# Influence of the Mission Profile on the Selection of the Leakage Inductance for DAB converter

Adriana Campos, Piotr Dworakowski, Besar Asllani, Konstantin Vershinin

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Adriana Campos, Piotr Dworakowski, Besar Asllani, Konstantin Vershinin. Influence of the Mission Profile on the Selection of the Leakage Inductance for DAB converter. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0254. hal-05087224

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# Influence of the Mission Profile on the Selection of the Leakage Inductance for DAB converter

Adriana Campos, Piotr Dworakowski, Besar Asllani, Konstantin Vershinin

SuperGrid Institute

23 rue Cyprian

Villeurbanne, France

E-Mail: adriana.campos@supergrid-institute.com

URL: https://www.supergrid-institute.com/

## Acknowledgements

The authors would like to acknowledge the FOR²ENSICS project, which is funded under the European Union's Horizon Europe research and innovation programme under grant agreement No 101075672.

## Keywords

«Dual Active Bridge (DAB)», «Mission profile», «MVDC», «Efficiency», «Solid State Transformer».

## Abstract

The Solid-State Transformer (SST) is a key technology to support the massive deployment of Renewable Energy Sources (RES) and the electrification of several sectors. The Dual Active Bridge (DAB) is a promising topology to be used in Medium Voltage DC (MVDC) networks. However, depending on the modulation and the voltage ratio range, the DAB can present high reactive power and low efficiency at light loads. The leakage inductance is a key design parameter to optimize the overall converter performance. This paper presents a methodology to choose the leakage inductance for four mission profiles (PV, EV, residential and commercial) based on proposed weighted duration coefficients. The methodology considers a DC voltage variation and the change in reactive power and ZVS zones. The results show that the leakage inductance and the MFT design are different for profiles that operate mostly at low powers, such as EV.

## Introduction

The utility grid is going through a profound transformation with the massive integration of Renewable Energy Sources (RES), and a target of 90% of RES in the energy mix by 2050 to reach the net-zero emissions goal [1]. Moreover, the energy demand is expected to increase

significantly with the electrification of several sectors and the widespread of datacentres [2]. Since many of these sources and loads are natively DC, their interconnection will likely be done with a DC network or a hybrid AC/DC network [3].

Solid State Transformers (SSTs) are a key enabler to the introduction of a new DC or hybrid DC/AC grid [3]. Thanks to the use of semiconductor devices, SSTs provide several interesting capabilities for the future network such as voltage and current regulation, which is useful for power flow control, voltage sag compensation and fault current limitation [4], [5]. It can also be bidirectional, transmitting power from the source to the load, like in the current utility grid, or from the load (prosumer) back to the network [5].

The Dual Active Bridge [6] is a promising topology, not only because it is bidirectional, but also because it allows to have low component stresses, small filter components, low switching losses, high efficiency, galvanic isolation and high power density [7], [8]. Recent work on series connection of semiconductor devices shows a proof of concept that would allow to use this converter topology in Medium Voltage DC (MVDC) systems [9], [10]. Different DAB-based converter topologies are also being considered for use in MVDC [11].

The most common modulation used for the DAB is the Single-Phase Shift (SPS), where both bridges are operated with a square wave and a duty cycle of 50%. The power transfer between the bridges is controlled with the phase shift angle $δ$ [12], [13]. However, SPS modulation makes the converter perform sub-optimally at low load with a non-unitary voltage ratio, since the conditions to achieve Zero Voltage Switching (ZVS) are not fulfilled. This is a problem, since many converters are meant to be operated over a wide load range, staying a good percentage of time at low power levels [14].
This problem has been widely addressed in the literature. It has been proposed to improve the performance of the converter at light load and non-unitary voltage ratio, mostly by minimizing the RMS current with alternative modulation and control strategies. In [15] a current stress optimization based on SPS control was done resulting in an improved converter efficiency. In [16] the derivation of the optimal phase-shift ratios was done to achieve the global minimum reactive power, and with that the minimum current stress in the DAB. In [17] and [18] a combination of the triangular and trapezoidal modulations was proposed along the operating range to reduce losses at low power.

