Magnetic Saturation Region Research Articles

Examination of Non-Sinusoidal Current Drive in Direct Current excited Reluctance Motor

A Direct Current excited Reluctance Motor (DCRM) powered by three-phase sinusoidal currents is expected to have a higher torque density than a Switched Reluctance Motor (SRM) powered by unipolar currents because they can achieve a greater angular variation of magnetic co-energy even in the magnetic saturation region. In this study, a non-sinusoidal current drive method for DCRM is proposed to increase torque. The non-sinusoidal current waveform is defined by a Fourier series function, and the optimum coefficients of the current function are solved using nonlinear programming. According to simulation results, the average torque of a DCRM driven by optimized non-sinusoidal current waveform is increased. Furthermore, the current balance between the armature coil and the excitation coil is investigated. As a result, the average torque is increased by up to about 25% when compared to conventinal sinusoidal current drive.

Torque Control Method for Switched Reluctance Motor based on Equivalent Inductance of Magnetic Co-energy

This paper proposes a torque ripple suppression method for a switched reluctance motor (SRM) with only measurable parameters. A large third-order torque ripple is generated via a conventional method with constant dq0-axis current, which is the dq-axis current and zero-phase current converted from the three-phase current of the SRM. The proposed method derives the zero-phase current with the third-order harmonic to suppress the torque ripple from a torque equation by considering the spatial harmonics of the inductance profile up to the fourth order and torque/current ratio in the entire region. Additionally, the average torque equation is derived from the inductance expressing the magnetic co-energy at the magnetic saturation. Consequently, the experimental results confirm that the torque ripple is reduced by 86.5% in the linear region and by 83.2% in the magnetic saturation region compared to the conventional method with the constant dq0-axis current. Finally, the derived average torque equation agrees with the experimental results, including the error of 5.2%.

Expansion of Motor High-Efficiency Area by Inserting Magnetic Composite Material into Rotor

Variable magnetic flux motors have been proposed to achieve high-efficiency operation over a wide drive range ranging from high torque to high-speed. This paper clarifies the high efficiency area expansion effect of a variable flux motor with a magnetic composite material inserted in the rotor. To achieve the effect of enlarging the maximum efficiency range, this motor uses magnetic composite materials with much lower saturation magnetic flux density and iron loss than electromagnetic steel plate. This paper reports the magnetic and mechanical properties of the magnetic composite material using Fe–Si–Al alloy, considering low iron loss. The simulation results clarified the variable magnetic flux characteristics for reducing loss at high-speed rotation by actively utilizing the magnetic saturation region of the magnetic composite material. The efficiency improvement in the high-speed region is attributed to the suppression of spatial harmonics without significantly reducing the q-axis inductance. Furthermore, the proposed motor achieves both the expansion of the high-efficiency range and relaxation of mechanical stress by increasing the thickness of the bridge part adjacent to the permanent magnet.

Modified Winding Function Analysis of Synchronous Reluctance Motor for Design Iteration Purposes

This article proposes a hybrid analytical modeling procedure for the performance parameter estimation of synchronous reluctance machine, including its operation in the region of magnetic saturation. The proposed model better estimated the torque profile through improved translation and stepped transition of rotor flux barriers. The non-linear operation is simulated by considering the global saturation and estimating the machine’s operating point on the magnetization curve of the core material. The procedure formulation focuses on improving the accuracy and rapidness of the iterative design process. The obtained results are validated against an already established design analysis technique, finite-element analysis, and the frequency spectrum analysis of practical machine results. With the improved accuracy and the least requirement of simulation runtime and computational resources, the modeling procedure can be utilized as an initial design iteration tool.

Electromagnetic Characteristic Analysis of BFSLRM

Flux concentrated structure is adopted in the design of bidirectional flux switching linear-rotary motor, which not only brings high torque/thrust density, but also increases stator iron material magnetic saturation. In order to decrease the magnetic maturation level of the motor, the stator pole width, stator pole axial length, permanent magnet (PM) width, PM axial length and stator yoke height are selected as the analysis variables, which are closely related to the two magnetic saturation regions of the stator section based on the initial analysis. The expressions of flux density in the two magnetically saturated regions of the stator core related with the selected five structure variables are derived by numerical fitting method based on the initial simulation result calculated by finite element method. Then the optimization structure variable values are achieved, a prototype and its test experiment are carried out, which verifies that the torque and thrust densities are improved and the numerical fitting method is efficient and accurate for magnetic saturation calculation.

