Implementation and Performance Comparison of Five DSP-Based Control Methods for Three-Phase Six-Switch Boost PFC Rectifier

Laszlo Huber, Misha Kumar, and Milan M. Jovanović

Delta Products Corporation P.O. Box 12173

5101 Davis Drive Research Triangle Park, NC 27709, USA

Abstract – In this paper, implementation and performance comparison of five control methods for the average-current-controlled three-phase six-switch boost PFC rectifier are presented. The considered average-current-control methods include implementations with three independent controllers, with six-step PWM, and with three-step PWM all in stationary (a,b,c) reference frame, as well as average-current control in rotating (d,q) reference frame with zero-sequence-signal (ZSS) injection-based PWM and with space vector modulation (SVM). It is shown that the average-current control with three independent controllers exhibits the lowest total harmonic distortion (THD) of input currents, whereas, the average-current control in the rotating (d,q) reference frame with ZSS injection-based PWM and SVM exhibit the highest power factor. It is also shown that the average-current control with three independent controllers requires the shortest calculation time. The measurements were performed on a 3-kW, three-phase, six-switch, boost PFC rectifier prototype controlled by the TMS320F2808 DSP from TI.

I. INTRODUCTION Today, active three-phase PFC rectifiers need to meet

very challenging performance requirements. In the majority of applications, the input current of active three-phase PFC rectifiers is required to have a total harmonic distortion (THD) less than 5% and a power factor (PF) greater than 0.99 [1]. One of the most cost-effective topologies that can meet these requirements is the three-phase six-switch boost PFC rectifier [2], which is usually implemented without neutral-point connection.

Many control methods that can achieve a high quality of input currents in the three-phase six-switch boost PFC rectifier are available [3], [4]. One direct current control method, well suited for digital implementation, is the average-current control [6], [7].

The average-current control of the three-phase six-switch boost PFC rectifier can be implemented in different reference frames such as stationary (a,b,c), stationary (α,β), and rotating (d,q) reference frame. The implementation in stationary (a,b,c) reference frame is done with three current controllers [5], [8]-[12], whereas the implementation in stationary (α,β) reference frame employs two current controllers and requires signal transformations from 3-phase to 2-phase stationary coordinate system [3], [4]. Finally, implementation in rotating (d,q) reference frame employs two current controllers [3], [4], [9], [13] and requires signal transformations from 3-phase stationary to 2-phase rotating coordinate system [14].

Generally, in three-wire implementations (i.e., without neutral-point connection) in stationary (a,b,c) reference frame, it is possible to have only two out of three controllers actively shaping the current at a given time because the sum of the phase currents is zero. The desired current in the phase of the inactive controller is automatically obtained as the negative sum of the actively controlled currents. One implementation of this control method is based on dividing the line cycle of input phase voltages in six 60o-segments (six-step PWM) [8]-[10], as shown in Fig. 1. In each 60o-segment, the controller in the phase of the highest absolute value voltage is disabled, i.e., switches in the corresponding leg are turned off, which results in reduced switching losses. Another implementation of this control method is based on dividing the line cycle of input phase voltages in three 120o-segments (three-step PWM) [10] as shown in Fig. 2. In each 120o segment, the controller in the phase of the most positive (or most negative) phase voltage is disabled, i.e., the switches in the corresponding leg are turned off. The

t

30

a0v b0v c0v

-30 90 150 210 270 330 0

I II III IV V VI

o o o o o o o

Fig. 1 60o segments of six–step PWM.

t

60

a0v b0v c0v

0 180 300 360

I II III I

o o o o o

envpv

(a)

t

0 120 360

I II III

o o o 240 o a0v b0v c0v

envnv

(b) Fig. 2 120o segments of three-step PWM referenced to: (a) positive envelope, (b) negative envelope of input phase voltages.

978-1-4799-6735-3/15/$31.00 ©2015 IEEE 101

major benefit of the three-step over the six-step PWM is that it exhibits much reduced input-current transients at the segment transitions which improves THD and PF performance and reduces susceptibility to false segment detection [10].

Although in three-wire power-systems the three phase currents are not independent, three independent current controllers can also be employed [5], [11], [12]. As shown in [5], the whole rectifier system is stable if the equivalent single-phase control loops are stable.

In both stationary (a,b,c) and (α,β) reference frames, the current controllers can be implemented with P and PI compensation. In [12], it was shown that in the three-phase six-switch boost PFC rectifier with average-current control and with mismatched input-voltage and input-current sensing gains, the current controller with P compensation exhibits lower THD of input currents and higher PF compared to that with PI compensation. In addition, when the current references are sinusoidal, the PI compensator cannot achieve zero steady-state error due to the finite gain at the line frequency [15].

