SPWM电压源供电的永磁直线同步电机特性研究
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摘要
随着永磁材料、电力电子技术、微电子技术的迅猛发展,开关阵列构成的正弦脉宽调制的电压源逆变器(SPWM-VI)与高效节能、结构简单、可靠性强、推力密度大的永磁直线同步电机(PMLSM)为一体的系统受到广大学者的青睐。对具有供电电压源非正弦、工作频率低、行程有限、出入端效应、铁芯开断、端部半填槽等特点的PMLSM的特性开展研究具有重要意义。
本文以SPWM-VI供电的单初级PMLSM(SPPMLSM)驱动的水平运输系统与不连续初级PMLSM(DPPMLSM)驱动的垂直无绳运输系统为研究对象。建立了SPPMLSM的分区域模型,推导了SPPMLSM气隙及次级区域的磁场解析通解。建立了初级齿槽区域有限元方程,利用初级表面与气隙的交界面条件把解析通解方程与初级齿槽区域的矩阵方程联立,获得解析-有限元混合法的整体矩阵方程。采用解析-有限元混合法与单一有限元法分别求解样机的初级表面与气隙中线上的磁密分布。计算结果表明,本文提出的针对SPPMLSM的解析-有限元混合法,既有解析法的快速性,又具备有限元法的高精度、适应复杂边界条件的特性,是一种具有良好应用前景的磁场求解方法。
采用有限元法结合间接法研究SPPMLSM磁阻力的端部分量特性,提出了在出入端区域,半无限长初级PMLSM的磁阻力端部分量不满足周期性条件、傅立叶级数分析法不再适用的重要结论。研究了磁阻力的端部分量与永磁体长度、初级铁芯长度间的关系,提出了通过改变初级铁芯端部齿槽形状来减小磁阻力端部分量的有效措施,分析了此措施下磁阻力齿槽分量的影响和变化规律。采用三次B样条函数对SPPMLSM磁阻力的端部分量在出入端区域进行函数逼近,获得其近似解析式。在SPPMLSM的初、次级完全耦合区域,采用三角多项式作最小平方逼近,获得磁阻力的端部分量在初、次级完全耦合区域的解析模型。采用叠加法与有限元法结合分析DPPMLSM的磁阻力分量,获得磁阻力波形及磁阻力的各个分量的周期性和幅值随着次级动子相对位置变化情况,发现多段初级的磁阻力波形正弦度好,在段间切换时由于初级不连续引起扰动非常小。该结论对DPPMLSM性能分析和优化设计具有一定的借鉴意义。
采用谐波分析法建立了SPWM-VI数学模型,搭建了SPWM-VI的SIMULINK仿真模型。采用状态变量时步有限元法,考虑电机的端部阻抗,建立了SPWM-VI-SPPMLSM的数学模型,提高了二维磁场的计算精度,获得SPPMLSM的三相绕组磁链数据作为样本数据。在搭建初、次级完全耦合的模型时,采用FFT得到磁链对于电流和动子空间位置的偏导数,进行曲线拟合获得磁链的解析式,建立状态空间方程;在初、次级不完全耦合区域,磁链数据作为支持向量回归机函数逼近的样本数据,建立了基于非线性磁链的SPWM-VI-SPPMLSM状态相量数学模型。
研究了SPWM逆变器供电下SPPMLSM的稳态和动态特性。比较了SPWM-VI、正弦电压源两种供电电源下SPPMLSM的稳态特性及在不同载波频率下的SPPMLSM稳态特性;对SPPMLSM不同负载工况的稳态特性进行深入研究,采用负载角的手段可以清晰得到负载角跟SPPMLSM所加负载大小之间的关系。分析了稳态速度特性振荡的原因,指出SPPMLSM磁阻力的端部分量是影响动子稳态运行速度振荡的主要因素;分析了SPPMLSM考虑绕组电阻影响的低速特性。研究了SPPMLSM的负载突变动态特性,结果表明只要突加负载不超过最大额定负载,数值越大系统进入稳态运行的时间越短,突加负载段的速度波动越小;突卸负载时,易造成系统稳定性变差。
分析了DPPMLSM的结构特点及段间间隔的设计原则,建立了以非线性磁链为状态变量的DPPMLSM状态方程,运用SIMULINK建立其仿真模型。利用模型研究DPPMLSM的上行电动、下行反接发电回馈制动等工况,仿真数据与试验结果进行比较,验证了所建模型的正确性与精确度。采用有限元法结合运动系统的能量解析式对DPPMLSM垂直提升系统的失电保护过程进行深刻分析,获得DPPMLSM失电后每段初级绕组短接后的仿真和试验曲线,分析发现提升机失电下坠的稳定速度与外接电阻的阻值有关,找出了外接电阻与DPPMLDM失电保护制动性能的关系。动子速度在初级切换的过渡过程中速度突变较大,对系统的发电制动稳态运行不利,分析了发电制动过程中动子速度突变的原因及特点。
针对PMLSM的特有结构及工作频率低等特点,提出了一种有效测量PMLSM空载电势的新方法。利用微机测试装置完成SPPMLSM驱动的水平运输系统与DPPMLSM驱动的垂直提升系统数据的采集、处理。试验验证了理论的正确性和所建模型的有效性、实用性。
As the rapid development of permanent magnetic materials, power electronics technology and microelectronic technology, the integrated system is favored by the great majority of scholars, which consists of the sinusoidal pulse width modulation voltage source inverter (SPWM-VI) composed with switch arrays and the permanent magnet linear synchronous motor (PMLSM) with high efficiency and energy-saving, simple structure, reliability and thrust density. It attaches much importance to the research of the characteristics of PMLSM whose features are non-sinusoidal power supply, low frequency, limited itinerary, and entry and exit effect, cut cores, half-filled end section and so on.
The main target of this dissertation is the horizontal transport system driven by SPWM-VI-powered single primary PMLSM (SPPMLSM) and the ropeless vertical transport system driven by the non-continuous primary PMLSM (DPPMLSM).This dissertation proposes a fast, high-precious analysis-finite-element mixed method for SPPMLSM magnetic field, set up a partitioned model of SPPMLSM, deduce the analytic general solution of air space of SPPMLSM and secondary regional magnetic field, put up with the finite-element formula of primary spline region, combine the analytic general formula with the matrix equation of primary spline