# Analysis of optimization techniques applied to the DAB converter

Rossano M Sotoriva, Mateus C Orige, Leonardo A Bender, Gierri Waltrich, Samir A Mussa

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Rossano M Sotoriva, Mateus C Orige, Leonardo A Bender, Gierri Waltrich, Samir A Mussa. Analysis of optimization techniques applied to the DAB converter. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0221. hal-05095870

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# Analysis of optimization techniques applied to the DAB converter

Rossano M. Sotoriva¹, Mateus C. Orige¹, Leonardo A. Bender¹, Gierri Waltrich¹, Samir A. Mussa¹

Federal University of Santa Catarina¹ - Florianópolis, Brazil

E-mail: {rossano.sotoriva.97, mateusconstantinoorige, leobender1997, gierri} @gmail.com, samir@inep.ufsc.br

**Index Terms**—Optimization method, Dual Active Bridge (DAB), DC-DC converter, Bi-directional converters, Modulation.

**Abstract**—This paper compares computational approaches for optimizing DAB converters, focusing on efficiency and loss minimization. Additionally, a comparison between Single Phase Shift (SPS) and Extended Phase Shift (EPS) modulations was performed. The applied optimization techniques applied include Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Fmincon Global Search, all converging to the same optimal solution, differing only in processing time. A 2 kW prototype, with parameters obtained from the optimization for both EPS and SPS modulations, underwent testing for different voltage gains.

## I. INTRODUCTION

In response to the numerous challenges in creating a sustainable environment by reducing CO₂ emissions, many new challenges have risen such, as a high demand in the electric grid by the adoption of electric vehicles [1] with its own challenges such as battery autonomy [2].

Research has been conducted across various technological fields, including bidirectional isolated DC-DC converters. These converters can provide benefits such as reduced volume, cost, and weight, along with low conversion noise, high power density, and high efficiency. As a result, they are well-suited for a range of applications, including bus connections, voltage conversion, power transmission, and electrical isolation in DC distribution networks [3], [4].

Bidirectional isolated DC-DC converters can be utilized from energy generation to distribution due to this diverse range of applications. Within the bidirectional isolated DC-DC converters, the Dual-Active Bridge has shown to be a versatile option with applications on diverse fields namely, electric vehicles charging stations

[5], battery energy storage systems on microgrids [6], or photovoltaic systems [7] along with other applications.

Due to the myriad of possible applications and specific necessities of each of them, it is an interesting option to employ the use of computational approaches to the converter design, minimizing power losses by evaluating various material and component combinations, achieving optimal designs for specific applications [8], [9].

During the converter optimization, it is possible to consider different modulation methods. In the case of DAB, there are several modulation techniques [10], with emphasis on single phase shift (SPS), extended phase shift (EPS), dual phase shift (DPS), and triple phase shift (TPS).

Additionally in this work, a comparison of the optimization techniques PSO, GA, and fmincon *Global Search* will be conducted, evaluating both the optimal solution obtained by each technique and the associated computational cost. The objective function to be optimized is the maximization of the efficiency of a DAB converter operating with SPS and EPS modulation. To validate the results, experimental data from a 2 kW prototype will be analyzed at four different output voltage operating points.

## II. DUAL ACTIVE BRIDGE - DAB

The DAB converter, as illustrated in the Fig. 1, is a bidirectional converter capable of power transfer between its two bridges, it has numerous capabilities such as, galvanic isolation, zero voltage switching (ZVS) operation, and high flexibility with modulation schemes [11].

The power transfer in the DAB converter can be controlled by various methods, such as adjusting the phase shift angle ($\phi$) between the primary and secondary bridges, modulating the inner phase shift, or changing the switching frequency [12]. Among these methods there is:

* The Single-Phase Shift (SPS) modulation, which is the simplest method of control for the DAB con-
<figure><img src="image_2.png" /><figcaption>Fig. 1: Dual Active Bridge (DAB) converter.</figcaption></figure>

verter, is achieved by adjusting the phase shift angle between the two bridges of the converter. However, the main drawback of this technique is that the ZVS operation range becomes limited and there are high losses on lighter loads, making necessary the use of other modulation methods for a better efficiency of the converter [13];

* The Extended Phase Shift (EPS) can provide a wider range of ZVS operation and in addition to the phase shift between the two bridges of the converter, an inner phase shift is implemented on the legs of a bridge of the converter creating another voltage level [14];

* The Dual Phase shift (DPS) modulation has a similar approach to the EPS, this time implementing an inner phase shift between the legs of both bridges, further expanding the ZVS zone of the converter and attaining higher efficiency for the converter on lighter loads [15];

* The Triple Phase Shift (TPS) has a phase shift between the two bridges of the converter and an inner phase shift on each of its legs, granting this modulation technic three degrees of freedom, which makes it really versatile and much more complex to implement [16].

