快速交—直流PWM整流感应发电机系统的高性能控制中英文翻译.doc

第32页中文译文快速交直流pwm整流感应发电机系统的高性能控制摘要：本篇主要描述了一种快速的交直流感应发电机整流系统的直流电压调节控制方法，该整流系统中发电机的铜耗可减到最小。通过输入输出线性化的补偿，使得同步参考结构中的等价模型体线性化、解耦，达到高性能的转速矢量控制。稳态分解提供了发电机的操作规则，计算机仿真已证明了不同负载条件以及转速变化下的控制策略的有效性。文章还展示了一些实验结果。索引词：感应发电机，交直流pwm整流器，励磁，输入输出线性化，巴特沃思多项式，磁饱和、绪论越来越多的研究和实际应用已转移到可再生能源系统，例如风能。又由于发电机具有低成本，维护费用少，结构简单牢固，无刷（鼠笼式）等固有的优点，增加了感应电机特别是发电机的使用。感应电机的转差率决定了它是以发电机还是电动机运转，正的转差率说明电机以电动机形式运转，而负的转差率标志着电机工作在发电状态。众所周知，感应电机可以用作自激发电机，也就是说（a）通过定子接线端三个连接电容（b）通过使用反用换流器/整流器系统，发电机能够被励磁1。在使用反用换流器/整流器系统的情况下，直流侧的电容是否作为三相电容取决于反用换流器的开关信号，整流器的单相直流电容给感应电机提供必需的励磁。大量广泛的观察说明，过去超过25年里在自激，电压组合建模，感应电机的稳态分析等不同领域所做的大量工作已经被展示在2。而且，在以前的出版著作中，描述过感应发电机整流系统的矢量控制。该系统用于产生直流而且它的整流器也提供励磁3。该系统特别适用于风能方面的研究应用，因此来研究变化的转子转速的反应控制器。4中也做了感应发电机整流器在方向场控制下的稳定性研究，强调了感应发电机在高速应用时存在可能的不稳定性。本文中采用的控制方法已经详细展示，阐明了在系统的等效模型中，用输入输出线性化的方法将非线性部分从线性部分中分离出来。经测试，在电机负载变化以及转速变化的情况下，提出的控制策略依然可行。电机运转在最低铜耗下5。通过调节转子使用最小损耗功能，可达到损耗最小。稳态分析处理自激发电机在饱和条件下的运行状况6。研究了感应电机输出功率的容量以及在不同负载条件下电机操作时各个参数的作用。本篇分析主要突出了励磁量对系统的励磁需求的作用，该系统以调制信号的大小衡量励磁要求。通过固定磁链，电机励磁需要的调制量能被确定下来。连同饱和作用，研究了系统在最低铜耗下的情况。本篇按以下方式组织：第二和第三部分分别详细地描述了三相快速整流器模块和感应发电机。在第三部分中也提到了组合系统模块。第四部分做了电机的稳态分析。第五部分明确地表述了控制策略，第六部分通过仿真和实验结果证明了提出的控制策略。、三相快速整流器模型在系统中三相快速整流器用于交直流转换。每个整流器由六个活动开关（反并联续流二极管）组成，开关控制采用基于载波控制的三角正弦脉冲宽度调制方式（即pwm方式）。上、下桥臂的三个开关器件的作用分别被定义为和，开关只有在开通时才起作用，当它关断时不起作用。而且，同一桥臂上下两个开关器件不能同时导通。在三相参考坐标系中，根据开关所起的作用，整流器的电压等式可表述为：开关作用经连续傅立叶变换后可近似为一个平均值和一个时变值。在三角正弦pwm方式中，随时间变化的调制信号和三角波做比较生成的信号控制开关通断。根据直流电压和相应的调制指标(mqs, mds)，将（13）式转化到同步参考坐标系中，q轴和d轴电压可被表述为：转化到同步参考坐标系下，整流器直流侧的电压等式可以描述为：是整流器负载。 、三相感应发电机模型除电流方向不同外，三相感应发电机的模型方程式和感应电动机一样。系统模型如图1展示。图1 交直流感应发电机整流系统同步参考坐标系中发电机的方程式可以表述为： 是电机转速，是qd坐标中电机电压的角频率， 分别是q，d轴上的转子磁链，分别是q，d轴上的定子电流。就像早期所提出的，这种控制方法考虑将转子磁通和控制（定子）电流设置为控制变量。根据所要求的状态变量感应发电机的模型方程式可以表述为：其中在方程式（8）（12）中的参数按下式定义：、稳态励磁稳态分析是采用感应发电机按（14）（16）所示的复杂模型方程式进行的，在（16）式中考虑了气隙磁通饱和的作用。考虑到电机的饱和效应及最小铜耗的条件，分析主要在于决定发电机励磁所要求的调制指标的大小值。图 2 是一个2马力的感应电机在饱和条件下磁感随磁通量的变化曲线。电压方程式在参考坐标系下的变化角度体现了q轴随磁通链变化的校准。因此，假定d轴的磁通量是零，则d轴的磁感恒定。而q轴上磁感是磁通的函数，可近似由多项式（13）表示。 是转差频率，可定义为。图2 磁感的倒数随磁通量的变化曲线稳态下可导出，（14）（16）中p为零。考虑到电机气隙磁链的磁饱和，分解的目的在于使电机运转时的总铜耗最小。当转子转差的导数为零时，电机的总铜耗（如式17所示）最小。选择合适的电机转差率可以实现这种条件，如式18所示。如图三所示，转差率是磁感的函数。图3 转差率随磁通量的变化曲线为了获得调制指标（m）的大小和磁通量的关系，（16）式中的定子电流根据定子磁通量表达。重新整理（15）式得：将（19）式带入（14）式中得：定子电流用定子磁通表达为：将（20）式带到（21）式，并将（16）式中的定子电流消去，可得等式： 用方程式（22），可以达到在最小铜耗的条件下，通过改变调制指标量的大小产生磁通量变化的效果。当磁链改变时磁感的对应数值能够被计算出来。用磁感的值，可以计算在最低铜损时的转差和对应的调制指标。假定恒定的转子转速，图4展示了变化的负载电阻和变化的磁通量对调制指标m的作用。图4所示，随着负载电阻的增加，调制指标的计算值减小。从图4也可看出，在恒定负载下，两个不同的磁感值可以获得相同的调制指标。图7说明了不同磁感的作用。同样地，图5展示了某个恒定的磁通下转速的变化效果。此时，取磁通量为一个恒定的值0.25wb。根据等式（22）中的电感，负载电阻和调制指标的平方的乘积组成的表达式 ，给出了在分解中用到的另外一个参数。这个参数可以用来衡量系统以固定的转速和转差率运转时的负载电阻。图6显示了不同的转差率对产生的影响。图4 转差率折算到最小铜耗下，负载电阻变化时，调制指标m的值随磁通链的变化曲线图5 在最小铜耗下，电机负载电阻变化，磁通量为恒值 0.25wb时，调制指标m的大小随转速的变化曲线。图6 电机转速恒定，转差率变化时，随磁通链的变化曲线在磁通量固定，负载恒定的情况下，转速只与曲线上的一个点对应，每个点都对应确定的电流和磁通量。因此d轴转子的参考磁通能用（18）和（19）式计算。根据最小铜耗下的转差率，算出对应的磁通量如下式所示。对于曲线上的每个点，都有一个直流电压的工作范围。用磁通量表达定子电流如（25）式所示，将（25）式带入（16）式得出一个用磁感和调制指标量表达直流电压的等式（26）。在式（26）中，通过改变调制指标的q轴分量并计算相应的d轴分量，可以得到直流电压的范围。也就是说当时同一个调制指标对应两个不同的磁感磁通链的值。磁通链越高，电压越高，在大多数情况下，这是不可取的也是不可行的。从图7可以看到磁通链对直流电压范围的影响。图7显示了不同的负载电阻下，磁通量较小时直流电压变化的等高线。图7 转速恒定，负载电阻在范围变化时，直流电压随调制指标m的q轴分量的变化曲线、控制方案的公式表述用提出的控制方案，如图8所示，可以达到通过控制调制信号的q轴和d轴分量控制直流电压的目的。控制方案采用转子磁通链和定子电流作为控制变量。感应发电机的模型方程式（8）（12）是非线性的，用输入输出的线性去耦技术可以获得输入控制变量和输出控制变量间的一个控制关系8。用这种方法，古典的线性控制系统理论可以用在决定每个控制器的结构和pi控制器的固定增益参数方面。当被控参数是直流电压和转子磁通量和时，这儿的控制变量是 。从方程式（8）（12）中，控制器的输出可以定义为：将（45）式代入（6）式中得：直流电压控制器的输出可用于计算q轴参考电流。从（1011）式，推导出转差频率和d轴参考定子电流为：通过（8）和（9）式，q轴和d轴的电压分量的控制式可以表达为：定义控制器增益如下，推导出状态变量的传递函数如（33）所示：将pi控制器转移函数的系数与butterworth多项式9的系数作比较，可以决定pi控制器的持续增益。