Other works have focused on the selection of the optimal leakage inductance of the DAB, since it is one of the most important aspects in the design of the converter. The leakage inductance value directly affects the reactive power flow and thus the reactive current and the resulting losses of the converter. In [13] and [8] an analytical formula to find the optimal leakage inductance with a power controller that ensures zero reactive power was proposed. This results in minimum conduction losses in all load conditions. In [19] analytical formulas were also derived to obtain the optimal value of leakage inductance considering the deviations of the DC link voltage in nominal operation.

In [20] a holistic design approach was proposed to optimize the conduction losses of a DAB. The leakage inductance and turns ratio of the transformer were taken as design variables. A different approach was proposed in [21] by adding an auxiliary inductance in parallel of the magnetizing inductance to achieve ZVS at light load. This extra inductance would only be connected at light load and would allow to effectively extend the ZVS range.

This paper proposes a simple approach, where the SPS modulation is selected as the modulation technique and the choice of the leakage inductance of the MFT is optimized based on the mission profile and the nominal DC bus voltage variations. The novelty resides firstly, in the proposal of weighted coefficients for each mission profile to have a better understanding of the losses. Secondly, the weighted average losses are minimized for each mission profile, all while considering a DC voltage variation, as well as the change in reactive power and ZVS zones with the leakage inductance value. Furthermore, no complex modulations or time-consuming optimizations are needed for this.

This paper is organized as follows. First, the case study and converter specifications are presented. Then, the mission profiles are introduced, and new weighted duration coefficients are proposed for each mission profile. Then, the different design considerations and the impact of the leakage inductance in the design are explained. Finally, a leakage inductance range is defined to minimize the average weighted losses, and the final value is chosen with the MFT design optimization.

## Case study and specifications

The proposed case study includes a DC SST interfacing a 10 kV MVDC network with a 1.5 kV LVDC bus in which typical DC loads or sources such as Electric Vehicles (EVs), residential and commercial loads or Photovoltaic panels (PV) are connected, as shown in Fig. 1.

<figure><img src="image_2.png" /><figcaption>Fig. 1: MVDC network with DC SST</figcaption></figure>

## Converter specification

The topology considered for the DC SST is a DAB converter as shown in Fig. 2. The converter is bidirectional, and it is composed of two bridges and a Medium Frequency Transformer (MFT). The leakage inductance of the MFT is represented by the inductance $L_{lk}$. As it can be seen, a series connection of six devices is considered in the MV bridge in order to reach to desired voltage level.

<figure><img src="image_3.png" /><figcaption>Fig. 2 DAB converter considered for the case study</figcaption></figure>

The specifications for the converter are shown in Table I. As it can be seen, a variation of 10% is considered in the MV bus, while it is assumed that the LV bus control keeps the voltage constant around 1.5 kV. It is also assumed that the converter could operate continuously at the points 10 kV ±10% on the MV bus. The nominal power of the SST is 250 kW and the switching frequency is fixed at 10 kHz. As regards the semiconductor devices, a 3.3 kV SiC MOSFET power module is used in the LV bridge, while for the MV bridge a
series connection of six discrete 3.3 kV SiC MOSFET devices is done.

<table><caption>Table I: Specification for DC SST</caption><tr><td>Nominal power</td><td>250 kW</td></tr><tr><td>Nominal voltage LV bus</td><td>1.5 kV</td></tr><tr><td>Nominal voltage MV bus</td><td>10 kV ± 10%</td></tr><tr><td>Operating frequency</td><td>10 kHz</td></tr><tr><td>Device LV bridge</td><td>Hitachi Energy<br>5SFG-0500X330100<br>SiC MOSFET<br>3.3 kV, 500 A<br>Power module</td></tr><tr><td>Device MV bridge</td><td>GeneSiC<br>G2R50MT33K<br>SiC MOSFET<br>3.3 kV, 44 A<br>Discrete device</td></tr><tr><td>Modulation technique</td><td>Single Phase Shift (SPS)</td></tr></table>