Overall, the operating range and efficiency of the DAB converter are highly dependent on the modulation technique employed, each with its own benefits and drawbacks. For example, SPS modulation offers simplicity and ease of control but when operating on lower loads it presents higher losses.

In contrast, more advanced techniques like EPS, DPS or TPS modulation can improve efficiency across a broader operating range, though at the cost of increased control complexity and implementation effort. Therefore, the selection of the modulation technique must balance the trade-offs between efficiency, operational range, and system complexity, depending on the specific application requirements.

### III. OPTIMIZATION

In this section we will discuss the optimization techniques utilized for comparison in this study, along with the overall algorithm for the optimization of the DAB converter.

The optimization presented in this work is designed with the objective of reducing the power losses with the converter design, maximizing the efficiency ($η$), the objective function (1), maintaining fixed values for input voltage ($V_i$) and Power output ($P_o$), while variating the voltage output ($V_o$).

* $V_i = 400$ V;

* $P_o = 2$ kW;

* $V_o = [300 350 400 450]$ V;

$$ \max f_{ob}(i) = \eta(i) \Rightarrow \left( \eta \mid_{V_o=V_o(i)} \right). \quad (1) $$

#### A. Optimization techniques

The DAB converter is optimized for SPS and EPS modulations, using three optimization methods: PSO, GA, and the Find Minimum of Constrained Nonlinear Multivariable Function (Fmincon) Global Search in MATLAB.

Both PSO and GA are evolutionary algorithms based on biological principles, they are heuristic methods widely used for problem-solving suitable in various applications [17].

Even though both algorithms have similar principles, they approach the problem and work to a solution differently. PSO operates by generating a swarm of particles, each characterized by a position and a velocity. The movement of each particle is governed by its velocity, which determines its transition to a new position. Upon reaching a new position, both the individual best position of each particle and the global best position of the swarm are updated accordingly. The velocity of each particle is subsequently adjusted based on its previous experiences and the information shared within the swarm. This iterative process continues until a predefined stopping criterion is satisfied. [18].

GA is an optimization technique inspired by natural selection, following the principle of the survival of the fittest. It operates on a population of candidate solutions (chromosomes), which evolve over successive iterations through genetic operators such as selection, crossover, and mutation. The process begins with a randomly initialized population, where each chromosome's fitness is evaluated. Two chromosomes are then selected based on their fitness, and a crossover operator is applied to
generate offspring. A mutation operator is subsequently used to introduce variability. This process repeats until a new population is formed. By dynamically adjusting the probabilities of crossover and mutation, GA enhances the search process and improves the likelihood of reaching an optimal solution. Its ability to evaluate multiple individuals simultaneously provides strong global search capabilities [19].

In contrast, the Fmincon function is a gradient-based method designed to find the minimum of a constrained nonlinear problem, differing from the previous algorithms in its reliance on gradient information [20].

To evaluate each algorithm method, in the case of the PSO and GA the swarm size and population size were established as being the same, along with the number of iterations and generations [21]. In the case of the Fmincon function the same number of iterations was used, with the modifying option to enable global search on the algorithm, this way evading the algorithm locking on a local minima of the function objective [22].

## B. Optimization algorithm

The optimization process shown in Fig. 2 involves the determination of four construction parameters at each operation point $i \in \{1, 2, 3, 4\}$, $V_i = 400$ V, $P_o = 2$ kW, $\forall i$ and $V_o[i]$. The nomenclatures used were defined as follows: number of turns in the inductor ($N_L$), length of the inductor gap ($l_g$), number of turns in the primary ($N_p$) and number of turns in the secondary ($N_s$) transformer windings. Given that multiple solutions exist for the converter, the routine identifies the best combination for each operating point $i$, and also optimizes a unique frequency ($f_{s,i}$) for each operating point; the frequency being a variable that can be changed aside from the construction parameters. During the EPS modulation optimization one extra parameter will be optimized, the inner phase shift ($\tau$) of the legs of the converter.

