# Zero Current Modulation Control Strategy for Dual Active Bridge Dynamic Operation

Jakob Vellinger, Simon Schramm

► To cite this version:

Jakob Vellinger, Simon Schramm. Zero Current Modulation Control Strategy for Dual Active Bridge Dynamic Operation. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0262. hal-05085294

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Submitted on 26 May 2025

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# Zero Current Modulation Control Strategy for Dual Active Bridge Dynamic Operation

Jakob Vellinger, Simon Schramm

HM Munich University of Applied Sciences

Lothstraße 64

80335 Munich, Germany

Tel.: +49 89 1265 3512

E-Mail: {jakob.vellinger,simon.schramm}@hm.edu

***Index Terms***—DC-DC, Dual Active Bridge (DAB), Modulation scheme, Control strategy, DC grid component.

***Abstract***—This paper presents a novel approach to the operation of the DAB topology. It reformulates known switching patterns for real-time computation of the analytical expressions, allowing dynamic power changes and start-up capability with 0V on one side. The approach is systematically derived, with selection logic and laboratory results provided.

## I. INTRODUCTION

Galvanically isolated DC-DC converters in the kilowatt power range are gaining increasing significance in the context of the energy transition. These converters are essential for applications such as (fast) charging of electric vehicles, integration of large-scale battery storage systems, and the connection of electrolysers or fuel cells to centralized DC bus systems. Furthermore, recent research has investigated the potential advantages of DC grids over traditional AC grids, particularly in industrial settings, where the role of such converters is also of high relevance [1].

Depending on the application, either unidirectional or bidirectional power flow may be required. Some applications involve nearly constant input or output voltages, while others, such as battery systems, photovoltaic systems, electrolysis, or fast-charging applications, may experience significant variations in input or output voltages. Operating conditions vary from constant rated power operation to very dynamic power flow control [2].

In this paper, we build upon some well established operating modes and introduce a novel application of them. The aim of this research is to introduce this innovative operating strategy, which allows a direct transition between operating modes from one switching period to the next. We analytically describe the relevant

operating modes for different power levels and directions, considering the specific conditions outlined in this paper. This analytical description is also applied to the control system of the DC-DC converter to achieve the aforementioned functionality during operation.

In the dual active bridge (DAB) topology examined in [3], phase shift modulation (PSM) is employed, wherein the input and output voltages of the transformer are phase-shifted relative to each other. This operating mode is well known, facilitates high power transfer through the converter and can be easily integrated into conventional control structures, such as those using PI controllers. However, the efficiency of PSM is highly dependent on the operating conditions, including the input and output voltages, the transformer turns ratio, and the desired power level.

For applications that necessitate a wide input voltage range or exhibit significant variations in transmitted power, as previously mentioned, PSM may be substantially less efficient than alternative operating modes discussed in the literature, e.g. in [4]. Advanced operating modes can be a remedy here, but require more effort in the software implementation of these operating patterns, and above all the optimal selection of the operating patterns as soon as the operating point changes. Important properties that distinguish the modulation modes are the number of degrees of freedom, their soft switching range and their solvability, either by (offline) optimization and look-up tables or analytically. Exemplary for this is [5], where closed form solutions for different modes with soft switching capability over a wide input voltage range are given.

Optimization strategies vary based on application needs. Efficiency optimization is based on a simulation model to calculate power losses offline and select the optimal modulation scheme [6]. Other methods try to en-
able (zero voltage) soft switching over a wide operating range [5]. Reactive power minimization reduces reactive power flow between primary and secondary magnetic components. These current optimization schemes show a high efficiency when compared to other optimization methods [7].

In the event of dynamic change in power requirements and the associated modulation pattern change, the control parameters often need to be changed continuously until a transition is possible, c.f. [8]. This work focuses on a control strategy that allows for the nearly instant change of modulation modes based on a zero current normalization of well known switching patterns.

The structure of this paper is outlined as follows: Chapter 2 introduces the Dual Active Bridge (DAB) converter, elaborating on its fundamental operation and deriving the most common operating modes, with particular consideration given to the proposed control concept. In Chapter 3 the overall strategy is discussed, utilizing operating mode maps as applied in the actual control system. Chapter 4 focuses on the implementation of these modes in the hardware system alongside representative results from real-world measurements. Lastly, the paper concludes with a forward-looking perspective on ongoing and future developments in the system's implementation.