## Mission profile

Four mission profiles for MVDC networks have been defined, namely PV, EV charging, residential and commercial profiles. The PV profile corresponds to a high-density installation of PV [22]. For the EV charging profile, an average has been made between different charging options, in particular, profiles of EV residential charging, EV commercial charging, EV fast charging and charging station have been considered [23], [24], [25]. The residential profile considers a mix of residential loads as well as residential EV charging and a minority of PV production. To derive this mission profile, ENEDIS (French DSO) open data has been used [26]. Finally, the commercial profile is characterised by a minimum load which is always present, and it is also a mix between a commercial load, commercial EV charging, fast EV charging and PV generation. Same as for the residential profile, the ENEDIS open data has been used to derive this profile [26]. For both the residential and commercial profiles, a normalised load was produced for a 1 kW of the installed load considering the peak of the production.

Table II shows the four profiles in terms of the time spent in each power point. This means for example that the converter connected to a PV panel works at 5% of its nominal power during 3% of its runtime in a year. It is important to note that the runtime is different for each mission profile. For the PV and EV applications, the converter would work only 50% of the time or less, while for the residential and commercial profiles it could operate continuously. Then an

estimation of the time spent in each operating point was computed.

<table><caption>Table II: Duration-based MVDC mission profiles</caption><thead><tr><th rowspan="2">Power, %</th><th colspan="4">Duration (time spent), %</th></tr><tr><th>PV</th><th>EV</th><th>Residential</th><th>Commercial</th></tr></thead><tbody><tr><td>5</td><td>3</td><td>20</td><td></td><td></td></tr><tr><td>10</td><td>6</td><td>22</td><td></td><td></td></tr><tr><td>15</td><td></td><td></td><td>21</td><td></td></tr><tr><td>20</td><td>13</td><td>18</td><td></td><td></td></tr><tr><td>30</td><td>10</td><td>10</td><td></td><td></td></tr><tr><td>40</td><td></td><td></td><td>27</td><td></td></tr><tr><td>50</td><td>48</td><td>17</td><td></td><td>54</td></tr><tr><td>65</td><td></td><td></td><td>31</td><td></td></tr><tr><td>70</td><td></td><td></td><td></td><td>35</td></tr><tr><td>80</td><td></td><td></td><td>10</td><td></td></tr><tr><td>100</td><td>20</td><td>13</td><td>11</td><td>11</td></tr></tbody></table>

## Proposed weighted duration profile

It is of interest to know the duration that the converter spends in each operating (power) point since the efficiency of the converter is different in each of these points. The so-called European efficiency [22] takes this into account and gives an averaged operating efficiency based on the time spent on each point. It is defined for PV inverters as follows:

$$ \eta_{EU} = 0.03\eta_5 + 0.06\eta_{10} + 0.13\eta_{20} + 0.1\eta_{30} + 0.48\eta_{50} + 0.2\eta_{100} \quad (1) $$

The drawback of the European efficiency is that it does not give a good indication of the losses, because the efficiency at each point is computed taking as a base the operating power at each point. Logically the losses in absolute value are greater at high power than at low power, even if the converter operates a good amount of time at low power. In order to have a better indication of the losses, new coefficients are proposed here for each profile, where the duration is weighted with the operating power. The new coefficients of duration are derived with equation (2):

$$ C = \frac{P_{op,i} \cdot Duration_i}{\sum_{i=1}^{n} P_{op,i} \cdot Duration_i} \quad (2) $$

Where C is the new (weighted) duration coefficient, $P_{op,i}$ is the operating power point and Duration is the time spent in each operating point.
The resulting coefficients are presented in Table III. As it can be seen, the new (weighted) duration is greater for high power points, providing a better representation of the losses in absolute value. These new coefficients also give more weight to the operating points that will determine the thermal sizing of the converter.

