Search results for: Harmonic Power

Authors: T. Mohammed Chikouche, K. Hartani

Abstract:

In order to solve the instantaneous power ripple and achieve better performance of direct power control (DPC) for a three-phase PWM rectifier, a control method is proposed in this paper. This control method is applied to overcome the instantaneous power ripple, to eliminate line current harmonics and therefore reduce the total harmonic distortion and to improve the power factor. A switching table is based on the analysis on the change of instantaneous active and reactive power, to select the optimum switching state of the three-phase PWM rectifier. The simulation result shows feasibility of this control method.

Keywords: Power quality, direct power control, power ripple, switching table, unity power factor.

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Authors: Hossein Mohammadpour, Rahman Dashti

Abstract:

Power transformers are among the most important and expensive equipments in the electric power systems. Consequently the transformer protection is an essential part of the system protection. This paper presents a new method for locating transformer winding faults such as turn-to-turn, turn-to-core, turn-totransformer body, turn-to-earth, and high voltage winding to low voltage winding. In this study the current and voltage signals of input and output terminals of the transformer are measured, which the Fourier transform of measured signals and harmonic analysis determine the fault's location.

Keywords: turn-to-turn faults, short circuit, Fourier transform, harmonic analysis.

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Authors: Zahzouh Zoubir, Bouzaouit Azzeddine, Gahgah Mounir

Abstract:

The use of more and more electronic power switches with a nonlinear behavior generates non-sinusoidal currents in distribution networks, which causes damage to domestic and industrial equipment. The multi-level shunt power active filter is subsequently shown to be an adequate solution to the problem raised. Nevertheless, the difficulty of adjusting the active filter DC supply voltage requires another technology to ensure it. In this article, a photovoltaic generator is associated with the DC bus power terminals of the active filter. The proposed system consists of a field of solar panels, three multi-level voltage inverters connected to the power grid and a non-linear load consisting of a six-diode rectifier bridge supplying a resistive-inductive load. Current control techniques of active and reactive power are used to compensate for both harmonic currents and reactive power as well as to inject active solar power into the distribution network. An algorithm of the search method of the maximum power point of type Perturb and observe is applied. Simulation results of the system proposed under the MATLAB/Simulink environment shows that the performance of control commands that reassure the solar power injection in the network, harmonic current compensation and power factor correction.

Keywords: MPPT, active power filter, PV array, perturb and observe algorithm, PWM-control.

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Authors: A. K. Al-Othman, Nabil A. Ahmed, A. M. Al-Kandari, H. K. Ebraheem

Abstract:

Selective harmonic elimination-pulse width modulation techniques offer a tight control of the harmonic spectrum of a given voltage waveform generated by a power electronic converter along with a low number of switching transitions. Traditional optimization methods suffer from various drawbacks, such as prolonged and tedious computational steps and convergence to local optima; thus, the more the number of harmonics to be eliminated, the larger the computational complexity and time. This paper presents a novel method for output voltage harmonic elimination and voltage control of PWM AC/AC voltage converters using the principle of hybrid Real-Coded Genetic Algorithm-Pattern Search (RGA-PS) method. RGA is the primary optimizer exploiting its global search capabilities, PS is then employed to fine tune the best solution provided by RGA in each evolution. The proposed method enables linear control of the fundamental component of the output voltage and complete elimination of its harmonic contents up to a specified order. Theoretical studies have been carried out to show the effectiveness and robustness of the proposed method of selective harmonic elimination. Theoretical results are validated through simulation studies using PSIM software package.

Keywords: PWM, AC/AC voltage converters, selectiveharmonic elimination, direct search method, pattern search method, Real-coded Genetic algorithms, evolutionary algorithms andoptimization.

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Authors: Setareh Gorji Ghalamestani, Lieven Vandevelde, Jan Melkebeek

Abstract:

In this work, an experimental technique is applied for the measurements of the vibrations and deformation of a test transformer core. Since the grid voltage contains some higher harmonics, in addition to a purely sinusoidal magnetisation of the core the presence of third harmonic is also studied. The vibrations of the transformer core for points as well as the surface scan of the leg show more deformation in the corners of the leg than the middle of the leg. The influence of the higher harmonic of the magnetisation on the core deformation is also more significant in the corners of the leg. The core deformation shape under a sinusoidal magnetisation with a higher harmonic is more wavy and fluctuating than that under a purely sinusoidal magnetisation.

