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Electric machines emulators (EMEs) based on hardware-in-the-loop (HIL), which effectively act as emulators to mimic the actual motor behavior of Interior Permanent Magnet (IPM) machines. EME is frequently used to evaluate motor controller and motor control methodologies prior to development. The inverse magnetization motor model, which is used as the basis for real-time simulation in this paper's proposal for an electric machine emulator system based on HIL, uses FEA to create the motor model data. The nonlinear features of the motor may be successfully replicated with this motor model, and the accuracy of the electric machine emulator can be enhanced by using a straightforward and trustworthy motor controller. The real-time simulation tool typhoon HIL is used in the study to develop a hardware-in-the-loop simulation platform for an IPM electric machines emulator.
Copyright: 2024 Guo et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Machines emulator is composed of electronic components and a real-time simulation device running the motor model, which can modify the motor parameters and load according to the test requirements. The EME replaces the real motor connected to the motor controller under test, simulates the output characteristics of the motor under different operating conditions at the port, and completes the motor controller test safely and undamaged. In terms of the input port of the test devices, the EME resembles to a genuine motor. In addition, motor control scheme testing at the pre-development stage can help to decrease development time and faults, making electric machines emulator research highly significant for real-world industrial applications [8].
To solve the drawback of time-consuming finite element real-time simulation, analyzing the variation of d-q axis Flux linkage with d-q axis current as well as rotor position by finite element and applying the simulation results to the motor simulator by curve fitting function is an effective solution [22].
In order to solve the above problems, a nonlinear motor model with high fidelity, considering IPM magnetic saturation, space harmonics and cross-coupling is proposed in this paper, based on the Flux Linkages of the motor. The core parameters of the motor model are obtained from finite element calculations, and the nonlinear factors such as magnetic saturation, cross-saturation, cross-coupling, and cogging torque are reflected by the nonlinear relationships of inductance, Flux Linkages, and torque with current and rotor position. Compared with other modeling approaches, the motor model proposed in this paper does not require FEA online simulation, and the nonlinear parameters of the motor are stored in tables that can be used offline; and combines the advantages of simple mathematical model form to simplify the derivation of equations and reduce the amount of table data generated by FEA results, which is simple to implement and improves the model accuracy and simulation efficiency. In addition, a simple and reliable current tracking algorithm is used to control the inverter to accurately track the commanded current to ensure the speed and accuracy of the electric machine emulator current tracking. The real-time simulation device running the motor model is connected to the device under test, making up a HIL real-time simulation platform with simple and easy to implement features.
The organization of this paper is as follows. Section 2 presents an overview of the electric machines emulator system architecture. Section 3 presents the theoretical analysis and modeling process based on the Flux Linkages nonlinear motor model. Section 4 presents the electric machines emulator controller design, containing improved internal mode control and the Luenberger torque observer. Section 5 presents the real-time simulation of the proposed system as a means of validation, and the section contains the transient and steady-state experimental results are analyzed and discussed. Section 6 finally concludes this paper.
The nonlinear simulation model of a motor serves as the foundation for the electric machine emulator constructed during this research, which produces the needed current by sampling the port voltage as an input variable. This study refers to the EME of this mode as the VTC (Voltage to Current) mode as the three-phase inverter utilized to replicate the electrical characteristics of the motor is similar to a regulated current source in this case. The indicated electric machines emulator in this study aims to evaluate the motor controller and drive inverter in all respects in a lossless environment.
With the goal to emulate the port characteristics of the permanent magnet synchronous motor, Fig 1 shows a three-phase voltage inverter with base L filtering coupled to the driver that will be presented to the test. The rotor winding of the virtual motor is symbolized by the inverter circuit in the structural block diagram of the electric machines emulator, the induced electric potential is constituted by the capacitance of the filtered coupling circuit, the stator inductance is indicated by the inductance L of the filtered coupling circuit, and the internal resistance R of the inductor L is referred to by the virtual permanent magnet synchronous motor.