<table><caption>Table III: Weighted duration mission profiles</caption><thead><tr><th rowspan="2">Power, %</th><th colspan="4">Weighted duration, %</th></tr><tr><th>PV</th><th>EV</th><th>Residential</th><th>Commercial</th></tr></thead><tbody><tr><td>5</td><td>0</td><td>3</td><td></td><td></td></tr><tr><td>10</td><td>1</td><td>7</td><td></td><td></td></tr><tr><td>15</td><td></td><td></td><td>7</td><td></td></tr><tr><td>20</td><td>5</td><td>12</td><td></td><td></td></tr><tr><td>30</td><td>6</td><td>10</td><td></td><td></td></tr><tr><td>40</td><td></td><td></td><td>26</td><td></td></tr><tr><td>50</td><td>48</td><td>34</td><td></td><td>45</td></tr><tr><td>65</td><td></td><td></td><td>35</td><td></td></tr><tr><td>70</td><td></td><td></td><td></td><td>40</td></tr><tr><td>80</td><td></td><td></td><td>15</td><td></td></tr><tr><td>100</td><td>40</td><td>34</td><td>17</td><td>15</td></tr></tbody></table>

Based on these weighted duration coefficients, a new weighted averaged efficiency can be calculated for the converter, with a better indication of the absolute value of the losses. For the PV inverter this efficiency would be defined as follows:

$$ \eta_{PV} = 0.01\eta_{10} + 0.05\eta_{20} + 0.06\eta_{30} + 0.48\eta_{50} + 0.4\eta_{100} \quad (3) $$

Similarly, the efficiency for the other mission profiles can be defined based on the weighted duration coefficients shown in Table III.

Fig. 3 illustrates the difference between the coefficients presented in Table II and Table III for the different mission profiles. As mentioned before, the weighted duration coefficients (in blue) magnify the impact of the higher power operating points that will be more constraining for the thermal sizing of the converter, and it reduces the percentage of the low operating points.

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3 Duration (time-based) and weighted duration for the four mission profiles</figcaption></figure>

## DAB design considerations

One of the most important degrees of freedom for the design of the DAB converter is the selection of the leakage inductance and its corresponding nominal phase shift $\delta$. To select it, there are several considerations that should be taken into account such as control limitations, physical dimensions and the effect of the leakage inductance on the semiconductor losses. These considerations are presented in more detail in the following sections.

### Control limitations

With single phase shift modulation, the power transfer between the bridges in either direction is controlled with the phase shift $\delta$. Fig. 4 shows the active, reactive and apparent power for a DAB as a function of the phase shift. As it can be seen, the maximum power transfer occurs at 90°. Beyond that angle, the active power decreases and the reactive power increases, so there is no interest in going beyond this angle. This is then set as the upper limit for the nominal phase shift $\delta$.
<figure><img src="image_6.png" /><figcaption>Fig. 4 P, Q and S vs. δ for DAB</figcaption></figure>

On the other hand, the phase shift cannot be too small, since a very small δ translates into a challenging angle resolution required for smooth control. A lower limit of 4 µs is set for the phase shift. For an FPGA running at 50 MHz, this limit allows to have 200 steps between the minimum and the maximum power (0 to 250 kW), which is a good resolution. Table IV shows the upper and lower limits for the nominal phase shift and its corresponding leakage inductance $L_{lk}$ based on the control limits. Clearly this limit depends on the material chosen for the control, if a different electronic card with a better resolution is chosen, the lower control limit could be brought down.

<table><caption>Table IV Control limits for δ and $L_{lk}$</caption><thead><tr><td>Limit</td><td>δ</td><td>$L_{lk}$</td></tr></thead><tbody><tr><td>Min</td><td>14.4° (4 µs)</td><td>36 µH</td></tr><tr><td>Max</td><td>90° (25 µs)</td><td>225 µH</td></tr></tbody></table>

## Physical limitations

Apart from the control limitations presented in the previous section, there are physical limitations to the value of leakage inductance. A very low value of leakage inductance may not be feasible or manufacturable, while a very big value can lead to a complex design with bigger dimensions, more use of raw materials, higher price and low performance. These physical constraints of the MFT in terms of leakage inductance can be identified during a pre-design phase of the transformer.

