Single Phase Unity Power Factor Control for Dual Active Bridge Converter

M. H. Kheraluwala R.W. De Doncker

General Electric Company Corporate Research and Development

P. 0. Box 8 Schenectady, NY 12301

Abstract - An ac line fed switching power supply with a single power converter stage, is described which operates with high input power factor while maintaining good regulation of the desired output dc voltage. The single power converter is a dual active bridge dc-to-dc converter (DABC), comprising high- frequency transformer-coupled input and output bridge converters. The DABC receives a rectified ac line voltage via a diode-bridge rectifier connected to a smal l , high-frequency filter capacitor. The two active bridges, generating "edge-resonant'' square waves at their transformer terminals are appropriately phase-shifted from each other to simultaneously perform the high-efficiency dc output regulation, while maintaining unity power factor at the ac input. The soft-switching nature of the converter allows increased performance (in terms of efficiency and stresses) and reduction in size/weight at operating frequencies, in the range of 50-250 kHz. The paper addresses the design, control and performance issues of the proposed high power factor power supply.

I. Ih'TRODUClTON

To comply with future regulations on low and high frequency distortions of main ac power lines and electromagnetic interference requirements, it is necessary to improve waveform quality of ac-to-dc converters. In general, there are two approaches to solving this problem. The first approach entails increasing size and reactance value of passive filter elements, i.e. inductors and capacitors, in order to reduce the high frequency content of the ac input waveforms. Disadvantageously, this approach becomes increasingly expensive at higher power levels and creates other side effects for which compensation must be provided, such as high in- rush currents, low bandwidth and poor power factor. The second approach entails providing a separate front-end power factor correcting converter [ 11. Even though filter size can be reduced by switching at a high frequency, the disadvantage of this approach is lower efficiency and added cost by virtue of the two-stage conversion process.

Accordingly, to minimize the number of active power devices it is desirable to provide for a single stage converter

[2,3] controlled to produce unity power factor while regulating the desired output dc voltage. The advantages of single stage systems are improved efficiency, high power density, low cost and high operating bandwidths. Since the double line frequency (e.g. 120 Hz) energy storage is provided at the output of the converter, the single stage systems are particularly suitable for high power applications requiring output dc voltages of 50 V or above, such as in distributed power architecture, electric vehicle battery chargers, etc.

II. PROPOSED CONVERTER

A . Topology and Operation

The proposed high power factor power supply, shown in Fig. 1, consists of a line voltage rectifier followed by a single power converter sruge which is controlled to actively waveshape the line current while regulating its output dc voltage. The single power converter stage is the Dual Active Bridge dc-to-dc Converter (DABC) [4-61, shown in its half- bridge form. The Ci input capacitors are small high frequency capacitors providing a high-frequency filtered input dc voltage Vi that is pulsating at twice the ac line frequency (e.g., 120 Hz) to the converter. The output capacitors CO provide a high-frequency filtered output dc voltage V,. The double line frequency energy storage capacitor CSt is connected at the output terminals.

The DABC with its buck and boost capability inherently provides the required characteristics for high power factor operation, in addition to combining the output voltage regulation function. Moreover, the soft-switching operation of the converter lends itself for achieving high power densities at high switching frequencies anywhere in the range of tens of kilohertz to hundreds of kilohertz depending on the power levels and type of switching device (MOSFETs, IGBTs). The phase-shift between the edge-resonant square wave voltages VI and V2 across the high-frequency transformer windings is controlled so as to regulate the output dc voltage while realizing near unity power factor under the soft-switching constraints of the DABC.

0-7803- 1462-x/93$03.00 01993IEEE 909

Fig.

V

1 Circuit schematic of proposed high power factor power supply. The dc to dc power converter is the Dual Active Bridge converter.

B . Basic Unity Power Factor Control

Fig. 2 illustrates a control scheme for controlling the dual active bridge converter of Fig. 1 to operate at unity power factor. Using the output dc voltage error a proportional- integral compensator generates a current signal Iac that controls the magnitude of the desired ac line current. The rectified ac line voltage Vi, attenuated by a factor K, modulates the signal Iac providing an ac line current command Ii*. To regulate the output voltage VO, while maintaining unity power factor, a phase-shift control block generates from the ac current command Ii* the appropriate phase-shift signal Q between the high frequency voltages V1 and V2 of the DABC.

I Fig. 2 Block diagram of high power factor controller with

regulated output voltage for the proposed converter.

