Letters
Modified Single-Loop Current Sensorless Control for Single-Phase
Boost-Type SMR With Distorted Input Voltage
Hung-Chi Chen, Member, IEEE, Chih-Chieh Lin, and Jhen-Yu Liao
Abstract—The first single-loop current sensorless control
(SLCSC) for single-phase boost-type switching-mode-rectifier (SMR) had been proposed in the prior paper. SLCSC with si-nusoidal input voltage possesses good performance, but its per-formance with distorted input voltage should be improved. In this paper, a modified SLCSC is proposed and implemented in a field-programmable gate array (FPGA)-based system to obtain better performance than SLCSC. Instead of the phase-shift signal in SLCSC, the inductor voltage amplitude signal becomes the out-put of proportional-plus-integral (PI)-type voltage controller in the modified SLCSC. The provided simulation and experiment results demonstrate the modified SLCSC.
Index Terms—Current sensorless control, switching mode
rectifier.
I. INTRODUCTION
A
QUALIFIED ac/dc conversion includes functions of input current shaping and output voltage regulation. The use of switching-mode rectifier (SMR) is an effective mean to perform the qualified ac/dc conversion. Boost-type SMRs are the most popular circuit topology among all the others due to the con-tinuous current in the inductor [1]. In order to save the input signals and pins, many current sensorless controls [2]–[5] had been proposed in this literature and are tabulated in Table I.The current sensorless controls using the special function d|sin θ|/dθ are able to yield sinusoidal input current, even when the input voltage is distorted [2], [3]. On the other hand, those sensorless current controls with the assumption of sinusoidal input voltage have poor performance with distorted input volt-age. In addition, the inductor resistance and the conducting voltages of switches and diodes are considered in [5], but are neglected in [2]–[4]. Sinusoidal input voltage is assumed in the proposed single-loop current sensorless control (SLCSC) [5], and significant increase of current harmonics can be found in the experimental results when the input voltage is distorted.
Manuscript received March 7, 2010; revised August 4, 2010; accepted August 17, 2010. Date of current version June 22, 2011. This work was supported by the National Science Council (NSC), Taiwan under Grant NSC98-2221-E-009-180-MY2. Recommended for publication by Associate Editor C. A. Canesin.
The authors are with the Department of Electrical Engineering, National Chiao Tung University (NCTU), Hsinchu 30010, Taiwan (e-mail: hcchen@ cn.nctu.edu.tw; [email protected]; [email protected]).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2010.2070079
In this paper, the proposed SLCSC is modified to obtain good performance with distorted input voltage. Instead of the phase-shift signal in SLCSC, the inductor voltage amplitude signal becomes the output of the proportional-plus-integral (PI)-type voltage controller and the special function d|sin θ|/dθ is also used in the modified SLCSC.
First, the effects of inductor-voltage amplitude on the in-put current waveform are analyzed and modeled with consider-ing the inductor resistance and conduction voltages. The result shows that the sinusoidal input current can be inherently yielded in modified SLCSC, even when the input voltage is distorted. Then, a PI-type voltage controller is included to regulate the output voltage by tuning this inductor voltage amplitude. Fi-nally, some simulated and experimental results have been given to demonstrate the performance of the modified SLCSC.
II. MODIFIEDSLCSC
A. Boost-Type SMR
The boost-type SMR is plotted in Fig. 1, where it can be seen as a single-switch boost-type converter cascaded to a bridge rectifier. Resistors Rs1, Rs2, Ro1, and Ro2 with resistances of several megaohms are used to sense the input voltage vs and the output voltage Vo. In order to represent the resistance of the practical inductor, a resistor rLis connected to an ideal inductor
L in series.
In boost-type SMR, the input current is(t) can be mathemat-ically represented as
is(t) = sign(vs(t))iL(t) (1) where sign(·) is a sign operator and
sign(X) =
+1, when X≥ 0
−1, when X < 0. (2) During the positive input voltage, the input current is flows through D3, rL, L, T , and D2, and through D3, rL, L, D, load, and D2, when the switch T is turning on and turning off,
respectively. Similarly, the current is flows through D1, T , L,
rL, and D4, and through D1, load D, L, rL, and D4, when the
switch T is conducting and blocking, respectively.
