AC Voltage and Current Sensorless Control of Three-Phase PWM Rectifiers

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1 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 6, NOVEMBER AC Voltage and Current Sensorless Control of Three-Phase PWM Rectifiers Dong-Choon Lee, Member, IEEE, and Dae-Sik Lim Abstract In this paper, a novel control scheme of three-phase PWM rectifiers eliminating both the ac input voltage and current sensors is proposed. The phase angle and the magnitude of the source voltage are estimated by controlling the deviation between the rectifier current and its model current to be zero. The input currents can be reconstructed from switching states of the PWM rectifier and the measured dc link currents. To eliminate the calculation time delay effect of the microprocessor, the currents ahead one sampling period are estimated by a state observer and then are used for feedback control. The proposed control scheme reduces the system cost and improves its reliability. The feasibility of the proposed ac sensorless technique for three-phase PWM rectifiers has been verified through experiments using a high performance DSP chip. Index Terms AC sensorless, PWM rectifier, source voltage estimation, state observer. I. INTRODUCTION THE THREE-PHASE PWM rectifier is increasingly used for industrial applications since it has advantages such as constant dc voltage control, sinusoidal line current control, unity power factor control, and bi-directional power flow [1]. For normal operation, it basically requires three kinds of sensors for detecting ac voltages, ac currents and dc voltage. A dc voltage sensor is demanded for the dc voltage feedback control and excessive voltage protection. The two ac voltage sensors are needed to detect the phase angle of the source voltage, which is taken as a reference frame of the controller, and thus to perform input power factor control. The two line current sensors are required for the input current control for boosting action and excessive current protection. Using all of these sensors makes the system bulky and expensive. In addition, the sensing signal is usually subject to the noise and furthermore incidental missing of the signal may deteriorate the system reliability. Therefore, it is desirable to reduce the number of sensors as far as possible. A few research results have been reported to eliminate either source voltage sensors [2] [4] or line current sensors [5] [8]. However, no method eliminating both of them has been yet presented as far as authors know. In this paper, a novel method to eliminate both ac voltage and current sensors is proposed, which uses only the dc-side sensors. The phase angle and the magnitude of the source voltage are estimated by controlling the deviation between the rectifier current Manuscript received March 19, 2001; revised March 28, This work was supported by the Yeungnam University Research Grants in Recommended by Associate Editor S. Y. Hui. D.-C. Lee is with the School of Electrical Engineering and Computer Science, Yeungnam University, Kyongbuk , Korea ( dclee@yu.ac.kr). D.-S. Lim is with the Bokuk Electric Ind. Co. Ltd., Daegu , Korea. Digital Object Identifier /TPEL Fig. 1. Three-phase PWM rectifier without ac-side sensors. and its model current to be zero. On the other hand, the line currents are reconstructed using the measured dc output currents and the switching states of the PWM rectifier. To eliminate the calculation time delay effect of the DSP, the line currents ahead one sampling period are estimated by a state observer, and then the predicted currents are used for feedback control. The validity of the proposed ac sensorless technique has been verified through experimental results for 1.5 [kva] IGBT PWM rectifier system controlled by a DSP TMS320C31. II. THREE-PHASE PWM RECTIFIERS A. System Modeling Fig. 1 shows the power circuit of the three-phase PWM rectifier. The voltage equations are given by,, and are the source voltage, the line current, and the rectifier input voltage, respectively and 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 A transformation matrix based on the estimated phase angle, which transforms three-phase variables into a synchronous (1) (2) (3) /02$ IEEE