Keywords: Vibrations and noise, transformer, vibration measurements, laser vibrometer, higher harmonic.

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Authors: H. Fathabadi

Abstract:

In this paper, we consider a designed and implemented phase-cutting dimmer. In fact, the dimmer is closed loop and a microcontroller calculates and then regulates the firing delay angles of each channel. Depending on the firing angle, the harmonic distortion in the input current will not comply with international standards, such as IEC 61000-3-2 (class C equipments). For solving this problem, eight harmonic compensators have been added to the dimmer. So, the proposed dimmer has a little harmonic distortion in the input current whereas conventional phase-cutting dimmers are not so. Sensitivity and removed THD of the proposed dimmer will be presented.

Keywords: Dimmer, compensator, harmonic, dimming.

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Authors: Gaddafi S. Shehu, T. Yalcinoz, Abdullahi B. Kunya

Abstract:

Multilevel inverters such as flying capacitor, diodeclamped, and cascaded H-bridge inverters are very popular particularly in medium and high power applications. This paper focuses on a cascaded H-bridge module using a single direct current (DC) source in order to generate an 11-level output voltage. The noble approach reduces the number of switches and gate drivers, in comparison with a conventional method. The anticipated topology produces more accurate result with an isolation transformer at high switching frequency. Different modulation techniques can be used for the multilevel inverter, but this work features modulation techniques known as selective harmonic elimination (SHE).This modulation approach reduces the number of carriers with reduction in Switching Losses, Total Harmonic Distortion (THD), and thereby increasing Power Quality (PQ). Based on the simulation result obtained, it appears SHE has the ability to eliminate selected harmonics by chopping off the fundamental output component. The performance evaluation of the proposed cascaded multilevel inverter is performed using PSIM simulation package and THD of 0.94% is obtained.

Keywords: Cascaded H-bridge Multilevel Inverter, Power Quality, Selective Harmonic Elimination.

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Authors: O. Arikan, C. Kocatepe, G. Ucar, Y. Hacialiefendioglu

Abstract:

In this paper, influence of harmonics on medium voltage distribution system of Bogazici Electricity Distribution Inc. (BEDAS) which takes place at Istanbul/Turkey is investigated. A ring network consisting of residential loads is taken into account for this study. Real system parameters and measurement results are used for simulations. Also, probable working conditions of the system are analyzed for 50%, 75%, and 100% loading of transformers with similar harmonic contents. Results of the study are exhibited the influence of nonlinear loads on %THDV, P.F. and technical losses of the medium voltage distribution system.

Keywords: Distribution system, harmonic, technical losses, power factor (PF), total harmonic distortion (THD), residential load, medium voltage.

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Authors: Rishikesh Pandey, Maneesha Gupta

Abstract:

A new low-voltage floating gate MOSFET (FGMOS) based squarer using square law characteristic of the FGMOS is proposed in this paper. The major advantages of the squarer are simplicity, rail-to-rail input dynamic range, low total harmonic distortion, and low power consumption. The proposed circuit is biased without body effect. The circuit is designed and simulated using SPICE in 0.25μm CMOS technology. The squarer is operated at the supply voltages of ±0.75V . The total harmonic distortion (THD) for the input signal 0.75Vpp at 25 KHz, and maximum power consumption were found to be less than 1% and 319μW respectively.

Keywords: Analog signal processing, floating gate MOSFETs, low-voltage, Spice, squarer.

