A dynamic mathematical model and vector block diagrams for class of hybrid‐field synchronous motors

This paper proposes a new dynamic mathematical model and new block diagrams for a newly emerging class of salient‐pole hybrid‐field synchronous motors (HFSM) that have rotor field by both permanent magnet and winding. The proposed mathematical model has the following completeness and generality. (1) It consists of three consistent basic equations such as circuit, torque, and energy‐transmission equations. (2) It deals with pole saliency and contains nonsaliency as a special case. (3) It is a dynamic model and contains a static one as a special case. (4) It is established in the general reference frame including stator and rotor reference frames as special cases. The proposed new block diagrams using vector signals for salient‐pole HFSM are established based on the model. It has the following attractive features. (1) It succeeds in realizing clear configurations with physically meaningful vector signals, which are helpful for understanding motor electromagnetic mechanisms and useful for designing controllers for the salient‐pole HFSM. (2) Vector signals utilized as transfer signals between blocks are defined in the general reference frame. Consequently, the vector‐signal block diagrams in the frame can be directly and easily reduced to the ones in such a specific frame as stator and rotor frames. (3) It is compact. Two typical and compact but sufficiently general vector‐signal block diagrams are newly presented. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 152(2): 47–57, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20112     

New sensorless vector control methods based on a new minimum‐order flux state observer in the “D‐module” for permanent magnet synchronous motors

This paper proposes new sensorless vector control methods that can be applied to both salient‐pole and non‐salient‐pole permanent magnet synchronous motors (PMSM). The proposed method estimates the phase of rotor flux by the “D‐module observer,” which is newly developed for sensorless vector controls of PMSM. The “D‐module observer” has the following attractive features. (1) It is a new state observer requiring no additional approximation to the motor mathematical model. (2) It is a minimum‐order state observer. (3) Observer gain guaranteeing proper estimation in a wide operating range except for singular zero‐speed can be a simple constant, and can be easily designed. (4) It utilizes motor parameters in the simplest manner. (5) Its structure is very simple and is realized at the minimum computing cost. (6) It can be applied to both salient‐pole and non‐salient‐pole PMSM. (7) It can be realized in both rotor and stator reference frames. Detailed designs and analyses for the “D‐module observer” and “D‐module observer”‐based sensorless vector control systems in both rotor and stator reference frames are given. Their validity and usefulness are examined and confirmed through extensive experiments. © 2005 Wiley Periodicals, Inc. Electr Eng Jpn, 151(2): 46–62, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20046     

Sensorless controls of salient‐pole permanent magnet synchronous motors using extended electromotive force models

In this paper, we propose a new mathematical model for synchronous motors and a sensorless control method based on it. To control permanent magnet synchronous motors, knowledge of rotor position and velocity are necessary. Heretofore, expensive sensors have been used to detect rotor position information. Although many sensorless control methods based on the electromotive force (EMF) have been developed for non‐salient‐pole permanent magnet motors, they cannot be applied for salient‐pole motors without approximation because of complications in the mathematical model; this is turn may lead to problems of instability. To solve this problem, we propose an extended electromotive force model for synchronous motors. The proposed model has a simple structure, making position estimation possible without approximation. Experimental results show that the proposed model and method are valid. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 146(3): 55–64, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10257     

A new initial‐rotor‐position estimation method for SPM synchronous motors using spatially rotating high‐frequency voltage: A dynamic simulator approach taking flux saturation phenomena into account

First, this paper proposes a new dynamic mathematical model of surface‐mounted permanent magnet synchronous motors (SPMSMs) with flux saturation phenomena, in a stationary reference frame. Second, based on the dynamic model, this paper establishes new dynamic simulators taking flux saturation phenomena into account, which act as very powerful tools for developing initial‐rotor‐position estimation methods for SPMSMs. Third, this paper proposes a new initial‐rotor‐position estimation method for SPMSMs. The proposed method is so simple that it inputs a spatially rotating high‐frequency voltage to SPMSMs, measures current output, and can estimate directly rotor position of N‐pole through norm evaluation of the current. The method exploits flux saturation phenomena inherent to SPMSMs and is insensitive to all motor parameters. According to experiments, the maximum estimation error is about ±0.035 rad (±2^○) in terms of mechanical angle, which is comparable to sensor mounting error and is sufficiently small for initial drive of SPMSMs. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 160(3): 63–73, 2007; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20241     

带整流器励磁的同步发电机转子过电压的分析

本文分析表明,带整流器励磁的同步发电机,当两相短路或三相短路以及短路切除恢复到电网电压的瞬态过程中,在励磁绕组两端可能感生高反向电压。并着重指出,同步电机的动态参数,特别是瞬态过程在转子铁芯中产生的涡流效应和运行方式显著地影响着转子过电压的大小。然而,这些动态参数又与同步电机转子结构形式有很大关系。就转子过电压危险的程度而言,隐极同步发电机比凸极同步发电机要小.     