Within each cycle of the fundamental input voltage the average input current to the dual active bridge converter is function of the phase-shift signal Q according to [4]:

1 -J B

41 where 1: is the average output dc current, and d is the ratio of

the output voltage V:, referred to the primary side of the transformer, to the input voltage Vi. Using a small input capacitor Cj the DABC input voltage Vi is a rectified line voltage waveform. For unity power factor operation, the input current, Ii, should follow Vi,

Ii = Ip Isin(ot)l (2)

where Ip is the desired peak of the ac line current, and o is the ac line frequency in radians per second. Refemng to Fig. 2,

where Vp is the magnitude of the ac line voltage, K is the attenuation factor, and Iac is the compensated error from the output voltage loop. Combining (1) and (2) yields a control equation for the phase angle control block to maintain a substantially constant output voltage and unity power factor:

0 5 o t 5 ” 2

91 0

C . Soft-switching Control Limits

1 Output Bridge Boundary i

The dual active bridge soft-switching boundaries [4-61 limit control over the angle Q at low input currents. The operating boundary of the input bridge is given by,

1 d<- 1 - 2 2 -

7c

(5)

As stated above, the input voltage Vi is a rectified ac waveform. Hence, the voltage ratio d varies within each double line frequency period according to:

(6) v: d - Vp Isin(wt)l e

From ( 5 ) and (6) the minimum phase-shift angle Qmin to satisfy the input bridge soft-switching constraint is derived as:

(7)

Similarly, the operating boundary of the output bridge is given by,

d > l - % . 7c (8)

From (6) and (8) the minimum phase-shift angle b i n to

2 A 3 A 4 k 5 A 6 A 71A I 'I

satisfy the output bridge soft-switching constraint is derived as

(9) qmin 5 (1- vp Isin(wt)?- vop

Both (7) and (9) define the time varying phase-shift boundaries for sinusoidal input voltage operation of the dual active bridge converter. Fig. 3 illustrates the soft-switching boundaries and the soft-switching area in the d-9 plane for the DABC that is specified in Appendix A. The input bridge and output bridge boundaries are shown separately. Unity power factor phase shift control trajectories, according to (4) and (6) are drawn in Fig. 3 for different peak values of the sinusoidal ac input current. Fig. 4 illustrates the variation of d, the control angle Q and the control limit Qmin as a function of time over one half-cycle of the line voltage for different input current amplitudes.

Whenever Q is required by the unity power factor control equation (4) to be smaller than bin, hard switching events will occur that are associated with resonant capacitor discharge into the power devices, diode reverse recovery losses and increased EMI. When using transistor devices (MOSFETs and IGBTs) these turn-on phenomena may be controllable and their losses can be tolerated as for the input bridge they occur simultaneously at low input voltages and at low input currents. The hard switching losses in the output bridge occur at low current or can be avoided by proper selection of the transformer turn ratio.

1 .

d

0 0.5 1 1.5 W a d )

Fig. 3. Soft-switching boundaries in the d-Q, plane and control trajectories for different load conditions (parameters

according to Appendix A).

0 nI4 nl2 3nI4 n Angle o t (rad)

Fig. 4. Variation of d, the phase-shift control angle $ and boundary b i n over one half-cycle of the input ac voltage

(parameters according to Appendix A).

91 1

I 1.6 L I I I

0 xi4 xi2 3x14 7[:

Angle w t (rad)

Fig. 5. Variation of the control angle Q and @min over one half-cycle of the input ac voltage for different turn ratios of

the high frequency transformer.

For specified output and input voltages and power levels (determined by the peak ac current) the transformer ratio has a strong influence on the phase-shift soft-switching control range. If the transformer ratio is selected such that the peak ac input voltage never exceeds the primary transformed output voltage, then the constraint related to the output bridge does not exist as the voltage ratio d never drops below unity. However, in this case, the soft-switching control range becomes quickly limited at lower input currents. In Fig. 5 three boundary curves are plotted corresponding to three different transformation ratios (41 , 3:1, and 2:l). If the transformation iatio is low (2:l) the control range at high input currents (e.g. 8.3 A) widens but the control range at low input currents (e.g., 2 A) narrows at high input voltages (when Q, equals 7d2) due to the output bridge constraint. Fig. 5 shows that for the DABC specified in Appendix A a transformation ratio of 3: 1 is preferable because the phase- shift angle is controllable under soft-switching conditions over a relatively wide range of input currents.

Fig. 4 and Fig. 5 show that at high load currents soft- switching operation of the DABC with unity power factor control can be achieved over almost the entire cycle of the fundamental input wave . At low input currents, e.g. 1 A peak sinusoidal reference, soft-switching operation of the DABC can be obtained only during two narrow instances of the half-cycle. Hence, to realize unity power factor operation over the entire power range the converter is forced to operate under hard-switching only at low input currents.

