Regulating Transformers in Sequence Domain
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1 ECE523: Lecture 25; Page 1/8 pu 1 Regulating Transformers in Sequence Domain A three-phase voltage regulating transformer has a per unit leakage reactance of.1, and steps the voltage from 69 kv to 35 kv. It has a MVA rating of 1 MVA and is connected in delta on the 69 kv side and Y on the 35 kv side. X L.1pu 1 1ipu jx L Tap change does not change phase shift angle. Just voltage magnitude b 69kV Y 1nominal e j3 deg e j3deg Y 1nominal 1i i i 1i pu Y 2nominal e j3deg e j3 deg Y 2nominal 1i i i 1i pu Y nominal Y nominal 1i pu A. Determine the per unit equivalent circuit parameters and sketch the circuit if the high voltage winding is has a tap changer, and is regulated to be at +7.5%. Also create the two-port matrix. a t_a 69kV a t_a c a c a.932 ( 1.75) ( ) b
2 ECE523: Lecture 25; Page 2/8 - equivalent circuit terms: Right leg: c a 2 c a.69ipu Left left: 1 c a.698ipu Series leg: c a 9.32ipu same both directions since c a is real BUS LV -3 o Y = -j 9.32 pu Y = -j.698 pu +3 o BUS HV Y = j.69 pu Note that the phase shift operator stays the same. Matrix terms: Y 11 Y 22 = c a 1 c a = 2 c a = c a YL c a = c a 2 again, c a is real. Y parta1 c a YL e j3 deg c a e j3deg c a 2 Y parta1 1i i i 8.653i pu
3 ECE523: Lecture 25; Page 3/8 Y 1 parta pu arg Y 9 parta deg Y parta2 c a e j3 deg 1i c a YL e j3deg c a 2 Y parta i i 8.653i pu Y parta c a 2 Y parta 8.653i pu Powerworld file implemented to verify the results. - MW - Mvar sla ck 69. kv kv 69/35 kv Bus A 1.75 tap B us B - MW Mvar LTC Control Status = Manual Set P and Q load to zero Note that Powerworld puts the tap on the "From Bus" side. Positive Sequence Y bus matrix. Bus A. j j8.6 Bus B.65 + j8.6. j8.65 Matches the results calculated above.
4 ECE523: Lecture 25; Page /8 Negative Sequence Bus A. j j8.6 Bus B.65 + j8.6. j8.65 Zero Sequence Bus A. + j.. + j. Bus B. + j.. j8.65 B. Determine the per unit equivalent circuit parameters and sketch the circuit for a phase angle regulator with a 15 degree phase shift, and a to rating. The transformer has an effective leakag reactance of.25pu (combining windings) 1 Z par j.25pu Y par Y par ipu Z par b par First look at case without a phase shift ϕ nom deg 1 t nom cos ϕ t nom 1 nom a t_par a t_par t nom e j ϕ c par c par 1 nom ( ) b par - equivalent circuit terms: Right leg: c par 2 c par Left left: 1 c par Y par Y par pu pu Series leg: c par Y par ipu same both directions since c a is real
5 ECE523: Lecture 25; Page 5/8 Y bus matrix terms: Y 11 Y 22 = c par Y par 1 c par Y par = Y par 2 c par = c par Ypar c par Y par = c par 2 Y par Positive sequence matrix: Y par1_deg Y par c par Y par i c par Ypar c par 2 Y Y par par1_deg i i i pu Phase Shifting Transformer in Powerworld Ybus for degree condition: Same positive, negativeand zero (depending on transformer connections) Positive Sequence Generator Bus. j.. + j. Load Bus. + j.. j.
6 ECE523: Lecture 25; Page 6/8 Now look at case with +15 degree shift ϕ 15 15deg 1 t 15 cos ϕ t a t_par15 a t_par15 t nom e j ϕ c par15 c par ( ) b par 15 arg c par15 deg Positive sequence - equivalent circuit terms: Right leg: c par15 2 c par15 Y par ( i) pu Left left: 1 c par15 Y par ( i) pu Series leg: c par15 Y par ( i) pu Y bus matrix terms: Y 11 c par15 Y par 1 c par15 Y par Y 11 ipu Still equal Y par Y 22 2 c par15 c par15 Y par c par15 Y par Y 22 i c par15 2 Y par i Positive sequence matrix: Y par1_15deg Y par c par15 Y par i c par15 Ypar c par15 2 Y par1_15deg Y par i i i pu
7 ECE523: Lecture 25; Page 7/8 Y par1_15deg 9 argy par1_15deg deg Negative sequence pi equivalent terms: Right leg: c par15 2 c par15 Y par ( i) pu Left left: 1 c par15 Y par ( i) pu Series leg: c par15 Ypar ( i) pu Negative sequence matrix: Y 11_2 Y 22_2 c par15 Ypar 1 c par15 Y par Y 11_2 ipu c par15 Ypar c par15 2 c par15 Y par Y 22_2 i Still equal Y par c par15 2 Y par i Y par2_15deg Y par c par15 Ypar i c par15 Y par c par15 2 Y par2_15deg Y par i i i pu Y par2_15deg 9 argy par2_15deg deg
8 ECE523: Lecture 25; Page 8/8 The zero sequence impedance will depend on the connections of the transformers that constitute the phase angle regulator, and will require test data on the zero sequence behavior of the different windings. Powerworld result with +15 degree shift Positive Sequence Generator Bus. j j3.86 Load Bus 1. + j3.86. j. Negative Sequence Generator Bus. j j3.86 Load Bus 1. + j3.86. j. Both match the results above.
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