Magnetic Cross Saturation Research Articles

Virtual-Axis Injection Based Online Parameter Identification of PMSM Considering Cross Coupling and Saturation Effects

Existing online parameter identification methods of permanent magnet synchronous motors (PMSMs) are generally based on the voltage equations, the precision of which is affected by the cross coupling and magnetic saturation effects. In order to deal with this issue, a virtual-rotary-axis high-frequency signal injection (VHFSI) based online parameter identification method is proposed in this paper, where the cross coupling and magnetic saturation effects on the traditional d-q axis model are analyzed. On this basis, an optimized voltage model under the composite magnetic field rotary axis is introduced. In the proposed method, the cross-coupling angle and the d-q axis inductances can be identified by injecting the high-frequency signal into the constructed virtual rotary axis. In addition, the complex Simpson integral algorithm is adopted to obtain the information of the incremental and apparent inductances. Finally, the permanent magnet flux linkage can be estimated based on the composite magnetic field rotary axis voltage equations. The effectiveness and feasibility of the proposed method are verified by the experiments on a 2.2-kW PMSM drive.

Analysis of Test Results of the Developed Synchronous Reluctance Motor for Public Transport Application

Abstract The paper describes the design and control method of the synchronous reluctance machine with improved efficiency compared to traction induction motor for electric vehicle application. Magnetic field finite element modelling is used in the design process. The paper presents load characteristics calculation method for the design process, considering the cross magnetic saturation effect. Control algorithm with constant d-axis current control method is developed in the research. The prototype of the machine is constructed and tested.

Mathematical Models of Synchronous Reluctance Motor Considering Iron Loss and Cross-Magnetic Saturation with Reciprocity Relation of Mutual Inductance

A unique approximation function for the d- and q-axes inductances for a synchronous reluctance motor (SynRM) is shown. This inductance approximation function has excellent features, such as continuous and differentiable over the entire current range when taking into account cross-magnetic saturation and satisfactory reciprocity relation of the mutual inductance. It is also possible to derive an equivalent inverse inductance function that can estimate the d- and q-axes currents from d- and q-axes stator flux linkages. Using the proposed inductance approximation function, the authors derive two mathematical models. The first is a strict model in which the state and input variables are the respectively load current and stator voltage. The second is a simple model in which the state and input variables are respectively the flux linkage and stator voltage, which are derived using the equivalent inverse inductance function. These models are applied to simulate the transient performances considering the iron loss and cross-magnetic saturation. The experimental and simulated results with a flux-barrier SynRM validate the proposed method.

Image Registration Technique to Improve a Self-Sensing Estimation for Model Predictive Controlled Interior PMSM Drives

Current responses based self-sensing control estimates rotor position by detecting magnetic saliency of a machine. However, the estimation error can be resulted from several nonideal factors, especially magnetic cross-saturation, as effects of these factors show up in current responses. This article applies image registration technique to improve the accuracy of a self-sensing estimation for model predictive control (MPC) interior permanent magnet synchronous machines (IPMSM) drives by minimizing impacts of nonideal factors on measured current responses. In commissioning process, two images are generated. The inverter voltage vectors in MPC excite current responses, represented by a set of vectors that generate a response image. Nonideal factors that result in estimation errors also deform the response image. A primitive image based on resolver output can be considered as a template. An image registration technique is investigated to register deformed images with corresponding primitive images, and transformations contain operations of rotation, scale, translation, and shear can be derived. During the drive, the deformed pixel points are online mapped to new pixel points by applying these operations. The current responses after transformation are less subject to nonideal factors. As a result, impacts of these deformation factors that contribute to estimation errors can be reduced. Finally, the application of image registration technique to the self-sensing estimation is verified on a 3.7-kW IPMSM drive.

Lagrangian Model of an Isolated DC-DC Converter With a 3-Phase Medium Frequency Transformer Accounting Magnetic Cross Saturation

This article presents a nonlinear equivalent circuit model of an isolated dc-dc converter with a 3-phase medium frequency transformer. The model takes into account the magnetic cross saturation of the 3-phase core-type magnetic circuit. The model is suitable in detailed electromagnetic transient simulations of power systems involving isolated dc-dc converters. The model is developed using the Lagrange energy method. It involves a matrix of dynamic inductances containing a nonlinear term resulting from core magnetization and a linear term resulting from leakage flux. The model parameters are determined based on a series of magnetostatic finite element method simulations. This approach is convenient when applied to high power transformers offering a limited characterization effort, or if the transformer prototype does not exist. The experimental validation performed on a novel 3-phase MFT prototype in a 100 kW 1.2 kV 20 kHz dual active bridge converter has proved the validity of the model and model parameters. The no-load steady-state and inrush tests and the full-load test show a very good fit between the simulated and experimentally measured waveforms. The comparison with a classical simplified model neglecting magnetic cross saturation shows a significant difference in the no-load inrush test.

