Phase Variable Model Research Articles

Phase-Variable Modeling and Comparative Study between a PMa-CPA and a CPA Alternator by Simulation Analysis

This paper presents the phase-variable modeling of a permanent magnet-assisted claw-pole alternator in PSIM simulation software tool with the performance compared with a claw-pole alternator model, which is a special case of the permanent magnet-assisted claw-pole alternator model with the rotor permanent-magnet flux constant setting equal to zero. The constructed model can be simulated as a real alternator directly connected to a diode-bridge rectifier or switch-mode rectifier circuit for the integrated power application system simulation analysis. The proposed model contains two features, one of which is that the stator and rotor windings are circuit-based. The other one feature is that the mechanical torque input is based on a mathematical function. In this model, the rotor position-dependent variable inductor is replaced by a separate voltage source according to the voltage source absorption theorem. The simulation shows that the proposed model has faster torque step response and higher power efficiency than the claw-pole alternator model. The proposed model can be employed to the application of the control design and simulation study of voltage regulation in automobiles. The simulation results with 15-V command and the load sudden change verify the correction of the proposed model.

FLC based speed control of Induction Motor

Speed control of induction motor is utilized for blowers, fans and many other applications. AC voltage regulators are used in induction motors to arrange the speed. This technique features the shrewd controllers such as the Fuzzy controller ac voltage controllers to produce the firing signals for thyristors concerning a given operating torque, speed of the motor, and the load. Fuzzy models have been intended to accomplish the proposed calculation. MATLAB/SIMULINK is utilized to reproduce the proposed strategies. The upside of such controller is its straightforwardness, security, and high precision contrasted with the regular numerical figuring of the firing signals which is a complex and tedious errand particularly in online control applications. The significant attribute of the FLC system is to improve robustness. The mathematical model of the drive framework is created utilizing the phase variable model. The created model is simulated using MATLAB/SIMULINK; since it provides a convenient tool to analyze the system precisely so the outcomes obtained are very satisfactory and promising.

Steady State Analysis Of Single Phase IPM Motors By D-Q Harmonic Balance Method

A concise steady-state analysis of a single-phase line-start permanent magnet (SPLSPM) machine is conducted from a developed d-q model using the d-q harmonic balance technique. The d-q model was developed in rotor reference frame from a phase variable model of the machine. SPLSPM whose performance indices were characterized by high torque ripples has detailed analysis docile mostly in computer simulations quite unlike the three-phase types. The main cause is not far-fetched, it was due to nonexistence of precise mathematical model in d-q rotor frame of the motor due to the unbalanced field winding, the rotor saliency and the presence of the capacitor in the auxiliary windings. Even after model has been developed, the simple traditional procedure of setting all time varying component to zero for steady-state analysis fails because the rotor position dependence on the inductance expressions could not be eliminated. The d-q harmonic-balance technique was then applied. An important feature of the harmonic balance technique was that it decoupled all equations to simple sine waveforms in a style that resembled Fourier series. Results yield torque pulsation, current and load characteristics in the steady state.

Performance analysis of single phase interior permanent magnet synchronous generator

This work presents the performance analysis of a single phase interior permanent magnet synchronous generator. The stator magneto motive force (MMF) waveform of the single phase winding function was developed. The mathematical model in phase variables by which the performance of the generator can be investigated under various operating conditions was developed. Self-excitation of the generator was achieved through pre-excitation by the permanent magnet in the rotor, and then regulated by connecting 30μF capacitor across the terminals of the stator winding. The performances of the generator under constant speed, constant capacitor value and varying power factor loads was investigated. The voltage build-up characteristics and dynamic loss of load performance was studied. The magnitudes of the output power, real power, load voltage and load current increases with increase in load power factors while the phase voltage, phase current, capacitor current and the reactive power decreases with increase in power factor loads. The generator has shown to be capable of stand-alone power source. Simulations were carried out using the Simulink® toolkit in MATLAB® software. Keywords: Interior permanent magnet, phase variable model, single phase, load characteristic, dynamic loss of load

Nonlinear Dynamic Model of PMBLDC Motor Considering Core Losses

The phase variable model is used commonly when simulating a motor drive system with a three-phase permanent magnet brushless dc (PMBLDC) motor. The phase variable model neglects core losses and this affects its accuracy when modeling fractional-slot machines. The inaccuracy of phase variable model of fractional-slot machines can be attributed to considerable armature flux harmonics, which causes an increased core loss. This study proposes a nonlinear phase variable model of PMBLDC motor that considers the core losses induced in the stator and the rotor. The core-loss model is developed based on the detailed analysis of the flux path and the variation of flux in different components of the machine. A prototype of fractional slot axial flux PMBLDC in-wheel motor is used to assess the proposed nonlinear dynamic model.