在这个控制方案中控制器的传递函数是二次的，因此将控制器传递函数的分母系数与二次butterworth多项式（34）作比较。在butterworth方法中，传递函数的特征值一律位于s平面的左半部分，并且在一个以原点为中心，为半径的圆周上。图8 感应发电机系统的控制方案、仿真和实验结果我们已经用matlab/simulink，对于针对感应发电机交直流整流系统提出的控制方案实施了仿真。图9中的仿真结果展示了感应发电机的起动过程。从0到0.45秒转速以倾斜的直线上升到240rad/s，一直到2s转速保持在240rad/s。图9的也展示了在系统起动响应过程中q轴和d轴电压分量的变化，电磁转矩的变化，并且直流电压在0.3秒时达到稳态值。图10展示了在负载和转速变化时控制方案的动态响应。当转速恒定系统运行在稳态时，在1s将负载电阻从100变化到25，则转速在2s时从240rad/s变化到200rad/s，又在4s时从200rad/s增加到240rad/s。为了适应负载和转子速度的改变，受控直流电压有效地追踪变化指令，图示为200v。图8所示的控制方案已经用一个40mhz的dsp芯片tms320 lf2407aevm实现。这个2马力的感应发电机被用于控制整流器输出的220v的直流电压。实验波形如图11所示。图9 起动过程的仿真结果 从头开始：（a）q轴电压，（b）d轴电压，（c）转速，（d）电磁转矩，（e）直流电压，（f）相电压。图10 负载和转速变化时系统的动态响应 （a）q轴电压，（b）d轴电压，（c）转速，（d）电磁转矩，（e）直流电压，（f）相电压。对应于发电机的初始励磁，电容器的耐压值指示为20v，发电机以1319rmin的速度运转。图11展示了感应发电机以1319 rmin的转速运转时的稳态波形。直流电压稳定在 220 v并跟踪参考电压的变化。线电压恒定在110 v。a相电流是一个3安培的稳态值。（d）显示了对应于顶端设备的调制信号。图11中，线电压有一些高频分量，这是由快速整流器的开关暂态造成的。图11 2马力感应发电机稳态响应波形参考直流电压 = 220，转速 = 1319 rpm，负载电阻 = 80（a）直流电压（137.5 伏/格）；（b）线电压（350伏/格）；（c）a相电流（7.5安/格）；（d）a相调制信号（1.36/格）、结束语本文提供了在电机最小总铜耗的条件下，系统的一种详细分解方法，并经过一步步的推算得到系统的控制方案。此发电机整流器系统已经经过不同负载条件和不同转速的测试。转速改变而直流电压稳定证明了控制器的鲁棒性很好。在仿真和实验结果中也展示了负载变化对系统的影响。用最小铜耗条件下转子磁通的d轴参考分量的计算值，已经说明实现了铜耗最小。分解中也考虑到饱和效应，通过磁感的q轴分量随磁通链变化而改变解决。本文也展示了磁通链变化和不同的负载条件下发电机系统的自然响应。整流器调制指标的大小可以衡量发电机需要的励磁，所以发电机的励磁情况能用调制指标值详细地表示。附 录实验中用的是230v，4极，2马力的三相感应电机，具体参数为：定子电阻 转子电阻 不饱和磁感 定子每相漏电感 转子每相漏电感 直流电容值 c = 7800f英文原文high performance control of a boost ac-dcpwm rectifier-induction generator systemjyoti sastry, olorunfemi ojo, zhiqiao wudepartment of electrical and computer engineering/center for energy systems researchlaboratory for electric machines and power electronicstennessee technological universitycookeville, tn 38505, u.s.aphone: (931)-372-3869, fax: (931)-372-3436, e-mail: abstractthis paper presents a control methodology for the dc voltage regulation of an induction generator-ac-dc- boost rectifier system in which the copper loss of the generator is minimized. with the aid of an input-output linearization technique, which linearizes and decouples the model equations in the synchronous reference frame, a rotor flux vector control type high performance is achieved. steady-state analysis provides some insights into the operability regime of the generator. the effectiveness of the control scheme under different load conditions as well as varying rotor speeds has been demonstrated by computer simulations. some experimental results are included. index words: induction generator, ac-dc pwm rectifier, excitation, input-output linearization, butterworth polynomials, magnetizing flux saturation.i. introductiongrowing research and real application interests in alternative energy systems such as wind energy has increased the use of the induction machine as a generator because of inherent advantages of such as low cost, reduced maintenance, rugged and simple construction, brush-less rotor (squirrel-cage) and so on.the operation of an induction machine as a motor or generator is determined by the operating slip of the machine.a positive operational slip would indicate the operation of the machine as a motor, and a negative slip would indicate the generating mode of the machine.it is well known that an induction machine can be made to work as a self-excited generator, i.e. the generator can be excited by the (a) connection of three capacitors at the stator terminals of the machine (b) by using an inverter/rectifier system 