Dynamic DC-link Voltage Adjustment for Electric Vehicles Considering the Cross Saturation Effects

The demands of remarkable reliability and high power density of traction systems are becoming more and more rigorous. The conflicting requirements imposed on the control strategy are higher accuracy and higher efficiency over the whole speed range. However, parameter variations caused by the cross coupling and magnetic saturation effect (omitted from the cross saturation effects in the following) are usually neglected in conventional control strategies, which could reduce the control precision. In order to fully consider the influence of parameter changes on the motor control and derive an approach that could realize the maximum efficiency during the whole speed range, this paper proposes a dynamic DC-link voltage adjustment strategy considering the cross coupling and magnetic saturation effects. The strategy can be categorized into three parts. Firstly, the torque request is transformed to the optimal current reference signal. Secondly, the differences between the setpoint and the real-time feedback signals of torque and voltage can be applied in the linearized function in the did,q coordinate. The solution guides the current vector into the optimal direction under the current and voltage limits to ensure the safety and reliability of the motor. Finally, last, the bus voltage can be modified according to the asked terminal voltage. A 10 kW prototype which instrumented a bidirectional DC-DC converter to regulating the bus voltage has been studied. The simulation and experiment results verify that the proposed control strategy can reduce the inverter losses in low speed region by offering the low bus voltage and track the actual maximum torque control trace more accurately, meanwhile, the flux weakening region can be delayed in high speed region by applying a high bus voltage. It helps the motor realize the high utilization rate of the DC-link voltage and guarantees the system reliability and robustness.

A Novel Optimal Current Trajectory Control Strategy of IPMSM Considering the Cross Saturation Effects

Abstract: The nonlinearity and uncertain variation of machine parameters are always caused by cross coupling and magnetic saturation effects, which are easily neglected in the conventional control strategy. In this paper, a current trajectory control strategy (CTCS) is proposed to take the cross coupling and magnetic saturation effects into account under voltage and current constraints. It can be considered as a calculating method considering parameter variation and separating among each iteration step which treats the calculated result of the former step as the initial value of the next step. At first, the torque command is translated into the current reference. Then, the increments between the target value and real value of the torque and the voltage are respectively calculated, which are subsequently converted into the current modification vector in did, diq framework for further analysis. In order to take the influence caused by cross coupling and magnetic saturation effects on the CTCS into consideration, self and mutual inductances are analyzed by finite element analysis (FEA). The results of the simulation and experiment show that the rapid response and robustness on reference speed variation could be achieved by employing the proposed CTCS, and the seamless switching between the constant torque and flux-weakening operation can also be realized.

Modeling of a Dual Stator Induction Generator with and Without Cross Magnetic Saturation

This paper discusses general methods of modelling magnetic saturation in steady-state, two-axis (d & q) frame models of dual stator induction generators (DSIG). In particular, the important role of the magnetic coupling between the d-q axes (cross-magnetizing phenomenon) is demonstrated, with and without cross-saturation. For that purpose, two distinct models of DSIGs, with and without cross-saturation, are specified. These two models are verified by an application that is sensitive to the presence of cross-saturation, to prove the validity of these final methods and the equivalence between all developed models. Advantages of some of the models over the existing ones and their applicability are discussed. In addition, an alternative is given to evaluate all saturation factors (static and dynamic) by just calculating the static magnetizing inductance which is simply the magnitude of the ratio of the magnetizing flux to the current. The comparison between the simulation results of the proposed model with experimental results gives a good correspondence, especially at startup.

Maximum Efficiency Drives of Synchronous Reluctance Motors by a Novel Loss Minimization Controller With Inductance Estimator

This paper presents a method to maximize the driving efficiency of synchronous reluctance motors (SynRMs) having cross-magnetic saturation effects. A novel loss minimization controller that generates the optimum current vector is proposed. In the proposed controller, either an off- or online inductance estimator can be adopted. In both cases, the proposed controller can determine the optimum current vector quickly and automatically, and is capable of both maximizing the driving efficiency and also realizing high-precision torque control. In addition, when the proposed controller with the online inductance estimator is employed, a troublesome offline inductance measurement test is omissible. The validity of the proposed method is verified from simulation and experimental results on a 1.1-kW flux-barrier-type SynRM.

