3.2.1. Hardware Design

Figure 2 shows the schematic of the DC/DC converter. A three-branches in parallel bridge topology to generate the battery output voltage emulation has been designed. Switching frequency of the IGBTs (SEMIKRON SEMIX302GB12E4s) are 20 kHz, working in the non audible spectrum. A carrier phase-shift scheme is adopted to make the equivalent switching frequency up to 60 kHz, reducing the output voltage ripple, and also the selection of IGBTs with less current capability but better switching efficiency.

**Figure 2.** Topology of the DC/DC converter of the proposed EVE: a three-branches two-level in parallel bridge topology.

The output filter is an LC filter, with three coils connected in parallel to the output capacitor. It is a second-order low-pass filter with a resonance frequency *ωres* given by Equation (1):

$$
\omega\_{\rm res} = \sqrt{\frac{3}{L\mathbb{C}\_{\rm out}}} \tag{1}
$$

The resonance frequency of the filter needs to be placed at least one tenth of the switching frequency in order to have a sufficient rejection of the switching components. To avoid resonance problems of the filter, *ωres* is also placed lower than the control frequency of the system. It allows the control to compensate the resonance current implementing a virtual resistance (*Rvirtual*), which is placed in series with each inductor. This control method improves the overall efficiency of the system, avoiding physical resistance in the filter to dampen the resonance. However, due to the lower *ωres*, the overall dynamic is reduced but is still enough to guarantee the stability and fidelity of the test. In order to

decide the *Rvirtual*, Figure 3 shows the bode plot of the LC filter (Equation (2)) with different resistance values.

$$G\_{DCfilter}(\mathbf{s}) = \frac{1}{\frac{LC\_{out}}{\mathfrak{A}}\mathbf{s}^2 + \frac{R\_{virtual}C\_{out}}{\mathfrak{A}}\mathbf{s} + 1} \tag{2}$$

Ideally, it can be seen in Figure 3 that with a higher R the system is damper. However, a high *Rvirtual* will also increase the measurement noise of the current, decreasing the steady state performance. A trade-off between dampening and performance has been chosen, selecting a *Rvirtual* = 1 Ω. The frequency response of the filter with the selected resistance is shown in Figure 4, obtaining resonance gain close to 10 dB.

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**Figure 3.** Sweep of the LC filter transfer function with different values of *Rvirtual*: 0.1 Ω in blue, 0.251 Ω in red, 0.63 Ω in orange, 1.58 Ω in purple, 3.98 Ω in green, and 10.0 Ω in light blue.