Dynamic Modeling of a Five-Phase Induction Machine With a Combined Star/Pentagon Stator Winding Connection

The combined star/pentagon connection of five-phase induction machines was recently demonstrated as a promising compromise between conventional star and pentagon connections. It combines the advantages of both star and pentagon connections without any additional hardware for winding changeover. This connection is based on two five-phase single layer concentrated winding sets shifted in space by π/10 and connected in a combined star/pentagon configuration to provide five-phase terminals. Since the combined star/pentagon connected induction machine is fundamentally an asymmetrical ten-phase machine, the machine mathematical model possesses additional subspaces, which affect the behavior of the machine especially under open line conditions. Starting from the conventional five-phase and m -bar squirrel cage induction machine model, the phase-variable model of the combined star/pentagon connection is introduced in this paper. The corresponding equivalent dq model with five decoupled subspaces, which can account for air gap harmonics up to ninth order, is then derived. Finally, it was shown that the machine model could be simply approximated with only two subspaces similar to a conventional five-phase induction machine with sinusoidally distributed winding, where the flux produced by the nonfundamental subspace could be neglected. The model is verified using a 1 kW prototype five-phase induction machine.

A Voltage-Behind-Reactance Model of Five-Phase Induction Machines Considering the Effect of Magnetic Saturation

Five-phase induction machines are generally modeled using multiple dq planes or using a phase variable model. This paper considers modeling five-phase induction machines using a voltage-behind-reactance (VBR) configuration. This configuration lends itself suitable for time-domain circuit-based simulators as the MATLAB/Simulink SimPowerSystems (SPS) toolbox. The stator electrical dynamics are represented in five-phase coordinates, while the rotor electrical circuit is modeled using rotor flux linkage as the state variable and expressed in the dq stator reference frame. The VBR model is equivalent to a conventional dq model; however, it facilitates the connection of an external inductance without affecting numerical accuracy and calculation efficiency. It also facilitates the simulation of different winding connections, series-connected multimotors, and open phase(s) conditions. The model is, first, derived for a magnetically linear system and then it is extended to include the effect of magnetic saturation. The flux correction method is used to represent the effect of magnetic saturation with a simple modification to represent the effect of cross coupling between fundamental and third sequence planes due to saturation effect. The dynamic cross saturation is considered by adding compensating terms that depend on magnetizing inductance variation. The proposed model is experimentally verified using a prototype 1.5-hp five-phase induction machine under different operating conditions.

Thermal Kinetics Phase Field Model for the Metals' Solidification - Mathematic Derivation of the Dendrite Growth Phase Field Variable Diffusion Model

Phase field equations for simulation of dendritic growth have a history of nearly twenty years. The existing phase field equations are directly derived through the Ginzburg-Landau equations. However, though widely used, the physical meaning of each variable in the equations is not clear. So the domestic and foreign researchers have made a lot of mistakes and interpretation. In this paper, with the solid fraction as a phase field variables in the field, based on thermodynamics and heat transfer theory, author gives a rigorous scientific phase variable diffusion model of the pure metal solidification and its derivation process.

Demagnetization Control for Reliable Flux Weakening Control in PM Synchronous Machine

A process for permanent magnet (PM) demagnetization control for optimal and reliable flux weakening control in permanent magnet synchronous machines (PMSM) is presented. A physics-based model was developed to estimate the magnetic flux operating point of the PM poles during the operation of PMSM. The model is enabled to dynamically estimate the average and the partial PM demagnetization due to reverse armature field as well as the PM temperature rise. The model is a function of physical geometry and material of the PMSM, physics of demagnetization, and the ambient temperature. The demagnetization assessment and control is verified on a V-type PMSM using the modified FE-based coupled thermal-field-circuit phase variable model and the time step FE analysis.