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Authors: Nesapriya. P., S. Rajalaxmi

Abstract:

This paper is based on the bridgeless single-phase Ac–Dc Power Factor Correction (PFC) converters with Fuzzy Logic Controller. High frequency isolated Cuk converters are used as a modular dc-dc converter in Discontinuous Conduction Mode (DCM) of operation of Power Factor Correction. The aim of this paper is to simplify the program complexity of the controller by reducing the number of fuzzy sets of the Membership Functions (MFs) and to improve the efficiency and to eliminate the power quality problems. The output of Fuzzy controller is compared with High frequency triangular wave to generate PWM gating signals of Cuk converter. The proposed topologies are designed to work in Discontinuous Conduction Mode (DCM) to achieve a unity power factor and low total harmonic distortion of the input current. The Fuzzy Logic Controller gives additional advantages such as accurate result, uncertainty and imprecision and automatic control circuitry. Performance comparisons between the proposed and conventional controllers and circuits are performed based on circuit simulations.

Keywords: Fuzzy Logic Controller (FLC), Bridgeless rectifier, Cuk converter, Pulse Width Modulation (PWM), Power Factor Correction, Total Harmonic Distortion (THD).

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Authors: S. Selvaperumal, M. S. Sivagamasundari

Abstract:

In this paper, selective harmonic elimination pulse width modulation technique is employed to eliminate lower order harmonics like third by determination of solving non-linear equations. The cascaded H-bridge five level inverter is driven by the Peripheral Interface Controlled (PIC) Microcontroller 16F877A. The performance of single phase cascaded H-bridge five level inverter with relevant to harmonics and a variety of switches with solar cell as its input source is simulated by employing MATLAB/Simulink. A hardware model is developed to verify the performance of the developed system.

Keywords: Multilevel inverter, cascaded H-Bridge multilevel inverter, total harmonic distortion, selective harmonic elimination pulse width modulation, MATLAB.

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Authors: Mihaela Popescu, Alexandru Bitoleanu, Mircea Dobriceanu, Vlad Suru

Abstract:

The aim of this paper is to identify an optimum control strategy of three-phase shunt active filters to minimize the total harmonic distortion factor of the supply current. A classical PIPI cascade control solution of the output current of the active filterand the voltage across the DC capacitor based on Modulus–Optimum criterion is taken into consideration. The control system operation has been simulated using Matlab-Simulink environment and the results agree with the theoretical expectation. It is shown that there is an optimum value of the DC-bus voltage which minimizes the supply current harmonic distortion factor. It corresponds to the equality of the apparent power at the output of the active filter and the apparent power across the capacitor. Finally, predicted results are verified experimentally on a MaxSine active power filter.

Keywords: Active filtering, Controller tuning, Modulus Optimum criterion, Optimum control.

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Authors: M.A.A. Younis, N. A. Rahim, S. Mekhilef

Abstract:

This paper presents the design and analysis of a parallel connected inverter configuration of. The configuration consists of parallel connected three-phase dc/ac inverter. Series resistors added to the inverter output to maintain same current in each inverter of the two parallel inverters, and to reduce the circulating current in the parallel inverters to the minimum. High frequency third harmonic injection PWM (THIPWM) employed to reduce the total harmonic distortion and to make maximum use of the voltage source. DSP was used to generate the THIPWM and the control algorithm for the converter. Selected experimental results have been shown to validate the proposed system.

Keywords: Three-phase inverter, Third harmonic injection PWM, inverters parallel connection.

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Authors: K. G. Firouzjah, A. Sheikholeslami

Abstract:

The perfect operation of common Active Filters is depended on accuracy of identification system distortion. Also, using a suitable method in current injection and reactive power compensation, leads to increased filter performance. Due to this fact, this paper presents a method based on predictive current control theory in shunt active filter applications. The harmonics of the load current is identified by using o–d–q reference frame on load current and eliminating the DC part of d–q components. Then, the rest of these components deliver to predictive current controller as a Threephase reference current by using Park inverse transformation. System is modeled in discreet time domain. The proposed method has been tested using MATLAB model for a nonlinear load (with Total Harmonic Distortion=20%). The simulation results indicate that the proposed filter leads to flowing a sinusoidal current (THD=0.15%) through the source. In addition, the results show that the filter tracks the reference current accurately.

Keywords: Active filter, predictive current control, low pass filter, harmonic omitting, o–d–q reference frame.

