDB-SM) uses the principles of PKE to incorporate the fundamental uncertainty of economic behaviors of farmers regarding the investments they make and the climate change they face, particularly as regards water ecosystem services. MDB-SM provides a framework for macroeconomic policies, especially for long-term fiscal policy and for policy directed at the sustainability of agricultural water, as measured by socio-economic well-being considerations, which include sustainable consumption and investment in the river basin. The model can also reproduce other ecological and economic aspects and, for certain parameters and initial values, exhibit endogenous business cycles and ecological sustainability with realistic characteristics. Most importantly, MDBSM provides a platform for the analysis of alternative economic policy scenarios. These results reveal the importance of understanding water ecosystem adaptation under climate change by integrating a PKE macroeconomic analytical framework with the system dynamics modelling approach. Once parameterised and supplied with historical initial values, MDB-SM should prove to be a practical tool to provide alternative long-term policy simulations of agricultural water and socio-economic well-being.

Keywords: Agricultural water, Macroeconomic dynamics, Modeling, Investment dynamics, Sustainability, Unemployment, Economics, Keynesian, Kaleckian.

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Authors: Kholod M. Abu-Alnaja

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In this work, we derive two numerical schemes for solving a class of nonlinear partial differential equations. The first method is of second order accuracy in space and time directions, the scheme is unconditionally stable using Von Neumann stability analysis, the scheme produced a nonlinear block system where Newton-s method is used to solve it. The second method is of fourth order accuracy in space and second order in time. The method is unconditionally stable and Newton's method is used to solve the nonlinear block system obtained. The exact single soliton solution and the conserved quantities are used to assess the accuracy and to show the robustness of the schemes. The interaction of two solitary waves for different parameters are also discussed.

Keywords: Crank-Nicolson Scheme, Douglas Scheme, Partial Differential Equations

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Authors: Akbar H. Borzabadi, Omid S. Fard

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In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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Authors: Ali Reza Mehrabian, Caro Lucas

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In this paper a new control strategy based on Brain Emotional Learning (BEL) model has been introduced. A modified BEL model has been proposed to increase the degree of freedom, controlling capability, reliability and robustness, which can be implemented in real engineering systems. The performance of the proposed BEL controller has been illustrated by applying it on different nonlinear uncertain systems, showing very good adaptability and robustness, while maintaining stability.

Keywords: Learning control systems, emotional decision making, nonlinear systems, adaptive control.

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Authors: Nemat Abazari, Reza Abazari

Abstract:

In this work, we successfully extended one-dimensional differential transform method (DTM), by presenting and proving some theorems, to solving nonlinear high-order multi-pantograph equations. This technique provides a sequence of functions which converges to the exact solution of the problem. Some examples are given to demonstrate the validity and applicability of the present method and a comparison is made with existing results.

Keywords: Nonlinear multi-pantograph equation, delay differential equation, differential transformation method, proportional delay conditions, closed form solution.

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Authors: Tomohiro Hachino, Hitoshi Takata, Shigeru Nakayama, Ichiro Iimura, Seiji Fukushima, Yasutaka Igarashi

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This paper presents a nonparametric identification of continuous-time nonlinear systems by using a Gaussian process (GP) model. The GP prior model is trained by artificial bee colony algorithm. The nonlinear function of the objective system is estimated as the predictive mean function of the GP, and the confidence measure of the estimated nonlinear function is given by the predictive covariance of the GP. The proposed identification method is applied to modeling of a simplified electric power system. Simulation results are shown to demonstrate the effectiveness of the proposed method.

Keywords: Artificial bee colony algorithm, Gaussian process model, identification, nonlinear system, electric power system.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

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Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: Shishen Xie

Abstract:

In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations

Keywords: variation iteration method, decomposition method, nonlinear integro-differential equations

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: H∞ fuzzy control, LMI, Takagi-Sugano (TS) fuzzy model, nonlinear dynamic systems, state-derivative feedback.

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Authors: A. N. K. Nasir, M. A. Ahmad, R. M. T. Raja Ismail

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The research on two-wheels balancing robot has gained momentum due to their functionality and reliability when completing certain tasks. This paper presents investigations into the performance comparison of Linear Quadratic Regulator (LQR) and PID-PID controllers for a highly nonlinear 2–wheels balancing robot. The mathematical model of 2-wheels balancing robot that is highly nonlinear is derived. The final model is then represented in statespace form and the system suffers from mismatched condition. Two system responses namely the robot position and robot angular position are obtained. The performances of the LQR and PID-PID controllers are examined in terms of input tracking and disturbances rejection capability. Simulation results of the responses of the nonlinear 2–wheels balancing robot are presented in time domain. A comparative assessment of both control schemes to the system performance is presented and discussed.

Keywords: PID, LQR, Two-wheels balancing robot.