1. in the case of the inverter/rectifier system, the dc side capacitor appears like three phase capacitors due to the switching signals of the inverter, and the single dc capacitor of the rectifier provides the required excitation for the induction generator. an extensive overview illustrating the vast amount of work done in different areas over the last 25 years such as self-excitation, voltage buildup modeling, steady state analysis of an induction machine has been presented in 2.also, in previously published work, the vector control of the induction generator rectifier system to produce dc power in which the rectifier also provides the excitation has been reported 3. the system has been studied specifically for applications related to wind energy, thereby studying the controller response for varying rotor speeds. also the stability of an induction generator-rectifier under field orientation control has been studied in 4, highlighting the possible instability of an ind uction generator used in high-speed applications. the control method adopted in this paper has been laid out in detail, illustrating the inp ut-output linearization method used in separating the linear from the non-linear terms in the system model equations. the proposed control scheme has been tested for its effectiveness by varying load conditions as well as varying the rotor speed of the machine. the mach ine has been operated at a condition of minimum copper loss 5. the condition of minimum loss is achieved by regulating the command rotor flux using a loss minimization function. the steady state analysis deals with the operation of the self-excited generator under conditions of saturation 6. the induction machine has been studied for its output power capability and the effect of the parameters of the machine on the operation of the machine under different load conditions. the analysis in this paper aims at highlighting the effect of the magnetizing flux on the excitation requirements of the system with the magnitude of the modulation signal as a measure of the required excitation. by fixing the magnetizing flux linkage the required modulation index for excitation of the machine can be determined. along with the effect of saturation, the system has been studied under a condition of minimum copper loss. the organization of this paper is as follows; sectio ns ii and iii detail the models of the three-phase boost rectifier and induction generator respectively. the model of the combined system has also been included in section iii. section iv deals with the steady state analysis of the machine. section v gives the formulation of the control scheme, and section vi validates the proposed control scheme using simulatio n and experimental results. ii. model of three-phase boost rectifierthe three-phase boost rectifier is used as the ac-dc converter in the system. each rectifier comprises of six active switches (with their anti-parallel diodes) that are switched using carrier-based sine-triangle pulse width modulation (pwm). the switching functions of the three top and three bottom devices are defined as and and respectively. the switching function has a value of one when the switch is turned on and it is zero when it is turned off. also, the switching function of the bottom device is complimentary to that of the top device. the voltage equations for the rectifier in the abc reference frame can be expressed in terms of the