## Semiconductor losses

As mentioned before, the leakage inductance can greatly affect the semiconductor losses. The value of the leakage inductance is directly proportional to the amount of reactive power (and current) that flows through the semiconductor devices and through the MFT. Fig. 5 illustrates this by showing the active and reactive power for a 250 kW converter with two different leakage inductance values. On the left, a low value is chosen. As it can be seen, with low values the reactive power remains low, limiting the losses for unitary voltage ratio. On the other hand, a big value of leakage inductance, like the one shown

in the figure on the right, results in a much higher reactive power.

<figure><img src="image_7.png" /><figcaption>Fig. 5 P, Q and S for different leakage inductances</figcaption></figure>

Moreover, the value of leakage inductance also affects the ZVS operating regions of the converter, as illustrated in Fig. 6. As it can be seen, when the voltage ratio is unitary (k=1), both bridges of the converter have ZVS, and thus reduced switching losses. However, when the voltage ratio is non-unitary, the ZVS is lost at low powers, regardless of the value of leakage inductance. What changes is the percentage of the operating region that loses ZVS. For example, with the 36 µH leakage inductance, the ZVS is lost very quickly at non-unitary voltage ratio, for operating powers lower than ~0.7pu. For a leakage inductance of 70 µH, the ZVS is lost at non-unitary values for powers lower than ~0.3pu. Finally, this value reduces even further for the 100 µH case, losing ZVS for operating powers lower than ~0.2pu. The trend is clear, the greater the leakage inductance, the greater the region in which both bridges of the DAB have ZVS.

<figure><img src="image_8.png" /><figcaption>Fig. 6 ZVS zones for different leakage inductances</figcaption></figure>

As it can be seen, there is a trade-off between the reactive power (and current) and the ZVS operating regions. This is why it is of great importance to consider the mission profile in which the converter will operate, so the leakage inductance value can be chosen to minimize the losses in the expected operating powers.

## Leakage inductance selection

Taking into account the design considerations presented in the previous section, and the weighted duration mission profiles shown in Table III, it is of interest to see the averaged weighted losses of the converter for different leakage inductance values and for each of the mission profiles proposed. Fig. 7 shows the
semiconductor losses (conduction plus switching) for both bridges of the DAB for three values of voltage ratio k, unitary and the upper and lower limits.

<figure><img src="image_9.png" /><figcaption>Fig. 7 Averaged weighted semiconductor losses vs. leakage inductance for different mission profiles</figcaption></figure>

From the figure, it can be observed that for the case of unitary voltage ratio, the averaged weighted losses increase with the leakage inductance. This is expected, since the reactive power increases with the leakage inductance, but the losses increase very slowly, remaining under 1% for k=1. For non-unitary voltage ratios, the losses are higher for low values of leakage inductance, due to the high reactive current and the loss of ZVS. As the leakage inductance increases the losses for k≠1 decrease and eventually reach a plateau.

Regarding the difference between profiles, it is interesting to see that the EV profile presents higher losses than the other profiles. This is due to the fact that for this profile the converter operates most of the time at low power. The commercial profile on the other hand, presents the lowest losses for low values of leakage inductance. This is because for this profile the converter never operates under 50% of the

nominal power, ensuring that for most operating points there is ZVS. The PV and residential profiles result in very similar losses.

The next step to select the leakage inductance of the MFT is to determine an acceptable range of values depending on the optimization objective. In this case it is considered that the aim is to minimize the losses as much as possible. Table V shows the target ranges selected if the maximum averaged weighted losses are set to 1.5%. As it can be seen, the residential and commercial profiles already have losses under this threshold for the minimum feasible leakage inductance, while the EV requires a big inductance to remain under the limit. Since the semiconductor losses reach a plateau for all the profiles, it is considered that there is no interest in choosing leakage inductance values beyond 100 µH.