D. Near Unity Power Factor Control Methods

When hard-switching losses cannot be tolerated, unity power factor control cannot be maintained. Three altemative control methods to operate the converter under soft-switching conditions at all times are evaluated next. In the first method the DABC is controlled according to the sinusoidal current control explained above but the converter stops operation every time a soft-switching boundary is met, i.e., whenever Cp < $min. In the second method, referred to as the extended sinusoidal current control, the phase-shift control angle Q is temporarily forced to follow the soft-switching boundary Qmin whenever Q tends to be less than $min. The third control method keeps the angle I$ constant and the converter is switched off every time a soft-switching boundary is met. In all three methods, the input current will not track the sinusoidal reference over the entire period leading to greater line current distortion.

Sinusoidal current control within the soft-switching boundaries leads to input ac current waveforms that ideally, i.e. neglecting switching frequency ripple, can be represented by the waveform shown in Fig. 6.

Sinusoidal Control

-1 .n 2%

8 = at (rad)

Fig. 6. Idealized input line current for sinusoidal current control (Ip - 8.3 A, parameters according to Appendix A).

At the instant 0, the DABC phase-shift Cp equals $min. Hence, the deadtime angle Os for different peak values Ip of the input current can be calculated eliminating Qmin from (4) and (7).

The ac input power for different peak ac currents can be expressed as a function of the deadtime angle 8,:

10

(1 1) Pin = vP IP - 2 e, + sin (2 e,)]

I I I

Constant Phase-Shift Control

Fig. 8 illustrates the relationship between the input power and the deadtime angle according to (10) and (1 1). The input RMS current, the power factor PF, and total harmonic distortion THD, for sinusoidal current control are given as:

Extended sinusoidal current control typically produces input current waveforms according to Fig.7. With this control, the phase-shift control angle follows temporally the soft-switching boundaries (5) and (8) instead of shutting down the converter.

10 I I I

Extended Sinusoidal Control n

4 - / I t

i t -1

IT 2n 8 = a t (rad)

Fig. 7. Idealized input line current for extended sinusoidal control (Ip = 8.3 A, parameters according to Appendix A).

Whenever the soft-switching boundaries are met, the input current is solely determined by the input and output voltages according to:

1 v,' sin*(wt)

v,P

Hence, the converter soft-switching operation can be extended during the fundamental ac input cycle only with loss of control over the ac input current. However, for every peak value of the input ac current an optimal extended control angle 8, can be found that maximizes the power factor PF. Numeric calculations were performed to determine the optimal extended control deadtime 8, as a function of input power of the DABC. The resulting relationship is shown in Fig. 8.

1-

0.8-

8 2 W 5 0.5

I I

0.3

0

I I I I I I I I

Constant Phase-Shift 8,

1 200 400 600 800 Pin (W)

Fig. 8. Deadtime angles for sinusoidal, extended sinusoidal and constant phase shift current control as a function of input

power (parameters according to Appendix A).

n 2n 8 = at (rad)

Fig. 9. Idealized input line current for constant phase-shift control (Ip = 7 A, parameters according to Appendix A).

91 3

E 901

a

85 J

Extended sinusoidal

Id I I I

0 200 400 600 800 1000 Pin (W)

5 c '

Extended sinusoi

301

20 I I I I 0 200 400 600 800 lo00

Pin (W)

Fig. IO. Power factor as a function of input power. Fig. 1 1. THD as a function of input power.

Taking into account the soft-switching boundaries, the E. Simulation Results peak input current and input power are functions of the constant angle control range according to: Detailed simulations were performed to verify the results

obtained from the idealized analysis. The simulations include the control dynamics, the effects of the finite output capacitance value, the DABC high switching frequency patterns and the ac line input inductance. The parameters used in the simulation correspond to Appendix A for an operating condition that corresponds to Ip = 6 A. Figs. 12, 13 and 14 illustrate the simulated input line current waveforms for each control

F . Experimental Results

(16) 1 2v I

P, = cos(e,) (I7)

The input RMS current and the PF can be expressed as a function of the deadtime angle 8, :

(18)

(19) A proof-of-concept breadboard was assembled for the

specifications and parameters listed in Appendix A, for a nominal output power of 500 W. The input and output switching bridges of the DABC were assembled as full bridges with IRFP450 (MOSFETs) on the input and IRFPI50 on the output. The input high frequency filter capacitor Ci was selected as 2 pF and the output high frequency filter capacitor

ceramic X7R type. The output energy storage capacitor Cst, was selected as mF. The resonant snubber capacitors across each device are a combination of the inherent drain-to- source capacitance enhanced by external 1 nF capacitors of the Silver-mica type.