To achieve zero steady-state error with PI compensation, the control is usually implemented in the rotating (d,q) reference frame, where the sinusoidal signals are transformed to dc signals [3], [4], [13]. However, zero steady-state error can also be achieved in the stationary (a,b,c) and (α,β) reference frames, if instead of PI compensation, a proportional plus resonant (PR) controller is employed [4], [15]-[17].

When the control is implemented in the rotating (d,q) reference frame, the output signals of the current controllers, after being transformed from the rotating (d,q) back to the stationary (a,b,c) reference frame, can be further

processed by zero-sequence-signal (ZSS) injection-based PWM or by space vector modulation (SVM). It can be shown that the ZSS-injection-based PWM and SVM are equivalent [18].

In this paper, implementation and performance comparison of five control methods for the average-current-controlled three-phase six-switch boost PFC rectifier are presented. Three control methods in the stationary (a,b,c) reference frame and two in the rotating (d, q) frame are considered. The stationary (a,b,c) reference frame methods include implementations with three independent controllers, with six-step PWM, and with three-step PWM, whereas the rotating (d, q) frame methods include implementations with ZSS-injection-based PWM and with SVM. Experimental performance evaluation of the input-current THD and PF, as well as DSP calculation time, was performed on a 3-kW, three-phase, six-switch, boost PFC rectifier prototype controlled by the TMS320F2808 DSP from TI.

II. POWER STAGE AND CONTROL CIRCUIT

The simplified circuit diagram of the three-phase six-switch boost PFC rectifier is shown in Fig. 3. The switches are implemented with IGBTs in a six-pack module [19]. The switching frequency is selected as fsw = 20 kHz, which is the maximum recommended fsw for the IGBT module. The input phase voltage range is 120 ± 15% Vrms, 45-65 Hz, the nominal output voltage is 400 V, and the maximum output power is 3 kW.

The block diagram of the control circuit in the stationary (a,b,c) reference frame is also shown in Fig. 3. Average-current control is implemented using digital signal processor (DSP) TMS320F2808 from TI [20]. For average-current control, the input phase-phase voltages, phase

* - notation for digital values

p

n

LINE VOLTAGE PHASE CURRENT

OUTPUT VOLTAGE

Sap Sbp Scp

San Scn

v o

v a0

v b0

v c0

L

L

L

i a

i b

i c

Sbn

+

-

a

b

c

C p

C n

ANTIALIASING FILTER

LOW-PASS FILTER

ANTIALIASINGFILTER

Phase A

VOLTAGE CONTROLLER

ADC

1FSR

13

ADC

Phase B

Phase C

v oref *

v EA *

i aref *i *

a K AB

C 2m

v a0 *

B

A C

v ca*

v ab*

v o*

ADC

1FSR

1FSR

*v a0 AVG

CURRENT CONTROLLER

DPWM

Sap

v ZSS*

v a0 *

ZSS INJECTION

DUTY-CYCLEFEEDFORWARD +

ZSSv a0 * v *

v oref *

+

GENERATOR

ZERO-SEQUENCE SIGNAL (ZSS)

v ZSS*

v b0 *

v c0 *

Offset1.5V

FSR 2

Offset1.5V

1 *

2

dan*

S an

dCCa*

DSP

VOLTAGEFEEDFORWARD

SENSING SENSING

SENSING

KcsKvs

Kd

Fig. 3 Simplified circuit diagram of power stage (La=Lb=Lc=1mH, Cp=Cn=2240H) and block diagram of control circuit in stationary (a,b,c) reference frame.

102

currents, and the output voltage are sensed. The respective sensing gains are denoted as Kvs, Kcs, and Kd, as shown in Fig. 3. The sensed voltages and currents are converted to digital signals through the 12-bit analog-digital converter (ADC) of the DSP. The input voltage range of the ADC is 0-3 V, i.e., the full-scale range FSR = 3 V. As only positive voltages can be applied to the input of the ADC, the bipolar phase-phase voltages and phase currents are scaled to ±FSR/2 and level shifted by FSR/2. The output signals of the DSP are the digital PWM (DPWM) gate signals for the bottom switches Sxn, xϵ{a,b,c}. The DPWM operates with a triangular carrier. As the clock frequency of the DSP is fsysclock = 100 MHz, the peak value of the triangular carrier is Cpk = 1/2·fsysclock/fsw = 2500. All the sensed signals are sampled at the peak of the triangular carrier. The corner frequency of the input- and output-voltage antialiasing filters is fAAFin = 3 kHz and fAAFout = 550 Hz, respectively, whereas the corner frequency of the low-pass filter of the sensed inductor-currents is fLPF = 92.5 kHz.