In order to minimize losses for each of the operation points, a modulation strategy is implemented, where it's possible to adjust both the phase shift ($\phi$) and the frequency ($f_s$) of the converter. As can be seen in the DAB single phase shift power transfer equation given by

$$P_o(\phi, f_s) = \frac{V_i \cdot V_o \cdot \phi \cdot (\phi - \pi)}{2\pi^2 \cdot f_s \cdot L \cdot n} \quad (2)$$

the power flow in the DAB converter depends on both the phase shift ($\phi$) and the switching frequency ($f_s$). By adjusting both parameters, a high level of flexibility can be achieved, thereby enhancing the converter's overall performance under SPS modulation. When implementing EPS modulation, an additional variable must be considered: the internal phase shift ($\tau$) between the converter

<figure><img src="image_3.png" /><figcaption>Fig. 2: Optimization flowchart.</figcaption></figure>

legs in the bridge with the highest voltage. This internal phase shift affects power transfer, and the extended phase shift power transfer equation for the DAB converter is given by

$$P_o(\phi, \tau, f_s) = \frac{V_o^2 \cdot \phi^2 - \pi V_o \cdot \phi + V_i \cdot n \cdot \gamma_{\varrho}}{4\pi^2 \cdot f_s \cdot L \cdot n}, \quad (3)$$

where $\gamma_{\varrho} = (\phi^2 + \tau^2 - \pi\tau - \phi \cdot \tau)$.

The phase-shift angle for each operation point $i$ is calculated using a frequency ($f_{s,i}$), an output voltage ($V_{o,i}$) and an output power ($P_{o,i}$). Then, the following elements are calculated:

* the peak current in the primary power switches ($i_{p,pk}$);

* the RMS value of current in the primary power switches ($i_{p,rms}$);

* the peak current in the secondary power switches ($i_{s,pk}$);

* the RMS value of current in the secondary power switches ($i_{s,rms}$);

* the peak-to-peak density flux in the inductor ($\Delta B_L$);

* the derivative of the density flux in the inductor ($dB_L(t)/dt$);
* the inductor current in $n^{th}$ harmonic ($i_{L,n}$);

* the peak-to-peak density flux in the transformer ($\Delta B_{trs}$);

* the derivative of the density flux in the transformer ($dB_{trrs}(t)/dt$);

* and the transformer current in ($i_{trrs,n}$) at $n^{th}$ harmonic.

With these values, it is possible to assess whether the magnetic elements saturate or if any element in the converter exceeds the temperature limit. If any of these conditions are met, the algorithm rejects the iteration, and the parameters undergo a new selection before being retested.

### C. Losses and thermal models

The study incorporates models for losses and thermal effects, embracing both semiconductor and magnetic losses.

#### 1) Semiconductor losses:

* Conduction losses: This losses are calculated upon the on-resistance ($R_{ds-on}$) of the switches and the RMS value of the currents at the switches and can be expressed by the equation,

$$P_{cond} = R_{ds-on} \cdot I_{rms,i}^2. \quad (4)$$

* Switching losses: This losses are calculated based on the energy characteristics as specified in the manufacturer's datasheets for the switches. The switching losses is given by

$$P_{sw} = (E_{on,i} + E_{off,i}) \cdot f_s. \quad (5)$$

Based of the flowchart exhibited on the Fig. 3 the switching losses are calculated depending on the $V_{sw}$ and $I_{sw}$.

<figure><img src="image_4.png" /><figcaption>Fig. 3: Switching loss flowchart.</figcaption></figure>

To further reduce the switching losses it is possible to achieve ZVS on the switches turn-on, depending on the polarity of the inductor's current ($i_L$) [23]. If the current of a switch is negative while being activated, Zero Voltage Switching (ZVS) will occur. The ZVS range for each phase shift can be acquired by the equations:

$$ZVS_{p,s} \Rightarrow \left\{ \begin{array}{l} \text{for } d < 1 \Rightarrow \begin{cases} \phi ZVS_{p} > \frac{d\pi - \tau}{2 \cdot d} \\ \phi ZVS_{s} > \frac{\tau - d \cdot \pi}{2} \end{cases} \\ \\ \text{for } d > 1 \Rightarrow \begin{cases} \phi ZVS_{p} > \frac{d\tau - \pi}{2 \cdot d} \\ \phi ZVS_{s} > \frac{\pi - d \cdot \tau}{2} \end{cases} \end{array} \right. \quad (6)$$

Where when the phase shift $\phi$ condition is true, ZVS is achieved at each side of the converter, the voltage ratio defined as $d = n \cdot \frac{V_o}{V_i}$. It is noted that, for $\tau = \pi$, the ZVS expression presented is equivalent to that of the SPS modulation.

