**6. Conclusions**

This paper proposes new three-phase PFAs for URDN with the presence of linear and non-linear loads and D-STATCOM devices. These PFAs can give both fundamental and harmonic power flow solutions with/without the presence of D-STATCOM devices. The developed BNM and BRNM make both the FPFA and HPFA simple. These matrices are developed by exploiting the radial topology in distribution networks. This method uses the

basic concepts of circuit theory, and they can be easily understood. In this paper, the linear loads are modeled as a series combination of resistance and reactance, and non-linear loads are modeled as constant current sources with its magnitude and angle obtained from the current spectra. The harmonic current injections from the D-STATCOM are assumed as zero. The proposed FPFA and HPFA are tested on the IEEE−13 bus URDN, and the results are found to be accurate with the literature. The test studies are carried on the IEEE−13 bus and IEEE−34 bus URDN, and the results of the case studies show thatthere is an improvement in the fundamental voltage profile, a reduction in the fundamental and harmonic power loss, and a reduction in THD% with the integration of D-STATCOM devices.

**Author Contributions:** R.S. and K.V. designed the problem under study, performed the simulations and obtained the results. R.S. and K.V. wrote the paper, which was further reviewed by A.Y.A. and A.E.-S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

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