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Letters An Optimized Phase-Shift Modulation For Fast Transient Response in a Dual-Active-Bridge Converter Xiaodong Li and Yi-Fan Li
Abstract—In this letter, two different phase-shift modulation used for the transient response of a dual-active-bridge dc/dc converter and their effects on the dynamics of the converter are discussed and compared. It is found that the settling time for both cases depends on the value of the equivalent series resistance of the power inductor. To minimize the transient time, a modified asymmetric double-side modulation is proposed, which enables the converter to transfer smoothly from one steady state to another one regardless of the equivalent series resistance of the power inductor. Experimental results of the dynamics of the converter using different transient modulation techniques are also included for the purpose of validation.
I. INTRODUCTION HE bidirectional dc/dc converter may find wide applications in industries, for example the renewable energy generation systems, where the energy storage system (ESS) is needed for battery charging or discharging [1], [2]. Among many bidirectional dc/dc converters, the dual-active-bridge (DAB) dc/dc converter has been attracting attentions of engineers and researchers since introduced two decades ago [3]–[9]. The DAB converter is feature with easy control, high efficiency, and high power density. A typical full-bridge DAB dc/dc converter serving as an interface between two voltage sources with its equivalent circuit is shown in Fig. 1. The two actively controlled full bridges are linked by means of a high-frequency (HF) transformer and a power inductor. The power inductor Ls including the leakage inductance acts as the main energy transfer device. The resistor rs is an equivalent resistance including the series equivalent resistance of Ls and the total winding resistance of the HF transformer. Normally, it is small enough to be neglected in steadystate analysis. However, it is important in transient to settle down the average inductor current to zero and prevent the saturation of the HF transformer. The conventional control is to manipulate the two bridges to generate two square-wave voltages vA B and vX Y as shown in Fig. 2. There is a phase shift existing be-
T
Manuscript received October 16, 2013; revised December 7, 2013; accepted December 7, 2013. Date of current version January 29, 2014. This work was supported by Science and Technology Development Fund of Macau SAR under Grant 067/2011/A. Recommended for publication by Associate Editor C. C. Mi. The authors are with the Faculty of Information Technology, Macau University of Science and Technology, Macau, China (e-mail:
[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.2013.2294714
Fig. 1.
Dual-active-bridge dc/dc converter and its equivalent circuit.
Fig. 2.
Steady-state waveforms of a DAB converter.
tween the two square-wave voltages, which is the controllable parameter to manipulate the power flow. If vA B leads vX Y , the net power flows from the primary to the secondary; if vA B lags vX Y , the net power flows from the secondary to the primary. Apparently, the control of the phase shift is realized by precisely controlling the time delay between the two gating signals Gs1 and Gsa . To the best of knowledge of the author, there is no detailed discussion in the literature about how to change the the phase shift during the change of a load level, and how the change of phase shift would affect the converter transient response.
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is assumed fixed and the gating signals of the secondary bridge is delayed by dT at the time of to . The dashed lines in Fig. 3 represent the original waveforms. The transient duration Tt is defined as the time period between two minimum values of the inductor current, in which the gating signals are modified. The current at the beginning of the transient duration is assumed to be Io and the currents at the boundary points between each interval in Tt can be expressed as
Fig. 3. Single-side modulation for the increase of phase shift in a DAB converter at M < 1.
