Modeling and Semi-Analytic Stability Analysis for Dynamics of AC Machines

In this article, a semi-analytical technique is proposed to predict stable sustained periodic responses of AC electrical machines. Based on such desired outputs, the proper selections of machine variables are captured, such as the perturbation parameter arisen from the relative movement between the stationary and rotating parts. Compared to the experimental results, the derived analytical results are relatively well-fitted with the studied practical cases.

[1]  Mohamed El-Borhamy,et al.  On the existence of periodic solution and the transition to chaos of Rayleigh-Duffing equation with application of gyro dynamic , 2020 .

[2]  Essam M. Rashad,et al.  Modeling and design considerations of a photovoltaic energy source feeding a synchronous reluctance motor suitable for pumping systems , 2012 .

[3]  Danny Sutanto,et al.  Steady-state and transient analysis of self-excited induction generators , 1989 .

[4]  Mohamad Reza Banaei,et al.  Dynamic modeling of wind turbine based axial flux permanent magnetic synchronous generator connected to the grid with switch reduced converter , 2015 .

[5]  Shingo Ito,et al.  Noise analysis and efficiency improvement of a pulse-width modulated permanent magnet synchronous motor by dynamic error budgeting , 2017 .

[6]  Ji-Huan He,et al.  Variational iteration method for autonomous ordinary differential systems , 2000, Appl. Math. Comput..

[7]  Mohammad Mehdi Rashidi,et al.  The modified differential transform method for investigating nano boundary‐layers over stretching surfaces , 2011 .

[8]  A. L. Mohamadein,et al.  Analysis of series-connected wound-rotor self-excited induction generator , 1993 .

[9]  H. Bremer,et al.  Instability maps of a system of Mathieu‐Equations using different perturbation methods , 2011 .

[10]  J. Cole,et al.  Approximate solutions to Mathieu's equation , 2017, Physica E: Low-dimensional Systems and Nanostructures.

[11]  Ivana Kovacic,et al.  Mathieu's Equation and Its Generalizations: Overview of Stability Charts and Their Features , 2018 .

[12]  David Rakhmilʹevich Merkin,et al.  Introduction to the Theory of Stability , 1996 .

[13]  Jose Antonio Sanchez,et al.  Simultaneous measurement of forces and machine tool position for diagnostic of machining tests , 2005, IEEE Transactions on Instrumentation and Measurement.

[14]  Ji-Huan He.  Variational iteration method—Some recent results and new interpretations , 2007 .

[16]  A. K. Gupta,et al.  Comparison between homotopy perturbation method and optimal homotopy asymptotic method for the soliton solutions of Boussinesq–Burger equations , 2014 .

[17]  Y. Gong,et al.  Estimation of Rotor Temperature of Permanent Magnet Synchronous Motor Based on Model Reference Fuzzy Adaptive Control , 2020 .

[18]  D. Baleanu,et al.  The variational iteration method for solving n-th order fuzzy differential equations , 2012 .

[19]  Mohamed El-Borhamy,et al.  Chaos Prediction in Fractional Delayed Energy-Based Models of Capital Accumulation , 2021, Complex..

[20]  Abdul-Majid Wazwaz,et al.  The variational iteration method for solving linear and nonlinear ODEs and scientific models with variable coefficients , 2014 .

[21]  Abdul-Majid Wazwaz,et al.  The variational iteration method for analytic treatment for linear and nonlinear ODEs , 2009, Appl. Math. Comput..

[22]  Hossein Jafari,et al.  A new method for calculating general lagrange multiplier in the variational iteration method , 2011 .

[23]  S. Abbasbandy,et al.  New perturbation‐iteration solutions for nonlinear heat transfer equations , 2012 .

[24]  On the existence of new integrable cases for Euler-Poisson equations in Newtonian fields , 2019, Alexandria Engineering Journal.

[25]  Mohamed El-Borhamy,et al.  Floquet analysis of linear dynamic RLC circuits , 2020, Open Physics.

[27]  Vasile Marinca,et al.  On the flow of a Walters-type B’ viscoelastic fluid in a vertical channel with porous wall , 2014 .

[28]  Rui Shao,et al.  Robust Fault Detection for Permanent-Magnet Synchronous Motor via Adaptive Sliding-Mode Observer , 2020 .

[29]  N. Mahmoudian,et al.  Energy-rate method and stability chart of parametric vibrating systems , 2008 .

[30]  Kaiyuan Hou,et al.  Steady-State Stability of Sending-End System with Mixed Synchronous Generator and Power-Electronic-Interfaced Renewable Energy , 2020 .

[31]  A. L. Mohamadein,et al.  Application of Floquet's theory to the analysis of series-connected wound-rotor self-excited synchronous generator , 1993 .

[32]  N. Herisanu,et al.  Optimal Homotopy Perturbation Method for a Non-Conservative Dynamical System of a Rotating Electrical Machine , 2012 .

[33]  Ji-Huan He,et al.  Variational iteration method: New development and applications , 2007, Comput. Math. Appl..

[34]  Nicolae Herisanu,et al.  Dynamic Response of a Permanent Magnet Synchronous Generator to a Wind Gust , 2019, Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems.

[35]  Klaus Zeman,et al.  Hierarchical design models in the mechatronic product development process of synchronous machines , 2010 .

[37]  Saeid Abbasbandy,et al.  Determination of optimal convergence-control parameter value in homotopy analysis method , 2013, Numerical Algorithms.

[38]  I. A. M. Abdel-Halim,et al.  A Novel Approach for the Analysis of Self-Excited Induction Generators , 1999 .

[39]  Mohamed El-Borhamy.  Chaos transition of the generalized fractional duffing oscillator with a generalized time delayed position feedback , 2020, Nonlinear Dynamics.

[40]  Mohamed El-Borhamy,et al.  Stability Analysis Of Delayed Fractional Integro-Differential Equations With Applications Of RLC Circuits , 2020 .