Example: Three Phase TrnasfomersWe have a small power system as shown in the figure: generator, two transformers, distribution line, and load. Ratings on the equipment are shown. The generator voltage is 13.8kV. a. Find the load voltage without the transformers. b. Find the load voltage WITH the tranformers. c. Find the generator load real and reactive power. 6 MVA 10 V A j 1 Vg 13.8 kV VT1L 13.8 kV SgR 50 MVA VT1H VT1L 10 3 239.023 kV VT2H VT1H 239.023 kV Xg 2.7 Ω VgLN Zload ( 4 j 1 ) Ω Vg 3 VT2L VT2H VgLN 7.967 kV 1 Xline 100 Ω XT1 0.07 Ω 13.8 kV 10 3 XT2 0.07 Ω Without the transformers, the line and load and generator are in series. Using voltage division on a line-to-neutral per phase circuit. Vload VgLN Z Zload Vload ( 91.239 311.929i) V load j Xline Vload 324.998 V Voltage Regulation Vout_noload VgLN Vregulation Vout_noload arg Vload 73.696 deg Vload Vload 3 Vregulation 2.352 10 % This is not good. Let's include the transformers. We must make a reflection of the line impedance. Let's reflect everything to the generator side. With identical transformers, the load impedance reflects across both transformers, cancelling out the effect. VT1H NT1 VT1L NT1 17.321 Xline Xline_eq NT1 NT2 NT1 Again, using voltage division, load j XT2 j Xline_eq j XT1 Zload Vload VgLN Z Vload ( 7.662 0.83i) kV Vload 7.706kV Vregulation arg Vload 6.184deg VgLN Vload Vload Vregulation 3.386% 2 Xline_eq 0.333Ω Find the load power. Sload Vload 3 2 Sload ( 41.922 10.481i ) MVA Zload Find the generator power. Vload Iload Zload 3 Iload 1.754 10 646.022i A NT1 Igen Iload NT2 3 Igen 1.754 10 646.022i A Calculate the combined real and reactive power. Sgen 3 VgLN Igen Sgen ( 41.922 15.441i ) MVA