**6. Conclusions**

This paper investigates the filters for the DI-OEWT topology used in the photovoltaic grid-tied applications. The equivalent circuits of the existing Type-1 and Type-2 filter are derived in detail, and the corresponding harmonic suppression transfer functions are given. Some findings can be obtained from analyzing these equivalent circuits and the transfer functions, as well as comparing with the LCL filter used in the multi-parallel inverter topology. It can be found that Type-1 filter does not make judicious use of the merit (output harmonic cancellation) of the DI-OEWT topology, because its two individual sets of shunt capacitors break the cancellation loop. Another finding is that the two inverter-side inductors of the Type-2 filter are actually connected in series and can be merged into one single inductor to further reduce the filter volume and cost.

From the analysis of the existing filters and with consideration of the large leakage inductance value of the high power MV transformer, a new high order filter (named Type-3 filter) for DI-OEWT topology is also proposed. Unlike the existing filters, in which the transformer leakage inductance is set as the grid-side inductor, the Type-3 filter set the leakage inductance as the inverter-side inductor. Such an arrangemen<sup>t</sup> can maximize the transformer leakage inductance utilization, so as to reduce the requirement of the extra inductance.

A brief parameter design method for the three kinds of filters is also introduced. With the design examples of the three filters, the extra inductance requirement of the Type-3 filter can have a 58.35% higher reduction than the Type-1 and Type-2 filters. In addition, a fault tolerance scheme for DI-OEWT topology is also presented in the paper, but only Type-1 and Type-3 filters are applicable for the scheme. Finally, through evaluating the three filters in terms of the inductance requirement, magnetic core number and applicability for the fault tolerance scheme, the proposed Type-3 filter has a certain advantage over the existing Type-1 and Type-2 filters.

Experimental results of a 30 kW D3L inverter prototype verify the effectiveness of the proposed filter design method and validity of the analysis.

Besides the stability analysis, damping methods of the dual-inverter with the filters are also important issues, we will focus on these topics in future research.

**Author Contributions:** Conceptualization, B.W. and X.Z.; data curation, B.W.; formal analysis, B.W.; funding acquisition, X.Z. and R.C.; methodology, B.W.; experiment, B.W. and C.S.; writing—original draft, B.W.; writing—review & editing, B.W.

**Funding:** This work was funded by the National Natural Science Foundation of China (NO. U1766207).

**Acknowledgments:** The authors declare no acknowledgments.

**Conflicts of Interest:** The authors declare no conflict of interest.