region by using the interface of primary surface and air space to get the whole matrix formula of analytic-finite-element mixed method, calculate the magnet distribution between the primary surface of the sample and the midline of air space with the analytic-finite-element mixed method and single-finite-element method, respectively. With concrete calculation, it is very promising that the analytic-finite-element mixed method for magnet field solution show that the analysis is fast and the finite-element method is highly precious and versatile for the complicated marginal conditions.
Characteristics of the end region of SPPMLSM detent force is researched employing the finite-element method incorporated with indirect method, and that Fourier analysis method is not available is found out when at the entry and the outer, the detent force in the end region of half-infinite long primary PMLSM do not meet the periodicity. Then the dissertation goes to the relation between the detent force in the end region and the length of permanent magnet and primary core, come up with the efficient solution to reduce the detent force of the end region by altering the shape of tooth-slot component on the end of the primary core and analyze the effect and rule of tooth-slot component of the detent force under by using this solution, deduce the approximate analysis formula with the function approximating the end region of the SPPMLSM detent force by cubic B-spline function. And in the primary and secondary absolute coupling areas of SPPMLSM, the trigonometric polynomial as minimum square approximation is taken, and the analytic model of the detent force of the end region is worked out in the primary and secondary absolute coupling areas, then the periodicity of the waveform of the detent force and all the elements of the detent force and amplitude by the analysis of all the elements of the detent force of DPPMLSM is elicited with the combination of the method of superposition and method of finite-element. As the relative position of secondary mover changes, that the multi-end primary detent force approach to sine is found, and is simply perturbed by the non-continuous primary in the short-time, which cast the practical meaning for the analysis of the capability of DPPMLSM and optimizing the design.
For the building-up of nonlinear model of SPWM-VI-PMLSM, firstly, the mathematic model of SPWM-VI by the harmonic analysis is set up and the simulate model of SPWM-VI’s SIMULINK is put up, secondly, the mathematic model of SPWM-VI-SPPMLSM is established with state variable by time-stepping finite element method considering the impedance of the end of motor. As result, the precision of two-dimension magnet field is improved and the three-phase winding flux linkage data of PMLSM is collected as the sample datum. In the course of putting up the primary and secondary absolute coupling model, the flux linkage is fit the curve based on the partial derivative of the current and location of mover and lead to the analytic formula of flux linkage, so the equations of state space are accomplished. At the outer and entry zone, the flux linkage as the sample data of supporting vector machine regression function approximation set up the state phasor mathematic model of the nonlinear SPWM-VI-SPPMLSM.