Multiobjective Design Optimization of Coupled PM Synchronous Motor-Drive Using Physics-Based Modeling Approach

This paper deals with an optimal design of surface-mounted permanent magnet motor geometry for achieving minimum torque ripple, minimum RMS value of phase current, and minimum total harmonic distortion of phase currents, simultaneously. A classic multiobjective function is formed as a combination of these single objectives. A dynamic physics-based phase variable modeling approach is used to indirectly couple the motor geometry in the finite element domain to the drive circuit in a simulink environment. The physical behavior of motor is calculated by nonlinear transient FE analysis with motion. A fast hybrid genetic-particle swarm optimization process is developed for shape optimization of the motor. The results before and after optimization show the expected performance improvements while reducing magnet material and copper size.

Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics

A detailed model in direct-phase variables of a synchronous reluctance motor operating at mains voltage and frequency is presented. The model includes the stator and rotor slot openings, the actual winding layout and the reluctance rotor geometry. Hence, all mmf and permeance harmonics are taken into account. It is seen that non-negligible harmonics introduced by slots are present in the inductances computed by the winding function procedure. These harmonics are usually ignored in d– q models. The machine performance is simulated in the stator reference frame to depict the difference between this new direct-phase model including all harmonics and the conventional rotor reference frame d– q model. Saturation is included by using a polynomial fitting the variation of d-axis inductance with stator current obtained by finite-element software FEMAG DC®. The detailed phase-variable model can yield torque pulsations comparable to those obtained from finite elements while the d– q model cannot.

A Vector Control Method of LPMBDCM Considering Effects of PM Flux Linkage Harmonic and Cogging Force

This paper presents a general vector control principle of surface-mounted permanent magnet (SPM) motors with arbitrary back-electromotive-force (back-EMF) waveform, then applies it to minimize the force pulsation of three-phase linear permanent magnet brushless dc motors (LPMBDCMs). The principle is derived from the force equation in the dot product form of the current vector and the permanent magnet (PM) flux linkage derivative vector. It indicates that the mutual force is proportional to the amplitude of current vector, and the ohmic loss is at the minimum when the current vector is aligned with the PM flux linkage derivative vector. Based on a d'q' asynchronously rotating reference frame considering the effects of PM flux linkage harmonic, a new id' = 0 vector control method with the cogging force compensation is proposed according to the principle. From the results of simulation with an accurate finite element (FE) based phase variable model, the validity of the proposed control method is verified compared with the conventional PWM current control for a LPMBDCM.

Design and Analysis of a Claw Pole Permanent Magnet Motor With Molded Soft Magnetic Composite Core

Soft magnetic composite (SMC) materials and SMC electromagnetic devices have undergone substantial development in the past decade. Much work has been conducted on designing and prototyping various types of electrical machine. However, the iron cores were often made by cutting existing SMC preforms that were formed by compacting SMC powder in simple cylinder or bar-shape molds, and the magnetic properties of the cores may deteriorate significantly during the cutting process. To investigate ldquoindustry production-readyrdquo products, this paper presents the design and analysis of a claw-pole permanent magnet (PM) motor with a molded SMC core of low mass density to replace the existing induction motor in a dishwasher pump. The magnetic properties of the molded SMC core are measured and utilized in the motor design and analysis. Finite element analysis (FEA) of magnetic field is carried out to accurately determine key motor parameters, and an improved phase variable model is applied to predict the motor performance. Both parameter computation and performance prediction are validated by the experimental results on the prototype.

Equivalent Hardware Representation of PM Synchronous Motors From the Physics-Based Phase Variable Model Obtained Through FE Computation

This paper presents an approach utilizing a machine model to achieve an equivalent hardware representation of machines as a computational prototyping tool. The purpose of our study is to find a way to perform hardware experiments of machine control without the actual machine. The proposed approach provides a way to test the control before the machine is fabricated, or in the cases where the controller needs to be experimentally tested before being implemented onto the actual machine. The equivalent hardware of a machine is built using a current controllable load, a controller, and a machine model in a hardware-in-the-loop (HIL) real time simulation environment. The equivalent hardware representation of the machine is achieved by controlling the currents of the controllable load to be the same as the currents of the actual machine under the same operating conditions. The machine model is used to provide the reference signal for the control. In this paper, the introduction of the proposed approach is presented focusing on three issues: the machine model, the procedure to enable the machine model to be compatible with the HIL real time simulation, and performance examination. Finally, the validity of the proposed approach is demonstrated with the voltage and current waveforms and the torque and speed profiles measured at the developed equivalent hardware of the machine. A 2-hp surface mounted permanent magnet (PM) synchronous motor is used as an example machine to present and verify our work.

