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AC Voltage and Current Sensorless Control ofThree-Phase PWM Rectifiers Dong-Choon Lee, Member, IEEE, and Dae-Sik Lim1 THREE-PHASE PWM RECTIFIERSA System ModelingFig. 1 shows the power circuit of the three-phase PWM rectifier. The voltage equations are given by (1)Fig. 1. Three-phase PWM rectifier without ac-side sensors.where , and are the source voltage, the line current, and the rectifier input voltage, respectively and are the input resistance and the input inductance, respectively. When the peak line voltage , angular frequency , and initial phase angle are given, assuming a balanced three-phase system, the source phase voltage is expressed as (2)Where (3)A transformation matrix based on the estimated phase angle ,which transforms three-phase variables into a synchronous dq reference frame, is (4)Transforming (1) into the reference frame using (4) (5)where p is a differential operator and . Expressing (5) in a vector notation (6)where, , (7)Taking a transformation of (2) by using (4) (8)Where (9)Expressing (6) and (8) in a discrete domain, by approximating the derivative term in (6) by a forward difference 9, respectively, (10) (11) Where T is the sampling period. Fig. 2. Overall control block diagram.B System ControlThe PI controllers are used to regulate the dc output voltage and the ac input current. For decoupling current control, the cross-coupling terms are compensated in a feed forward-typeand the source voltage is also compensated as a disturbance. For transient responses without overshoot, the anti-windup technique is employed 10. The overall control block diagram eliminating the source voltage and line current sensors is shown in Fig. 2. The estimation algorithm of source voltages and line currents is described in the following sections.2 PREDICTIVE CURRENT ESTIMATIONThe currents of and can not be calculated instantly since the calculation time of the DSP is required. To eliminate the delay effect, a state observer can be used. In addition, the state observer provides the filtering effects for the estimated variable.Expressing (5) in a state-space form, (12) (13)where, ,And y is the output. Transforming (12) and (13) into a discrete domain, respectively, (14) (15)where,Then, the observer equation adding an error correction term to is given by (16)Where K is the observer gain matrix and “ ” means the estimated quantity, and is the state variable estimated ahead one sampling period. Subtracting (15) from (16), the error dynamic equation of the observer is expressed as (17)where . Here, it is assumed that the model parameters match well with the real ones. Fig. 3 shows the block diagram of the closed-loop state observer.The state variable error depends only on the initial error and is independent of the input. For (17) to converge to the zero state, the roots of the characteristic equation of (17) should be located within the unit circle. Fig. 3. Closed-loop state observer. Fig. 4. Short pulse region. 4 EXPERIMENTS AND DISCUSSIONSA. System Hardware ConfigurationFig. 5 shows the system hardware configuration. The source voltage is a three-phase, 110 V.The input resistance and inductance are 0.06and 3.3 mH, respectively. The dc link capacitance is 2350F and the switching frequency of the PWM rectifier is 3.5 kHz.Fig. 5. System hardware configuration.Fig. 6. Dc link currents and corresponding phase currents (in sector V ).The TMS320C31 DSP chip operating at 33.3 MHz is used as a main processor and two 12-b A/D converters are used. One of them is dedicated for detecting the dc link current and the other is used for measuring the dc output voltage and the source voltages and currents, where ac side quantities are just measured for performance comparison.One of two internal timers in the DSP is employed to decide the PWM control period and the other is used to determine the dc link current interrupt. Considering the rectifier blanking time of 3.5 s, A/D