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Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Wind turbines with double output induction generators can operate at variable speed permitting conversion efficiency maximization over a wide range of wind velocities. This paper presents the performance analysis of a wind driven double output induction generator (DOIG) operating at varying shafts speed. A periodic transient state analysis of DOIG equipped with two converters is carried out using a hybrid induction machine model. This paper simulates the harmonic content of waveforms in various points of drive at different speeds, based on the hybrid model (dqabc). Then the sinusoidal and trapezoidal pulse-width–modulation control techniques are used in order to improve the power factor of the machine and to weaken the injected low order harmonics to the supply. Based on the frequency spectrum, total harmonics distortion, distortion factor and power factor. Finally advantages of sinusoidal and trapezoidal pulse width modulation techniques are compared.

Keywords: DOIG, Harmonic Analysis, Wind.

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Authors: Smko Zangana, Ergun Ercelebi

Abstract:

The alternating current is the main power in all industries and other aspects especially for the short and mid distances, but as far as long a distance which exceeds 500 KMs, using the alternating current technically will face many difficulties and more costs because it's difficult to control the current and also other restrictions. Therefore, recently those reasons led to building transmission lines HVDC to transmit power for long distances. This document presents technical comparison and assessments for power transmission system among distances either ways and studying the stability of the system regarding the proportion of losses in the actual power sent and received between both sides in different systems and also categorizing filters used in the HVDC system and its impact and effect on reducing Harmonic in the power transmission. MATLAB /Simulink simulation software is used to simulate both HVAC & HVDC power transmission system topologies.

Keywords: HVAC power system, HVDC power system, power system simulation (MATLAB), the alternating current, voltage stability.

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Authors: M. Suresh Kumar, K. Ramani

Abstract:

This paper proposed the comparison made between Multi-Carrier Pulse Width Modulation, Sinusoidal Pulse Width Modulation and Selective Harmonic Elimination Pulse Width Modulation technique for minimization of Total Harmonic Distortion in Cascaded H-Bridge Multi-Level Inverter. In Multicarrier Pulse Width Modulation method by using Alternate Position of Disposition scheme for switching pulse generation to Multi-Level Inverter. Another carrier based approach; Sinusoidal Pulse Width Modulation method is also implemented to define the switching pulse generation system in the multi-level inverter. In Selective Harmonic Elimination method using Genetic Algorithm and Particle Swarm Optimization algorithm for define the required switching angles to eliminate low order harmonics from the inverter output voltage waveform and reduce the total harmonic distortion value. So, the results validate that the Selective Harmonic Elimination Pulse Width Modulation method does capably eliminate a great number of precise harmonics and minimize the Total Harmonic Distortion value in output voltage waveform in compared with Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method. In this paper, comparison of simulation results shows that the Selective Harmonic Elimination method can attain optimal harmonic minimization solution better than Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method.

Keywords: Multi-level inverter, Selective Harmonic Elimination Pulse Width Modulation, Multi-Carrier Pulse Width Modulation, Total Harmonic Distortion, Genetic Algorithm.

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Authors: S. Chatterji, S. L. Shimi

Abstract:

As wind, solar and other clean and green energy sources gain popularity worldwide, engineers are seeking ways to make renewable energy systems more affordable and to integrate them with existing ac power grids. In the present paper an attempt has been made for integrating the PV arrays to the smart nano grid using an artificial intelligent (AI) based solar powered cascade multilevel inverter. The AI based controller switching scheme has been used for improving the power quality by reducing the Total Harmonic Distortion (THD) of the multi-level inverter output voltage.

Keywords: Artificial Intelligent (AI), Solar Powered Multi-level Inverter, Smart nano grid, Total Harmonic Distortion (THD).

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Authors: H. Abaali, M. T. Lamchich, M. Raoufi

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In this paper, we propose the Modified Synchronous Detection (MSD) Method for determining the reference compensating currents of the shunt active power filter under non sinusoidal voltages conditions. For controlling the inverter switching we used the PI regulator. The numerical simulation results, using Power System Blockset Toolbox PSB of Matlab, from a complete structure, are presented and discussed.

Keywords: Distorted, harmonic, Modified Synchronous Detection Method, PI regulator, Shunt Active Power Filter, unbalanced.

