ZVS-Optimized Constant and Variable Switching Frequency Modulation Schemes for Dual Active Bridge Converters

This paper proposes two modulation schemes for Dual Active Bridge (DAB) converters, with the aim of maximizing Zero Voltage Switching (ZVS) operation over a wide operational range. The first is a ZVS-optimized constant frequency modulation scheme, constructed based on the boundary conditions of ZVS operation. This scheme maximizes the number of ZVS events across a broad operational range and is easy to implement. Additionally, a variable frequency modulation scheme is proposed, enabling continuous full ZVS operation for the DAB converter at full power and eliminating the loss of ZVS due to transitioning between modulation regions. This functionality extends the full ZVS range, yielding improved Electromagnetic Interference (EMI) performance and overall power efficiency. The synergy of the proposed modulation schemes is particularly well-suited for applications like off-board Electric Vehicle (EV) charging. Experimental validation, conducted on an 11-kW DAB converter prototype with an output voltage range of 250 V to 950 V, demonstrates the efficacy of the proposed schemes in achieving ZVS and boosting converter efficiency.

Most EVs launched last decade have a nominal battery voltage of around 400 V. Currently, high-end EV manufacturers are increasingly adopting 800 V battery architectures due to their benefits: reduced vehicle weight and faster battery charging times using public DC-fast charging infrastructures.This is especially advantageous as public charger cable current ratings are limited by thermal management.Therefore, today the public DC-type EV charging infrastructures should be able to supply power efficiently to both 400 V and 800 V EV battery classes.
One of the main challenges for the DAB converter in the public EV charging application is maintaining the highefficiency performance and zero voltage switching (ZVS) ability in an extended power and voltage regulation range.The conventional single phase shift (SPS) modulation method is the simplest modulation method, which regulates the voltage and power level by controlling [1], [2], [3].At unity voltage gain scenarios, the SPS modulation can provide ZVS over most of the operating range.Fig. 1(c) shows the typical operational waveform of the SPS modulation method where all transistors operate in ZVS turn-on.
The DPS modulation of DAB converter is introduced In [7] to eliminate reactive power in light load operations.The DPS adjusts D 1 and D 2 (D 1 = D 2 ) between 0% and 100% while controlling .It offers wider power transmission and more power transfer than SPS with the same and current stress as per [20].[33] identifies four DPS modulation modes and proposes an optimized scheme using magnetizing current.
However, [30] suggests that DPS is generally inferior to EPS due to higher current stress.
The EPS mode 2 modulation, as proposed in [5], extends the soft switching range of the DAB converter by adjusting and D 1 /D 2 based on the largest DC voltage.Although it enhances the ZVS range, it encounters hard-switching issues under light loads.Subsequent works have optimized and extended its soft switching capabilities, with EPS mode 1 enabling ZVS even in light load scenarios where EPS mode 2 fails [6], [12].The asymmetric EPS modulation introduces a DC offset, necessitating a blocking capacitor [29].Finally, the studies in [31], [32] employ magnetizing current to further extend the ZVS range, but this approach leads to sub-optimal transformer design and elevated current stresses.
Several researchers have proposed distinctive modulation schemes that amalgamate modulation methods to optimize efficiency performance for DAB converters relative to SPS modulation.The authors of [4], [9] recommend a blend of triangular (a boundary case between TPS mode 1 and 3) and trapezoidal (a specialized case of TPS mode 3) current modulation for optimal system efficiency.However, only four and two out of eight transistors can achieve ZVS in trapezoidal and triangular modes, respectively, with the remaining transistors only achieving Zero Current Switching (ZCS).In [11], to extend the soft-switching range to the zero-load condition and to reduce rms and peak currents, the recommendation is to operate in TPS mode 1 at low power due to its full ZVS ability and concurrently minimized rms current, and in EPS mode 2 (a special case of TPS mode 4) at high power.At maximum power, EPS mode 2 naturally transitions into SPS.However, the analysis of the critical ZVS condition is not accurate, as it overlooks the output capacitance of the transistors.This omission can result in sub-optimal ZVS performance during practical implementation.To mitigate the conduction and copper losses, [13] employs TCM (TPS mode 3) for low power, OTM (TPS mode 4) for medium power, and CPM (SPS) for high power, even though some switches do not achieve ZVS in TPS mode 3. Additionally, the formulation of the modulation scheme is intricate for practical implementation.The studies in [19], [24], [26] optimize current stress using varying combinations of EPS and TPS modes.[28] employs SPS for heavy loads and transitions to EPS2, EPS1, and TPS1 as the load decreases.However, implementing the transition between the nine modulation modes using a state machine is not straightforward, and the ZVS loss during the transition is not thoroughly explored.[35] introduces a modulation scheme for DAB converters that maximizes the ZVS range and achieves quasi-optimal inductor rms current, amalgamating TPS1, EPS1, EPS2, and SPS.In [36], universal analytical expressions for TPS modulation are derived, and an RMS current-minimized scheme, grounded in GOC equations, is introduced.However, it prioritizes RMS current reduction, potentially compromising optimal ZVS performance.Asymmetric duty modulation, explored in [37], [38], provides additional flexibility through duty cycle adjustments, resulting in reduced RMS current and an expanded soft-switching range.However, its complexity, compared to symmetrical duty modulations, poses challenges to implementation.The ZVS analysis in [38], based on the stored energy equation, omits energy considerations from the non-switching bridge, leading to inaccuracies acknowledged by the authors.Although [38] demonstrates full ZVS operation, it is confined to BUCK mode operation with a voltage regulation range from 0.5 to 1.
