An impact of the line resistance on the power flow calculations with installed phase-shifting transformer in different voltage levels power systems

In modern power systems, phase-shifting transformers are installed not only in the extra high voltage lines, but some of these devices can be built for lower voltage levels (e.g., 40 kV). Due to big voltage difference, in the power flow analyses, not only phase-shifting transformer properties, but also line parameters, including resistance, should be considered. For high voltage power systems, the line reactance is much greater than its resistance (the ratio is even greater than 10), while it is smaller in lower voltages. This fact should be taken into account during any calculations of power flows in such systems. This article considers 400 kV, 220 kV, and 70 kV transmission lines with installed asymmetrical phase-shifting transformers to present the line resistance impact on the final power flow calculations. Also, the IEEE 5-bus power system is tested to prove the dependency of line resistance on power flow calculations and bus voltage values. The highest voltage levels calculation results show that the assumption of omitting line resistance is correct (the relative error is equal to 2%), while for the 70 kV system, the same error results even 30%. What is more, the line resistance for medium voltage power systems cannot be omitted. What is more, the resistance effect is intentionally not taken into account in some power flow calculations presented in the literature.