In order to develop the modified SLCSC, some assumptions are initially made.
1) The output voltage Vois assumed to be equal to the voltage command Vo∗due to the bulk capacitor Co.
TABLE I
SUMMARY OFCURRENTSENSORLESSCONTROL[2]–[5]
Fig. 1. Boost-type SMR with modified SLCSC.
2) The switching frequency fs(=1/Ts) is assumed to be much larger than the line frequency f and the input voltage is seen as constant during each switching period.
3) Both the sums of conduction voltages for the turning-ON loop and the turning-OFF loop are assumed to be equal to VF.
The control signal vcontin Fig. 1 is the output of the modified
SLCSC and it is connected to the comparator (−) terminal. A fixed-frequency fixed-amplitude carrier signal vtriis at the
com-parator (+) terminal. Based on the assumption 2), the average duty ratio ¯d during each switching period Ts can be expressed as
¯
d = 1− vcont. (3)
Applying Kirchhoff’s voltage law to the turning-ON loop and turning-OFF loop yields the turning-ON inductor voltage vL ,O N and turning-OFF inductor voltage vL ,O FF, respectively
vL ,O N =|vs| − VF − iLrL (4)
vL ,O FF =|vs| − VF − iLrL− Vo∗. (5) Then, the average inductor voltage ¯vL can be expressed as
¯
vL =
vL ,O N× tO N+ vL ,O FF× tO FF
Ts
(6)
where tO N(= ¯dTs) and tO FF(=Ts− tO N) are the turning-ON
time and turning-OFF time, respectively. By substituting (3), (4), and (5) into (6), the average inductor voltage can be rewritten as
¯ vL =|vs| − VF − ¯iLrL − vcontVo∗. (7) Fig. 2. Modified SLCSC. TABLE II SIMULATEDPARAMETERS B. Modified SLCSC
According to the divider rule and the assumption of 1), the input signals vs and Voin Fig. 1 can be expressed as
vs =Rs2 Rs vs (8) Vo= Ro2 Ro Vo= Ro2 Ro Vo∗ (9)
where Rs = Rs1+ Rs2and Ro = Ro1+ Ro2, respectively. By substituting (8) and (9) into (7), the average inductor voltage ¯vL
Fig. 3. Simulated waveforms for sinusoidal input voltage. (a) 300 W. (b) 600 W. can be expressed as ¯ vL =|vs| Rs Rs2 − VF − ¯iL rL− vcontVo Ro Ro2 . (10) In order to yield the sinusoidal input current, the average inductor voltage ¯vLmust be the function of sign(vs) cos(2πf t) with amplitude ˆVL, i.e.,
¯
vL = ˆVLsign(vs) cos(2πf t). (11) By substituting (11) into (10) and arranging the terms, the control signal vcontis given as
vcont= vcont0+ Δvcont (12)
where the nominal control signal vcont0and the variable control
signal Δvcontare
vcont0 =|vs| Rs Rs2 1 Vo∗ (13) Δvcont= ˆ VL Vo∗ −s1(t)− rL 2πf Ls2(t) −VF Vo∗. (14) It is noted that both unit functions s1(t) =
sign(vs) cos(2πf t) and s2(t) =|sin(2πft)| are
synchro-nized to the zero-crossing points (ZCPs) of the input voltage and repeated with fixed frequency (i.e., double line frequency
TABLE III SIMULATEDTHDiVALUES
2f ). Thus, it is easy to generate functions s1(t) and s2(t) in a
digital system.
Fig. 2 shows the block diagrams of the modified SLCSC, where both functions s1(t) and s2(t) are generated by
synchro-nizing the ZCPs of the input voltage signal vsand lookup table. In order to generate a signal with double line frequency 2f, the frequency of the clock input CLK of the block “lookup table” is fs/(2f ), where fs is the sampling frequency (i.e., carrier frequency).