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Authors: Sukir Maryanto, Didik R. Santosa, Iyan Mulyana, Muhammad Hendrasto

Abstract:

Successive event of explosion earthquake and harmonic tremor recorded at Semeru volcano were analyzed to investigate the dynamical system regarding to their eruptive mechanism. The eruptive activity at Semeru volcano East Java, Indonesia is intermittent emission of ash and bombs with Strombolian style which occurred at interval of 15 to 45 minutes. The explosive eruptions accompanied by explosion earthquakes and followed by volcanic tremor which generated by continuous emission of volcanic ash. The spectral and Lyapunov exponent of successive event of explosion and harmonic tremor were analyzed. Peak frequencies of explosion earthquakes range 1.2 to 1.9 Hz and those of the harmonic tremor have peak frequency range 1.5 — 2.2 Hz. The phase space is reconstructed and evaluated based on the Lyapunov exponents. Harmonic tremors have smaller Lyapunov exponent than explosion earthquakes. It can be considerably as correlated complexity of the mechanism from the variance of spectral and fractal dimension and can be concluded that the successive event of harmonic tremor and explosions are chaotic.

Keywords: Semeru volcano, explosion earthquakes, harmonic tremor, lyapunov exponent, chaotic.

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Authors: Sukir Maryanto, Iyan Mulyana

Abstract:

Fractal analyses of successive event of explosion earthquake and harmonic tremor recorded at Semeru volcano were carried out to investigate the dynamical system regarding to their generating mechanism. The explosive eruptions accompanied by explosion earthquakes and following volcanic tremor which are generated by continuous emission of volcanic ash. The fractal dimension of successive event of explosion and harmonic tremor was estimated by Critical Exponent Method (CEM). It was found that the method yield a higher fractal dimension of explosion earthquakes and gradually decrease during the occurrence of harmonic tremor, and can be considerably as correlated complexity of the source mechanism from the variance of fractal dimension.

Keywords: Fractal dimension, Semeru volcano, explosionearthquake, harmonic tremor, Critical Exponent Method

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Authors: N. Janjamraj, A. Oonsivilai

Abstract:

This paper present the harmonic elimination of hybrid multilevel inverters (HMI) which could be increase the number of output voltage level. Total Harmonic Distortion (THD) is one of the most important requirements concerning performance indices. Because of many numbers output levels of HMI, it had numerous unknown variables of eliminate undesired individual harmonic and THD nonlinear equations set. Optimized harmonic stepped waveform (OHSW) is solving switching angles conventional method, but most complicated for solving as added level. The artificial intelligent techniques are deliberation to solve this problem. This paper presents the Particle Swarm Optimization (PSO) technique for solving switching angles to get minimum THD and eliminate undesired individual harmonics of 15-levels hybrid multilevel inverters. Consequently it had many variables and could eliminate numerous harmonics. Both advantages including high level of inverter and Particle Swarm Optimization (PSO) are used as powerful tools for harmonics elimination.

Keywords: Multilevel Inverters, Particle Swarms Optimization, Harmonic Elimination.

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Authors: Azali Saudi, Jumat Sulaiman

Abstract:

Harmonic functions are solutions to Laplace’s equation that are known to have an advantage as a global approach in providing the potential values for autonomous vehicle navigation. However, the computation for obtaining harmonic functions is often too slow particularly when it involves very large environment. This paper presents a two-stage iterative method namely Modified Arithmetic Mean (MAM) method for solving 2D Laplace’s equation. Once the harmonic functions are obtained, the standard Gradient Descent Search (GDS) is performed for path finding of an autonomous vehicle from arbitrary initial position to the specified goal position. Details of the MAM method are discussed. Several simulations of vehicle navigation with path planning in a static known indoor environment were conducted to verify the efficiency of the MAM method. The generated paths obtained from the simulations are presented. The performance of the MAM method in computing harmonic functions in 2D environment to solve path planning problem for an autonomous vehicle navigation is also provided.

Keywords: Modified Arithmetic Mean method, Harmonic functions, Laplace’s equation, path planning.