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Authors: Dong Sang Yoo

Abstract:

We consider nonlinear uncertain systems such that a  priori information of the uncertainties is not available. For such  systems, we assume that the upper bound of the uncertainties is  represented as a Fredholm integral equation of the first kind and we  propose an adaptation law that is capable of estimating the upper  bound and design a continuous robust control which renders nonlinear  uncertain systems ultimately bounded.

 

Keywords: Adaptive Control, Estimation, Fredholm Integral, Uncertain System.

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Authors: N. N. Omehe

Abstract:

CdSiP2 and CdsiAs2 are nonlinear optical materials for near and mid-infrared applications. Density functional theory has been applied to study the structure, band gap, and optical properties of these materials. The pseudopotential method was used in the form of projector augmented wave (PAW) and norm-conserving, the band structure calculations yielded a band gap of 1.55 eV and 0.88 eV for CdSiP2 and CdsiAs2 respectively. The values of ε1(ω)  from the doelectric function calculations are 15 and 14.9 CdSiP2 and CdsiAs2 respectively.

Keywords: Band structure, chalcopyrite, near-infrared materials, mid-infrared materials, nonlinear material, optical properties.

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Authors: Roza Dastres, Mohsen Soori

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Digital Signal Processing (DSP) is the use of digital processing systems by computers in order to perform a variety of signal processing operations. It is the mathematical manipulation of a digital signal's numerical values in order to increase quality as well as effects of signals. DSP can include linear or nonlinear operators in order to process and analyze the input signals. The nonlinear DSP processing is closely related to nonlinear system detection and can be implemented in time, frequency and space-time domains. Applications of the DSP can be presented as control systems, digital image processing, biomedical engineering, speech recognition systems, industrial engineering, health care systems, radar signal processing and telecommunication systems. In this study, advanced methods and different applications of DSP are reviewed in order to move forward the interesting research filed.

Keywords: Digital signal processing, advanced telecommunication, nonlinear signal processing, speech recognition systems.

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Authors: Rajneesh Sharma, M. Gopal

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Markov games are a generalization of Markov decision process to a multi-agent setting. Two-player zero-sum Markov game framework offers an effective platform for designing robust controllers. This paper presents two novel controller design algorithms that use ideas from game-theory literature to produce reliable controllers that are able to maintain performance in presence of noise and parameter variations. A more widely used approach for controller design is the H∞ optimal control, which suffers from high computational demand and at times, may be infeasible. Our approach generates an optimal control policy for the agent (controller) via a simple Linear Program enabling the controller to learn about the unknown environment. The controller is facing an unknown environment, and in our formulation this environment corresponds to the behavior rules of the noise modeled as the opponent. Proposed controller architectures attempt to improve controller reliability by a gradual mixing of algorithmic approaches drawn from the game theory literature and the Minimax-Q Markov game solution approach, in a reinforcement-learning framework. We test the proposed algorithms on a simulated Inverted Pendulum Swing-up task and compare its performance against standard Q learning.

Keywords: Reinforcement learning, Markov Decision Process, Matrix Games, Markov Games, Smooth Fictitious play, Controller, Inverted Pendulum.

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Authors: Da-Xue Chen, Guang-Hui Liu

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In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.

Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.

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Authors: Rahul Bansal, Sudipta Majumdar

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This paper presents the closed form nonlinear expressions of bipolar junction transistor (BJT) differential amplifier (DA) using perturbation method. Circuit equations have been derived using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law (KCL). The perturbation method has been applied to state variables for obtaining the linear and nonlinear terms. The implementation of the proposed method is simple. The closed form nonlinear expressions provide better insights of physical systems. The derived equations can be used for signal processing applications.

Keywords: Differential amplifier, perturbation method, Taylor series.

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Authors: A. Puras Trueba, J. R. Llata García

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A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Jinfeng Wang, Yang Liu, Hong Li

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In this article, we propose a new approximate procedure based on He’s variational iteration method for solving nonlinear hyperbolic equations. We introduce two transformations q = ut and σ = ux and formulate a first-order system of equations. We can obtain the approximation solution for the scalar unknown u, time derivative q = ut and space derivative σ = ux, simultaneously. Finally, some examples are provided to illustrate the effectiveness of our method.

Keywords: Hyperbolic wave equation, Nonlinear, He’s variational iteration method, Transformations

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Authors: S.Ali Al-Mawsawi

Abstract:

In this paper, a new developed construction model of the UPFC is proposed. The construction of this model consists of one shunt compensation block and two series compensation blocks. In this case, the UPFC with the new construction model will be investigated when it is installed in multi-machine systems with nonlinear load model. In addition, the steady–state performance of the new model operating as impedance compensation will be presented and compared with that obtained from the system without compensation.

Keywords: UPFC, PWM, Nonlinear load, Multi-Machines system

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