Component modifications and variable switching frequency modulation have also been explored in the literature to enhance the DAB converter's performance.[10] employs variable AC link reactance with a dual leakage transformer to mitigate peak transformer currents during light load SPS operation.[22] introduces a modulation scheme utilizing a voltage offset across the DC blocking capacitor, allowing for a broader soft-switching range with simple implementation.Expanding the ZVS range by decreasing magnetizing inductance is also possible [32], [33], [40].However, these methods require hardware changes, such as specific transformer designs and additional capacitors, possibly reducing power density and increasing current stress.An alternative is to manipulate the switching frequency without hardware alterations.[17] proposes finding the optimal design trade-off among switching loss, conduction loss, and drive loss by manipulating the switching frequency.However, the possibility of maximizing the ZVS range is not explored.The work in [18], [20] proposes including variable switching frequency in SPS and EPS modulation to extend the soft-switching range.However, the ZVS analysis is based on inductive and capacitive energy equations, which are inaccurate due to the omission of energy provided by the non-switching bridge.
In conclusion, compared to the operation with only SPS method, an appropriate modulation scheme, comprising SPS, DPS, EPS, and TPS methods significantly enlarges the ZVS range and reduces current stress in the DAB converter.However, it is still challenging to achieve a full ZVS operation in a wide voltage regulation range application such as EV charging due to the inevitable ZVS lost during the transition between these modulation methods.Most of the proposed modulation schemes in the literature focus on the optimization of current stresses, leading to sub-optimal ZVS performance.And the modulation scheme are practically hard to implement.
Moreover, there is no study covering the wide voltage range operation of the DAB converter from 250 V to 1000 V, which is necessary for the off-board EV charging application.
In the context of EV charging applications, converters or power modules are expected to operate at full power for the majority of charging scenarios, particularly in common situations such as home charging and workplace charging [41].In these scenarios, low to medium power chargers with a capacity of up to 50 kW are commonly used, and they operate at their full power until the batteries of the EVs reach a high state of charge (SOC).This behavior is evident in charging profiles from various sources such as [42], [43], [44], where 50 kW chargers continue to operate at full power until the EV's SOC exceeds 80%.In fast to ultra-fast charging scenarios, the individual power modules within the charger also operate at full power most of the time, particularly when implementing the multi-step constant current (MSCC) charging strategy [45].Under this strategy, power modules run at full power until the required charging power decreases, at which point they are sequentially turned off.Charging profiles from sources like [46], [47], [48], [49] exemplify these charging scenarios.Consequently, operating with a reduced number of ZVS events at full power operating points is undesirable due to its adverse effects on both Electromagnetic Interference (EMI) performance and power efficiency.It is crucial to achieving continuous ZVS operation for minimizing the switch-bridge cross-talk caused by the hard switching and achieving high efficiency performance throughout the charging process.
This paper proposes to combine the TPS mode 1, EPS mode 1, EPS mode 2 together to form a ZVS-advantageous constant switching frequency modulation scheme.These three modes are chosen because their operational ranges are naturally connected, meaning there will not be any abrupt change of phase shifts during the changing of modes.With this modulation scheme, the DAB converter is able to operate with full ZVS for all eight switches in most of the operational points.However, two or four out of eight switches can lose ZVS during the transition region where the DAB changes between the EPS mode 1 and 2. To address this issue, for the dominating full power charging scenarios, the variable switching frequency is introduced into the modulation scheme to ensure full ZVS performance.Since in the EV charging application, the converter will operate in full power condition most of the time, this modulation scheme will ensure reliable operation of the EV charger without introducing modification on the converter components or topology.
The main contributions of this paper are as follows: r The proposal of a ZVS-optimized constant frequency modulation scheme and its construction method based on straightforward ZVS analysis.The proposed scheme aims to maximize ZVS events in the DAB converter while ensuring easy practical implementation.
r The proposal of a variable switching frequency modula- tion scheme and its construction method to address the lost of ZVS issue during mode transition in the constant frequency modulation scheme.This variable switching frequency modualtion scheme ensures full ZVS operation of the DAB converter in a wide voltage range during the full power charging process to improve the EMI performance.
r The experimental testing of the proposed modulation schemes on an 11 kW DAB prototype with a wide output voltage range (250-950 V).This wide voltage range test of the DAB converter was not yet elaborated on in the literature.This is particularly important because it demonstrates the feasibility of the proposed modulation schemes for the future EV market.This paper is arranged as follows.In Section II, the analytical expressions of the DAB converter in TPS mode 1 and 4 are introduced, including the operational conditions of D 1 /D 2 / , the calculations of inductor current i L values, and the ZVS requirements for different switching actions.The boundary conditions to operate with full ZVS for all eight switches are derived based on the analytical current calculation and the general ZVS requirements.Section III presents the proposed ZVS-optimized constant frequency modulation scheme and the analytical method to construct it.Moreover, the issue of the ZVS lost during the transition of modulation methods is explained in detail.Section IV presents the proposed variable switching frequency modulation scheme and the method of its construction.In Section V, the modulation schemes are tested on a DAB prototype, and the results are presented.The ZVS and efficiency performance of the proposed modulation scheme are verified and compared.The conclusion is presented in Section VI.