Torque analytical model and self‐decoupling characteristics analysis of a bearingless switched reluctance motor

In this paper, a bearingless switched reluctance motor (BRSM) with sharing suspension windings, which simplifies the winding structure and reduces the complexity of the control circuit, is analysed. A torque analytical model is derived using the Maxwell stress tensor method, which provides better results, compared with the linear model in the magnetic saturated conditions. A finite element analysis (FEA) model of the prototype is built and used for comparison with the torque analytical model. The results show that the torque analytical model provides accurate results in the entire magnetic saturation region, which verify the feasibility of this model. In addition, the self-decoupling characteristics of this type of motor are illustrated using analytical model analysis, FEA and experimental analysis. The results indicate that BSRMs with sharing suspension windings can be flexibly controlled without using complex self-decoupling algorithms of conventional BSRMs. The presented work provides a theoretical basis for the control strategy.

Calculation of magnetizing and leakage inductances of induction machine using finite element method

Distinguishing between the stator and rotor leakage inductances of induction machines is a challenge, and it becomes more difficult in the case of magnetic saturation that arises in some applications such as self-excited induction generators (SEIG). This paper presents a direct and simple procedure to determine the inductances of induction machines in magnetic saturation region, by combining the experimental tests and finite element modeling of the machine at a synchronous speed. The proposed method uses radial component of the magnetic flux density in air gap to calculate the magnetizing inductance. Also, the stator slot and end-winding leakage inductances are derived by calculating the linkage flux of the stator phases for the three-phase balanced induction machine. The effectiveness of the proposed method is verified by simulation and experimental investigation of SEIG.

Analysis and design method of a combined radial–axial magnetic bearing based on asymmetric factor

Combined radial–axial magnetic bearings (MBs) use a common bias magnetic circuit to provide radial and axial bias magnetic flux. Different from separate MBs, there is a constraint relation between the radial and axial bias flux. Meanwhile, there is also a constraint relationship between the radial and axial maximum bearing capacity. Therefore, the design method for separated MB is not suitable for a combined radial-axial MB (CRAMB). In this study, a design method of the CRAMB based on an asymmetric factor was proposed. The definition of the asymmetric factor was proposed. In order to avoid the radial and axial magnetic flux into the weak magnetic field and saturation region, the optimum range of the asymmetric factor is analysed. The influence of the asymmetry factor on stiffness is analysed; the prototype designed by this method can run stably. The validity and accuracy of the design method are verified by experimental results.

A Novel Approach to MTPA Tracking Control of AC Drives in Vehicle Propulsion Systems

In today's hybrid or fully electric vehicles, two types of propulsion machines can mainly be found: induction machines (IM) and interior permanent magnet synchronous machines. They are highly utilized and operated in magnetic saturation regions where inductance parameters change nonlinearly. The energy efficiency of both drives depends strongly on the choice of reference currents within field-oriented control. The paper shows two approaches for the determination of well-adjusted current components for both machines. First, model-based optimization is performed. It uses machine models considering saturation and loss models including the inverter. Second, a newly developed online-optimization scheme based on a discrete search method is presented. Simulation results show its advantages over recently published solutions for both machine types. Finally, experimental results at a drive test bench are presented. They prove the fast convergence and correct function of the proposed method.

Design and Construction of the Main Magnet for a 230-MeV Superconducting Cyclotron

For the applications of proton therapy and proton irradiation, and based on the RD then, the construction progress and the B–H curve measurement results of the warm iron over the magnetic saturation region are outlined; the R&D of the superconducting coils system and the design of the field mapping system are also briefly introduced.

Detection of Inner Cracks in Thick Steel Plates Using Unsaturated AC Magnetic Flux Leakage Testing With a Magnetic Resistance Gradiometer

In order to ensure the safety of infrastructure, it is important to be able to detect both surface and inner cracks in the thick steel plates used. However, it is difficult to use conventional magnetic measurement techniques for inspecting inner cracks in steel because of its high permeability as well as owing to the variations in it. To solve this problem, we developed a method called unsaturated ac magnetic flux leakage (MFL) testing based on a magnetic resistance gradiometer for analyzing the inner cracks in steel. The proposed method uses a sensor probe consisting of a semicircular yoke with induction coils at each end, and a gradiometer with two anisotropic magnetic resistance sensors for detecting the components perpendicular to the steel surface. The conventional MFL testing method requires a strong power source for observing the MFL in the magnetic saturation region. In contrast, in this paper, a gradiometer-based method for detecting the differential intensity and phase is used to detect low levels of magnetic leakage using a weak power source when the test steel sample is unsaturated. During the measurements, a deep inner crack could be detected by decreasing the frequency. The line-scanned differential signal exhibited a peak just above the crack position and was observed to be depth dependent. Based on these results, the method could be used to determine the position of the crack as well as its depth.