## II. DAB TOPOLOGY AND PRINCIPLE OF OPERATION

Figure 1a shows the circuit schematic of the DAB converter under consideration. The two full-bridges apply edge-resonant, quasi-square wave voltages at the terminals of the high-frequency (HF) ac-link (or: HF-link) circuit. The latter consists of a HF transformer with a turns ratio of $n = n_1 : n_2$ and an optional (external) series inductor $L$. The input bridge (index 1) generates the voltage $v_{HF1}(t)$ which appears between nodes A and B with an amplitude equal to the dc voltage of the input $V_{DC1}$. Voltage $v_{HF2}(t)$, which appears between nodes C and D, is generated by the output bridge (index 2) with an amplitude equal to the output dc bus voltage $V_{DC2}$. The amplitudes of both dc voltages are abbreviated below with the respective index of the bridge $V_{1,2} = V_{DC1,2}$.

Assuming the ideal case, where the magnetizing inductance of the transformer is infinite, the winding resistances are zero, and the core losses are non-existent, the segment between ports A to D can be represented by an equivalent series inductance $L$. In addition, parasitic elements (e.g. transformer winding capacitance) are

neglected and the output side terminal voltage is referred to the input side:

$$v'_{HF2}(t) = v_{HF2}(t) \cdot n \quad (1)$$

Similarly, the equivalent series inductance is also referenced to the primary side. To further simplify the analysis, it is generally assumed that the duration of the resonant transition is considerably shorter than the period of the quasi-square waves. This allows to replace the voltage-sourced bridges on both sides with ideal voltage sources $v_{HF1}$ and $v_{HF2}$. As a result, the lossless DAB model is obtained as depicted in fig. 1b.

According to the lossless model, power transfer is directly related to the averaged current of the ac-link $i_{HF1} = i_L$, which is solely dependent on the voltage drop across the inductor $v_L$. For a time instant $t_i$, $i_L$ is defined as

$$i_L(t_i) = i_L(t_{i-1}) + \frac{v_L}{L}(t_i - t_{i-1}) \quad (2)$$

### A. Modulation

The DAB's original mode of operation (mode) is commonly known as Phase Shift Modulation (PSM) and has already been described extensively in the literature, see e.g. [9]. It is still widely used due to its simple control, where the power transfer is solely controlled by the phase-shift angle $\phi$ between (the two falling edges of) the square-wave voltages. Various other modes have been proposed since, each with specific advantages and disadvantages. A frequent goal is to increase the soft-switching range [5], which is often limited to a certain voltage ratio $d = V'_2/V_1$ or transferable power. Different modes are combined to cover a larger operating or soft switching range and utilize each mode's respective advantages. For a seamless transition between modes, a smooth transition of the inductor current has to be guaranteed.

Usually, the start of a switching cycle is oriented to a falling or rising voltage edge of the primary or secondary voltage, the other switching events are expressed or calculated using phase shift from the starting point. As a result, PSM and other modes have a nonzero initial current in general.

In this work, a different approach is proposed, which results in the same principle patterns, but has significant advantages regarding the change of modes: the essential criterion of the switching pattern calculation is that each switching period starts and ends uniformly with a current of 0 A, regardless of the selected switching pattern. Furthermore, the current $i_L(T_s/2) = 0$ for all modes.
<figure><img src="image_2.png" /><figcaption>Fig. 1: (a) DAB Converter Topology (b) Lossless DAB model</figcaption></figure>

This has significant advantages: the operating mode and the transmitted current can be changed instantaneously from one switching cycle to the next.

The modes used in this work are defined for positive power flow (dir = 1, if $P > 0$), power is transferred from the input (index 1) to the output bridge (index 2). A piecewise linear behavior of the inductor current $i_L$, as a result of the constant voltage drop $v_L = v_{HF1} - v'_{HF2}$ is assumed for each section of the switching cycle. This is permissible if voltage amplitudes $V_{DC1,2}$ and control variables $x$ are constant in each section. Each switching cycle starts at $t_0 = 0$ and ends at $T_s$. Note that switching instances (times) can be expressed as angular quantities, given by $\alpha = \omega_s t_\alpha$, which are normalized with regard to the switching cycle. Furthermore, the effective voltage time area over the inductor must be the same for both half switching cycles in order to prevent dc current and possible transformer core saturation. Operation with variable switching frequency $f_s$ is also possible with this approach, the calculation of the timing starting from zero current at the beginning of each period is carried out taking into account the desired switching frequency, which could in principle be modified for each switching period. The voltages $v_{HF1,2}$ and inductor current $i_L$ repeat every half switching cycle with reversed signs. These properties allow calculations (e.g. power, mode timings) to be based only on the first half of the switching period and to be extended by simple means of geometric considerations to the whole period. Similarly, control parameters for positive power flow can be rearranged to obtain parameters for negative power flow.