II. ANALYTICAL EXPRESSIONS OF THE TPS MODE 1 AND 4
The EPS mode 1 and 2 modulations are special cases of TPS mode 1 and 4 modulations, which can be observed in Fig. 1.Thus, the analyses of TPS mode 1 and 4 are presented in this paper as they are more general and cover the cases for EPS mode 1 and 2. In order to be categorized into TPS mode 1 and 4 as shown in Fig. 1(g) and (i), the values of the phase shifts need to fall within the operational conditions summarized in Table 1.
For the SPS, TPS mode 1, and mode 4, two types of switching actions occur, the switching of a switching leg (a half-bridge), and the switching of a H-bridge.When the switching action of a half-bridge happens, the voltage of that H-bridge will change between zero and ±V .And when the switching action of a H-bridge happens, the voltage of it will change between +V and −V .Table 2 summarised the analytical expressions for the instantaneous current values of i L at each switching action.
According to the different voltage changes, the general ZVS requirements for the switching actions are summarized in Table 3. Z is the characteristic impedance of the LC resonant circuitry during the half-bridge switching actions, and it can be calculated by (1).For the deriving of the expressions in Table 3, the conventional inductive and capacitive stored energy equation for ZVS analysis are used by numerous papers [18], [20], [38].It is usually written as 0.5LI 2 > 0.5nC oss V 2 ds , in which L is the leakage or external inductance value, and n is the number of transistors involved during the switching transition.This equation oversimplifies the energy exchange during the switching transition because it ignores the energy provided by the non-switching bridge, leading to inaccurate ZVS analysis.In this paper that energy is taken into consideration.As shown from the ZVS conditions listed in Table 3 , the ZVS current requirement expressions include the non-switching bridge voltage as well.
Combining the current values and the ZVS requirements for the switching actions, sets of inequations can be derived to ensure ZVS at each switching action.The boundary conditions for the DAB converter to operate with full ZVS for all eight switches can be derived for different modulation methods based on these sets of equations.

A. FULL ZVS BOUNDARY CONDITIONS FOR TPS MODE 1
When V in > nV out Combining the current values and the ZVS requirements for the three switching actions, (v 2 : 0 → +nV out ), (v 1 : 0 → +V in ), (v 1 : +V in → 0), the following inequation system can be derived for ensuring the full ZVS performance.
k is defined as the voltage ratio as in (5), and k w is the worst case value of k.
Substituting k using the worst value k w in this equation system, the following boundary conditions can be derived: Since D 2 is always larger than D 1 when V in > nV out , The value of allowed for the equation system to hold true can be calculated by solving the following equation: Solving this equation, the boundary condition for the value of can be derived as (9).And the maximum value of for the converter to operate in the TPS mode 1 modulation, TPS(max) , can also be obtained from (9).
When V in < nV out Similarly, the following equation system can be derived for ensuring the full ZVS performance of the TPS mode 1 modulation when V in < nV out .
Based on this inequation system, the following boundary conditions can be derived:

B. FULL ZVS BOUNDARY CONDITIONS FOR EPS MODE 2
When V in > nV out Combining the current values and the ZVS requirements for the three switching actions, (v 1 : 0 → +V in ), (v 2 : −nV out → +nV out ), (v 1 : +V in → 0), the following equation system can be derived for ensuring the full ZVS performance. ( Based on this equation system, the following boundary conditions can be derived, and the minimum value of D and for the DAB converter to operate in the EPS mode 2 modulation with full ZVS, D EPS2(min) and EPS2(min) , can also be calculated.
Based on this inequation system, the following boundary conditions can be derived:

III. THE ZVS-OPTIMIZED CONSTANT FREQUENCY MODULATION SCHEME
There are infinite combinations of and D 1/2 that can operate the DAB converter at a certain operational power, switching frequency, input and output voltage.A construction method is thus needed to guide the selection of the advantageous values of and D 1/2 for the modulation scheme based on the optimization objectives.A straightforward construction method is proposed based on the full ZVS boundary conditions derived in the last section to construct a ZVS-optimized constant switching frequency modulation scheme.This modulation scheme features continuity of the phase shift values, meaning no abrupt change of phase shift value will happen during the operation.And full ZVS operation can be achieved in the majority of the operational range.