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Authors: Daniel Zammit, Cyril Spiteri Staines, Maurice Apap

Abstract:

This paper presents a study on Proportional Resonant (PR) current control with additional PR harmonic compensators for Grid Connected Photovoltaic (PV) Inverters. Both simulation and experimental results will be presented. Testing was carried out on a 3kW Grid-Connected PV Inverter which was designed and constructed for this research.

Keywords: Inverters, Proportional-Resonant Controllers, Harmonic Compensation, Photovoltaic.

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Authors: Hanny H. Tumbelaka, Masafumi Miyatake

Abstract:

This paper proposes a three-phase four-wire currentcontrolled Voltage Source Inverter (CC-VSI) for both power quality improvement and PV energy extraction. For power quality improvement, the CC-VSI works as a grid current-controlling shunt active power filter to compensate for harmonic and reactive power of loads. Then, the PV array is coupled to the DC bus of the CC-VSI and supplies active power to the grid. The MPPT controller employs the particle swarm optimization technique. The output of the MPPT controller is a DC voltage that determines the DC-bus voltage according to PV maximum power. The PSO method is simple and effective especially for a partially shaded PV array. From computer simulation results, it proves that grid currents are sinusoidal and inphase with grid voltages, while the PV maximum active power is delivered to loads.

Keywords: Active Power Filter, MPPT, PV Energy Conversion.

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.

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Authors: Mahdi Zolfaghari, Seyed Hossein Hosseinian, Hossein Askarian Abyaneh, Mehrdad Abedi

Abstract:

This paper presents a virtual active power filter (VAPF) using vehicle to grid (V2G) technology to maintain power quality requirements. The optimal discrete operation of the power converter of electric vehicle (EV) is based on recognizing desired switching states using the model predictive control (MPC) algorithm. A fast dynamic response, lower total harmonic distortion (THD) and good reference tracking performance are realized through the presented control strategy. The simulation results using MATLAB/Simulink validate the effectiveness of the scheme in improving power quality as well as good dynamic response in power transferring capability.

Keywords: Virtual active power filter, V2G technology, model predictive control, electric vehicle, power quality.

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Joshi Manohar. V., Sujatha. P., Anjaneyulu K. S. R

Abstract:

The range of the output power is a very important and evident limitation of two-level inverters. In order to overcome this disadvantage, multilevel inverters are introduced. Recently, Cascade H-Bridge inverters have emerged as one of the popular converter topologies used in numerous industrial applications. The modulation switching strategies such as phase shifted carrier based Pulse Width Modulation (PWM) technique and Stair case modulation with Selective Harmonic Elimination (SHE) PWM technique are generally used. NR method is used to solve highly non linear transcendental equations which are formed by SHEPWM method. Generally NR method has a drawback of requiring good initial guess but in this paper a new approach is implemented for NR method with any random initial guess. A three phase CHB 11-level inverter is chosen for analysis. MATLAB/SIMULINK programming environment and harmonic profiles are compared. Finally this paper presents a method at fundamental switching frequency with least % THDV.

Keywords: Cascade H-bridge 11- level Inverter, NR method, Phase shifted carrier based pulse width modulation (PSCPWM), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv).

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Authors: Md. Alal Hosen

Abstract:

In this paper, a modified harmonic balance method based an analytical technique has been developed to determine higher-order approximate periodic solutions of a conservative nonlinear oscillator for which the elastic force term is proportional to x^1/3. Usually, a set of nonlinear algebraic equations is solved in this method. However, analytical solutions of these algebraic equations are not always possible, especially in the case of a large oscillation. In this article, different parameters of the same nonlinear problems are found, for which the power series produces desired results even for the large oscillation. We find a modified harmonic balance method works very well for the whole range of initial amplitudes, and the excellent agreement of the approximate frequencies and periodic solutions with the exact ones has been demonstrated and discussed. Besides these, a suitable truncation formula is found in which the solution measures better results than existing solutions. The method is mainly illustrated by the x^1/3 force nonlinear oscillator but it is also useful for many other nonlinear problems.

Keywords: Approximate solutions, Harmonic balance method, Nonlinear oscillator, Perturbation.

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