PF = 2 CO+,) 4 7 n ( n - 2 e c )

Eliminating the deadtime angle 8, yields an expression for PF and THD as a function Of input power* Note that maximum power is reached when 8, equals zero. In this case,

n'2)* the converter its maximum power transfer capability and is operating under soft-switching conditions over the entire cycle of the input voltage wave.

the input C u m n t becomes a square wave (phase shift 4 CO was selected as 27 PF, both of the AVX, multi-layer

Figs. I O and 11 illustrate the relationship between input power, power factor PF and THD for the three control

conclude that the extended sinusoidal current control achieves methods explained above' From Figs' lo and One can The breadboard was operated with a constant g00 phase-

shift control. Fig. 15 shows the line voltage vac and line the highest power factor (lowest THD) Over the entire power current Iac under nominal operating conditions. The measured range Of the power throughput be achieved

with 'Onstant phase-shift control higher instead

power factor and THD under these conditions is 0.939 and 36.6%. The measured results correlate well with those from

of 650 W), however at the expense of higher waveform distortion.

theidealizedanalysis.

91 4

200 1 , IO 5

h

4 O 8 U

- 5

-200 I 1-10 0 4.17 8.34 12.5 16.7

Time (msecs)

Fig. 12. Input line current with sinusoidal current control. Calculated power factor PF - 93.71 %, THD = 36.49 %.

0 4.17 8.34 12.5 16.7 Time (msecs)

Fig. 13. Input line current with extended sinusoidal control. Calculated power factor PF = 97.58 %, THD = 21.1 %.

200

100 h L s o > -100

-200 0 4.17 8.34 12.5 16

Time (msecs)

IO

5 h

4 U

- 5

-10 .7

Fig. 14. Input line current with constant phase-shift control. Calculated power factor PF = 96.63 %, THD = 25.41 %.

Fig. 15. Oscillograms of the measured line voltage Vac (top, 50 V/div) and line current Iac (bottom, 5 Ndiv).

Time scale : 2 mddiv.

111. CONCLUSIONS

A single-stage DABC high power factor power supply is presented which shows high performance in terms of overall power factor, efficiency and dynamic response under load and line disturbances. Unity power factor control can be achieved over the entire cycle only when hard-switching events can be tolerated. Three control schemes are derived to achieve near unity power factor control while maintaining soft-switching operation of the converter. The extended current control achieves the highest power quality. The constant phase shift control method achieves medium waveform quality but reaches higher power transfer capability and can be realized with simpler control. Simulations and experimental results are presented to corroborate the idealized analysis.

ACKNOWIEDGMENT

The authors would like to thank Mr. Gany Grandy for his assistance in the assembly and testing of the breadboard.

Appendix A

To illustrate key characteristics of the unity power factor, high frequency DABC a unit rated at 500 W is considered throughout the paper. It is assumed that both primary and secondary devices are MOSFETs. Important parameters that are used both for the idealized calculations and the simulations are listed below.

91 5

Nominal RMS input ac voltage: Nominal output Power: Nominal output dc voltage: Nominal switching frequency: Primary transformed leakage inductance: Transformation ratio: Input line inductance: Input line resistance: Input dc filter capacitor: Output dc filter capacitor:

REFERENCES

v,, = 120 v P 0 = 5 0 0 W Vd, - 50 Vdc fsw = 250 WZ Lp'9W Np:Ns = 9:3 bine 100 W

Cin - 2 P Cst = 10 mF

Rljne = 0.5 SZ

S.D. Freeland, I. "A Unified Analysis of Converters with Resonant Switches, 11. Input-Current Shaping for Single- Phase AC/DC Converters," Ph.D. Thesis, California Institute of Technology, 1988.

M.J. Schutten, R.L. Steigerwald, M.H. Kheraluwala, "Characteristics of Load Resonant Converters Operated in a High Power Factor Mode," IEEE Tran. on Power Electronics, April 1992, Vol. 7, No. 2, pp. 304-3 14.

M.H. Kheraluwala, R.L. Steigerwald, R. Gurumoorthy, "A Fast-Response High Power Factor Converter with a Single Power Stage," IEEE PESC Conf. Records, 1991, pp.769-779.

R.W.A.A. De Doncker, D.M. Divan, M.H. Kheraluwala, "A Three-phase Soft-Switched High-Power-Density dddc Converter for High-Power Applications," IEEE Tran. on Industry Applications, Jan/Feb 1991, Vol. 27, No. 1, pp. 63-73.

K. Vangen, T. Melaa, A. Adnanes, "Soft-switched High- frequency, High Power DC/AC Converter with IGBT," IEEE PESC Conf. Records, 1992, pp. 26-33.

M.H. Kheraluwala, R.W.A.A. De Doncker, D.M. Divan, "Analysis, Design and Experimental Evaluation of a High-Power High-Frequency DC/DC Converter," EPE Conf. Records, 1991, pp. 568-573.