A. CONSTRUCTION OF THE MODULATION SCHEME
This modulation scheme consists of three regions.The converter will operate in the EPS mode 2 region at high power and in the TPS mode 1 region at low power.An EPS mode 1 region is in between to connect them.To achieve the optimal ZVS performance in the whole range, a straightforward method of constructing the modulation scheme is proposed, in which the values of phase shifts in each region are determined by linear interpolation between two anchor operational points.Compared to using Lagrange multiplier method to minimize current stress [39], this method does not require complex calculation.Thus, it is a simple and effective way to construct ZVS-optimized modulation schemes.
For the EPS mode 2 region, the first anchor point is where the converter's power is maximized.It can be written as (28).
The other anchor point of the EPS mode 2 region is defined by EPS2(min) and D EPS(bdr) .EPS2(min) is the minimum value according to (21) or (27) depending on the value of k, and D EPS(bdr) is the value of D to in the EPS transition mode as shown in Fig. 1(e).Thus, this anchor point can be written as (29).
Note that, since it is EPS mode, one of D 1/2 equals to 1 depending on the value of k, and the non-unity D is calculated according to (29).
With the two anchor points, the non-unity value of D 1/2 inside the EPS mode 2 region can be calculated based on the value of by linear interpolation by: The TPS mode 1 region starts at = 0 and ends at TPS(max) defined by ( 9) or (15), at which point either D 1 or D 2 will be equal to 1.With these two anchor values defined for the TPS mode 1, the values of D 1 and D 2 inside the TPS mode 1 can be obtained based on the minimum values to ensure full ZVS operation, which can be calculated based on | | value and ( 6) and ( 7) or ( 14) and (13).
The EPS mode 1 region bridges these two regions.The values of D 1/2 can be calculated using linear extrapolation between the two anchor points of the EPS mode 2 and TPS mode 1 regions.The resulting equations for D 1/2 are shown in (31).TPS(max) is the maximum value of | | to operate in the full ZVS region of TPS mode1, which can be calculated by ( 9) or (15).D 1/2,TPS(max) is the maximum value of D 1/2 to operate in the full ZVS region of TPS mode 1, and it can be calculated by substituting | | with TPS(max) in ( 6) and ( 7) or ( 14) and ( 13).+ D 1/2,TPS(max) (31) Using this construction method, the phase shift values of the constant frequency modulation scheme can be calculated for different k values.Furthermore, by applying the power calculation equation in Table 1, the corresponding power level at each operational point can be calculated.Fig. 2 shows four examples of the constant frequency modulation scheme and the values of phase shift for different values of k.It can be seen that when k < 1 and the DAB converter is operating in the BUCK mode, it operates in EPS mode 2 when the power is high and transitions into EPS mode 1 and further into TPS mode 1 when the power level decreases.A special case of the modulation scheme is when k is close to 1, as shown in Fig. 2(c).In this case, the minimum value of | | required for the full ZVS operation in EPS mode 2 is close to zero based on ( 21) and ( 27).This indicates that the converter will operate mostly in EPS mode 2, and will not transition into TPS mode 1.When V out further increases and the DAB converter is in the BOOST mode, the maximum power of the converter can be easily reached with a small value of , meaning the converter might operate mostly in the TPS mode 1 region and transition into EPS mode 1 or EPS mode 2 when the power level is approaching its maximum.In the example of Fig. 2(d) where V out is high, the DAB converter operates in TPS mode 1 in its power range, and at the maximum power, the operation is at the edge between the TPS mode 1 and EPS mode 1 region.