Low-Speed Sensorless Control With Reduced Copper Losses for Saturated PMSynRel Machines

Permanent-magnet-assisted synchronous reluctance (PMSynRel) machines are generally well suited for sensorless operation at all speeds since the rotor topology possesses a magnetic saliency. However, magnetic saturation can result in a vanishing differential saliency which renders sensorless control at certain operating points difficult (or even impossible) at low speed. In this paper, an optimization procedure, based on results from finite-element (FEM)-based simulations, is proposed. As output, current reference trajectories are obtained in which copper losses are kept at minimum, while the capability for sensorless control is still maintained. The results from the FEM-based simulations are in good agreement with the corresponding experimental results. For the experimental prototype in consideration, the torque limit when operating sensorless at low speed is increased substantially from below 45% to around 95% of its rated value with only slightly increased copper losses. Additionally, the impact of position-dependent harmonics on the magnetic cross saturation (affecting the steady-state position estimation error) is found to be substantial. This highlights that this spatial variation should be taken into consideration for accurate prediction of performance during sensorless operation even if the winding of the machine is of the conventional distributed type.

Analytical Study Considering Both Core Loss Resistance and Magnetic Cross Saturation of Interior Permanent Magnet Synchronous Motors

This paper presents a method for evaluating interior permanent magnet synchronous motor (IPMSM) performance over the entire operation region. Using a d-q axis equivalent circuit model consisting of motor parameters such as the permanent magnetic flux, copper resistance, core loss resistance, and d-q axis inductance, a conventional mathematical model of an IPMSM has been developed. It is well understood that in IPMSMs, magnetic operating conditions cause cross saturation and that the iron loss resistance - upon which core losses depend - changes according to the motor speed; for the sake of convenience, however, d-q axis machine models usually neglect the influence of magnetic cross saturation and assume that the iron loss resistance is constant. This paper proposes an analysis method based on considering a magnetic cross saturation and estimating a core loss resistance that changes with the operating conditions and speed. The proposed method is then verified by means of a comparison between the computed and the experimental results.

On-line Parameter Estimation Method for IPMSM Based on Decoupling Control

This paper proposed on-line parameter estimation method to compensate the magnetic cross-saturation effect on the interior permanent magnet synchronous motor (IPMSM) control system for electric vehicle. The decoupling control model for IPMSM with magnetic saturation compensation based on SVPWM (Space Vector PWM) method is established. Though comparing the simulation results between model with saturation compensation of parameter estimation and ones without saturation compensation, it is verified that the control performance with saturation compensation is more stable and more accurate than that of without compensation over speed operating region especially at higher speed. The on-line parameter estimation method based on decoupling control improves the system following-up performance, robustness and the control accuracy effectively.

A method to determine direct‐ and quadrature‐axis inductances of permanent magnet synchronous motors

AbstractThe equivalent circuit constants of permanent magnet synchronous motors are needed in the calculation of operation characteristics, construction of a control system, etc. These constants can be computed from the data on structural form and materials. However, measurements are necessary to obtain highly precise values. Methods for measurement of the d‐ and q‐axis inductances can be roughly divided into rotational and standstill methods. The standstill methods have the advantage that they are easy to carry out. However, it is difficult to consider magnetic saturation and distortion of the change in the armature winding inductance. The accuracy of the standstill method can be improved if these effects can be readily taken into account.This paper describes a standstill method for measuring accurate d‐ and q‐axis synchronous inductances of permanent magnet synchronous motors. By utilizing the fact that the EMF interference terms in the motor voltage equation considering the distortion of the inductance change are equal to zero when the rotor is in a specific position, the proposed method determines the inductances considering both magnetic saturation and inductance distortion effects from simple off‐line standstill testing. In addition, this method is capable of taking cross‐magnetic saturation into account when used with the necessary testing equipment. The proposed method was implemented on a 0.4‐kW interior permanent magnet synchronous motor with concentrated stator winding. The validity of the proposed method was demonstrated by comparing the measured and calculated results of the no‐load and on‐load characteristics. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(3): 41–50, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20969

Inductance Calculation Method of Synchronous Reluctance Motor Including Iron Loss and Cross Magnetic Saturation

This paper presents the novel method inductance calculation of a synchronous reluctance motor (SynRM). Synchronous inductances (Ld and Lq) are exceedingly important factor of SynRM to drive. Because of self axis current as well as the other axis current, inductances of d-axis and q-axis of SynRM are varied. Using an equivalent circuit model for expressing d-axis and q-axis inductance variation, the authors elicit suitable equation considering iron loss and cross magnetic saturation. Parameters of motor to use calculation are gained by AC signal test.