<table><caption>Table V Target ranges of $L_{lk}$ for semiconductor losses≤1.5%</caption><thead><tr><td>Profile</td><td>L<sub>lk,min</sub></td><td>L<sub>lk,max</sub></td></tr></thead><tbody><tr><td>PV</td><td>43 µH<br>(0.3239 pu*)</td><td>100 µH<br>(0.9237 pu)</td></tr><tr><td>EV</td><td>71 µH<br>(0.5752 pu)</td><td>100 µH<br>(0.9237 pu)</td></tr><tr><td>Residential</td><td>36 µH<br>(0.2670 pu)</td><td>100 µH<br>(0.9237 pu)</td></tr><tr><td>Commercial</td><td>36 µH<br>(0.2670 pu)</td><td>100 µH<br>(0.9237 pu)</td></tr></tbody></table>

With these ranges and the general specifications presented in Table VI, it is now possible to do a pre-design of the MFT [27]. A curve with possible MFT designs has been obtained for each mission profile as shown in Fig. 8. Each curve shows the maximum efficiency limit for different possible design points that are within the determined range for leakage inductance. As it can be seen, the averaged weighted efficiency for all of them is of at least 99.5%.

<table><caption>Table VI General specifications for MFT</caption><tr><td>Turn ratio</td><td>3:20 +5% / -7%</td></tr><tr><td>Averaged weighted efficiency</td><td>≥99.5%</td></tr><tr><td>Max ambient temperature</td><td>40°C</td></tr></table>

As it can be seen, for the PV, residential and commercial profiles, there are possible design points starting from a volume of around 75 dm³. For the EV profile on the other hand, the design points begin at 110 dm³. In terms of efficiency, the EV designs have the lowest maximum reachable efficiency, of just over 99.7%. For the

<footnote>*The base apparent power varies with the value of leakage inductance.</footnote>
other profiles, the efficiency goes over 99.8% and even 99.85% for the residential and commercial profiles. The difference in design points between the EV profile and the other profiles is due to the minimum leakage inductance specified for this profile, which is much greater than for the other profiles. In this case, by optimizing the losses, there is an important increase in the volume of the transformer compared to the other profiles.

<figure><img src="image_10.png" /><figcaption>Fig. 8 MFT design curves for different mission profiles</figcaption></figure>

Since the volume is proportional to the quantity of raw material needed to manufacture the MFT, it is also a good indicator of cost. Given that all the designs are shown to comply with the desired efficiency, a design with the smallest volume and highest efficiency is chosen for each profile to optimize the design. In the curves of Fig. 8, the chosen designs are shown as points for each mission profile. They correspond to the points located most towards the left and to the top. The results are presented in Table VII. The efficiency corresponds to the weighted average for each mission profile presented in Table III, with a unitary voltage ratio.

<table><caption>Table VII L<sub>lk</sub>, MFT volume, weight and efficiency for each mission profile</caption><thead><tr><th>Profile</th><th>PV</th><th>EV</th><th>Res</th><th>Comm</th></tr></thead><tbody><tr><td>L<sub>lk</sub> (μH)</td><td>43.2</td><td>71.2</td><td>36.2</td><td>36.2</td></tr><tr><td>Vol<sub>MFT</sub> (dm<sup>3</sup>)</td><td>78</td><td>111</td><td>77</td><td>77</td></tr><tr><td>Weight<sub>MFT</sub> (kg)</td><td>52</td><td>92</td><td>57</td><td>57</td></tr><tr><td>η<sub>bridges</sub> (%)</td><td>99.26</td><td>99.29</td><td>99.31</td><td>99.28</td></tr><tr><td>η<sub>MFT</sub> (%)</td><td>99.58</td><td>99.57</td><td>99.64</td><td>99.65</td></tr><tr><td>η<sub>Total</sub> (%)</td><td>98.84</td><td>98.86</td><td>98.95</td><td>98.93</td></tr></tbody></table>

The results show that the optimal designs that minimize the volume with a good efficiency seem to remain close to the lower limit of the leakage inductance. In the end, all the designs have a total efficiency over 98.5% and under 99%. Not surprisingly, the MFT design chosen for the EV

charging profile is the heaviest and occupies the most footprint. The performances of the residential and commercial converters are very similar to each other. The results for the PV are also similar to these last two.