B. LOSS OF ZVS DURING TRANSITION
Even though it is possible for all the switches of the DAB converter to have ZVS when it is operated in the TPS mode 1, EPS mode 1, and EPS mode 2, certain switches will lose the ZVS when the operation is at the boundary between two modes.A straightforward way to explain the loss of ZVS is that, in such boundary regions, the switching actions of the H-bridge I are very close to, or even overlapping, that of the H-bridge II.For the EPS boundary mode illustrated in Fig. 1(c), the switching action of (v 1 : 0 → +V in ) overlaps that of (v 2 : −nV out → +nV out ), and (v 1 : 0 → −V in ) overlaps that of (v 2 : +nV out → −nV out ).It can be seen from Table 3 that the switching action (v 1 : 0 → +V in ) requires a negative current value for ZVS, while the switching actions (v 2 : −nV out → +nV out ) requires a positive current value.Therefore, the ZVS requirement for one of the switching actions can not be fulfilled, and ZVS for certain switches will be lost.Similarly, operating at the edge of the operation region where the switching actions of the two H-bridges are very close will lead to insufficient current values for different ZVS requirements, resulting in partial  4.
ZVS or even hard switching.Therefore, this proposed constant frequency modulation scheme introduces improvements to the number of ZVS events compared to other modulation methods, but the loss of ZVS for certain transistors during the transition of modulation regions is inevitable.
Based on the method of construction of the modulation scheme, it is clear that the converter is able to operate with full ZVS in the TPS mode 1 region.This is because all the values of D 1/2 and in this region fulfill the ZVS requirements shown in ( 6), ( 7) and ( 9) or ( 14), (13),and (15).
However, full ZVS will not always be achieved in the EPS mode region.The reason lies in the choice of the anchor points.As explained in Section III-A, the second anchor point for the EPS mode 2 region is at | | = EPS(min) , and D 1/2 = 1 − 2 EPS(min) .In this operational point, even though the ZVS requirement for as shown in (21) or ( 27) is fulfilled, the ones for D 1/2 as written in (19) and ( 20) or ( 25) and ( 26) are not guaranteed.This indicates that 2 or 4 transistors on the primary side might lose ZVS when the operation is close to this anchor point of EPS mode 2 region.This operational point is still chosen as the anchor point of EPS mode 2 region because the resulting modulation scheme offers better overall ZVS performance in the whole operational range.The alternative anchor point is at | | = EPS2(min) with D 1/2 = D EPS2(min) fulfilling the ZVS requirements of ( 19) and ( 20) or ( 25) and (26).With this anchor point, all the operational points inside the EPS mode 2 region will achieve full ZVS.However, part of the resulting operational region that bridges this anchor point to that of the TPS mode 1 can only achieve ZVS on two out of eight transistors.
To explain this phenomenon, the constant frequency modulation scheme at V out = 250 V, k = 0.446 and f sw = 25 kHz?enlrg -10pt?> is shown in Fig. 3 together with the important boundaries of and D.Moreover, the number of switches that can achieve ZVS is also marked in the specific regions.It can be seen that by following the proposed method of scheme construction, the DAB converter will operate with 8/8 ZVS in the whole TPS mode 1 region and most of the EPS mode 2 region, but will operate with 6/8 ZVS in edge of the EPS mode 2 region and the EPS mode 1 region.However, if the alternative anchor point of EPS mode 2 is used, the resulting modulation scheme (indicated by the dashed blue line) will include a specific region inside the EPS mode 2 region where the only 2/8 transistors can achieve ZVS.Note that it is still possible to achieve partial ZVS for the other six switches.
The loss of ZVS happens not only when the power level changes while k is fixed, but also when k changes and the power level is fixed.Fig. 4 shows the phase shift values at different V out for the constant frequency modulation scheme at the full power operation.When V out is low, the DAB converter needs to operate with high values of and in the EPS mode 2 region to deliver the maximum rated power.However, as V out further increases, the maximum power operational point will shift from EPS mode 2 region into EPS 1.During the transition from EPS mode 2 to EPS mode 1 (700 V < V out < 870 V), the converter will lose ZVS on two transistors during the full power operation according to the calculation based on the ZVS requirements in Table 3.It can be seen that, the loss of ZVS during mode transition can cover a significant operational range as illustrated in Fig. 4.This will bring detrimental impacts on the EMI and efficiency performance of the DAB converter, especially when it is used in the EV charging application due to the reasons explained in the Introduction.4.

IV. THE VARIABLE FREQUENCY MODULATION SCHEME FOR FULL POWER OPERATION
To prevent the DAB from operating at the edge of the operational regions where certain switches will lose ZVS during full power operation, the phase shift can be increased or decreased so that the operation moves more deeply into ZVS-beneficial regions.However, the operational power of the DAB converter will be changed by changing .Table 1 shows the conditions of D 1 , D 2 , and the power calculation of the TPS mode 1 and mode 4. It can be seen that the phase shift is a proportional control parameter for the power of the DAB operation.Therefore, it is not possible to maintain ZVS by only changing .To solve this issue, the switching frequency f sw can be utilized.

A. WORKING PRINCIPLE
As can be seen from the equations of power calculation in Table 1, the power is inversely proportional to f sw .Thus, The switching frequency f sw can be utilized as an additional control parameter to shift the operation of the DAB converter to the ZVS-beneficial modulation modes without changing the power level.f sw can either be increased or decreased to help maintain the ZVS performance.The first one is to increase f sw when the DAB converter is about to enter the boundary mode from EPS mode 2, which decreases the output power, requiring an increase in to achieve the same power.As a result, the operation will remain in the EPS mode 2 region where full ZVS can be achieved.Similarly, f sw can be reduced and needs to be reduced to maintain the same power.The lower value of will help to maintain the operation in the full ZVS part of the TPS mode 1 region.
From the ZVS point of view, whether f sw is increased or decreased is inconsequential as long as ZVS is achieved.However, each approach has their pros and cons.In the case of decreasing f sw , the switching losses on the transistors can be mitigated, but the dB/dt and magnetic flux density stress of the transformer core increases.This means the magnetic components must be designed at the lowest switching frequency and most critical flux density to avoid saturation, resulting in the oversizing of magnetic components.Conversely, increasing f sw will amplify the switching losses, but due to lower dB/dt and flux density stress at higher f sw the magnetic components can be designed similarly to those in the conventional constant frequency modulation.Therefore, aside from the EMC filter circuitry, no hardware change is required when f sw is increased, and this maintains the converter's power density and lowers the design complexity.This paper focuses on the case of increasing f sw .