The dissertation goes to the research of stability and dynamism of SPPMLSM supplied by SPWM voltage source inverter, comparative researching the stability of SPPMLSM powered by the sinusoidal voltage source and SPWM-VI respectively and the stability of SPPMLSM on different carrier frequency, in-depth studying the stability of SPPMLSM on different load condition, using the load angle to analyze the relationship between the load angle and the volume of the load on SPPMLSM, inspecting the cause of oscillation of the steady velocity, pointing out that the end region-component of the detent force of SPPMLSM play the main part in the mover steady velocity oscillation, and construing the characteristic of low speed interfered by the winding resistance of SPPMLSM . Then the research results of the dynamic charactersitics of load suddenly changing are shown that the bigger the numerical value is, the shorter time the system runs stably, the softer the speed fluctuation of shock load is, and given that shock load is less than the maximum of rated load. When uninstall the load, the system is easily to go to low-stability.
The dissertation builds up the nonlinear model of SPPMLSM whose state variable is composed with nonlinear flux linkage, analyzing the structure of SPPMLSM and the designating rule of intersegment interval, forming the space state equations of SPPMLSM, and the emulate model with SIMULINK. Lastly, the dissertation testifies the validity and precision of the models by comparing the simulated data and the experimental results, working over the conditions like the uplink electric of SPPMLSM and the power generation regeneration baking by downlink reverse connect. The dissertation gives the systematic research on the feature of braking operation of DPPMLSM when lose power, studied the blackout protection of vertical hoisting system of DPPMLSM with the combination of finite-element method and the energy analytic-formula of motion system, analyzed the emulate and trial curve when every primary winding is short circuited after the blackout of DPPMLSM ,found out the steady falling-down speed of hoister lossing power which is related with the resistance value of external resistance and the relation between external resistance and the protection breaking performance of DPPMLSM when in power off. And the motor speed change greatly in the transition of primary switch, and has bad effect on the steady operation of the electrical generation braking of the system. The dissertation also generalizes the reason and the feature of speed mutation of mover.
Experimental research is focused on the characterstics of PMLSM such as specific structure and limited displsce in low-frequency operation condition, and a new way to measure the no-load electromotive force of PMLSM is proposed, the collecting and dealing with the datum of the horizontal transportation system are finished driven by SPPMLSM and the vertical ropeless hoisting system driven by DPPMLSM, which are detected by the person computer, the validity of the theory and the efficiency and practicality of the established models is demonstrated.
本文以SPWM-VI供电的单初级PMLSM(SPPMLSM)驱动的水平运输系统与不连续初级PMLSM(DPPMLSM)驱动的垂直无绳运输系统为研究对象。建立了SPPMLSM的分区域模型,推导了SPPMLSM气隙及次级区域的磁场解析通解。建立了初级齿槽区域有限元方程,利用初级表面与气隙的交界面条件把解析通解方程与初级齿槽区域的矩阵方程联立,获得解析-有限元混合法的整体矩阵方程。采用解析-有限元混合法与单一有限元法分别求解样机的初级表面与气隙中线上的磁密分布。计算结果表明,本文提出的针对SPPMLSM的解析-有限元混合法,既有解析法的快速性,又具备有限元法的高精度、适应复杂边界条件的特性,是一种具有良好应用前景的磁场求解方法。