永久磁石同期モータの直軸および横軸インダクタンス算出法

The equivalent circuit constants of permanent magnet synchronous motors are needed in the calculation of operation characteristics, construction of a control system, etc. These constants can be computed from the data on structural form and materials. However, measurements are necessary to obtain highly precise values. Methods for measurement of the d- and q-axis inductances can be roughly divided into rotational and standstill methods. The standstill methods have the advantage that they are easy to carry out. However, it is difficult to consider magnetic saturation and distortion of the change in the armature winding inductance. The accuracy of the standstill method can be improved if these effects can be readily taken into account. This paper describes a standstill method for measuring accurate d- and q-axis synchronous inductances of permanent magnet synchronous motors. By utilizing the fact that the EMF interference terms in the motor voltage equation considering the distortion of the inductance change are equal to zero when the rotor is in a specific position, the proposed method determines the inductances considering both magnetic saturation and inductance distortion effects from simple off-line standstill testing. In addition, this method is capable of taking cross-magnetic saturation into account when used with the necessary testing equipment. The proposed method was implemented on a 0.4-kW interior permanent magnet synchronous motor with concentrated stator winding. The validity of the proposed method was demonstrated by comparing the measured and calculated results of the no-load and on-load characteristics. © 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 171(3): 41–50, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20969

A Predictive Torque Control for the Synchronous Reluctance Machine Taking Into Account the Magnetic Cross Saturation

A predictive torque and flux control algorithm for the synchronous reluctance machine is presented in this paper. The algorithm realizes a voltage space phasor preselection, followed by the computation of the switching instants for the optimum switching space phasor, with the advantages of inherently constant switching frequency and time equidistant implementation on a DSP-based system. The criteria on how to choose the appropriate voltage space phasor depend on the state of the machine and the deviations of torque and flux at the end of the cycle. In order to obtain an appropriate model of the machine, it has been developed on a d-q frame of coordinates attached to the rotor and takes into account the magnetic saturation in both d-q axes and the cross-saturation phenomenon between both axes. Therefore, high-performance torque control is achieved, and the torque ripple is reduced. Simulated and experimental results using a DSP/field-programmable-gate-array-based control and a commercially available machine show the validity of the proposed control scheme

A Method to Calculate Transient Characteristics of Synchronous Reluctance Motors Considering Iron Loss and Cross-Magnetic Saturation

This paper presents a method to calculate the transient characteristics of synchronous reluctance motor (SynRM). Using an approximate equation suitable for expressing d- and q-axes inductance variation, the authors derive a nonlinear state equation considering both iron loss and cross-magnetic saturation. All electrical motor parameters used for the calculation are measured from tests. Calculation results on transient and steady-state characteristics of a vector-controlled flux-barrier type 1.1-kW SynRM are verified with experimental results.

A Three-Phase Core-Type Transformer Iron Core Model With Included Magnetic Cross Saturation

A Three-Phase Core-Type Transformer Iron Core Model With Included Magnetic Cross Saturation

Maximum Efficiency Operation of Vector-Controlled Synchronous Reluctance Motors Considering Cross-Magnetic Saturation

The direct and quadrature axes inductances of flux barrier type Synchronous Reluctance Motors (SynRM) change depending on the magnitude of both direct and quadrature axes currents under the influence of the cross-magnetic saturation. This paper presents a maximum efficiency operation method of SynRMs with cross-magnetic saturation. An improved approximate equation that accurately expresses the inductance variation caused by cross-magnetic saturation is utilized for calculating the Maximum Efficiency Operation Current (MEOC, i.e., the d-axis current at maximum efficiency) at each load point. A vector control system in which the steady-state driving efficiency is maximized by selecting a d-axis current command from the obtained MEOC is shown. By considering cross-magnetic saturation the proposed method not only maximizes the efficiency but also improves the torque control accuracy. The validity of this method is demonstrated with calculated and measured results of on-load characteristics.

Determination of direct and quadrature axis inductances of synchronous reluctance motors with allowance for cross saturation

AbstractThe d‐axis inductance of reluctance motor is affected by not only the d‐axis current but also the q‐axis current, because of cross magnetic saturation between the direct and quadrature axes. This situation is similar for the q‐axis inductance. The authors propose a method to determine the d‐axis inductance related to the d‐ and q‐axis currents and the q‐axis inductance related to the d‐ and q‐axis currents from a standstill test. This method involves the following four steps. First a rectangular‐wave voltage, alternated between plus and minus, is applied to the two armature winding terminals after breaking the rotor in the d‐axis position. Secondly, the voltage and current between the terminals are measured. Thirdly, the d‐axis inductance related with d‐axis current is calculated from the voltage and current. Finally, the process above is repeated when a DC current flows from the remaining armature terminal to neutral point terminal and the d‐inductance related to the d‐ and q‐axis currents is derived. A similar treatment applies when determining the q‐axis inductance related to the d‐ and q‐axis currents in the q‐axis rotor position. The method is implemented on a 1.1 kW–178 V–6.3 A‐4P–2200 min−1 flux barrier type reluctance motor. Results of load performance on a vector controlled reluctance motor measured by on‐load tests and calculated from the d‐ and q‐axis inductances obtained by the proposed method clearly demonstrate the validity of the proposed method. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 149(4): 52–59, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.10377