The voltage controller is implemented with PI compensation (for better regulation of the output voltage), whereas, the current controller is implemented with P compensation because of its benefits compared to PI compensation as explained in [12]. The average-current control implementation also includes voltage feedforward (VFF) [6], duty-cycle feedforward (DFF) [21], and zero-sequence-signal (ZSS) injection [18]. Generally, VFF can make the output voltage practically insensitive to line-voltage variations. However, VFF with P-compensated current controller is effective only if DFF is also implemented, as shown in [12].

Generally, ZSS injection is employed to extend (up to 15%) the input and/or output control range of the converter [18]. In addition, ZSS injection improves the THD of input-currents [12]. The ZSS signal vZSS, shown in Fig. 3,

is obtained from the input phase voltages and the output reference voltage. Using different segments of the positive and negative envelopes of the input phase voltages, different ZSS signals and, consequently, different control methods can be obtained. The ZSS signal for the average-current control method with three independent controllers, with six-step PWM and with three-step PWM referenced to venvp and venvn is shown in Figs. 4(b)-4(e), respectively. It should be noted that the ZSS-injection benefits in average-current control methods with six-step and three-step PWM can also be obtained by employing phase-to-phase current controllers without ZSS injection instead of phase-current controllers with ZSS injection [10] since the phase-to-phase current-controller implementation exhibits inherent ZSS-injection property.

The block diagram of the control circuit in the rotating (d,q) reference frame is shown in Fig. 5. The phase angle of the input phase voltages, required for the signal transformations from stationary (a,b,c) to rotating (d,q) reference frame and vice versa is obtained by using a three-phase phase-locked loop (PLL) [22]. Both the voltage and current controller are implemented with PI compensation. It should be noted that the control circuit in Fig. 5 does not include DFF. Generally, DFF is employed when current controllers with PI compensation are used in the stationary (a,b,c) reference frame to reduce the phase shift between a phase voltage and phase current caused by the controller and, consequently, to improve the THD and PF. Because in rotating (d,q) reference frame the signals are dc, DFF is not necessary.

As shown in Fig. 5, the d and q components are decoupled, which simplifies the design of the current controllers. However, it should be noted that it was observed in both simulation and experimental circuit that in the described design the decoupling of d and q components has practically no effect on the performance of the circuit in steady state operation and during line and load transients. Therefore, the decoupling of the d and q components can be omitted if the additional calculation time for decoupling is critical for the total duration of the interrupt service routine.

The procedure for decoupling the d and q components is described in Appendix A. The scaling factor KL in Fig. 5 is obtained in Q12 format, scaled to the peak value of the triangular carrier Cpk, as

pkcs

L CK

FSRK 122 . (1)

Finally, it should be noted that the control circuit in the rotating (d,q) reference frame in Fig. 5 does not include ZSS injection because a common signal injected into three phase (a,b,c) controllers is mapped to a zero vector in (a,b,c)-to-(d,q) transformation. The ZSS signal is added to the duty cycles generated in the (d,q) reference frame after the duty cycles are transformed from rotating (d,q) back to stationary (a,b,c) reference frame, as shown in Fig. 6(a). Using different segments of the positive and negative

Fig. 4 ZSS injection methods: (a) Positive envelope venvp and negative

envelope venvn of input phase voltages, (b) VZSS for three independent controllers, (c) VZSS for six-step PWM, (d) VZSS for three-step PWM

referenced to venvp, (e) VZSS for three-step PWM referenced to venvn.

2

vvv envnenvp

ZSS

envnenvpenvnoref

envnenvpenvporef

ZSS

vvifv2

V

vvifv2

V

v

envporef

ZSS v2

Vv

envnoref

ZSS v2

Vv

)v,v,vmax(v 0c0b0aenvp

)v,v,vmin(v 0c0b0aenvn

103

envelopes of the duty cycles da, db, and dc, different ZSS signals and, consequently, different control methods can be obtained.

It can be shown that for any arbitrary ZSS-injection- based PWM there is an equivalent SVM with an appropriate distribution of the zero switching state vectors [18]. The block diagram of the SVM circuit is shown in Fig. 6(b). In this paper, symmetrical ZSS signal, obtained as the negative average of the positive and negative envelopes of the duty cycles da, db, and dc, similarly as in Fig. 4(b), and the equivalent conventional continuous SVM are used [18]. The equivalence between the symmetrical ZSS-injection-based PWM and the conventional continuous SVM is explained in Appendix B.