转子齿宽对双凸极永磁轮毂电机性能的影响

转子齿宽对基于磁阻工作原理的双凸极永磁轮毂电机特性有重要影响。以二维有限元计算方法为基础,画出空载时电机的场图分布,给出第三气隙与转子齿宽的数值关系,得到不同转子齿宽时的绕组磁链曲线和对应的绕组反电势波形,同时讨论转子齿宽与绕组磁链变化率和反电势波形的关系,这些结论为设计出性能更趋完善的双凸极永磁电机提供了参考。     

择多函数在无刷直流电动机控制中的应用

转子位置信息的获得是无位置传感器无刷直流电动机控制的关键技术,一般采用基于位置检测电路的反电势检测法,而择多函数法省掉了位置检测电路,运用反电势信号及逻辑运算关系判定测试条件"真"到"假"的变化,消除噪声对反电势信号的影响,获得正确的反电势过零点。该方法在基于DSP的无位置传感器无刷直流电动机控制平台上进行实验验证,实测数据证明该方法可以在2~3倍负载条件下有效滤除反电势虚假过零点,获得准确的反电势过零点,性能可靠,灵活性和实用性较高。     

Position sensorless control of interior permanent magnet synchronous motor using extended electromotive force

Driving a permanent magnet synchronous motor (PMSM) requires the rotor position information to control the motor torque, and this is generally detected by mechanical position sensors such as an encoder or a resolver. However, these sensors increase the machine size and the cost of the drive, and reduce reliability of the system. Therefore, many papers about position sensorless drive method of PMSM have been published. This paper presents a position sensorless control of interior permanent magnet synchronous motor (IPMSM). A mathematical model of IPMSM using the extended electromotive force (EMF) in the rotating reference frame is utilized to estimate the rotor speed and position. This model has a simple structure integrating position information into the extended EMF term. Therefore, the sensorless control based on the mathematical motor model can be implemented simply. The estimation method proposed is based on the principle that the error of the current is proportional to that of extended EMF. This method was carried out using a 6‐pole, 400‐W, 1750 r/min test motor system. It was found that sensorless speed control was achieved from 80 r/min to 1800 r/min under 0 to 100%loads. © 2007 Wiley Periodicals, Inc. Electr Eng Jpn, 161(3): 41–48, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20406     

凸极式永磁无刷直流电机直接转矩控制研究

提出并分析研究了一种凸极式永磁无刷直流电机定子磁链幅值不控型直接转矩控制策略。结合凸极式永磁无刷直流电机及其两相导通工作特点,全面建立起两相导通时电压矢量对电磁转矩控制理论。采用转矩单环控制,根据转矩滞环比较输出和定子磁链位置给出所施加的电压矢量,实现转矩的快速控制。推导出两相静止坐标系下电磁转矩计算模型,并针对实际无刷电机转子反电势既非理想梯形波,又非正弦波的情况,提出采用查表方式获得转矩观测所必需的转子反电势和转子磁链方法。实验结果表明,所提控制方案具有快速的动态响应和良好的稳态性能。     

Potentiality of a new minimum‐order back‐EMF state observer taking acceleration into account for sensorless vector control of permanent‐magnet synchronous motors

This paper proposes new sensorless vector control methods for permanent‐magnet synchronous motors (PMSMs), which are based on a new minimum‐order back‐EMF state observer taking acceleration into account, and examines potentiality of the improved back‐EMF observer through experiments. Conventional sensorless vector control methods for PMSMs using an estimate of back‐EMF are established under the assumption of constant speed or zero acceleration, and consequently cannot operate properly at modes requiring rapid speed change especially in low speed region. On the other hand, the proposed back‐EMF observer has the following features: (1) it is a new back‐EMF state observer taking acceleration into account and requiring no additional approximation to motor mathematical model; (2) it is a minimum‐order state observer; (3) it utilizes motor parameters in the simplest manner; (4) it can be applied to both salient‐pole and non‐salient‐pole PMSMs; (5) it can be realized in both rotor and stator reference frames. Detailed designs and analyses for the improved state observer and the sensorless vector control systems in both rotor and stator reference frames are given. In relation to the sensorless vector control systems, this paper newly proposes a double‐integral‐type PLL method and an integral‐feedback‐type acceleration/speed estimation method. Their potentialities are examined through experiments. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 164(4): 78–92, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/ eej.20630     

A new generalized high‐frequency voltage injection method and mirror‐phase estimation method for sensorless drive of salient‐pole PMSMSs