2 884 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 6, NOVEMBER 2002 Fig. 2. Overall control block diagram. reference frame, is Transforming (1) into the reference frame using (4) is a differential operator and. Expressing (5) in a vector notation, (4) (5) (6) (7) B. System Control The 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 feedforward-type and 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. III. SOURCE VOLTAGE ESTIMATION The source voltage estimation is based on regulating the deviation between the rectifier current and the model current to be zero [2]. From (10), the rectifier current is expressed as Taking a transformation of (2) by using (4) (8) The model current corresponding to (12) is given by (12) Expressing (6) and (8) in a discrete domain, by approximating the derivative term in (6) by a forward difference [9], respectively, (9) Let the source voltage have the -axis component only (13) (14) is the sampling period. (10) (11) Even though we attach the subscript to the model variables, it may be deleted by assuming that the model parameters coincide well with those of the real system. In this case, the relationship of the voltage and current vectors for both the systems is shown in Fig. 3.

3 LEE AND LIM: AC VOLTAGE AND CURRENT SENSORLESS CONTROL 885 Fig. 4. Space voltage vectors. Fig. 3. Vector diagram. Subtracting (13) from (12) (15) From (15), it should be noted that is proportional to the estimation error of the source voltage. Substituting (11) and (14) into (15), (16) If, then (16) can be expressed as (17) Fig. 5. Switching pulses and dc link currents., (18) Since it is obvious from (16) that the - and -axis current errors are directly proportional to the magnitude error and the phase angle error, respectively, each variable to be estimated can be found by using PI regulators as follows: (19) (20) and are the PI gains for the magnitude estimator, and and are those of for the phase angle estimator. IV. LINE CURRENT RECONSTRUCTION A. Reconstruction of Line Currents Just as the output current of PWM inverters can be reconstructed from the switching states and the dc link currents, so can the input current of PWM rectifiers [5] [8]. The dc link current is expressed as (21) means a switching state (1 or 1) of each leg of the rectifier. For the zero voltage vectors, the dc current is zero since the dc output side is isolated from the source. Fig. 4 shows a space voltage vector diagram for three-phase PWM rectifiers. For example, let a reference voltage vector be located in region. In this case, the effective voltage vectors of and are used for switching. Fig. 5 shows the switching state of each phase and corresponding dc link current. For the time duration of vector,,, and for vector,,. Fig. 6 describes the current flow in this case. The third line current is obtained by (22) This algorithm of the current reconstruction can be applied for the remaining sectors in voltage vector diagram. Table I shows the relationship between the switching state of each voltage vector and the corresponding dc link current. B. Modification of the Reconstructed Currents The equation (22) is valid only when the two line currents are sampled at the same time. However, it is seen from Fig. 5 that and can never be sampled simultaneously. Therefore, there exist some errors in the third line current calculated as (22). To eliminate the errors, the currents at the end point of each sampling period are predicted with the reconstructed line

4 886 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 6, NOVEMBER 2002 Likewise, the -line current at the calculated as th sampling instant can be (25). Then, the third line current,, can be found from (22). For the other sectors, the same algorithm for the line current reconstruction as above can be applied. V. PREDICTIVE CURRENT ESTIMATION The currents of (23) and (25) 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 [11]. In addition, the state observer provides the filtering effects for the estimated variable [9]. Expressing (5) in a state-space form,, (26) (27) Fig. 6. Current paths for (a) V (100) (b) V (110). TABLE I SWITCHING STATES AND DC LINK CURRENTS and is the output. Transforming (26) and (27) into a discrete domain [9], [12], respectively,, (28) (29) currents, applied average voltages, and time duration, as follows [11]: Then, the observer equation adding an error correction term to (28) is given by (30) and (23) (24) is the observer gain matrix and means the estimated quantity, and is the state variable estimated ahead one sampling period. Subtracting (30) from (28), the error dynamic equation of the observer is expressed as (31) which is the averaged -phase voltage applied from to the end point of the sampling period. Here, the source voltage is assumed to be constant over a sampling period and the dead time effect and the conduction voltage drop of the devices are neglected.. Here, it is assumed that the model parameters match well with the real ones. Fig. 7 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 (31) to converge to the zero state,