Dynamic Models of a Self-Excited Induction Generator Taking Iron Losses Into Account: a Comparative Study

This paper deals with the development of a dynamic model of a stand-alone self-excited induction generator (SEIG) taking into account iron losses. It is important to mention that for stable operation of the SEIG, the generator has to operate in the region of magnetic saturation. As a consequence, in any accurate analysis, iron losses must be included. This is particularly the case for small induction machines, where the magnitude of the current in the resistance representing the iron losses can not be neglected compared to that of the magnetising current. The iron losses are represented by means of inserting an equivalent loss resistance in the equivalent circuit of the SEIG. Three places are commonly used to insert the iron loss resistance; in parallel with the magnetising inductance, before the stator leakage inductance or before the stator resistance. Three models are consequently developed and are applied to a 3 kW induction generator. An experimental investigation is carried out to compare the performances of these three models in terms of accuracy and time consumption.

A Fixed-Switching-Frequency Integral Sliding Mode Current Controller for Switched Reluctance Motor Drives

A fixed-switching-frequency model-based sliding mode current controller with an integral switching surface for switched reluctance motor (SRM) drives is presented in this paper. Based on the equivalent circuit model of SRM, including the magnetic saturation and mutual coupling, an integral sliding mode current controller is designed. The stability of sliding mode controller is analyzed in two scenarios: 1) one with known motor parameters and 2) the other with bounded modeling error. In order to analyze the robustness of the sliding mode controller, the motor controller parameter constraints are derived and the stability analysis is demonstrated by considering motor parameter modeling errors. The sliding mode controller is validated by both simulation and experimental results with a 2.3-kW, 6000-r/min, three-phase 12/8 SRM over the wide speed range in both linear and magnetic saturation regions. Compared to the hysteresis current controller, the sliding mode controller demonstrates comparable transient response and steady-state response in terms of torque ripples, current ripples, root-mean-square error of current and torque. Moreover, the sliding mode controller has some advantages over the hysteresis controller, including constant switching frequency and much lower sampling rate.

An Offline Torque Sharing Function for Torque Ripple Reduction in Switched Reluctance Motor Drives

In this paper, an offline torque sharing function (TSF) for torque ripple reduction in switched reluctance motor (SRM) drives over a wide speed range is proposed. The objective function of an offline TSF is composed of two secondary objectives with a Tikhonov factor to minimize the square of the phase current (copper loss) and derivatives of current references (rate of change of flux linkage). The proposed TSFs with different Tikhonov factors are compared with the conventional TSFs including linear, cubic, and exponential TSFs in terms of efficiency and torque-speed performance while operating in both magnetic linear and saturation regions. Then, the Tikhonov factor is selected based on a tradeoff between the copper loss and torque-speed performance. The maximum torque-ripple-free speed of the selected offline TSF is validated to be seven times as high as the best case in these conventional TSFs. The performance of the offline TSF is verified by simulations and experiments with a 2.3-kW, three-phase 12/8 SRM. Results show that the proposed offline TSF can significantly reduce the torque ripple of SRM without increasing copper loss over a wide speed range.

Modeling and Simulation of a 16/12 Double Stator Switched Reluctance Motor

Abstract. Modeling of a switched reluctance motor (SRM) is to predict the motor performance with a reasonable estimate over a wide range of speed and torque. Obtaining the realistic model of SRM which operates in a region of magnetic saturation due to complex structural implementation progress is too complicated process, with long response time. This paper introduces a linear model of double-stator SRM (DSSRM) which will be applied on direct-drive washing machine application. The proposed method uses a developed simple magnetic equivalent circuit for modeling a DSSRM. The electromagnetic characteristics of the designed DSSRM are analyzed by finite element method (FEM) to validate the extracted results of the model. Finally, the experimental results with appropriate accuracy are achieved for modeling and magnetic analysis of the evaluated DSSRM.