The ZVS range can be plotted as shown in Figure 5, where the output power is normalized over the voltage ratio graph, since the phase shift is proportional to the output power. It is valid to note that the ZVS range can be further extended by applying different modulation schemes, such as EPS, DPS, or TPS control [24]. The ZVS region addition represented in black on the figure is due the EPS modulation scheme, while the ZVS region is achievable with the SPS modulation.

<figure><img src="image_5.png" /><figcaption>Fig. 5: ZVS range with normalized output power over voltage ratio.</figcaption></figure>

#### 2) Magnetic losses: On the present converter, there are two magnetic elements: the transformer and the inductor. In each of these elements there are losses in their windings and cores. The core losses are calculated using the improved Generalized Steinmetz Equation (iGSE) [25], [26].
<figure><img src="image_6.png" /><figcaption>Fig. 4: Semiconductor losses flowchart.</figcaption></figure>

For the winding losses, the Dowell's equation is employed, which takes into account the resistance of the litz wire winding used in the magnetics [27]. Since these resistances are frequency-dependent, the Fourier series of the current is considered for the inductor, primary windings of the transformer, and secondary windings of the transformer.

## IV. OPTIMUM DESIGN

To initialize the optimization process, the necessary specifications and materials where all acquired from the material and component datasheet. The materials used in this prototype are presented below. The power switches used were the C3M0030090K models, while the heatsink, for both the primary and secondary sides, was designated as LAM4K15012. For the inductor and transformer, the core employed was the E80/38/20-N87 model, combined with 392x37AWG Litz wires.

The boundary conditions for the optimization were established, allowing for an analysis within the defined operational range. These limits include $N_L \in [2, 15]$, $l_g$ [mm] $\in [0.02, 2]$, $N_p, N_s \in [2, 15]$, $f_s$ [kHz] $\in [20, 150]$, $\tau$ [°] $\in [0, 180]$. Also its defined on Table I a population/swarm size of 300 for each optimization parameter, it includes the $N_L, N_p, N_s, l_g, f_{s,i}$ and $\tau$.

In the first set of iterations, the minimized losses for the converter were defined as outlined in Tab. II. After the construction characteristics were stabilized, the algorithm was set to find the unique frequency ($f_{s,i}$) for each operating point (i), refining the overall optimization and minimizing the losses at each point. During the EPS modulation optimization, there was a slight difference in the inner phase shift ($\tau$) results for each optimization method; however, it is small and does not affect the test

results, having only a minor impact on the frequency at each operating point.

<table><caption>TABLE I: Optimization parameters.</caption><thead><tr><th rowspan="2">Method</th><th colspan="3">Algorithm parameters</th></tr><tr><th>Swarm size</th><th>Max Stall iterations</th><th>Max iterations</th></tr></thead><tbody><tr><td>PSO</td><td>300·ρ</td><td>50</td><td>200</td></tr><tr><td>GA</td><td>300·ρ</td><td>50</td><td>200</td></tr><tr><td>Fmincon (GS)</td><td>-</td><td>-</td><td>200</td></tr></tbody></table>

The swarm size and max iterations, used on PSO, are equivalent to the population size and max generations used on GA.

<table><caption>TABLE II: Optimum design summary.</caption><thead><tr><th colspan="4">Optimized construction parameters</th></tr><tr><th>Parameter</th><th>Value</th><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td>$N_p$</td><td>14</td><td>$N_s$</td><td>12</td></tr><tr><td>$N_L$</td><td>14</td><td>$l_g$</td><td>0.52 mm</td></tr><tr><td>$f_s$</td><td>60 kHz</td><td>$L_{DAB}$</td><td>87.69 μH</td></tr><tr><td>$\tau_{PSO}$</td><td>141.29°</td><td>$\tau_{GA}$</td><td>142.06°</td></tr><tr><td>$\tau_{Fmincon}$</td><td>141.71°</td><td></td><td></td></tr></tbody></table>

The results for each optimization method are presented in Tables III and IV, which include the theoretical outcomes for the converter with both SPS and EPS modulation. Upon analysing the initial results, it is observed that, when using the same construction characteristics and materials, all methods are viable, with nearly all parameters converging to similar solutions.

