Transformer Current & Voltage Practice

Wye connected windings: Have a common connection point Have two voltages available “L-L & L-N” Has only one current Line current

Delta connected windings: Have no common connection point Have only one voltage available “L-L” Delta can be closed “connected” in more than one way Has two currents Line current Phase or winding current

Definitions Delta: Phase voltage is line voltage but phase current is not line current. Line current ÷ √3= phase current Line voltage = Phase voltage Wye: Phase voltage is not line voltage but phase current is line current. Line voltage ÷ √3= phase voltage Line current = phase current

230 kV 13,280 23 kV HS Line 230 kV LS Line 23 kV Transformer 3 Ø 230/13280/23000 Gnd. Wye 25 MVA 230 kV N H1 H2 H3 X1 X2 X3 C B A a b c W1 W2 W3 W4 W5 W6 13,280 23 kV

Voltage on HS 115 kV. Only one voltage because it is delta HS Line 115 kV LS Line 12 kV Transformer: 3 3 Ø 115/12000/6928 Gnd. Wye 40MVA Voltage on HS 115 kV. Only one voltage because it is delta N H1 H2 H3 X1 X2 X3 C B A a b c W2 W3 W5 W6 201 116 16.6/1 1925 Voltage on LS 12,000 & 6,928 because it is wye connected Transformer Ratio 16.6/1

1255 LS Line 23 kV Transformer ? MVA N H1 H2 H3 X1 X2 X3 C B A a b c W2 W3 W5 W6 1255

Typical GSU Transformer Connection System X3 X2 X1 H3 H2 H1 a b c C B A W1 W2 W3 W4 W5 W6 Generator

Transformer Solutions Information: 230/23kV 25 MVA transformer What is the voltage A-B, B-C, C-A ? What is the voltage a-b, b-c, c-a? What is the voltage a-n, b-n, c-n? What is the voltage across W1, W2, W3? What is the voltage across W4, W5, W6? What is the current in line A, B, C ? What is the current in W1, W2, W3? What is the current in W4, W5, W6? 230 kV 23 kV 13,280 kV 230 kV 13,280 kV 25 MVA / 230 kV / √3 = 62.76 amps 25 MVA / 3 = 8.33 MVA /230 kV = 36.3 amps 25 MVA / 23 kV / √3 = 627.56 amps

Transformer Solutions Information: Δ-Υ 230/23kV 25 MVA transformer What is the voltage on High voltage line? What is the voltage on low voltage line? What is the voltage on low voltage phase? What is the voltage across W1, W2, W3? What is the voltage across W4, W5, W6? What is the current in line A, B, C ? What is the current in W1, W2, W3? What is the current in W4, W5, W6? 230 kV (Given) 23 kV (Given) 13,280 kV ( V 𝐿−𝐿 ÷ √3) 230 kV (Same as the line for Δ winding) 13,280 kV ( L-N voltage) 25 𝑀𝑉𝐴 ÷230,000÷ 3 =62.75 25 𝑀𝑉𝐴 ÷230,000 ÷√3÷√3=36.23 25 MVA / 23 kV / √3 = 627.56 amps

Transformer Solutions What is the current in line a, b, c? On the delta side of the transformer Same as winding W4, W5, W6= 627.556 amps The line current ÷ √3 = Winding Current ; 62.76 ÷ √3 = 36.23 Calculating three phase transformer MVA Voltage X Current X three windings 230,000 X 36.3 amps = 8,349,000 x 3 (windings)= 25,047,000 = 25 MVA 13,280 X 627.57 amps = 8,334,129 X 3 (windings)= 25,002, 388 = 25MVA

Transformer Ratio 3 Phase 230/23 kV 25 MVA Transformer is 230/ 23 kV Ratio is NOT this ration but is the ration of the voltages across the windings. W1 230 kV, W4 13,280 Ratio is 230,000 / 13,280 = 17.32/1 N H1 H2 H3 X1 X2 X3 C B A a b c W1 W2 W3 W4 W5 W6 Note: W4 current/ W1 current = 627.56/36.3 = 17.3 627.56 amps X 13,280 volts = 8.3 MVA 36.3 amps X 230,000 volts = 8.3 MVA 8.3 MVA X 3 (windings) =25 MVA

How Are They Connected? primary secondary H

N H1 H2 H3 X1 X2 X3 C B A a b c W1 W2 W3 W4 W5 W6

Both transformers are Δ-Υ but notice the Δ windings are not closed the same X1 X2 X3 C B A a b c W1 W2 W3 W4 W5 W6 N H1 H2 H3 X1 X2 X3 C B A a b c W1 W2 W3 W4 W5 W6

Single Phase Transformer information: HV 115 kV LV 7200 V Capacity 16,670 KVA primary secondary Primary amps 16,670,000 ÷ 115,000 = 145 amps Secondary amps 16,670,000 ÷ 7,200 = 2315 amps Turns Ratio 115,000 ÷7200 = 15.97/1 Calculating single phase transformer MVA Voltage X Current 115,000 X 145 amps = 16,675,000= 16.67MVA 7,200 X 2315 amps = 16,668,000 = 16.67 MVA Current ratio Check 2315÷145 = 15.97/1

Transformer Information For Practice Calculations 3Ø, Δ-Υ 115/12 kV 25MVA 3Ø, Δ-Υ 115/23 kV 40 MVA 3Ø, Δ- Δ 23/ 13.8 kV 5 MVA 3Ø Υ- Υ 4160/ 2400 5 MVA 3Ø, Δ- Δ 115/ 13.8 kV 10 MVA 1Ø Υ- Δ 230/22 kV 350 MVA Delta and Wye 3-phase circuits : Electronics Worksheet