In this letter, the issue of how to modulate the phase shift precisely during the transient period and the modulation’s effects on the converter dynamics would be addressed. The two different methods of phase-shift modulation and their effects on the converter dynamics are discussed and compared in Section II. An optimized asymmetric double-side modulation is then derived to minimize the settling time of the transient inductor current. In Section III, experimental results based on a TI eZdspS320F2812 development board are included for the purpose of validation. II. TWO DIFFERENT WAYS OF PHASE-SHIFT MODULATION AND THEIR EFFECTS ON THE CONVERTER DYNAMICS In Fig. 2, the steady-state waveforms of the DAB converter are presented. Based on different possible values of the converter gain M , the inductor current may have different shapes as shown. The converter gain is defined as M = nt V2 : V1 , where nt is the turns ratio of the HF transformer. The common choice of M in design is unity, which enables ZVS operation for switches in both bridges for all load level. However, it is almost impossible to hold M unchanged due to the variation of V1 and V2 . In this letter, it is assumed that the two voltages would not change abruptly and can be regarded as constant in transient. In close-loop control mode, the phase shift φ shall be adjusted automatically to respond to the request of a load level. Naturally, there are two ways to modify the phase shift φ: single-side modulation and double-side modulation. A. Single-Side Modulation In single-side modulation, the gating signals of one bridge are fixed, while the gating signals of the other bridge would be changed with respect to the fixed signal according to the requirement. In Fig. 3, the transient of the DAB converter with M < 1 using single-side modulation is shown with the assumption of rs = 0. The original phase shift is DT , where 2T is the switching period. It is assumed that the phase shift is requested to increase by dT to transfer more power from the primary side to the secondary side. The gating signals of the primary bridge
I1 = Io +
V1 + nt V2 (D + d)T Ls
(1)
I2 = I1 +
V1 − nt V2 (1 − d − D)T Ls
(2)
I3 = I2 −
V1 + nt V2 (D + d)T Ls
(3)
I4 = I3 +
nt V2 − V1 (1 − d − D)T . Ls
(4)
It can be found easily that I4 is same as Io after the transient duration of Tt = 2T . The maximum and the minimum inductor currents during the transient are given, respectively, a Itm ax =
V1 + (2D − 1 + 4d)nt V2 T = I2 2Ls
(5)
V1 + nt V2 (2D − 1) T = Io . 2Ls
(6)
Itm in = −
With the assumption of rs = 0, the changing pattern of iL s in Tt will repeat in the next regular period of 2T and the average inductor current is Itave =
nt V2 dT. Ls
(7)
If so, the nonzero dc component of the inductor current would result in the saturation of the HF transformer. However, it is not true in real application due to the nonzero rs . Actually the envelope of the inductor current waveform would shift down for a few cycles until the average inductor current becomes zero. The settling time of the transient depends on the value of rs . This procedure can be proved mathematically by solving a series of first-order differential equations with the help of the equivalent circuit in Fig. 1, which would not be included here due to the limited space. B. Symmetric Double-Side Modulation The double-side modulation requires that the gating signals of both bridges should be changed in transient to increase or decrease the phase shift. In the following section, a symmetric double-side modulation is discussed, i.e., the gating signals of each bridge should be adjusted by dT /2, respectively. In Fig. 4, the transient of the DAB converter with M < 1 using double-side modulation is shown with assumption of rs = 0. It is assumed that the phase shift is requested to increase by dT to transfer more power from the primary side to the secondary side. The gating signals of the primary bridge would be shifted ahead by dT /2, and the gating signals of the secondary bridge would be delayed by dT /2 . The current at the beginning of
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resistance of Ls is expected to be as small as possible. However, the settling time of inductor current during the change of phase shift would be quite long if the equivalent resistance is small. C. Optimized Asymmetric Double-Side Modulation
Fig. 4. Symmetric double-side modulation for the increase of phase shift in T t at M < 1.
the new period is Io , and the currents at the boundary points between each interval in Tt can be expressed as V1 + nt V2 I1 = Io + (d/2 + D)T Ls I2 = I1 +
V1 − nt V2 (1 − d − D)T Ls
I3 = I2 −
V1 + nt V2 (D + d)T Ls
nt V2 − V1 I4 = I3 + (1 − d − D)T . Ls
(8) (9)
∗ I4 = Im in
(2xd − 2d − 1)V1 + (1 − 2D + 2xd − 2d)nt V2 T 2Ls (16) ∗ and Im in is defined as the steady-state minimum inductor current when the phase shift is (D + d)T : I4 =
∗ Im in =
(11)
(−1 − d)V1 + (1 − 2D − d)nt V2 T = I4 . (13) 2Ls
As rs is assumed to be zero, the current waveform will enter into a steady state with the extrema given in (12) and (13) starting from the next cycle of 2T . The average current in the new steady state would be nt V2 − V1 dT. (14) Itave = 2Ls Apparently, the average current is zero only at M = 1. It would be positive for M > 1 and negative for M < 1. Thus, actually the envelope of the inductor current would move down (for M > 1) or move up (for M < 1) for a few cycles until the average inductor current becomes zero due to the nonzero rs in a real converter. Although the analysis until here are done based on the increase of phase shift and M < 1, the similar results can be obtained for the decrease of phase shift and any M . For the purpose of improving converter efficiency, the equivalent series
(15)
where the current at the end of the transient duration is
(10)
And, the maximum and the minimum inductor current in the transient duration of (Tt = 2T − dT /2) are given, respectively, as (1 − d)V1 + (2D − 1 + 3d)nt V2 T = I2 (12) Itm ax = 2Ls Itm in =