switching functions as:the switching function can be fourier- series approximated as in (3b) comprising of an average value and a time-varying component. the time varying component is the modulation signal, which compared with the triangle in the sine-triangle pwm scheme generates the switching function. transforming (1-3) to the synchronous reference frame, the q and d-axis voltages can be expressed in terms of the dc voltage and the corresponding component of the modulation index (mqs, mds ) as,the voltage equation on the dc side of the rectifier after synchronous reference frame transformation is given bythe load of the rectifier is .、model of three-phase induction genetratorthe model equations for a three-phase induction generator are the same as for an induction motor, except for the direction of the current flow. the system model is shown in figure 1.fig 1. induction generator-ac-dc rectifier systemthe equations for the generator expressed in the synchronous reference frame are 7:the rotor speed is , the angular frequency of the qd0 motor voltages is and the q-d rotor flux linkages are and . the stator q and d axis currents are and ,respectively.as mentioned earlier, the control scheme under consideration deals with the rotor fluxes and stator currents as control variables. the model equations for the induction generator can be expressed in terms of the desired state variables as:wherethe parameters and used in equations (8)-(12) are defined as:、steady state excitationthe steady state analysis is carried out using the complex form model equations of an induction generator (14)-(16). the effect of magnetic air-gap flux linkage saturation is taken into account 6. the analysis aims at determining the value of the magnitude of the modulation index required for the excitation of the generator, taking into account the effect of saturation and a condition of minimum total copper loss in the machine. under saturated conditions, the magnetizing inductance varies with the magnetizing flux as shown in figure 2 for a 2 hp induction machine. the reference frame transformation angle of the voltage equations assumes the alignment of the q-axis with the magnetizing flux linkage. hence, the d-axis magnetizing flux is assumed to be zero, and the d-axis magnetizing inductance is constant. however the q-axis magnetizing inductance is a function of the magnetizing flux, which is approximated by a polynomial given in (13). where is the slip frequency defined as .during steady-state, the derivatives, p in (14-16) are zero. alo ng with accounting for magnetic saturation of the air-gapflux linkage in the machine, the analysis aims at the operation of the machine at minimum total copper loss. the total copper loss (17) in the machine is minimum, when its derivative with the rotor slip is zero. this condition is achieved by appropriate selection of the operating slip of the machine, given by equation (18). the slip is plotted as a function of the magnetizing inductance in figure 3.fig 2. variation of the reciprocal of the magnetizing inductance with the magnetizing fluxfig 3. variation of the slip with the magnetizing flux.to obtain a relationship between the magnitude of the modulation index (m) and the magnetizing flux, the stator currents in equation (16) are expressed in terms of the stator fluxes. rearranging equation (15)substituting equation (19) in (14)the stator currents can be expressed in