When expanding the routine and optimizing the entire range of possible operations, the maps obtained from each algorithm showed consistent results, as illustrated in the maps on Figure 6, where (a), (b) and (c) represent the SPS optimization (d), (e) and (f) the EPS optimization,
<table><caption>TABLE III: Results for PSO, GA, and Fmincon for SPS modulation.</caption><thead><tr><th rowspan="2">i</th><th colspan="5">PSO</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>47.633</td><td>97.618</td><td>30.441</td><td>14.975</td></tr><tr><td>2</td><td>5.7143</td><td>46.058</td><td>97.697</td><td>34.907</td><td>14.694</td></tr><tr><td>3</td><td>5</td><td>61.490</td><td>96.926</td><td>42.195</td><td>15.630</td></tr><tr><td>4</td><td>4.4444</td><td>87.056</td><td>95.647</td><td>58.900</td><td>19.912</td></tr></tbody><thead><tr><th rowspan="2">i</th><th colspan="5">GA</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>48.134</td><td>97.593</td><td>30.166</td><td>14.826</td></tr><tr><td>2</td><td>5.7143</td><td>46.638</td><td>97.668</td><td>34.337</td><td>14.431</td></tr><tr><td>3</td><td>5</td><td>62.176</td><td>96.891</td><td>41.872</td><td>15.498</td></tr><tr><td>4</td><td>4.4444</td><td>88.275</td><td>95.586</td><td>59.879</td><td>20.291</td></tr></tbody><thead><tr><th rowspan="2">i</th><th colspan="5">Fmincon (Global Search)</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>48.939</td><td>97.553</td><td>25.966</td><td>12.592</td></tr><tr><td>2</td><td>5.7143</td><td>46.982</td><td>97.651</td><td>38.008</td><td>16.140</td></tr><tr><td>3</td><td>5</td><td>62.553</td><td>96.872</td><td>45.580</td><td>17.029</td></tr><tr><td>4</td><td>4.4444</td><td>88.292</td><td>95.585</td><td>60.479</td><td>20.532</td></tr></tbody></table>

<table><caption>TABLE IV: Results for PSO, GA, and Fmincon for EPS modulation.</caption><thead><tr><th rowspan="2">i</th><th colspan="5">PSO</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>31.451</td><td>98.427</td><td>42.632</td><td>9.261</td></tr><tr><td>2</td><td>5.7143</td><td>36.753</td><td>98.162</td><td>56.586</td><td>12.395</td></tr><tr><td>3</td><td>5</td><td>40.373</td><td>97.981</td><td>52.766</td><td>7.580</td></tr><tr><td>4</td><td>4.4444</td><td>53.023</td><td>97.349</td><td>61.408</td><td>8.613</td></tr></tbody><thead><tr><th rowspan="2">i</th><th colspan="5">GA</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>31.449</td><td>98.428</td><td>41.644</td><td>8.830</td></tr><tr><td>2</td><td>5.7143</td><td>36.540</td><td>98.173</td><td>56.229</td><td>12.439</td></tr><tr><td>3</td><td>5</td><td>40.465</td><td>97.977</td><td>52.207</td><td>7.535</td></tr><tr><td>4</td><td>4.4444</td><td>53.203</td><td>97.340</td><td>61.114</td><td>8.731</td></tr></tbody><thead><tr><th rowspan="2">i</th><th colspan="5">Fmincon (Global Search)</th></tr><tr><th>I<sub>o</sub> [A]</th><th>P<sub>Losses</sub> [W]</th><th>η [%]</th><th>f<sub>s</sub> [kHz]</th><th>φ [°]</th></tr></thead><tbody><tr><td>1</td><td>6.6667</td><td>31.444</td><td>98.428</td><td>42.087</td><td>9.020</td></tr><tr><td>2</td><td>5.7143</td><td>37.150</td><td>98.143</td><td>57.959</td><td>13.349</td></tr><tr><td>3</td><td>5</td><td>40.729</td><td>97.964</td><td>52.071</td><td>7.337</td></tr><tr><td>4</td><td>4.4444</td><td>53.286</td><td>97.336</td><td>60.684</td><td>8.391</td></tr></tbody></table>

where each of the figures presents a contour map of the converter, with (a) and (d) being the operating frequency, (b) and (e) the phase-shift regions and (c) and (f) the complete efficiency map for the converter optimization.