The operating points used in the following are based

on a sample application in which a BEV battery with a nominal voltage of 365 V ($V_2$) is connected to a 700 V ($V_1$) DC bus via a DAB converter with hardware parameters given in table V. Note, that the voltages are denoted as $V_{1,2}$ if the amplitudes of $|v_{HF1,2}|$ are assumed to be constant in the short time span of the switching cycle $T_s$ considered.

1) Phase Shift Modulation: The voltages $V_{1,2}$ are applied with a fixed duty cycle of $\tau_1/\pi = \tau_2/\pi = 0.5$. The transferred power is controlled by varying the phase shift ($x = \phi$) between $V_{1,2}$. Assuming the lossless model (cf. fig. 1b), the averaged input current $I_{DAB1}(\phi)$ can be calculated over half the switching period $T_s/2$.

$$I_{DAB1}(\phi) = \frac{2}{T_s} \int_{0}^{T_s/2} i_L(t) dt \quad (3)$$

The averaged DAB input power is then given by

$$P_1 = V_1 I_{DAB1} = \frac{V_1 V_2' \phi}{\omega_s L} \left(1 - \frac{|\phi|}{\pi}\right). \quad (4)$$

Now the required phase-shift angle $\phi$ required for a desired $P_1$ is obtained by rearranging eq. (4)

$$\phi = \frac{\pi}{2} \left( 1 - \sqrt{1 - \frac{8 f_s L |P_1|}{V_1 V_2' \phi}} \right) \operatorname{sgn}(P_1) \quad (5)$$

Figure 2a shows the HF-link for one switching cycle during PSM. The phase angle (or time) between the start of the period (rising edge $v_{HF1}$) and the first zero crossing of the current is defined by $\alpha$. By shifting all switching instances $t_0$ to $t_4$ by $\alpha$ ($t_\alpha$) to the left, PSM can be normalized in relation to zero current at the start and end of the period. This normalization is referred to
as Zero Current Modulation (ZCM), not to be confused with zero current switching (ZCS). ZCM versions of triangular and trapezoidal modulations are introduced in [10], including the effect of ohmic resistance on the equations.

$$t_{\alpha} = \frac{(-\pi + 2\phi)V'_{2} + \pi V_{1}}{2V_{1} + 2V'_{2}} \quad (6)$$

Figure 2 depicts both versions of PSM at the same operating point next to each other. The maximum power is reached with $\phi = \pi/2$, regardless of normalization. It is given by

$$P_{\max,PSM} = \frac{V_1 V'_2 n}{8 L f_s} \quad (7)$$

ZCM for PSM and other modes can also be achieved directly (without shifting by $t_{\alpha}$) when deriving the switching times by defining suitable constraints. The timings for ZCM PSM are given in table I, excluding already known start $t_0$, middle $T_s/2$ and end $T_s$ of each switching cycle. Some common terms are identified and defined up front to shorten the equations and allow for faster computation. The timings for the second-half can be easily derived from the first half, as shown in table I.

$$ \begin{aligned} e_1 &= (V_1 V'_2) & e_2 &= (V_1 + V'_2) \\ e_3 &= (V_1 - V'_2) & e_4 &= LP_1 f_s \end{aligned} $$

<table><caption>TABLE I: ZCM Timings - PSM</caption><tr><td>t<sub>1</sub> = -[√(e<sub>1</sub>(e<sub>1</sub> - 8e<sub>4</sub>) - V<sub>2</sub><sup>2</sup>) / (4V<sub>2</sub>e<sub>2</sub>f<sub>s</sub>)]</td><td>t<sub>3</sub> = T<sub>s</sub>/2 + t<sub>1</sub></td></tr><tr><td>t<sub>2</sub> = (e<sub>2</sub> - 4V<sub>2</sub>f<sub>s</sub>t<sub>1</sub>) / (4V<sub>1</sub>f<sub>s</sub>)</td><td>t<sub>4</sub> = T<sub>s</sub>/2 + t<sub>2</sub></td></tr></table>