This paper proposes a new generalized high‐frequency voltage injection method for sensorless drive of salient‐pole permanent‐magnet synchronous motors. The injected high‐frequency voltage has a unique spatially‐rotating elliptical shape, with the amplitudes of both the major and minor axes varying with the motor speed, and can be designed by selecting a design parameter. The high‐frequency current caused by the injected voltage, which has information on the rotor phase to be estimated, is speed‐independent, that is, is not affected by the motor speed at all. Consequently, the rotor phase can be estimated in a wide speed range from zero to the rated speed. By selection of the design parameter, the properties of the high‐frequency current can be adjusted appropriately to the associated motor‐drive system consisting of a motor and an inverter. As a versatile phase estimation method for estimating rotor phase using the high‐frequency current, the “mirror‐phase estimation method” is reconstructed and reproposed. © 2009 Wiley Periodicals, Inc. Electr Eng Jpn, 168(3): 67–82, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20803     

Current flow and losses in brushless exciters with polygon-connected windings and dc rectifiers

The current flow within a salient pole brushless exciter with polygon-connected winding is calculated. The winding is connected to a rectifier, which causes transients in the winding during switching. Brushless exciters are over-dimensioned for their rated operation. During ceiling conditions the required voltage may be two times higher and the exciter is strongly saturated. Therefore the normal asynchronous circuit theory is no longer applicable for a detailed study within the exciter itself. A nonlinear finite difference time stepping method with rotating rotor and diode circuits is applied instead. Basic theories for the combination between the circuit theory and field theory are summarized in one mathematical model. Calculation results are compared to measurements on a real power plant exciter for different operation conditions. Rolf Gantenbein has recently passed away.     

Complex vector model of the squirrel-cage induction machineincluding instantaneous rotor bar currents

In this paper, a new detailed mathematical derivation of the squirrel-cage induction machine d-q model is introduced. The model is based on coupled magnetic circuit theory and complex space-vector notation and takes into account the actual nonsinusoidal rotor bar distribution. It is shown for the first time that, given the structural symmetry of the induction machine, both stator and rotor circuits can be modeled by the simple set of only four coupled differential equations, i.e., the d-q model. More importantly, the number of equations does not depend on the number of rotor bars, and the model is valid even if the number of bars per pole is not an integer number. This enormous simplification is achieved without loss of generality nor loss of any information contained in the full set of equations, and it is valid for any operating condition. The actual n rotor bars and end-ring currents are fully included in the model, and they are obtained directly by using a simple vector transformation. In addition, the three-phase rotor equivalent parameters are obtained. Second-order effects, such as skin effect in the rotor bars, can be taken into account by simply modifying the bar and end-ring resistance values. An equivalent circuit based on the model is also derived     

Dynamic model for power systems with multiple FACTS controllers

Computer simulation and analysis of power systems are necessary for both planning and operation. This requires an appropriate mathematical model of the system that includes many inter-related linear/nonlinear differential and algebraic equations. Such mathematical model is also needed for the design of globally coordinated controllers to improve power system dynamic performance and stability. This paper presents a procedure for finding comprehensive dynamic models of power systems fitted with shunt and/or series connected FACTS controllers such as STATCOM, SSSC, and UPFC. In this procedure, individual components of a power system are modeled using appropriate frame of references. Then all related equations are transformed to a common network frame of reference and tied to each other through the Y-matrix of the transmission network. The procedure is tested on the Western System Coordinating Council (WSCC) test system including FACTS controllers by performing computer simulations of the system for three-phase short circuit faults. MATLAB/Simulink software package is used for the simulations.     

Inverse modelling and pulsating torque minimization of salient pole non-sinusoidal synchronous machines

Sinusoidal motor's mathematical models are usually obtained using classical d–q transformation in the case of salient pole synchronous motors having sinusoidal field distribution. In this paper, a new inverse modelling for synchronous motors is presented. This modelling is derived from the properties of constant torque curves in the Concordia's reference frame. It takes into account the non-sinusoidal field distribution; EMF, self and mutual inductances having non-sinusoidal variations with respect to the angular rotor position. Both copper losses and torque ripples are minimized by adapted currents waveforms calculated from this model. Experimental evaluation was carried out on a DSP-controlled PMSM drive platform. Test results obtained demonstrate the effectiveness of the proposed method in reducing torque ripple.     