An architecture that mimics voltage input-current output is chosen for the electric machines simulation system that is suggested in this study. The motor model contains information obtained through finite element simulation and run in the form of an offline look-up table model that is related to the magnetic saturation of the machine, geometrical characteristics, spatial harmonics, etc. The motor modeling principles will be further discussed in Section III. Results of the motor simulation have a high degree of realism and precision since the process of simulation specified in the article employs a dynamic model of the motor. Additionally, a simple L-filter links the controller under test with the motor simulation device. Accurate command current acquisition and port control form the basis of the motor simulator in VTC mode. The proposed motor simulator system in the present study is set using a simple and durable current tracking control method. The next sections supply an explanation of the design process and analysis for the controller in an active control mode.
The voltage and torque equations for the d-q axis, as described in Eq (1) and Fig 2, are a basis of the conventional modeling approach used for PMSM in the literature. A more standard magnetic circuit model, the conventional motor d-q axis model advantages include easy the calculation and a distinct relationship between motor the features.
Where ud,uq,id,iq are the voltages and currents in the d-q axis, Ld,Lq are the self-inductances in the d-q axis. ψf is the permanent Flux linkage, R is the motor stator resistance, ωe is the electric angular velocity, and p is the number of pole pairs.
The cross-direct axis inductance parameters of the PMSM are subject to nonlinearity with the change in cross- and direct-axis currents as the conventional PMSM linear modeling is based on the voltage equation noted by self-inductance. The common linear motor model, on the contrary fingers, ignores the saturation of the magnetic circuit and the cross-coupling between parameters and only considers consideration of the air-gap Flux Linkages and the basic component of the inductance. As the result, the actual motor and such a motor model might not appear to be precisely the same. The permanent magnet synchronous motor is a high-order, multivariable, nonlinear, and complex system in actual operation, and the conventional linear model can no longer satisfy the requirements of a high-precision, high-performance motor simulator system. These effects consist of space harmonics, magnetic circuit saturation, cross-saturation, and cross-coupling. Further, the model and its state parameters are too flawless and the simulation time scale in off-line simulation technology does not precisely correspond the actual time, which makes it difficult bringing about the veracity and confidence of simulation conclusions.
This common model is still mostly in differential form and is commonly referred to as the direct modeling a position of positive magnetization. With the linear motor model, the FEA model can obtain the Flux Linkages as long as the current and rotor position are included. This three-phase look-up table model utilizes a total of 36 differential expressions, three a variety of impedance tables, and nine offline tables. The model has an all-time high parameter the requirement and a poor model simulation efficiency.
In order to solve the above problems, a reverse magnetization PMSM model is proposed in this paper, based on magnetic flux as the state variable. The dynamic block diagram of the motor model is shown in Fig 3.
To describe it more intuitively, the equation of the Flux linkage is rewritten in matrix form. Meanwhile, to account for the cross-coupling effect between inductors, the effect of motor cross mutual inductance is added on this basis, and the matrix form of the Flux linkage equation is finally obtained as shown in Eq (3).
To determine the parameters considering the spatial harmonics, the FEA results, including the rotation angle θ are applied to the PMSM model. Thus, the self-inductance model can be expressed as a function of θ. Therefore, the voltage equation can be rewritten as in Eq (5).
Based on the above equation, this paper modeling in the integral form first needs to inverse the relationship to get, which is called the inverse magnetization modeling method, and its simulation is faster and more accurate compared to the differential form. Compared with the traditional linear model, the chain-based inverse magnetization PMSM model is shown in Fig 4 can reflect the nonlinear characteristics of the motor magnetic circuit saturation, cross-saturation, cross-coupling, tooth slot torque, etc.; compared with the three-phase finite element look-up table model, the motor Flux linkage model only requires two Flux linkages and two inductance tables, which greatly reduces the number of parameters required for the model, and combines the advantages of simple mathematical model form with the real-time.
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