5 LEE AND LIM: AC VOLTAGE AND CURRENT SENSORLESS CONTROL 887 Fig. 7. Closed-loop state observer. Fig. 8. Short pulse region. the roots of the characteristic equation of (31) should be located within the unit circle. VI. SOLUTIONS FOR PRACTICAL PROBLEMS A. Short Pulse Width When the reference voltage vector is adjacent to the active vectors, as shown in shaded area of Fig. 8, it is difficult to measure the dc link current since time duration for actual detection is too short. In Fig. 9(a), the pulse width corresponding to (110) vector is too short for normal detection. In fact, either one or both of and may be too short. In this case, the pulse position should be shifted so that the minimum pulse width can be guaranteed [13]. Fig. 9(b) shows that the pulse width for vector is widened to which is the minimum time needed to detect the current, the total duration ( for active voltage vectors is kept the same. Due to the pulse position shift, voltage generation error may occur. However, it has been observed that its effect is so small to be neglected. B. Estimation of Initial Phase Angle At starting of the system, there is no initial information on the phase angle of the source voltage. In this case, since uncontrollable currents may flow, a special stage of estimating the initial phase angle is needed as below. At first, apply an arbitrary voltage vector with a short pulse during the first sampling period and measure the dc currents. Then, with a different voltage vector, repeat the same process for the second sampling period. Next, reconstruct line currents from the switching pattern and measured dc currents. Before the end of the second sampling period, calculate the source voltage Fig. 9. Switching pattern (a) with a short pulse (b) with minimum pulse width. expressed in stationary Then, find the initial phase angle as reference frame as follows: (32) (33) Using this initial phase angle, from the third sampling period, proceed with the normal control process. VII. EXPERIMENTS AND DISCUSSIONS A. System Hardware Configuration Fig. 10 shows the system hardware configuration. The source voltage is a three-phase, 110 [V].The input resistance and inductance are 0.06 [ ] and 3.3 [mh], respectively. The dc link capacitance is 2350 [ F] and the switching frequency of the

6 888 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 6, NOVEMBER 2002 Fig. 10. System hardware configuration. Fig. 12. Sampling of dc link currents. Fig. 11. Dc link currents and corresponding phase currents (in sector V ). PWM rectifier is 3.5 [khz]. 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, 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]. B. Experimental Results Fig. 11 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. 12(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. 13. 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. 12(b). The cut-off frequency of the Butterworth s 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. 13 shows the estimated source voltage and current at starting. With the proposed initial estimation strategy, the starting operation is well performed. Fig. 14 shows the phase angle, magnitude, and waveform of the estimated source voltage, which coincide well with measured ones. Fig. 15 shows the source voltage and current waveform at unity power factor. Figs. 16 and 17 show transient responses for voltage reference changes and for load variations from 540 [W] to 1080 [W] and back to 540 [W], respectively. 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 the load current is added, which is possible without additional cur-

7 LEE AND LIM: AC VOLTAGE AND CURRENT SENSORLESS CONTROL 889 Fig. 17. Transient responses for load variation. Fig. 14. Estimated source voltage in steady state. (a) phase angle (b) magnitude (c) waveform. Fig. 15. Source voltage and current waveforms. (a) estimated (b) measured. Fig. 18. Estimated currents for input inductance variation. (a) 30% decrease (b) 30% increase. Fig. 16. Transient responses for dc voltage changes. rent sensor when the PWM rectifier is combined with the PWM inverter for ac motor drives. Fig. 18 shows the effect of the parameter variation on the current estimation. In case that the inductance value in the DSP is changed by 30% or 30%, the performance of current estimation and control keeps nearly the same characteristic as before.