### B. Triangular and Trapezoidal Phase Shift

In addition to the phase-shift used in PSM, the primary and secondary duty cycles can be used as control variables ($\mathbf{x} = \phi, \tau_1, \tau_2$) to a maximum of 0.5. Modes that utilize those three control variables are summarized as Tripple Phase Shift. Trapezoidal (TZM) and Triangular Current Modulation (TRM) are a subset of the Tripple Phase Shift, introduced in [4], with a distinct (trapezoidal, triangular) inductor current shape. The latter can be seen as a discontinuous mode of TZM and is again subdivided depending on the voltage ratio. Boost TRM (BOT) for $d > 1$ and Buck TRM (BUT) for $d < 1$. The normalized (in relation to zero current at the start/end of the period) versions are depicted in fig. 3.

TRM's maximum power transfer capability is also the minimum required power for TZM, which enables a smooth handover between TRM and TZM modulation.

$$P_{\max,TRM} = P_{\min,TZM} \quad (8)$$

and is given by

$$P_{\max,TRM} = \begin{cases} \frac{V_2^2 e_3}{4 L V_1 f_s}, & d < 1, \\ -\frac{V_1^2 e_3}{4 L V_2 f_s}, & d > 1 \\ 0, & d = 1. \end{cases} \quad (9)$$

Power delivery in TRM mode is not possible for $d = 1$. The timings given in table I and table II correspond to the respective markings in fig. 3b to fig. 3c. TZM maximum power transfer is given by

$$P_{\max,TZM} = \frac{V_1^2 V_2^2 n^2 (2 f_s t_d - 1)^2}{4 L f_s (V_1^2 + V_1 V_2 n + V_2^2 n^2)} \quad (10)$$

Despite the impression stemming from the name TPS, the power flow for TZM and TRM can be controlled with a single control variable, as the other two parameters are used to achieve zero current modulation at the start and end of each half-wave. Even higher efficiency can be achieved utilizing all three possible degrees of freedom, however, at the expense at computational heavy expressions that may require offline optimization. This work favors the computational advantage of the combined TZM and TRM modulation, which is beneficial for achieving this work's objective of rapid and flexible mode changes. The following closed-form expressions provide the timings for a desired power flow $P_1$.

<table><caption>TABLE II: Timings - TRM</caption><tr><td>t<sub>1</sub> = [√(V<sub>1</sub>e<sub>3</sub>e<sub>4</sub>f<sub>s</sub>) / (V<sub>1</sub>e<sub>3</sub>f<sub>s</sub>)]</td><td>t<sub>2</sub> = [V<sub>1</sub>t<sub>1</sub> / V<sub>2</sub>]</td></tr><tr><td>t<sub>4</sub> = T<sub>s</sub>/2 + t<sub>1</sub></td><td>t<sub>5</sub> = T<sub>s</sub>/2 + t<sub>2</sub></td></tr><tr><td>t<sub>1</sub> = [√(e<sub>4</sub>f<sub>s</sub>) / (V<sub>1</sub>f<sub>s</sub>)]</td><td>t<sub>2</sub> = -[V<sub>2</sub>t<sub>1</sub> / e<sub>3</sub>]</td></tr><tr><td>t<sub>5</sub> = T<sub>s</sub>/2 + t<sub>1</sub></td><td>t<sub>6</sub> = T<sub>s</sub>/2 + t<sub>2</sub></td></tr></table>

It is necessary to include the necessary $t_d$ in the timing equations (table III), which can be done by scaling the maximum power equations eqs. (9) and (10) by $(1 - 2t_d f_s)^2$ and thus reducing the possible maximum power.

### C. Zero Voltage Startup

Depending on the application's requirements the converter may need to bring itself in its normal operation range starting from very small or even zero voltage on one side. The following considerations assume $V_{DC2} = 0$, but can be applied for $V_{DC1} = 0$ as well. No power can be transferred for zero voltage in the in e.g. BOT or TZM mode. PSM generates high peak current in this condition with a maximum duty cycle of the primary bridge. A special case of Extended Phase Shift (EPS) is proposed
<figure><img src="image_3.png" /><figcaption>(a) General PSM</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>(b) Normalized PSM</figcaption></figure>

<caption>Fig. 2: HF-link – Phase Shift Modulation</caption>

$V_1 = 700 \text{ V}, V_2 = 400 \text{ V}, f_s = 100 \text{ kHz}, t_d = 200 \text{ ns}, I_{\text{ref}} = 21 \text{ A}$