B. CONSTRUCTION OF THE MODULATION SCHEME FOR FULL POWER OPERATION
The variable frequency modulation scheme is modified based on the constant frequency modulation scheme.Since the operation always remains in the EPS mode 2 region in the variable switching frequency modulation scheme, the anchor point of the EPS mode 2 region can be chosen to be the alternative one that fulfills the full ZVS requirements, which is at | | = EPS2(min) with D 1/2 = D EPS2(min) .In this way, the EPS mode 2 region is utilized more efficiently.
The value of phase shifts and f sw for the variable switching frequency modulation scheme for full power operation is obtained by iteration on the basis of the constant frequency modulation scheme in full power.Firstly, the constant frequency modulation scheme is constructed with the new anchor point and interpolation method.Secondly, the operational region/ZVS performance of the DAB converter operating at its maximum power in this constant frequency modulation scheme is checked.If the operation is not in the ZVSbeneficial EPS mode 2 region and full ZVS can not be achieved, f sw will be increased by an increment.Then will be increased accordingly and D 1/2 will be re-calculated based on the construction method for the constant frequency modulation scheme explained in Section III-A with the new f sw .This is done until the same power level before changing f sw is reached.Then, the ZVS requirements will be checked again.If full ZVS is not yet achieved, the previous step will be repeated, and f sw and will be further increased until full ZVS operation is reached.This process is looped through different values of k to cover the whole voltage regulation range.
Fig. 5 shows the resulting variable frequency modulation scheme for full power operation.It can be seen that starting from V out ≈ 700 V, f sw is increased from 25 kHz to around 50 kHz, allowing the converter to operate with an increased value of compared to Fig. 4. As a result, the full power operation remains in the ZVS-beneficial EPS mode 2 region for the whole output voltage range.This indicates that by using the proposed variable frequency modulation scheme, the DAB converter can always have full ZVS during the full-power operation in the whole output voltage range, which is essential for the EV charging application.
Note that it is possible to extend the variable switching frequency modulation to lower power with the same construction method.In this paper, it is only applied to the full power  operation because it is identified as the dominating operational scenario for EV charging.

V. EXPERIMENTAL VERIFICATION
An 11 kW DAB converter prototype is built to verify the ZVS performance of the proposed modulation schemes.This converter features a wide output voltage range from 250 V to 950 V, which ensures its effectiveness in charging both 400 V and 800 V EVs.Fig. 6 shows the DAB prototype.Table 4 summarizes the specification of the DAB prototype.
A lookup table based power control is implemented in the micro-controller TMS320F28379D for the DAB prototype.Fig. 7 shows the control method of the prototype.This method is simple and does not require much computational resources.To generate the required lookup table, a matrix containing the power at a given value of , V in and V out is created in Matlab.This is done with a very high resolution for .For each combination of V in and V out , the power vs curve is sampled at fixed power values using the 1D interpolation function.These values of are then stored in a 3D matrix used in the lookup table to determine based on the converter power reference, V in and V out .The values of D 1 and D 2 are paired with based on the construction of the modulation scheme.
During the charging operation, V in and V out of the DAB converter are measured.Together with the required charging power value P ref sent by the EV, the values of the phase shifts and switching frequency can be extracted from the lookup table.These values are then used to generate the PWM gate signals for the transistors.

A. RESULTS OF CONSTANT FREQUENCY MODULATION SCHEME
Firstly, the constant frequency modulation scheme is tested on the prototype to set up a benchmark of ZVS and efficiency performance.Fig. 8 shows the operational waveform of the DAB converter operated with the constant frequency modulation scheme.These nine waveforms are located in at the operational points shown in Fig. 2. As can be seen from Fig. 8(a)-(c), the converter transitions from TPS mode 1 to EPS mode 1 and further into EPS mode 2 when the power increases.In Fig. 8(a) and (c), where the converter operates deeply in TPS mode 1 and EPS mode 2, all transistors have ZVS as indicated by the zoom-in waveform of the H-bridge voltage and current.And it can be seen in Fig. 8(b), where the converter operates in EPS mode 1, the 0 → +V in switching action of the primary side half bridge does not meet the ZVS requirement of having a zero or negative inductor current value.As a result, two transistors on the primary side lose ZVS as indicated by the sharp voltage change of v 1 .In comparison, v R has a slower and smooth change with this small positive value of inductor current, indicating that ZVS is achieved.
As v out increases and k is close to 1, the converter operates only in EPS modes as seen in Fig. 8(d)-(f).In the low power scenario as shown in Fig. 8(d), the converter is operating in the EPS mode 1 and is very close to the EPS transition mode, as the switching action 0 → +V in occurs closely to the switching action −V out → +V out .According to the general ZVS equations listed in Table 3, the switching action −V in → 0 and 0 → +V in requires a slightly negative i L to achieve ZVS, but the switching action −V out → V out requires zero or positive i L to achieve ZVS.As a result, only the four transistors on the secondary side achieve ZVS while the four on the primary side cannot, which is indicated by the waveform of v 1 and v R in Fig. 8(d).When the power increases, the converter operates at the edge of the EPS mode 2. The switching action 0 → +V in that requires a negative i L is still close to the switching action −V out → V out which requires a positive i L , leading to the loss of ZVS for the two transistors on the primary side.However, the switching action −V in → 0 now obtains ZVS due to the sufficiently negative i L .When the power further increases and the converter operates deeply in the EPS mode 2, full ZVS is achieved as shown in Fig. 8(f).
In the case where V out is high, the only operates in the TPS mode 1 and at the edge of EPS mode 1 region, as it can be seen in Figs. 2 and 8(g)-(i).Full ZVS can be easily achieved when the power level is not high and the converter is operating deeply in the TPS mode 1 region.However, as the power increases, the converter moves to the edge of the TPS mode 1 and EPS mode 1, making it challenging to maintain full ZVS performance.As can be seen from Fig. 8(i), the switching action +V out → 0 occurs very close to +V in → −V in .The prior one requires a negative current value for ZVS, while later one requires a zero or positive current.Consequently, the two transistors of the half bridge on the secondary side achieve only partial ZVS as it can be seen in Fig. 8(i).
In summary, the constant frequency modulation scheme operates well, and full ZVS is achieved in the majority of the operational range.However, the loss of ZVS happens when the operation is at the boundary of two modulation regions.In the case of unity voltage gain, 4 out of 8 transistors might lose ZVS, and in other boundary operation cases, 2 out of 8 transistors will lose ZVS.The loss of ZVS during full power operation is also demonstrated.