From the average inductor voltage in (11), the resulting aver-age inductor current ¯iL and the average input current ¯iscan be
Fig. 4. Simulated waveforms for distorted input voltage. (a) 300 W. (b) 600 W. expressed as ¯iL = ˆ VL 2πf L|sin(2πft)| (15) ¯is = ˆ VL 2πf Lsin(2πf t) = ˆIssin(2πf t). (16)
It is noted that the yielded input current is is sinusoidal and synchronized to ZCPs of the input voltage. In addition, the in-put current amplitude ˆIs is proportional to the inductor voltage amplitude ˆVL, and thus, the average input power is also propor-tional to the inductor voltage amplitude ˆVL.
In order to keep the output voltage constant, the average input power must be equal to the average load power. Therefore, based on the balance between the input power and output power, a PI-type controller is included in the modified SLCSC to regulate the output voltage by tuning the inductor voltage amplitude ˆVL.
III. SIMULATIONRESULTS
In this section, some computer simulations in Physical Secu-rity Information Management (PSIM) software are performed to demonstrate the modified SLCSC. The simulated parameters are tabulated in Table II.
A. Sinusoidal Input Voltage
When the waveform of input voltage is sinusoidal, the simu-lated waveforms for average output power 300 and 600 W are plotted in Fig. 3(a) and (b), respectively. The normal control signal vcont0 is fixed regardless of the power level, but the
vari-able control signal Δvcontvaries with the power level and the
PI output ˆVL.
The yielded input currents are sinusoidal and in phase with the sinusoidal input voltage, and the current amplitude are pro-portional to signal ˆVL in (16). Therefore, due to the balance between the input power and output power in simulation, the output voltages Vo are well regulated to 300 V.
The simulated total current harmonic distortion (THDi) val-ues under various power levels are tabulated in Table III. In the simulation waveforms, the zero-crossing distortion increases with the power level, and thus, the simulated THDivalue also increases with the increase of power level.
B. Distorted Input Voltage
By replacing the sinusoidal input voltage with a distorted input voltage with total voltage harmonic distortion THDv ≈
4.0%, the simulated waveforms for 300 and 600 W are plotted
in Fig. 4(a) and (b), respectively, where the current waveforms in ZCP of input voltage are plotted in detail. The yielded input currents are sinusoidal and synchronizing to the distorted input
Fig. 5. Experimental results for sinusoidal input voltage for average output power. (a) 300 W. (b) 400 W. (c) 500 W. (d) 600 W.
voltage, and the current amplitude are proportional to the PI output ˆVL in (16). Due to the distorted input voltage, significant difference between the normal control signals vcont0 in Figs. 3
and 4 can be found.
TABLE IV MEASUREDTHDiVALUES
The simulated THDivalues of distorted input voltage accord-ing to various power levels are tabulated in Table III. Compared with Fig. 3, the waveforms of distorted input voltage in Fig. 4 show less zero-crossing distortion [6], and thus, the simulated
THDivalues of distorted input voltage are lower than those of sinusoidal input voltage.
IV. EXPERIMENTALRESULTS
In this section, some experimental results are provided to demonstrate the modified SLCSC, which had been digitally implemented in a field-programmable gate array (FPGA)-based system using Xilinx XC3S250E. The used parameters in the experiment are the same as those tabulated in Table I.
A. Sinusoidal Input Voltage
The sinusoidal input voltage is provided by the instrument of ac power source. Fig. 5 shows the experimental results for various output power where the average duty ratio ¯d, the con-trol signals vcont0, and Δvcont for 400 W are also plotted for
comparison. When the input voltage is near zero, the average duty ratio is 100% in order to keep the switch conducting within several switching period. As the input voltage increases, the average duty ratio decreases. After the input voltage turns to decrease from its peak value, the average duty ratio increases from its minimum value.