According to (14), the average current becomes zero naturally if M = 1, which means that the converter enters into the steady state immediately after the transient duration Tt . In order to realize such a smooth transient duration for M = 1, an asymmetric double-side modulation is proposed here for any nonunity converter gain. The case of increasing the phase shift by dT is still taken as an example. It is assumed that the secondary gating signals are delayed by x · dT and the primary gating signals are shifted ahead by (1 − x) · dT . It is found that the transient duration Tt will last for (2T − (1 − x)dT ) with four intervals: (x · d + D)T , (1 − d − D)T , (d + D)T , (1 − d − D)T . The sufficient and necessary condition to let the converter be in the steady state right after the transient duration is concluded as
−V1 + (1 − 2D − 2d)nt V2 T. 2Ls
(17)
After solving (15)–(17), the optimized x is found to be x=
1 V1 . = V1 + nt V2 1+M
(18)
Using this result, the optimized asymmetric double-side modulation is presented in Fig. 5. When the phase shift is required to increase by dT , the secondary gating signals shall be shifted d T , while the primary gating signals shall be backward by 1+M Md T . It can be proved easily that this opshifted forward by 1+M timized selection of x is suitable for the case of the decrease of the phase shift too. With this optimized asymmetric double-side modulation, the converter may transfer from one steady state to another steady state smoothly and quickly regardless of the value of rs as shown in Fig. 5. Though the inductor current is manipulated to have a zero average in previous analysis, the proposed modulation is different from predictive current control and has no requirement of current sampling. III. VERIFICATION THROUGH SIMULATION AND EXPERIMENT To validate the discussion in the previous section, the transient of a DAB converter is explored by computer simulation in PSIM first. The specifications of the DAB converter are V1 = 120 V, V2 = 72 V, nt = 1, T = 5 μs, Ls = 180 μH, C1 = C2 = 22 μF. In Fig. 6, plots of the inductor current in transient using different modulation techniques are presented.
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Fig. 5. Asymmetric double-side modulation for the increase of phase shift in a DAB converter at M < 1 with x = 1/(1 + M ).
The phase shift are changed from 30◦ to 120◦ to meet the requirement of a load level. For each modulation technique, the test are repeated with different rs at 0.001 Ω, 0.1 Ω, 1 Ω, respectively. It is clearly seen that a large rs will accelerate the transient procedure for the first two techniques and has little effect on the third one. Also, the third modulation has the shortest settling time. Moreover, a series of experimental tests have been done in the lab. The lab prototype has same specifications as the one used in simulation. The equivalent resistance rs is measured at 0.95 Ω. The tested DAB converter has a converter gain at M = nt V2 /V1 = 0.6. And in the transient duration, an request is assumed to be obtained from the front-stage controller, which asks for an increase of 90◦ phase shift from the current phase shift 30◦ . The execution of the phase shift change between the two groups of gating signals are implemented using an eZdspTMS320F2812 development board. The board is based on a TI TMS320F2812 microcontroller unit which has two built-in timers with PWM outputs. In the experiment only one timer is used in continuous up/down-counting mode which could generate a symmetric triangular wave as the carrier signal. When each PWM compare value stored in the main compare register is equal to the current value of the timer (i.e., the carrier), a compare match is triggered and the corresponding PWM output flips. At any time, the new compare value can be written into a shadow/buffer register which will update the main compare register upon the next period match or underflow match. Thus, it is possible to calculate and update the next compare value in the interrupt subroutine at each period match or underflow match in advance. The obtained experimental plots for the three modulation technique at the increase of the phase shift are given in Fig. 7. The steady-state peak inductor current will jump from 1 to 2 A. The conditions of single-side modulation and symmetric double-side modulation observed in Fig. 7 match the previous
Fig. 6. Simulation plots of is in transient using (a) single-side modulation, (b) symmetric double-side modulation, and (c) asymmetric double-side modulation. In each case, rs has three different values: 0.001 Ω (top), 0.01 Ω (middle) and 1 Ω (bottom).
analysis given in Figs. 3, 4, 6(a), and (b). The settling times for those two cases are approximately 20 cycles and 11 cycles, respectively. With the calculated optimized x = 1/1.6 = 62.5%, the transient procedure of the optimized asymmetric double-side modulation in Fig. 7 is almost instantly as expected.
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calculation and validated by experiments so that it may be integrated with any close-loop controller as the executive stage for a DAB dc/dc converter using conventional phase-shift control. REFERENCES
Fig. 7. Experimental plots of the transient inductor current in a DAB at M = 0.6 using (up-left) single-side modulation; (up-right) symmetric double-side modulation; (bottom) optimized asymmetric double-side modulation.
IV. CONCLUSION This letter discussed and compared two phase-shift modulation techniques, single-side modulation and symmetric doubleside modulation, used for the transient response of a DAB dc/dc converter. After the transient duration, the inductor current in both cases needs some time to settle down to the new steady state. A modified asymmetric double-side modulation is then proposed to minimize the settling time of the inductor current. If the converter gain is available, the converter may have fast dynamic response by using this proposed modulation during the transient of load level. The optimized modulation is proved by
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