B. RESULTS OF VARIABLE FREQUENCY MODULATION SCHEME
Fig. 9 shows the waveforms of the DAB converter operating with full power but different output voltage in the constant frequency (Fig. 9(a)-(c)) and variable frequency modulation scheme (Fig. 9(d)-(f)).
It can be seen from Fig. 9(a)-(c) that the converter in the constant frequency modulation scheme need to transition from EPS mode 2 to EPS mode 1 when V out increases during full power operation.This is not beneficial for the ZVS performance because 2 out of 8 transistors will lose ZVS as explained in Section III-B and seen in Fig. 9(a)-(c).In the case of EV charging where the full power operation takes up most of the charging process, the loss of ZVS brought by the constant frequency modulation scheme will have a more significant impact, especially on the EMI performance.
With the variable switching frequency modulation scheme, both f sw and are adjusted so that the operation of the converter is kept in the full ZVS region.As shown in Fig. 9(d)-(f), f sw as well as are increased compared to the constant frequency modulation scheme, moving the operation into the full ZVS EPS mode 2 region.This demonstrates that by using the variable switching frequency modulation scheme, the ZVS performance during the full power operation can be improved compared to the constant frequency modulation scheme.

C. EFFICIENCY PERFORMANCE
The measured efficiency performance of the proposed constant frequency modulation scheme in the whole operational range is shown in Fig. 10.It is evident that the overall efficiency performance is excellent.The converter's efficiency is above 95% in the whole range, and the highest efficiency is measured to be 98.8%.Most importantly, the efficiency performance when operating above 2 kW is well above 97%.This demonstrates that this modulation scheme can provide excellent efficiency performance to the DAB converter for the wide voltage range EV charging application.

VOLUME 4, 2023
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Relatively low efficiency can be observed when operating at very low values of V out and P, and also when V out equals or close to 550 V.For the high power low V out operation, the current stresses during the high power operation are problematic, leading to significant conduction losses and low efficiency performance.For the case when the power is low and V out is high, the high switching losses brought by the high blocking voltage result in the efficiency drop.When V out equals or close to 550 V, the voltage ratio k is close to 1.According to the constructed modulation scheme shown in Fig. 2(c), the converter will lose ZVS during low power operation, which is verified by the test shown in Fig. 8(d).This also contributes to the relatively low efficiency performance.
The efficiency performances of the two modulation schemes at full power operation are compared.Fig. 11 shows the tested efficiency at the full power operation for the constant frequency and variable frequency modulation scheme.To provide more insights into the efficiency performance, the converter's losses and efficiency are also calculated analytically and plotted.The detailed losses calculation models can be found in [50], [51].As it can be seen from Fig. 11, the estimated efficiency matches well with the testing results.Thus, the estimated loss breakdown can be used to help interpret the efficiency performance.
It can be seen from the tested efficiency that, the variable switching frequency modulation scheme slightly improves the efficiency performance when V out > 700 V.As V out continues to increase, the improvement of efficiency starts to reduce.When V out is as high as 950 V, the efficiency performance of the variable frequency modulation becomes slightly lower than that of the constant frequency one.The reason behind  is that, the converter starts to lose ZVS when V out > 700 V (as it can be seen in Fig. 9(a) and (b)), causing the switching losses to increase (as it can be seen from the switching loss P S,sw stack plot in Fig. 11).Whereas in the variable frequency modulation, by slightly increasing f sw , the ZVS is maintained for all transistors, resulting in lower switching losses overall.As V out continues to increase, the operation moves to the ZVS-beneficial region for the constant frequency scheme, but f sw and P S,sw continue increasing for the variable frequency scheme.An interesting fact to point out is that, as f sw increases, the transformer core loss P T,c is reduced due to the lowered flux density stress.This benefits the efficiency performance of the variable frequency scheme.Secondly, the efficiency performances for these two modulation schemes when V out < 700 V are different.This is mainly due to the different choices of the anchor point for the EPS mode 2 region, whose reason and details are presented in Section III-B.
Overall, Based on the tested efficiency, the average efficiency in full power operation for the constant frequency and variable frequency modulation schemes can be calculated to be 97.76% and 97.80%, respectively.This demonstrates that by adopting the variable frequency modulation scheme, not only full ZVS can be maintained for the whole voltage regulation range, but also the efficiency performance will not be sacrificed for the full power operation.