Compared with the experimental results with sinusoidal in-put voltage in [5], the resulting inin-put currents are more closed to the sinusoidal waveform in phase with the sinusoidal input voltage especially with low output power. Moreover, the current waveforms at low output power are significantly improved.
In the practical circuit, all the inductance, the equivalent in-ductor resistance, and the conduction voltages of diodes and switch are not constants and may vary with the instantaneous current. It means that parameter mismatches always exist in the system and have effects on the yielded current waveforms. However, the output voltage is well regulated by the PI-type controller from the experimental results.
Compared with the THDivalues from 14.3% (≈300 W) to 12.56% (≈600 W) in [5], the measured THDivalues tabulated in Table IV vary from 7.56% (300W) to 15.95% (600 W). There-fore, for experimental results with sinusoidal input voltage, the low-power performance is improved by the modified SLCSC.
In order to evaluate the transient performance of the modified SLCSC, the output power is suddenly increased from 300 to
Fig. 6. Experimental waveforms for sinusoidal input voltage with the output power change from 300 to 600W.
600 W and the experimented waveforms are shown in Fig. 6. In order to regulate the output voltage to voltage command 300 V, the inductor voltage signal ˆVL increases and the resulting input current amplitude also increases. However, the input current is in phase with the sinusoidal input voltage during the transient time.
B. Distorted Input Voltage
In this experiment, the distorted input voltage, as shown in Fig. 7, is obtained by connecting the boost-type SMR to the electric outlet in the laboratory, where the measured total voltage harmonic distortion is THDv ≈ 4.0%.
Fig. 7(a)–(d) shows the experimental results for output power 300, 400, 500, and 600 W, respectively, where the average duty ratio ¯d, the control signals vcont0, and Δvcontfor 400 W are also
plotted for comparison.
Compared with the measured THDi values from 20.4% (≈300W) to 12.0% (≈700 W) in [5], the measured THDivalues tabulated in Table IV vary from 7.00% (300 W) to 12.23% (600 W). Therefore, from the experimental results of distorted input voltage, the low-power performance is significantly improved by the modified SLCSC.
The current harmonics of the current waveforms in Figs. 5 and 7 are tabulated in Table V, where the harmonic limits of the IEC-61000-3-2 for Class A and Class D are also listed for comparison. The yielded current harmonics are well below the harmonic limits, and thus, the measured currents comply with the commercial standards.
It is noted that the yield input current is synchronized with the ZCPs, not in phase with the fundamental component of the distorted input voltage. Thus, the measured fundamental input currents of distorted input voltage are slightly larger than those of sinusoidal input voltage due to the displacement power factor. From the simulation results in Table III and the experimental results in Table IV, all the measured THDivalues of distorted input voltage are smaller than those of sinusoidal input voltage. It follows that the modified SLCSC with distorted input voltage has better performance than with sinusoidal input voltage.
Fig. 7. Experimental results for distorted input voltage for average output power. (a) 300 W. (b) 400 W. (c) 500 W. (d) 600 W.
In order to evaluate the transient performance with distorted input voltage, the load power is forced to have a step change from 300 to 600 W and the experimented waveforms are shown in Fig. 8. In order to keep the output voltage to voltage command
TABLE V
MEASUREDCURRENTHARMONICS
Fig. 8. Experimental waveforms for the distorted input voltage when the load is suddenly changed from 300 to 600W.
300 V, the output ˆVL of the PI controller increases and the resulting input current amplitude also increases to meet the requirement of power balance. However, the input current can be seen as being synchronized with the sinusoidal input voltage during the transient period.
V. CONCLUSION
The modified SLCSC has been proposed and implemented in this paper and it yields lower current harmonics than the prior SLCSC. In addition, the modified SLCSC with distorted input voltage possesses better performance than that with sinu-soidal input voltage. However, due to the parameter mismatch, the practical input current is near sinusoidal, and fortunately, the current harmonics are lower than the well-known harmonic limits.
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