conversion time of 2.6 s, and the other signal delay time, the minimum pulse width is set to 10 s.A. Experimental Results Fig. 6 shows measured dc link currents and phase currents. In case of sector V of the space vector diagram, the dc link current corresponds to for the switching state of and for that of . Fig. 7(a) shows the raw dc link current before filtering. It has a lot of ringing components due to the resonance of the leakage inductance and the snubber capacitor. When the dc current is sampled at the end point of the active voltage vectors as shown in the figure, the measuring error can be reduced. Fig. 7. Sampling of dc link currents. Fig. 8. Estimated source voltage and current at starting. To reduce this error further, the low pass filter should be employed, of which result is shown in Fig. 7(b). The cut-off frequency of the Butterworths second-order filter is 112 kHz and its delay time is about 2 sec. Since the ringing frequency is 258 kHz and the switching frequency is 3.5 kHz, the filtered signal without significant delay is acquired.Fig. 8 shows the estimated source voltage and current at starting. With the proposed initial estimation strategy, the starting operation is well performed. Fig. 9 shows the phaseangle, magnitude, and waveform of the estimated source voltage, which coincide well with measured ones.Fig. 10 shows the source voltage and current waveform at unity power factor. Figs. With the estimated quantities for the feedback control, the control performance is satisfactory. The dc voltage variation for load changes will be remarkably decreased if a feedforward control for theload current is added, which is possible without additional cur-rent sensor when the PWM rectifier is combined with the PWM inverter for ac motor drives.Fig. 9. Estimated source voltage in steady state. (a) phase angle (b)magnitude (c) waveform. Fig. 10. Source voltage and current waveforms. (a) estimated (b) measured.4 CONCLUSIONSThis paper proposed a novel control scheme of the PWM rectifiers without employing any ac input voltage and current sensors and with using dc voltage and current sensors only. Reducing the number of the sensors used decreases the system cost as well as improves the system reliability. The phase angle and the magnitude of the source voltage have been estimated by controlling the deviation between the rectifier current and its model current to be zero. For line current reconstruction, switching states and measured dc link currents were used. To eliminate the effect of the calculation time delay of the microprocessor, the predictive state observer was used. It was shown that the estimation algorithm is robust to the parameter variation. The whole algorithm has been implemented for a proto-type 1.5 kVAPWM rectifier system controlled by TMS320C31 DSP. The experimental results have verified that the proposed ac sensor elimination method is feasible.无交流电动势、电流传感器的三相PWM整流器控制 Dong-Choon Lee, Member, IEEE, and Dae-Sik Lim1 三相PWM 整流器A 系统模型图一所示为三相PWM整流器的主电路，电压等式给出如下： (1) 图1 无交流传感器三相PWM整流器其中e，i和v分别是源电压，线电流和整流器的输入电压，R和L分别是输入电阻和输入电感。当已知线电压峰值E，角频率和初始相位角时，假定三相系统是平衡的，则源相位电压可以表达为 (2)其中 (3)一种基于估计相位角的变换矩阵，将三相变量变换成一个同步的，坐标系，这个矩阵是 (4)将（1）式变为坐标系使用式（4） (5)其中p是一个微分算子且将（5）式写成矢量形式 (6)其中 , (7)用式（4）对（2）式进行变换 (8)其中 (9) 通过前向差分来接近微分的限幅，分别将（6）式和（8）式用离散域表示 (10) (11)其中，T是采样周期图2 总的控制模块图B 系统控制PI控制器是用来调节直流输出电压和交流输入电流的。对于解耦电流控制，交叉耦合项用前馈式补偿，同时，源电压作为扰动的补偿。对于没有过调的暂态响应，引入anti-windup技术。消除源电压和线电流传感器的总的控制模块图如图2所示。源电压和线电流的估计算法在以后的章节中介绍。2预测电流估计由于DSP存在计算时间，所以和不能立即计算。为了消除延迟的影响，可以使用状态监测器。另外，状态监测器可以对估计变量起到滤波作用。将式（5）用状态空间形式表达为 (12) (13)其中, Y是输出。分别将式（12）和式（13）分别变换成离散领域 (14) (15)其中, 则加入了误差调整的监测器等式为 (16)其中，k是监测器增益矩阵，“ ”是指估计量，是提前一个采样周期估计的状态变量。用式（15）和减去式（16），监测器的动态误差等式表述为 (17)其中这里，假设模型参数与真实系统吻合的很好。图7所示是闭环状态监测器的模块图。状态变量误差仅取决于初始误差，与输入无关。为了使式（17）趋于零状态，典型等式（17）的根应该限制在单位圆内。 图3 闭环状态监测器 图4短脉冲区域3实验与讨论A系统硬件构造 图5 系统硬件结构 图6 直流电流和相应相电流 (扇区5 ).图5所示是系统的硬件结构图。源电压是三相110V。输入电阻和电感分别为0.06和3.3mH。直流侧电容为2350F，PWM整流器的开关切换频率为3.5KHZ.使用TMS320C31 DSP芯片设定在33.3MHZ作为主处理器，同时