Most of the operating points fall within the frequency range between 20 and 60 kHz for both SPS and EPS modulation. When analysing the phase shift in SPS

modulation, it lies between 10 and 20 degrees across all operating points. However, in EPS modulation, the phase shift is below 10 degrees for every operating point except for $i = 2$. The most notable observation from these figures is the efficiency map of both modulations. The EPS modulation achieves higher efficiency at every point, reaching over 97%. Furthermore, EPS modulation extends this high efficiency to regions where SPS modulation would only achieve 92% to 94%.

Even thought the results obtained in each of the optimization methods are very similar, they are positive. There is not a single point where the algorithm not converged to a suitable point, and on all the results a high level of efficiency was obtained.

However, when considering the CPU time used to run each of them, it's noticeable there are more differences between them, the elapsed time necessary for each of the method is described on the Tab. V.

<table><caption>TABLE V: Optimization time.</caption><thead><tr><th colspan="3">Modulation</th></tr><tr><th colspan="2">SPS</th><th>EPS</th></tr><tr><th rowspan="2">Optimization method</th><th colspan="2">Elapsed time</th></tr><tr><th>CPU time</th><th>CPU time</th></tr></thead><tbody><tr><td>Particle Swarm Optimization</td><td>1h 15min 9s</td><td>4h 37min 14s</td></tr><tr><td>Genetic Algorithm</td><td>5h 29min 20s</td><td>1h 02min 57s</td></tr><tr><td>Fmincon (GS)</td><td>11h 52min 38s</td><td>12h 17min 39s</td></tr></tbody></table>

The runtime of each optimization method varies significantly; when evaluating the SPS results the fmincon function is the only gradient-based optimization method used in this study. It took 11.52 hours of CPU time to reach a solution within the defined hyperparameters, making it the slowest method. While the results are satisfactory. The implementation of fmincon can be more challenging due to its tendency to converge to local minima, a common issue with gradient-based methods. This limitation may require additional configurations to help the algorithm avoid local minima during the optimization process.

GA is the second option, it took 5.92 hours of CPU time to reach a solution within the defined hyperparameters using this heuristic method, without reaching the maximum number of stall generations in the population configuration. Despite its slower performance, the GA implementation is very similar to the PSO algorithm, making it easy to adapt between the two options.

PSO, like GA, is a heuristic method, but it proved to be the fastest optimization technique in the present study, significantly outperforming the other methods in terms of
<figure><img src="image_7.png" /><figcaption>Fig. 6: Complete operating range maps of the converter for SPS modulation: (a) frequency map, (b) phase shift map, (c) efficiency map; and for EPS modulation: (d) frequency map, (e) phase shift map, (f) efficiency map. Optimized operating points are highlighted within the respective regions.</figcaption></figure>

speed while still providing a suitable solution. It took the CPU 1.25 hours to reach a solution within the delimited hyperparameter. It is worth noting that neither PSO nor GA reached the maximum number of stall iterations in the algorithm, indicating effective convergence within the set limits.

When Evaluating the EPS results the fmincon function presented the worst result in this study, requiring 12.29 hours to complete the optimization, which when in comparison with SPS modulation is similar result.

The PSO algorithm took 4.62 hours to complete,

representing an increase in computation time compared to the SPS result. Since PSO relies on swarm-based convergence, particles explore the search space based on previous best solutions. The addition of one more variable increases the complexity of the search space, requiring precise tuning. One possible solution to this is reducing the swarm size, which would make each iteration faster but at the cost of reduced accuracy and less exploration of the search space.