采用有限元法结合间接法研究SPPMLSM磁阻力的端部分量特性,提出了在出入端区域,半无限长初级PMLSM的磁阻力端部分量不满足周期性条件、傅立叶级数分析法不再适用的重要结论。研究了磁阻力的端部分量与永磁体长度、初级铁芯长度间的关系,提出了通过改变初级铁芯端部齿槽形状来减小磁阻力端部分量的有效措施,分析了此措施下磁阻力齿槽分量的影响和变化规律。采用三次B样条函数对SPPMLSM磁阻力的端部分量在出入端区域进行函数逼近,获得其近似解析式。在SPPMLSM的初、次级完全耦合区域,采用三角多项式作最小平方逼近,获得磁阻力的端部分量在初、次级完全耦合区域的解析模型。采用叠加法与有限元法结合分析DPPMLSM的磁阻力分量,获得磁阻力波形及磁阻力的各个分量的周期性和幅值随着次级动子相对位置变化情况,发现多段初级的磁阻力波形正弦度好,在段间切换时由于初级不连续引起扰动非常小。该结论对DPPMLSM性能分析和优化设计具有一定的借鉴意义。
采用谐波分析法建立了SPWM-VI数学模型,搭建了SPWM-VI的SIMULINK仿真模型。采用状态变量时步有限元法,考虑电机的端部阻抗,建立了SPWM-VI-SPPMLSM的数学模型,提高了二维磁场的计算精度,获得SPPMLSM的三相绕组磁链数据作为样本数据。在搭建初、次级完全耦合的模型时,采用FFT得到磁链对于电流和动子空间位置的偏导数,进行曲线拟合获得磁链的解析式,建立状态空间方程;在初、次级不完全耦合区域,磁链数据作为支持向量回归机函数逼近的样本数据,建立了基于非线性磁链的SPWM-VI-SPPMLSM状态相量数学模型。
研究了SPWM逆变器供电下SPPMLSM的稳态和动态特性。比较了SPWM-VI、正弦电压源两种供电电源下SPPMLSM的稳态特性及在不同载波频率下的SPPMLSM稳态特性;对SPPMLSM不同负载工况的稳态特性进行深入研究,采用负载角的手段可以清晰得到负载角跟SPPMLSM所加负载大小之间的关系。分析了稳态速度特性振荡的原因,指出SPPMLSM磁阻力的端部分量是影响动子稳态运行速度振荡的主要因素;分析了SPPMLSM考虑绕组电阻影响的低速特性。研究了SPPMLSM的负载突变动态特性,结果表明只要突加负载不超过最大额定负载,数值越大系统进入稳态运行的时间越短,突加负载段的速度波动越小;突卸负载时,易造成系统稳定性变差。
分析了DPPMLSM的结构特点及段间间隔的设计原则,建立了以非线性磁链为状态变量的DPPMLSM状态方程,运用SIMULINK建立其仿真模型。利用模型研究DPPMLSM的上行电动、下行反接发电回馈制动等工况,仿真数据与试验结果进行比较,验证了所建模型的正确性与精确度。采用有限元法结合运动系统的能量解析式对DPPMLSM垂直提升系统的失电保护过程进行深刻分析,获得DPPMLSM失电后每段初级绕组短接后的仿真和试验曲线,分析发现提升机失电下坠的稳定速度与外接电阻的阻值有关,找出了外接电阻与DPPMLDM失电保护制动性能的关系。动子速度在初级切换的过渡过程中速度突变较大,对系统的发电制动稳态运行不利,分析了发电制动过程中动子速度突变的原因及特点。
针对PMLSM的特有结构及工作频率低等特点,提出了一种有效测量PMLSM空载电势的新方法。利用微机测试装置完成SPPMLSM驱动的水平运输系统与DPPMLSM驱动的垂直提升系统数据的采集、处理。试验验证了理论的正确性和所建模型的有效性、实用性。
As the rapid development of permanent magnetic materials, power electronics technology and microelectronic technology, the integrated system is favored by the great majority of scholars, which consists of the sinusoidal pulse width modulation voltage source inverter (SPWM-VI) composed with switch arrays and the permanent magnet linear synchronous motor (PMLSM) with high efficiency and energy-saving, simple structure, reliability and thrust density. It attaches much importance to the research of the characteristics of PMLSM whose features are non-sinusoidal power supply, low frequency, limited itinerary, and entry and exit effect, cut cores, half-filled end section and so on.
The main target of this dissertation is the horizontal transport system driven by SPWM-VI-powered single primary PMLSM (SPPMLSM) and the ropeless vertical transport system driven by the non-continuous primary PMLSM (DPPMLSM).This dissertation proposes a fast, high-precious analysis-finite-element mixed method for SPPMLSM magnetic field, set up a partitioned model of SPPMLSM, deduce the analytic general solution of air space of SPPMLSM and secondary regional magnetic field, put up with the finite-element formula of primary spline region, combine the analytic general formula with the matrix equation of primary spline region by using the interface of primary surface and air space to get the whole matrix formula of analytic-finite-element mixed method, calculate the magnet distribution between the primary surface of the sample and the midline of air space with the analytic-finite-element mixed method and single-finite-element method, respectively. With concrete calculation, it is very promising that the analytic-finite-element mixed method for magnet field solution show that the analysis is fast and the finite-element method is highly precious and versatile for the complicated marginal conditions.