8 890 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 17, NO. 6, NOVEMBER 2002 VIII. CONCLUSIONS This 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 [kva] PWM rectifier system controlled by TMS320C31 DSP. The experimental results have verified that the proposed ac sensor elimination method is feasible. REFERENCES [1] B. T. Ooi, J. C. Salmon, J. W. Dixon, and A. B. Kulkarni, A three-phase controlled-current PWM converter with leading power factor, IEEE Trans. Ind. Applicat., vol. 23, pp , Jan./Feb [2] T. Takeshita, T. Kobayashi, and N. Matsui, A scheme of power source voltage sensorless three-phase PWM ac/dc converter, Trans. IEE Jpn., vol. 114-D, no. 12, pp , [3] T. Noguchi, H. Tomoki, S. Kondo, and I. Takahashi, Direct power control of PWM converter without power-source voltage sensor, IEEE Trans. Ind. Applicat., vol. 34, pp , [4] T. Ohnuki, O. Miyashita, P. Lataire, and G. Maggetto, A three-phase PWM rectifier without voltage sensors, in Proc. EPE 97 Conf., 1997, pp [5] C. T. Pan, Modeling and analysis of a three phase PWM ac dc converter without current sensor, Proc. Inst. Elect. Eng. B, vol. 40, Mar [6] S. Bhowmik, A. van Zyl, R. Spee, and J. H. Enslin, Sensorless current control for active rectifiers, IEEE Trans. Ind. Applicat., vol. 33, pp , [7] B. Andersen, T. Holmgaard, J. G. Nielsen, and F. Blaabjerg, Active three-phase rectifier with only one current sensor in the dc link, in Proc. IEEE PEDS 99 Conf., Hong Kong, 1999, pp [8] W.-C. Lee, D.-S. Hyun, and T.-K. Lee, A novel control method for three-phase PWM rectifier using single current sensor, in Proc. IEEE PESC 99 Conf., Charleston, SC, 1999, pp [9] G. F. Franklin, J. D. Powell, and M. L. Workman, Digital Control of Dynamic Systems, 2nd ed. Reading, MA: Addision-Wesley, [10] D.-C. Lee and G.-M. Lee, Anti-windup of current regulators considering inverter saturation, in Proc. EPE 97 Conf., 1997, pp [11] J. K. Moynihan, S. Bolognani, R. C. Kavanagh, M. G. Egan, and J. M. D. Murphy, State observer based indirect current detection for PWM synchronous servo drives, in Proc. ICEM 91 Conf., Manchester, U.K., 1991, pp [12] T. Kawabata, T. Miyashita, and Y. Yamamoto, Digital control of threephase PWM inverter with LC filter, IEEE Trans. Power Electron., vol. 6, pp , Jan [13] F. Blaabjerg, J. K. Pedersen, U. Jaeger, and P. Thoegersen, Single current sensor technique in the dc link of three-phase PWM-VS inverters: A review and a novel solution, IEEE Trans. Ind. Applicat., vol. 33, pp , Dong-Choon Lee (S 90 M 95) was born in Korea in He received the B.S., M.S., and Ph.D. degrees in electrical engineering from Seoul National University, Seoul, Korea, in 1985, 1987, and 1993, respectively. He was a Research Engineer at Daewoo Heavy Industry, Korea, from 1987 to He also worked at the Research Institute of Science Engineering, Seoul National University, under a Post-Doctoral Fellowship for one year. Since 1994, he has been a faculty member of the School of Electrical Engineering and Computer Science, Yeungnam University, Kyongbuk, Korea. As a Visiting Scholar, he joined Power Quality Laboratory, Texas A&M University, College Station, in 1998 and the Electrical Drive Center, University of Nottingham, U.K., in His research interests include ac machine drives, control of power converters, active power filters, and wind power generation. Dae-Sik Lim was born in Korea in He received the B.S. and M.S. degrees in electrical engineering from Yeungnam University, Kyongbuk, Korea, in 1998 and 2000, respectively. He is currently with Bokuk Electric Technical Research Laboratory, Daegu, Korea. His research areas are the web control of engine generator systems and dynamic UPS systems.

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