Mathematical modeling of a novel bearingless switched reluctance motor

Purpose – The novel bearingless switched reluctance motor (BSRM) is proposed recently, which is different from the conventional BSRM in the stator structure and suspension winding arrangement. The reduced number of suspension windings makes the novel BSRM much simpler, so that the control circuit and algorithm are greatly simplified when compared to those of the conventional BSRM. This paper for the first time proposes the novel BSRM's analytic model, including the mathematical relationships among the winding currents, rotor angle, radial forces, and motor torque, to further achieve the suspending forces and torque control. The paper aims to discuss these issues. Design/methodology/approach – The magnetic equivalent circuit method is employed to obtain the self-inductances and mutual-inductances of the motor torque windings (main windings) and suspension windings (control windings). The straight flux paths are combined with the elliptical fringing flux paths to calculate the air-gap permeances, and the stored magnetic energy. Then, the mathematical expressions of radial forces and torque are derived. A novel BSRM prototype is analyzed through using the proposed analytical model and the finite element model. The results of both methods are compared to verify the proposed mathematical model. Findings – The proposed mathematical model of the novel BSRM considering unsaturated magnetic circuits is verified by finite-element analysis results. Research limitations/implications – The mathematical model represents the situation of magnetic circuit unsaturated and is not suitable for the magnetic circuit saturation. It cannot be used to control the motor which is working in the deep magnetic circuit saturation region. Practical implications – Building mathematical model is a necessary step for the motor's suspension and rotating control. The built model provides the fundamental for the preliminary control algorithm and experimental study of this novel BSRM. Originality/value – For the first time, the novel BSRM's mathematical model is proposed. It provides necessary fundamental for the motor's further analysis, design, and suspending and rotating controls.

Special features of linear magnetic birefringence in an α-Fe2O3:Ga single crystal

Experimental investigations of the field dependence of the linear magnetic birefringence (LMB) in an α-Fe2O3:Ga single crystal are presented. It is established that during crystal magnetization in the basal plane near directions perpendicular to the С2 axes in the region of magnetic field saturation, the LMB changes nonmonotonically. The observed special feature of the field LMB dependence is due to the reorganization of the magnetic α-Fe2O3:Ga structure during magnetization.

Characteristic Measurement System for Automotive Class Switched Reluctance Machines

Flux-linkage characteristics and torque characteristics (versus current and rotor position) of switched reluctance machines (SRM) can be regarded as the fingerprint of SRMs because they are indispensable fundamental data to model machine behavior for both simulation and control proposes. In contrast to other types of electrical machines, e.g. induction machines and synchronous machines, SRMs are basically characterized by a strongly nonlinear behavior due to typical operation in the magnetic saturation region. Hence, no analytical functions can be applied to describe the characteristics of SRMs precisely. An accurate SRM model inevitably needs the complete machine characteristics in form of data-intensive look-up tables to represent the machine behavior. Basically, the SRM characteristics can be calculated by Finite Element (FE) simulation. However, real SRM characteristics can be different from the simulation model due to secondary effects, e.g. non-uniform material and manufacturing tolerances, which are normally not considered in the FE-simulation model. Therefore, the experimental measurement is preferred. Measuring and preparing the SRM characteristics is a complicated and time-consuming task. The time-expense as well as possible human errors in determining the SRM characteristics can be greatly minimized, if the measurement procedures are automated.This paper presents an automated characteristic measurement system for determining SRM characteristics experimentally. The measurement system was designed for automotive class SRMs, e.g. starter-generators, hybrid or main propulsion motors. The applied measurement methods, the system design and construction are described in the paper. Furthermore, constraints and discussions concerning the measurement accuracy are treated.

Operation of induction generator in the magnetic saturation region as a self-excited and as a double output system

This paper presents the development of two dynamic models for simulating the operation of an induction machine with saturation considered, operating either as self-excited or as double output induction generator in autonomous wind systems. Both systems’ steady state as well as transient performance during switching on and off from the bank of capacitors or the power line, respectively, is studied considering different wind speed and excitation conditions. A polynomial approximation of the variation of mutual inductance versus magnetizing current is used for the proper account of the effects of core saturation. The transient voltage and current built-up of the two systems, the harmonic distortion as well as the damping of the transient process are obtained from a laboratory autonomous wind generating system. From a comparison between the outputs generated by the two systems the results show that the double output induction generator can be installed for the better use of the wind energy.

Radial Force and Torque of a Bearingless Switched Reluctance Motor Operating in a Region of Magnetic Saturation

Bearingless switched reluctance motors, which can control rotor radial positions with magnetic force, have been proposed. These motors are characterized by integration of switched reluctance motors and magnetic bearings. It is essential for a control system to consider magnetic saturation in real time in order to realize stable operation at a full torque load. Thus, this paper proposes a method for fast calculation of radial force and torque of a bearingless switched reluctance motor operating in a region of magnetic saturation. It is shown experimentally that the proposed method is effective in calculating the radial force and the torque under conditions of magnetic saturation.