Characteristics of the end region of SPPMLSM detent force is researched employing the finite-element method incorporated with indirect method, and that Fourier analysis method is not available is found out when at the entry and the outer, the detent force in the end region of half-infinite long primary PMLSM do not meet the periodicity. Then the dissertation goes to the relation between the detent force in the end region and the length of permanent magnet and primary core, come up with the efficient solution to reduce the detent force of the end region by altering the shape of tooth-slot component on the end of the primary core and analyze the effect and rule of tooth-slot component of the detent force under by using this solution, deduce the approximate analysis formula with the function approximating the end region of the SPPMLSM detent force by cubic B-spline function. And in the primary and secondary absolute coupling areas of SPPMLSM, the trigonometric polynomial as minimum square approximation is taken, and the analytic model of the detent force of the end region is worked out in the primary and secondary absolute coupling areas, then the periodicity of the waveform of the detent force and all the elements of the detent force and amplitude by the analysis of all the elements of the detent force of DPPMLSM is elicited with the combination of the method of superposition and method of finite-element. As the relative position of secondary mover changes, that the multi-end primary detent force approach to sine is found, and is simply perturbed by the non-continuous primary in the short-time, which cast the practical meaning for the analysis of the capability of DPPMLSM and optimizing the design.
For the building-up of nonlinear model of SPWM-VI-PMLSM, firstly, the mathematic model of SPWM-VI by the harmonic analysis is set up and the simulate model of SPWM-VI’s SIMULINK is put up, secondly, the mathematic model of SPWM-VI-SPPMLSM is established with state variable by time-stepping finite element method considering the impedance of the end of motor. As result, the precision of two-dimension magnet field is improved and the three-phase winding flux linkage data of PMLSM is collected as the sample datum. In the course of putting up the primary and secondary absolute coupling model, the flux linkage is fit the curve based on the partial derivative of the current and location of mover and lead to the analytic formula of flux linkage, so the equations of state space are accomplished. At the outer and entry zone, the flux linkage as the sample data of supporting vector machine regression function approximation set up the state phasor mathematic model of the nonlinear SPWM-VI-SPPMLSM.
The dissertation goes to the research of stability and dynamism of SPPMLSM supplied by SPWM voltage source inverter, comparative researching the stability of SPPMLSM powered by the sinusoidal voltage source and SPWM-VI respectively and the stability of SPPMLSM on different carrier frequency, in-depth studying the stability of SPPMLSM on different load condition, using the load angle to analyze the relationship between the load angle and the volume of the load on SPPMLSM, inspecting the cause of oscillation of the steady velocity, pointing out that the end region-component of the detent force of SPPMLSM play the main part in the mover steady velocity oscillation, and construing the characteristic of low speed interfered by the winding resistance of SPPMLSM . Then the research results of the dynamic charactersitics of load suddenly changing are shown that the bigger the numerical value is, the shorter time the system runs stably, the softer the speed fluctuation of shock load is, and given that shock load is less than the maximum of rated load. When uninstall the load, the system is easily to go to low-stability.
The dissertation builds up the nonlinear model of SPPMLSM whose state variable is composed with nonlinear flux linkage, analyzing the structure of SPPMLSM and the designating rule of intersegment interval, forming the space state equations of SPPMLSM, and the emulate model with SIMULINK. Lastly, the dissertation testifies the validity and precision of the models by comparing the simulated data and the experimental results, working over the conditions like the uplink electric of SPPMLSM and the power generation regeneration baking by downlink reverse connect. The dissertation gives the systematic research on the feature of braking operation of DPPMLSM when lose power, studied the blackout protection of vertical hoisting system of DPPMLSM with the combination of finite-element method and the energy analytic-formula of motion system, analyzed the emulate and trial curve when every primary winding is short circuited after the blackout of DPPMLSM ,found out the steady falling-down speed of hoister lossing power which is related with the resistance value of external resistance and the relation between external resistance and the protection breaking performance of DPPMLSM when in power off. And the motor speed change greatly in the transition of primary switch, and has bad effect on the steady operation of the electrical generation braking of the system. The dissertation also generalizes the reason and the feature of speed mutation of mover.
Experimental research is focused on the characterstics of PMLSM such as specific structure and limited displsce in low-frequency operation condition, and a new way to measure the no-load electromotive force of PMLSM is proposed, the collecting and dealing with the datum of the horizontal transportation system are finished driven by SPPMLSM and the vertical ropeless hoisting system driven by DPPMLSM, which are detected by the person computer, the validity of the theory and the efficiency and practicality of the established models is demonstrated.
引文
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