Determination of equivalent circuit constants of synchronous machines from the extended Dalton‐Cameron method

This paper presents a method of determining the equivalent circuit constants which accord with the physical construction of synchronous machines, using the dc decay testing method with the rotor in arbitrary position (proposed by the authors and called the extended Dalton–Cameron method). The conventional Dalton–Cameron method calculates the direct‐ and quadrature‐axis subtransient reactance from a standstill response test in any arbitrary rotor position using a single‐phase power supply. The extended Dalton–Cameron method determines the direct‐ and quadrature‐axis operational impedances for each slip from a standstill response test using a small‐capacity dc power supply. The direct‐ and quadrature‐axis operational impedance loci thus obtained synchronous machine constants (subtransient, transient, and synchronous reactances) are used to estimate the direct‐ and quadrature‐axis equivalent circuit constants which accord with the physical construction of synchronous machines. As an example, equivalent circuit constants are determined for a 10‐kW laminated salient‐pole‐type synchronous machine with damper winding. The validity of the equivalent circuit constants is confirmed by comparing the calculated resistance and leakage reactance of the field winding determined from the operational impedance when the terminals are short‐circuited, to those when the terminals are connected to an external resistance. © 2001 Scripta Technica, Electr Eng Jpn, 138(1): 56–67, 2002     

新型混合励磁同步电机的数学模型与等效分析

为改善高速永磁电机磁场调节困难的问题,提出一种新型混合励磁电机,转子上既有永磁极又有铁心极,磁路呈现典型的径向、周向和轴向三维特性,难以直接用解析法求取电感参数。根据新型混合励磁电机的磁路特点,提出一种等效分析方法,将复杂磁路的混合励磁电机等效为三种二维磁路电机轴向并列叠加。为了提高新型混合励磁电机电磁设计与性能分析的效率,推导了其数学模型与电感参数表达式。对一台10 k W混合励磁原理样机进行了有限元分析与实验研究,结果验证了所提数学模型与等效分析方法的正确性,为该类电机的设计和优化提供了理论支撑。     

A General Analytical Method for a Three‐Phase Line‐Start Permanent‐Magnet Synchronous Motor

A line‐start permanent‐magnet synchronous motor (LSPMM) consists of a stator with symmetrical three‐phase armature windings and a salient pole rotor with a permanent magnet for excitation and a starting winding similar to the squirrel‐cage winding of an induction motor. In this paper, a general analytical method based on tensor analysis is proposed for practical performance calculation of a three‐phase LSPMM. The general equation for the currents of the three‐phase LSPMM is derived from the transient impedance tensor expressed in polyphase symmetry axes, and the general equation for vibratory and nonvibratory torques is derived from the current equation. © 2013 Wiley Periodicals, Inc. Electr Eng Jpn, 185(4): 60–68, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21284     

Optimal current control methods of a non‐salient pole hybrid field‐synchronous motor for energy‐efficient and wide speed‐range operation

This paper proposes new practical optimal current control methods for a newly emerging class of non‐salient pole synchronous motors with hybrid rotor fields by both permanent magnet and winding. In practical situations with limited voltage, the extensively used permanent magnet synchronous motor hardly achieves an ideal performance that allows simultaneously both low‐speed high‐torque and wide speed‐range operations, due to its constant magnet field. Hybrid field synchronous motors (HFSM) have recently emerged to achieve ideal performance as practical motors with controllable hybrid rotor field. For HFSM, the same torque can be produced by a variety of currents due to nonlinearity between torque and currents. Consequently, appropriate determination of a set of stator and rotor current commands plays a key role in achieving possible energy‐efficient and wide speed‐range operation. Proposed methods determine the current commands corresponding to a given torque command such that total winding copper loss due to stator and rotor currents can be minimized if the exact solution exists; the best approximate torque can be produced if no exact solution exists. The determined current commands are optimal in the sense of energy efficiency or degree of approximation in wide speed‐range operation under voltage limit. New real‐time recursive algorithms searching the optimal current solution are also given. The proposed methods are analytical but practical, and their usefulness is verified through experiments. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 156(1): 70–83, 2006; Published online in Wiley InterScience ( www.interscience. wiley.com ). DOI 10.1002/eej.20156     

Mathematical model of five-level ac/dc converter in abc reference frame

This paper proposes a mathematical model for three-phase multilevel diode clamped ac/dc converter (DCC) in abc-reference frame, in order to study dynamic responses and stability of the system, where multilevel converters are employed. An attempt is made to model the converter adopting 5-level DCC and can be easily extended to DCC with any number of levels. The converter output and dc capacitor voltages are expressed in terms of input source currents and switching functions; which are basic inputs provided to a converter. Connection and capacitor currents of the converter have been analyzed. The effectiveness of the proposed mathematical model is verified by the computer simulations and experimental results. The obtained mathematical model has been validated with the physical converter model in MATLAB/Simulink environment and the prototype model using dSPACE DS under closed loop control system. The developed mathematical model equations are able to represent the physical converter with similar characteristics.