terms of the stator fluxes as:sub stituting (20 ) in (21) and eliminating the stator currents in (16), using equation (22) the effect of the changing magnetizing flux on the magnitude of the modulation index is obtained under a condition of minimum copper loss. the magnetizing flux linkage is varied and the corresponding values of magnetizing inductances are calculated. using the values of the magnetizing inductances, the slip and the corresponding modulation index is calculated for minimum total copper loss condition. figure 4 shows the effect of changing load resistance and changing magnetizing flux linkage on m assuming a constant rotor speed s can be seen from figure 4, an increase . as can be seen from figure 4, an increase in the load resistance decreases the values of the modulation index calculated. also from figure 4, at a constant load, the same value of modulation index is obtained for two different values of magnetizing inductance. the effect of the different magnetizing inductances is illustrated in figure 7.similarly, the effect of change in rotor speed for a constant magnetizing flux is illustrated in figure 5. in this case, the magnetizing flux is chosen to have a constant value of 0. 25 wb.expressing the product of the load resistance and the square of the modulation index in terms of the magnetizing inductance using equation (22), gives another parameter that can be used in the analysis. the parameter can be used as a measure of the load resistance that the system can be operated with for a fixed value of rotor speed and slip.the effect of the different operating slips on r0 is shown in figure 6.fig 4. variation of the magnitude of the modulation index m withthe magnetizing flute linkage for varying load (rl=35-65)resistances, and slip calculated under minimum loss.fig 5. variation of the magnitude of the modulation index m with rotor speed for a constant value of magnetizing flute 0.25 wb, for varying load resistances (rl =35-65) under minimum loss.fig 6. variation of ro with the magnetizing flux linkage for varyingslips at a constant rotor speed =200 rad/sec. fixing the magnetizing flux, at a constant load and rotor speed identifies with a single point on the m vs curve. each point corresponds to a certain current and flux. therefore the d-axis rotor reference flux can be calculated using equations (18) and (19). the flux is calculated corresponding to the operating slip at minimum loss.also for every point on the m vs curve, there is a range of dc voltages for that particular operating point. expressing the stator currents in terms of the magnetizing flux (25) and substituting in equation (16) results in an equation for the dc voltage in terms of the magnetizing inductance and modulation index (26). the range of do voltages is obtained by varying the q-axis component of the modulation index and calculating the corresponding d-axis component, in equation (26).for the same value of the modulation index there are two values of magnetizing inductance/magnetizing flux linkage.the higher magnetizing flux linkage yields a higher voltage,which in most applications is not acceptable and infeasible.the effect of the magnetizing flux linkage on the range of dc voltages can be seen in figure 7. the dc voltage contours are plotted for the lower value of the magnetizing flux, for plotted for the lower value of the magnetizing flux, for different load resistances. fig 7. var