A new hybrid analytical model (HAM) based on conformal mapping (CM) method and magnetic equivalent circuit (MEC) model is presented in this paper for electromagnetic modelling of cage rotor induction motors (CRIMs) used in electric submersible pumps (ESPs). For every operating point, the iron parts are modelled with a non-linear MEC model to calculate the equivalent virtual currents, which represent the influence of magneto motive force (MMF) drops and MMF sources in stator and rotor cores. The effects of the equivalent virtual currents on the air-gap magnetic field are then considered using the CM method and Hague's solution. This approach for calculating the air-gap field is also used to prepare a 3-D lookup table (3-D LUT) for each element of inductance matrix and derivative of inductance matrix in terms of rotor position. These LUTs are then used for transient modelling and analysis of CRIM under no-load and loading conditions. The accuracy of proposed HAM is validated by comparing the results obtained through HAM with corresponding results obtained from finite element method and experiment set-up. K E Y W O R D S conformal mapping (CM), hybrid analytical model (HAM), inductance, magnetic equivalent circuit (MEC) model, magnetic field, magnetic saturation This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
In this paper, a nonlinear dynamic of permanent magnet synchronous machine scalar drive systems (PMSMSDS) is investigated thoroughly. At first, the mathematical dynamic model of the PMSMSDS is developed and formulated for open-and close-loop cases. Then, constant and periodic load torque are considered for the analysis of the system. The Jacobian matrix and the Poincaré mapping of the system are calculated analytically to study the feasibility of nonlinear phenomena at each point of equilibrium for constant and periodic loads, respectively. Computer simulation is used to obtain bifurcation diagram, time response, and phase plane of the state variables to investigate the complex behavior of the system by changing some parameters. It is shown that by changing the parameters of reference speed command, supply voltage range, and speed controller gain, the response of PMSMSDS state variables will be routed to limit cycle, bifurcated, and chaotic. Numerical analysis is provided to confirm the simulation results.
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