The GA implementation for EPS modulation proved to be the fastest overall, taking only 1 hour and 4
<figure><img src="image_8.png" /><figcaption>Fig. 7: Experimental results for the DAB converter with SPS modulation for the cases of (a) 300 V, (b) 350 V, (c) 400 V, and (d) 450 V in the output voltage.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8: Experimental results for the DAB converter with EPS modulation for the cases of (a) 300 V, (b) 350 V, (c) 400 V, and (d) 450 V in the output voltage.</figcaption></figure>

seconds to complete the optimization. It was not only the fastest method for EPS modulation but also the fastest among all tested algorithms. GA evaluates multiple individuals independently, making it more efficient when using parallel computing compared to PSO. Unlike PSO, which explores the search space based on previous results, GA relies on mutation to jump through the search space in pursuit of a near-optimal solution. By incorporating an extra parameter in the optimization, GA better constrained the search space, leading to a faster solution.

## V. EXPERIMENTAL TESTS

To experimentally validate the solutions obtained by the optimization methods, a prototype was developed, shown in Fig. 9, operating with SPS and EPS modulation using the LAUNCHXL-F280049C from Texas Instruments.

The waveforms shown in Fig. 7 correspond to the tests conducted for the operating points with output voltages of 300 V, 350 V, 400 V, and 450 V, with SPS modulation, respectively in Fig. 8(a),(b),(c) and (d) with EPS modulation. Efficiency measurements were carried out using the four-wire method with the Yokogawa
WT1800 power meter, as shown in both Figures. In the SPS modulation at the 400 V (Fig. 7(a)) operating point, the lowest losses were observed, resulting in an efficiency of 97.20%. In contrast, at the 450 V point (Fig. 7(d)), the lowest efficiency was recorded, approximately 95.77%, due to increased losses in the magnetic components at this operating point.

In the EPS modulation at the 450 V (Fig. 8(a)) operating point, the lowest losses were observed, resulting in an efficiency of 97.60%. In contrast, at the 450 V point (Fig. 8(d)), the lowest efficiency was recorded, approximately 97.60%, due to increased losses in the magnetic components at this operating point.

Overall is noticeable that the EPS modulation offers higher efficiency in every point of operation tested with relative simplicity in order to implement when compared with the SPS modulation, compensating its implementation.

One important consideration regarding the wave-
forms presented in the figures is that, at the 350V and
400V operating points, even though the input voltage
is higher than the output voltage, the converter operates
in boost mode due to the transformer's turns ratio of
0.86. Additionally, it is worth noting that the dead time
adopted was conservative, set at 300 ns, which suggests
that the efficiency could be further improved with a more
optimized adjustment of this parameter.

<figure><img src="image_10.png" /><figcaption>Fig. 9: DAB converter prototype used for the validation of the optimization methods.</figcaption></figure>

VI. CONCLUSION

In this work, a comparison was made between
different optimization techniques applied to the DAB

converter using SPS and EPS modulation, along with
the modeling of component losses in the converter. All
the evaluated algorithms were effective in finding the
optimal solution, with the main difference between them
being the execution time. While optimizing for the SPS
modulation, PSO stood out by being about 11 times
faster than fmincon Global Search and approximately 4.5
times faster than GA. However when optimizing for the
EPS modulation GA stood out by being about 12 times
faster than fmincon Global Search and approximately 3.5
times faster than PSO.

With the optimal solution defined, practical results
were obtained, where the measured efficiency showed an
error of less than 1% compared to the value predicted by
the optimization, demonstrating the closeness between
theoretical and experimental models.

Genetic Algorithm (GA) is well-suited for optimiza-
tion problems due to its ability to evaluate multiple
individuals in parallel, making it highly efficient in com-
putational environments that support parallel process-
ing. Unlike Particle Swarm Optimization (PSO), which
updates particle positions based on past experiences,
GA introduces diversity through mutation, allowing it to
explore the search space more broadly and avoid local
optima.

The performance of PSO and GA varied depend-
ing on the problem’s dimensionality. PSO demonstrated
superior efficiency in lower-dimensional search spaces
due to its rapid convergence, effective balance between
exploration and exploitation, and fewer function evalu-
ations per particle. Its velocity-based updates allowed it
to navigate smaller search spaces efficiently. Conversely,
GA’s strong exploration capabilities through mutation
and crossover, along with its parallel evaluation of popu-
lations, made it less prone to premature convergence and
more effective in navigating larger search spaces. As a
result, GA proved to be more robust in high-dimensional
optimization scenarios, while PSO remained an efficient
choice for lower-dimensional problems.

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