It could also be possible to make a multi-application optimization, in this case, a single design would be chosen to be used for all the profiles. This option would have many benefits from an industrialization point of view. It would be possible to make a production chain for this single converter design, which would allow to reduce the unit's manufacturing costs. On the other hand, by looking at the curves in Fig. 8 and particularly at the EV one, it can be seen that in order to have a single design for all the mission profiles, a relatively large transformer would be needed, resulting in a sub-optimal power density for three out of the four profiles. Even though the resulting transformer would have high efficiency, the increase in volume could be limiting for some of the applications, and it could also worsen some other KPIs, such as the raw material utilization and the overall carbon footprint.

Finally, a third option would be to make a unique design for the profiles PV, residential and commercial and a different design for the EV. This option would allow to optimize volume and efficiency for all the profiles. Besides manufacturing the design chosen from Fig. 8, another way to optimize the EV profile design would be to consider a different modulation technique, more adapted to operation at low power with non-unitary voltage ratio. It is possible that by changing the modulation technique, the semiconductor losses get reduced at low power and thus a smaller leakage inductance might become feasible in terms of acceptable losses. More detailed studies would be needed to confirm this.

## Leakage inductance sensitivity analysis

It is important to mention that from a detailed design and manufacturing point of view, the built MFT may result in a different value of the leakage inductance with respect to the specified value. Also, regarding series production, there will be differences between the values of leakage inductance for different units, as an exact value of leakage inductance is hardly reproduceable due to geometrical differences. Manufacturers usually commit to a tolerance of ±10% of the specified value, which means that in the worst-case scenario two transformers of the same series
could have a 20% gap between their leakage inductances with respect to the specified value. A variation in the leakage inductance value will result in a variation of the semiconductor and transformer losses. Therefore, it is of interest to see how significant these variations are, with a tolerance of ±10%.

It is considered that a single mechanical structure will be used for a manufacturing line, and the variations in the leakage inductance value will depend on the precise geometry of the windings. Even though this will change the transformer losses, the variation is assumed to be marginal and therefore not considered in this analysis. Instead, this analysis will focus on the semiconductor losses variation.

Tables VIII to XI show the variation of the semiconductor losses (expressed in bridge efficiency) with the leakage inductance for each mission profile. Reminding that the shown efficiency corresponds to the unitary voltage ratio $k = 1$, it can be seen for all the profiles that the efficiency of the bridges decreases slightly as the leakage inductance increases. This change remains small, with a variation of up to 0.04 points in the efficiency.

However, since the DAB converter might operate continuously at non-unitary voltage ratios, it is also important to examine the losses variation for these cases. Looking closely at the PV profile in Fig. 7, it can be seen that the averaged weighted losses always remain under the specified threshold of 1.5% within the tolerance range. Therefore, the leakage inductance variation will have minimal influence on the semiconductor losses and it will not affect the thermal sizing of the converter.

<table><caption>**Table VIII Semiconductor losses variation with leakage inductance tolerance for PV profile**</caption><thead><tr><th></th><th>Min<br>(-10%)</th><th>Specified<br>L<sub>lk</sub></th><th>Max<br>(+10%)</th></tr></thead><tbody><tr><th>L<sub>lk</sub> (µH)</th><td>38.9</td><td>43.2</td><td>47.5</td></tr><tr><th>η<sub>bridges</sub> (%)</th><td>99.27</td><td>99.26</td><td>99.26</td></tr></tbody></table>

For the EV profile, it can be seen from Fig. 7 that reducing the value of leakage inductance would result in semiconductor losses over the 1.5% threshold for non-unitary voltage ratios. There is minimal variation in case of a higher value of leakage inductance. Considering this, it would be important to assess whether semiconductor losses over 1.5% would represent a significant change in the thermal sizing of the bridges (for non-unitary voltage ratio operating points).

<table><caption>**Table IX Semiconductor losses variation with leakage inductance tolerance for EV profile**</caption><thead><tr><th></th><th>Min<br>(-10%)</th><th>Specified<br>L<sub>lk</sub></th><th>Max<br>(+10%)</th></tr></thead><tbody><tr><th>L<sub>lk</sub> (µH)</th><td>64.1</td><td>71.2</td><td>78.3</td></tr><tr><th>η<sub>bridges</sub> (%)</th><td>99.31</td><td>99.29</td><td>99.27</td></tr></tbody></table>

For the residential profile, it can be seen that the averaged losses remain around 1.5% for lower or higher values of leakage inductance. Therefore, the thermal sizing of the converter would not be affected. However, it is important to note that the specified leakage inductance of 36.2 µH is very close to the minimum threshold of the specified target range (36 µH, see Table V) and therefore a reduction of 10% in the leakage inductance would result in a value under the specified control limit (see Table IV). In this case it would be preferable to have a tolerance range with values over the specified one, and not under, to avoid challenges related to the control.