<figure><img src="image_5.png" /><figcaption>(a) TRM - BOT</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>(b) TRM - BUT</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>(c) TZM</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>(d) EPS</figcaption></figure>

$V_1 = 700 \text{ V}, V_2 = 310 \text{ V (a)}, 390 \text{ V (b)}, 365 \text{ V (c)}, 10 \text{ V (d)}, f_s = 100 \text{ kHz}, t_d = 200 \text{ ns}, I_{\text{ref}} = 7 \text{ A (a, b)}, 21 \text{ A (c) and } 30 \text{ A (d)}$

<caption>Fig. 3: HF-Link – Normalized Modulation</caption>

to allow the converter to steadily increase the secondary voltage until normal operating range is reached, where TRM or TZM eventually become applicable. The timings

are given in table IV.

In general, EPS offers two degrees of freedom, duty cycle and phase-shift ($x = \phi, \tau_1$). The proposed version aligns
<caption>TABLE III: Timings - TZM</caption>

$$
\begin{aligned}
t_1 &= \frac{2\sqrt{-e_1 (e_1 e_4 f_s - V_1^2 (V_2^2 (f_s t_d - \frac{1}{2})^2 - e_4 f_s) + V_2^2 e_4 f_s)}}{2V_2 f_s (V_1^2 + V_2^2 + e_1)} \\
&\quad + \frac{V_2^3 - 2V_2^3 f_s t_d}{2V_2 f_s (V_1^2 + V_2^2 + e_1)} \\
t_2 &= -\frac{V_2 (2 f_s t_1 + 2 f_s t_d - 1)}{2 V_1 f_s} \qquad t_5 = T_s/2 + t_1 \\
t_6 &= T_s/2 + t_2 \qquad t_7 = T_s - t_d
\end{aligned}
$$

<caption>TABLE IV: Timings - EPS</caption>

$$
\begin{aligned}
t_1 &= \frac{e_1 + V_2^{\prime 2} + \sqrt{-8LP_1e_1f_s + V_1^2 - V_2^{\prime 4}}}{4e_1 f_s} & t_4 &= T_s/2 + t_1 \\
t_2 &= -t_1 \frac{e_2}{2f_s V_1} & t_5 &= T_s/2 + t_2
\end{aligned}
$$

the HF current $i_L$ in phase to the secondary voltage, minimizing reactive power and therefore RMS current flow. The modulation pattern is shown in fig. 3d. A pulse of negative primary voltage is applied in the first half cycle to balance the volt-seconds. And the maximum duty cycle is applied for the secondary bridge. Thus, zero current switching is achieved on the primary and zero voltage switching on the secondary side. Since the primary duty cycle is controlled, the peak current is limited.

### D. Modulation Summary

Closed-form expression for the switching instances of normalized versions PSM, TRM and TZM as well as a special startup sequence based on EPS have been introduced is the previous section. The normalization has no effect on the soft switching capabilities or the maximum power transfer of the different modes compared to versions already known in literature. The dead time is considered in the equations.

The main advantage of the presented normalization is the inherent possibility to change the mode after each switching period. The necessary condition zero current modulation is given by the normalization. The timing equations are given in a closed form. For the presented modes, the (computational heavy) calculation of $t_1$ and $t_2$ is sufficient as the other timings can be derived from this. This enables a straightforward implementation on the controller, which is discussed in more detail in the following section.

## III. OPERATION STRATEGY

The objective of the proposed operating strategy is to control the power flow between the converter terminals

<figure><img src="image_9.png" /><figcaption>Fig. 4: Control Sequence</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 5: HF Modulation - From BOT $t_{i-}$ to TZM $t_i$</figcaption></figure>

for a given operating point. Any conventional superimposed control strategy, e.g. voltage control can be used to determine this power reference point. The given power specification is translated into an active current reference $i_{DAB1,ref} = P_{1,ref}/V_{1,meas}$. One of the featured modes is selected and applied at each switching cycle $T_s$.