In the design of the voltage and current controllers, the digital redesign approach is used, i.e., the control loops are optimized in continuous-time domain (s-domain) and then their controllers are translated to discrete-time domain (z-domain) to obtain corresponding recursive expressions that are coded into the DSP.

III. PERFORMANCE COMPARISON OF FIVE CONTROL METHODS

Performance evaluation of the five control methods is performed with respect to their THD of input currents, PF, and DSP calculation time. Measured steady-state waveforms of the phase currents at nominal phase voltage of 120 Vrms and for 2-kW load are presented in Figs. 7(a)-7(e). Figures 7(a)-(e) also show corresponding measured THD and PF values. THD and PF measurements as a function of load current for the 10%-100% load range are presented in Figs. 8(a) and (b), respectively. It should be noted that the THD and PF values in Fig. 8 are obtained as average values of the measured THD and PF of individual phases.

It can be concluded from Figs. 7 and 8 that the average-current control with three independent controllers exhibits the lowest THD of input currents, whereas, the average-current control in the (d,q) reference frame with ZSS-injection-based PWM and SVM, as well as the three-step PWM generate slightly higher THD. The PF of the two control methods in the (d,q) reference frame is the highest, whereas, the PF obtained with the three independent controllers and with the three-step PWM is slightly lower. The THD and PF performance of the six-step PWM is inferior compared to that of the other methods. DSP calculation times, measured within an interrupt service routine from the ADC output to the DPWM input, are presented in Table I. It can be seen that the average-current control with three independent controllers requires the shortest calculation time, whereas, the six-step PWM requires the longest calculation time due to the additional code necessary to achieve reliable 60o-segment detection.

IV. SUMMARY

In this paper, implementation and performance comparison of five control methods for the average-current-controlled three-phase six-switch boost PFC rectifier are presented. Three control methods in the stationary (a,b,c) reference frame and two in the rotating (d, q) frame are considered. The stationary (a,b,c) reference frame methods include implementations with three independent controllers, with six-step PWM, and with three-step PWM, whereas the rotating (d, q) frame methods include implementations with ZSS-injection-based PWM and with SVM.

3-PHASE

KL

i d*

i a *

i b *

i c *

PLL

vd*

v q*

v b0*

v a0*

v c0*

d q*

dq

abc

db*

d a*

dc*

dq

abc

dq

abc

i * q

VOLTAGE

CONTROLLERvo*

v d*

i dref *

v EA *

2

K AB

C

m B

A C CURRENT

CONTROLLERd

d d*

KL L

Vo

CURRENTCONTROLLER

q

d CCd *

d CCq* vq

*qref i * = 0

LVo

voref*

d * decoupl,d

d * decoupl,q

Fig. 5 Block diagram of control circuit in rotating (d,q) reference frame.

db*

d a*

dc*

d aZSS*

d bZSS *

d cZSS *

GENERATOR

ZERO-SEQUENCE

SIGNAL (ZSS)

d ZSS *

1 *

2

(a)

db*

d a*

dc*

SECTOR

CALCULATION &

Sector

d aSVM*

DETECTION

DISTRIBUTION OF

ON-TIMES OF SSVs

d bSVM *

d cSVM *

(b)

Fig. 6 Block diagram of: (a) ZSS injection, (b) SVM circuit.

TO DPWM

TO DPWM

104

Experimental performance evaluation of the input-current THD and PF, as well as DSP calculation time was performed on a 3-kW, three-phase, six-switch, boost PFC rectifier prototype controlled by the TMS320F2808 DSP from TI.

It is found that the average-current control with three independent controllers exhibits the lowest total harmonic distortion (THD) of input currents, whereas, the average-current control in the rotating (d,q) reference frame with ZSS injection-based PWM and SVM exhibit the highest power factor. It is also found that the average-current control with three independent controllers requires the shortest calculation time.

V. APPENDIX A

The averaged circuit model of the three-phase six-switch boost PFC rectifier in rotating (d,q) reference frame is shown in Fig. A1 [13]. It should be noted in Fig. A1 that the d and q input circuits are coupled due to the appearance of controlled voltage sources Liq and Lid in the d and q input circuits, respectively. Because of this coupling, an

(b)

Ia Ic Ib

Ia Ic Ib

(d)

(e)

(a)

(c)

Ia Ic Ib

Ia Ic Ib

Ia Ic Ib

Six-step PWM

Three-step PWM

(d,q) - ZSS

(d,q) - SVM

Three independent

Fig. 7 Experimental waveforms during steady-state operation (120Vrms,

2kW) of phase currents Ia, Ib, Ic [A] with: (a) three independent controllers, (b) six-step PWM, (c) three-step PWM, (d) control in (d,q) reference frame with ZSS injection-based PWM, (e) control in (d,q) reference frame with SVM.