<table><caption>**Table X Semiconductor losses variation with leakage inductance tolerance for residential profile**</caption><thead><tr><th></th><th>Min<br>(-10%)</th><th>Specified<br>L<sub>lk</sub></th><th>Max<br>(+10%)</th></tr></thead><tbody><tr><th>L<sub>lk</sub> (µH)</th><td>32.6</td><td>36.2</td><td>39.8</td></tr><tr><th>η<sub>bridges</sub> (%)</th><td>99.32</td><td>99.31</td><td>99.30</td></tr></tbody></table>

Finally, for the commercial profile the same problem seen in the residential profile applies, the losses remain under 1.5% for non-unitary voltage ratios, but the minimum leakage inductance is under the specified control limit. Also in this case it would be preferred to have a leakage inductance variation towards higher values and not lower ones to ensure a smooth control.

<table><caption>**Table XI Semiconductor losses variation with leakage inductance tolerance for commercial profile**</caption><thead><tr><th></th><th>Min<br>(-10%)</th><th>Specified<br>L<sub>lk</sub></th><th>Max<br>(+10%)</th></tr></thead><tbody><tr><th>L<sub>lk</sub> (µH)</th><td>32.6</td><td>36.2</td><td>39.8</td></tr><tr><th>η<sub>bridges</sub> (%)</th><td>99.28</td><td>99.28</td><td>99.27</td></tr></tbody></table>

In general, it can be observed that the semiconductor efficiency is not greatly affected by the leakage inductance variation within ±10% tolerance. This is thanks to the fact that the specified value is in the plateau of the averaged weighted losses curve (Fig. 7), and therefore variations remain minimal. It is important however to consider potential challenges related
to small values of leakage inductance, such as control limits or high losses at non-unitary voltage ratios, caused by the loss of ZVS in this zone.

## Conclusion

In this paper the design of a DAB converter is done for four different mission profiles: PV, EV, residential and commercial. A proposal of weighted duration for each of these profiles has been done with the aim of having a better understanding of the losses of the converter in absolute value. The designs are done with the aim of minimizing the averaged weighted losses for each profile. Based on some general considerations such as control limitations and averaged weighted losses limit, a range of acceptable leakage inductance values has been selected for each mission profile. Then, maximum efficiency curves with feasible MFT designs were generated for each mission profile and an optimal design in terms of volume and efficiency was chosen. The results show that the overall converter designs have a high averaged weighted efficiency over 99.5%. In general, the optimal found leakage inductance values correspond to the lower threshold of the specified range, minimizing the size and weight of the MFT, while keeping a good efficiency over the specified limit. It is however important to consider the non-unitary voltage ratio losses to specify the leakage inductance range, since the averaged weighted losses are actually higher at low leakage inductance values due to the loss of ZVS.

It is interesting to see that among the analysed mission profiles, the design of the EV one stands out. This design requires a higher value of leakage inductance to reach the desired efficiency compared to the other profiles. This results in a heavier transformer and with a greater volume. In terms of weighted duration, the converter would operate most of the time at 50% or less of its nominal power for the EV charging profile.

Finally, to account for manufacturing tolerance ranges, a sensitivity analysis was carried out to see the variation of the semiconductor losses with a leakage inductance variation of ±10%. It was found that overall, the efficiency does not present a great variation with respect to the leakage inductance (0.04 points at most). However, in some cases the lower leakage inductance values might be under the specified control thresholds, or they might result in higher losses than desired for non-unitary voltage ratios. In these cases, it

would be preferable to have a tolerance towards higher values of leakage inductance and not towards lower ones.

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