The control logic in fig. 4 is repeated every execution $t_{step}$ of the controller. In a first step, the required current $i_{DAB1,ref}$ for the desired power flow is determined and the maximum current each mode can deliver at the given parameters is calculated. The sign of the power references indicates the direction *dir* of the power flow. Depending on the speed of the utilized controller, the timing equations and thus the power flow can be updated every switching cycle. This allows for nearly instantaneous power delivery (e.g. from 0 to nominal power) or power reversal within one switching cycle (e.g.: 10 µs). Figure 5 depicts the implemented process for a requested change in power at the beginning of the period $t_i -$. While the existing timings are applied, the new timings for the upcoming period $t_i$ are calculated in parallel.

Depending on the optimization goal, the optimal
mode is selected. Common approaches in literature have been shortly introduced in section I. The presented approach is independent of the selected optimization target as long as it can be implemented on the controller. This work utilizes a current minimization strategy, resulting in low conduction losses of both, the inductance and the semiconductors.

Besides the known hardware parameters (e.g. $n, L, f_s, t_d$) and the reference setpoint ($P_{1,ref}$) only the voltages $V_{1,2}$ have to be gathered by measurements. Only two timings, $t_1$ and $t_2$, are computationally expensive. The remaining six switching instances are either already known (start, half and end of each switching cycle as well as the dead time) or can be easily expressed by geometric considerations, see e.g. table II. The timings are always calculated for positive power flow and rearranged if dir indicates a negative power request. The gate signals are generated from the timings in accordance to the selected mode. The process is repeated at the beginning of the new switching cycle with an update of the voltage measurement.

The maximum current trajectory of each mode is shown in fig. 6 over the voltage ratio $d$ at a fixed voltage $V_{DC1} = 700$ V. PSM can be applied anywhere below its maximum current path, while TZM and TRM are exclusive. The lower limit of TZM is the maximum of both TRM modes BOT and BUT. The EPS mode is not shown since it is only applied for the rather extreme case of $V_2 \approx 0$ during startup. PSM is only used when TZM can not provide the requested power. Power request above the maximum of PSM are limited to the maximum current trajectory of PSM. Furthermore, all presented modes do not require offline simulation information and instead rely on online calculations of optimized switching times, avoiding the need for look-up table-based approaches.

## IV. EXPERIMENTAL VERIFICATION

The proposed modulation and operating strategie are implemented on a dc-dc DAB prototyp with the system specifications given in table V. Measurement results from a nearly instant change in power are shown in fig. 7. The DAB is initially operated at around 2.3 kW in mode BUT. For the requested power of 7 kW, mode TZM is chosen which is seamlessly applied after the last BUT switching cycle.

The measurement results verify the feasibility of presented approach. Both modes (BUT and TZM) feature zero current at the end and start of each respective switching cycle and can be applied directly one after the other. However, unaccounted influences such as ohmic

<figure><img src="image_11.png" /><figcaption>Fig. 6: Maximum current of each mode for $V_1 = 700$ V</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 7: HF Modulation for nearly instant power jump $V_1 = 400$ V, $V_2 = 175$ V, $f_s = 60$ kHz, $t_d = 200$ ns, from 2.3 kW (2 = BUT) to 7 kW (3 = TZM).</figcaption></figure>

<table><caption>TABLE V</caption><tr><td>Transformer Ratio n</td><td>2</td></tr><tr><td>Inductance L</td><td>25.2 uH</td></tr><tr><td>Switching Frequency f<sub>s</sub></td><td>60 kHz</td></tr><tr><td>Dead time t<sub>d</sub></td><td>200 ns</td></tr><tr><td>Primary Voltage V<sub>DC1</sub></td><td>400 V</td></tr><tr><td>Secondary Voltage V<sub>DC2</sub></td><td>175 V</td></tr></table>
resistance of semiconductors, switch capacitance and other parasitics result in deviation from the calculated modulation patterns. This can be seen from the deviation of the current at the calculated zero crossing ($i_L \neq 0$), among other things.

V. CONCLUSION

This paper investigates the implementation of switch-
ing patterns, well-established in the literature, on real
hardware by introducing a novel approach, termed Zero
Current Modulation. To this end, the relevant switching
patterns were mathematically derived, incorporating con-
straints that enable seamless transitions between patterns
within each switching cycle. The selection process of
switching patterns for specific operating points is demon-
strated and substantiated with empirical measurement
data. The results confirm the efficacy of the proposed
approach, enabling highly dynamic operation. Deviations
from the ideal switching patterns, caused by parasitic
effects, have been identified and are the subject of
ongoing research. The approach outlined in this paper
has the potential to promote the increased adoption of
Dual Active Bridge converters in practical applications.

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