THDa=2.95%PFa=0.9987

THDb=3.12% PFb=0.9982 THDc=3% PFc=0.9976

THDa=8.52%PFa=0.9926

THDb=6.83% PFb=0.9926 THDc=8.19% PFc=0.9923

THDa=3.79%PFa=0.9982

THDb=3.29% PFb=0.9976 THDc=3.56% PFc=0.9976

THDb=3.55% PFb=0.9986 THDc=3.6% PFc=0.9985

PFa=0.999

THDb=3.37% PFb=0.9987

THDc=3.36% PFc=0.9985

THDa=3.67%PFa=0.9989

THDa=3.38%

(a)

(b)

Fig. 8 Measured performance of five control methods as function of

load: (a) THDi [%], (b) PF.

Control Method Calculation time [µs]

Three independent controllers 17.6

Six-step PWM 23

Three-step PWM 20.6

Control in (d,q) with ZSS injection 22.36

Control in (d,q) with SVM 22.2

TABLE I - PERFORMANCE COMPARISON OF FIVE CONTROL METHODS WITH RESPECT TO DSP CALCULATION TIME

105

interaction exists between the d and q components, which makes the control design more complex. However, the control design can be simplified by using a decoupling network as shown in Fig. A2. The effect of the decoupling network in the d and q input circuits is such that in steady-state the d and q input circuits are completely decoupled, as shown in Fig. A3. The output circuit model with decoupling is obtained as shown in Fig. A4 after performing the following simple derivation,

qCCqdCCd

qo

dqCCqd

o

qdCCdqqdd

idid

iV

iLidi

V

iLididid

. (A1)

VI. APPENDIX B

The equivalence between the symmetrical ZSS-injection-based PWM and the conventional continuous SVM can be explained by observing the average voltage of a rectifier leg.

With symmetrical ZSS-injection-based PWM, rectifier leg voltage vaRn, for example, is obtained as

ZSSao

oo

ZSSaoapaRn vv

VV

V

vvVdv

0

0

22

1, (B1)

as shown in Fig. B1. With conventional continuous SVM, the ON-times of the

switching state vectors within a switching cycle Tsw are distributed as shown in Figs. B2(a) and B2(b), respectively for sectors I, III, V and sectors II, IV, VI. The hexagon of

Fig. A2 Input circuit model with decoupling.

Fig. A1 Averaged circuit model of the three-phase six-switch boost PFC rectifier in rotating (d,q) reference frame.

Fig. A3 Decoupled d and q input circuit models in steady state.

Fig. A4 Decoupled output circuit model.

Fig. B1 Rectifier leg voltage vaRn obtained by symmetrical ZSS-injection based PWM.

106

the switching state vectors is defined in Fig. B3. Time intervals Tk and Tk+1 in Fig. B2 represent the ON-times of the two non-zero switching state vectors of the k-th sector. The corresponding duty cycles are obtained as

)60sin( so

mk dd , (B2)

and

)sin(1 smk dd , (B3)

where dm is the modulation index, defined as

o

mm V

Vd

3 , (B4)

and s is the phase angle within a sector as shown in Fig. B3. Duty cycles dk and dk+1 normalized to dm are presented

in Fig. B4. Duty cycles of the zero switching state vectors are defined as

2

1 170

kk dd

dd , (B5)

To obtain rectifier leg voltage vaRn, duty cycle dap needs to be derived for each sector I-VI. For example, for sector I,

01 ddap , (B6)

as follows from Fig. B5. By applying (B5) to sector I,

2

1 2170

dddd

, (B7)

dap in sector I is determined as

Fig. B5 Switching of rectifier legs in Sector I.

Fig. B2 Distribution of ON-times of switching state vectors within a switching cycle Tsw with conventional continuous SVM: (a) Sectors I, III, V; (b) Sectors II, IV, VI.

Fig. B3 Hexagon of switching state vectors.

Fig. B6 Rectifier leg voltage vaRn obtained by conventional continuous SVM.

Fig. B4 Duty cycles of two non-zero switching state vectors in k-th sector.

107

22

1 21 dddap

. (B8)

Finally, rectifier leg voltage vaRn = dapVo is obtained as shown in Fig. B6.

By comparing leg voltages vaRn in Figs. B1 and B6, it can be observed that they are identical. Therefore, it can be concluded that the symmetrical ZSS-injection-based PWM and the conventional continuous SVM result in identical rectifier leg voltages, i.e., that the symmetrical ZSS-injection-based PWM and the conventional continuous SVM are equivalent.

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