Influence of inductance variation on performance of a permanent magnet claw pole soft magnetic composite motor

Winding inductance is an important parameter in determining the performance of electrical machines, particularly those with large inductance variation. This paper investigates the influence of winding inductance variation on the performance of a three-phase three-stack claw pole permanent magnet motor with soft magnetic composite (SMC) stator by using an improved phase variable model. The winding inductances of the machine are computed by using a modified incremental energy method, based on three-dimensional nonlinear time-stepping magnetic field finite element analyses. The inductance computation and performance simulation are verified by the experimental results of an SMC claw pole motor prototype.

다상 브러시리스 교류전동기의 시뮬레이션을 위한 혼합 모델

The emf of a permanent magnet multi-phase BLAC(Brushless AC) motor is generally a non-sinusoidal or a non-ideal trapezoid wave. So, conventional modeling using a sinusoidal or an ideal trapezoid emf can result in errors to simulate and analyze the properties of a multi-phase BLAC motor. To reduce the modeling error, this paper proposes a phase variable model, which is obtained from a hybrid modeling technique consisting of Finite Element Analysis(FEA) based circuits and equations. Since the phase model parameters including the emf waveform were obtained using FEA, the proposed hybrid modeling technique can be used to implement a simulation model for multi-phase BLAC motors with any emf voltage waveforms. Adequacy of the proposed model was established from the simulation and experimental results for a seven-phase BLAC motor.

A Practical Method for Building the FE-Based Phase Variable Model of Single Phase Transformers for Dynamic Simulations

A finite-element (FE)-based phase variable model of single-phase transformers is developed for fast and accurate dynamic simulation purposes. In the developed model, the winding flux linkages, psi1 and psi2 are used as the phase variables. Their values are obtained from a series of nonlinear FE computation over the full operating range of the transformer. An equivalent magnetizing current, iem is defined. The variation of flux linkages psi 1 and psi2 with the defined iem and the primary current i1 or the secondary current i2 are used to describe the magnetization nonlinearity of the core. Our study shows that the utilization of iem enables the FE-based phase variable model has the same accuracy as the full FE model without the necessity of excessive number of FE computations. The validity of the developed FE-based circuit model is verified through comparing with the full FE model and demonstrated by simulating the inrush current and the magnetizing currents at various saturation levels

Internal Short Circuit Fault Diagnosis for PM Machines Using FE-Based Phase Variable Model and Wavelets Analysis

This paper presents a procedure using the finite-element (FE)-based phase variable model combined with wavelet analysis to facilitate the fault diagnostic study for permanent magnet machines with internal short circuit faults. Our efforts are dedicated to the aspects of fault modeling and fault extraction. The FE-based phase variable model is developed to describe the PM machine with internal short circuit faults. This model is built with the parameters [inductances and back Electromotive Force (EMF)] obtained from FE computations of the machine with the same type of fault. The developed model has two features. It includes the detailed information of the fault including the location of the shorted turns and the number of turns involved. It keeps the accuracy of the FE model by taking only a fraction of time needed by FE operation. This is particularly desired for diagnosing faults in machines connected to a control circuit. The wavelet transform is used to perform machine current/voltage signature analysis. Excellent results were obtained providing information that would not be otherwise available except by measurement

An Improved FE-Based Phase Variable Model of PM Synchronous Machines Including Dynamic Core Losses

An improved finite-element (FE)-based phase variable model of PM synchronous machines is developed to provide an accurate machine model for drive and control applications. The improvements add the effects of core losses to the phase variable model as well as its variation with the rotor position, which are obtained from steady-state FE solutions of the machine covering a complete ac cycle. Details on the creation of the improved model, its implementation, dynamic core loss calculation using FE computation, in addition to applications are presented in the paper. The originality of this work is based on the fact that a fast and more comprehensive PM machine model has been proposed for machine control studies

FE-Based Modeling of Single-Phase Distribution Transformers With Winding Short Circuit Faults

This paper presents a fast and accurate phase variable model of single-phase distribution transformers with internal winding short circuit faults. The flux linkages of windings (including the winding formed with the shorted winding turns) are used as the phase variables. Their variation with the winding currents is used to represent the nonlinear magnetization of the iron core. The flux linkage variation is obtained from the solutions of a series of FE computation, covering the full operation range of the transformer with short circuit faults. It is described using tables and utilized by table look up in the developed model. An equivalent magnetizing current is defined to reduce the number of the FE computations for building the flux linkage tables. The implementation of the proposed FE-based model is studied and the verification is performed. Also, the application examples are presented