VI. CONCLUSION
The ZVS-optimized constant and variable switching frequency modulation schemes proposed for the DAB converter aim to enhance ZVS performance in EV charging applications while concurrently maintaining high efficiency.These schemes are formulated based on ZVS boundary conditions, ensuring ease of implementation.
Contrary to existing modulation schemes that focus on optimizing current stress, the proposed constant switching frequency scheme excels in achieving extensive ZVS operation across a wide voltage regulation range, ensuring ZVS on all eight transistors for the majority of the operational span.Nonetheless, this paper acknowledges the inevitable ZVS loss on two or four transistors during the modulation method transitions in the constant switching frequency modulation scheme, presenting challenges for EMI and efficiency.
To address this challenge, the paper introduces a variable switching frequency modulation scheme and outlines its construction methodology.The essence of this approach lies in the dynamic adjustment of the switching frequency to strategically steer the converter's into ZVS-favorable regions whenever ZVS is jeopardized.This dynamic approach ensures that ZVS is maintained for all transistors.Given that power modules predominantly operate at full capacity in EV charging scenarios, this variable switching frequency scheme is specifically designed for full-power operation in this study.
Experimental testing on an 11 kW, 250V-950 V DAB prototype validates the efficacy of the proposed modulation schemes.The ZVS performances are verified for both modulation schemes.The extensive ZVS range of the constant switching frequency modulation scheme and the loss of ZVS during mode transitions are illustrated.The full ZVS operation of the variable switching frequency modulation scheme is also demonstrated for full power operation.The efficiency performances of both modulation schemes are presented, demonstrating successful improvement of ZVS performance while maintaining excellent efficiency.
The results of this study provide substantial evidence supporting the feasibility and effectiveness of the proposed modulation schemes.These findings indicate that the proposed modulation schemes are promising solutions for enhancing the performance and reliability of DAB converters in the context of wide voltage range EV charging applications.

FIGURE 1 .
FIGURE 1. Schematics of the DAB converter and the typical operational waveform of SPS (c), EPS (d), (f), TPS (g), (h), (i) modulation in the advantageous modes, and two boundary modes denoted as SPS transition mode (b) and EPS transition mode (e).

FIGURE 2 .
FIGURE 2. The phase shift (D 1/2 and ) and power values for the constant frequency TPS + EPS modulation scheme, under different k values.f sw = 25kHz, and other specifications of the converter can be found in Table4.

FIGURE 3 .
FIGURE 3. Phase shift (D 1/2 and ) values for the constant frequency TPS + EPS modulation scheme when V out = 250 V, k = 0.446, f sw = 25 kHz.Specifications of the converter can be found in Table 4.The blue dashed line shows the alternative scheme when the anchor point of EPS mode 2 is changed.

FIGURE 4 .
FIGURE 4. Phase shift (D 1/2 and ) values for the constant frequency TPS + EPS modulation scheme at the full power operation, f sw = 25kHz.Specifications of the converter can be found in Table4.

FIGURE 5 .
FIGURE 5. Phase shift (D 1/2 and ) and f sw values for the variable frequency modulation scheme at the full power operation.Specifications of the converter can be found in Table4.

FIGURE 6 .
FIGURE 6. Picture of the 11 kW DAB converter prototype.

FIGURE 8 .
FIGURE 8. Waveform of the DAB converter operating with the proposed constant switching frequency TPS + EPS modulation scheme, with V in = 640 V and f sw = 25 kHz.v R and i R are the voltage and current measured from the secondary winding of the transformer.

FIGURE 9 .
FIGURE 9. Waveform of the DAB converter with the proposed constant modulation scheme (a)-(c), and variable switching frequency modulation scheme (d)-(f), with V in = 640V and P = 11kW (full power).v R and i R are the voltage and current measured from the secondary winding of the transformer.

98. 8 FIGURE 10 .
FIGURE 10.Tested efficiency of the constant frequency modulation schemes in the whole operation range.

FIGURE 11 .
FIGURE 11.Tested efficiency, estimated losses, and estimated efficiency of the constant frequency and variable frequency modulation schemes at full power.(a) constant frequency modulation scheme.(b) variable frequency modulation scheme.

FIGURE 12 .
FIGURE 12. Waveform of transient behaviours of the DAB converter with the proposed constant frequency modulation scheme (a)-(c), and variable switching frequency modulation scheme (d)-(f), with V in = 640V.v R and i R are the voltage and current measured from the secondary winding of the transformer.