Institute of Mechatronics and Information Systems. Transformers

Transcription

1 nstitte of Mechatronics and nformation Systems for internal se only Transformers Exercise A three-phase transformer has the following nominal ratings rated power S 60 kva, Calclate rated voltage ratio x,5 / V, 1 ± winding connection Dyn, rated freqency f 50 Hz, rated no- crrent i0 0, 75, rated core losses P W, rated short-circit voltage k 6, rated winding losses P k 600 W. 1. ratings of the spply needed to perform the nominal no- test,. parameters of the magnetising branch of the Γ type eqivalent circit,. ratings of the spply needed to perform the nominal short-circit test, 4. parameters of the branch of the Γ type eqivalent circit, 5. relative vales of the Γ type eqivalent circit parameters, 6. relative, percent vales of the voltage drops on the short circit elements of the Γ type eqivalent circit, 7. relative, percent vales of voltage drops nder and the voltage on the LV winding, when energised from the HV winding on tap 0 with rated voltage V and rated freqency f f 50 Hz, for the following s 1 a. 0, 8 ind. b. 0,5 0, 8 ind. c. and cosϕ 1 d. 0, 6 ind. e. 0, 8 cap.. k X k Fe 1ph ph E ph X m Edited by Witold Kbiak, Ph.D., M.Sc., Eng. 1

2 nstitte of Mechatronics and nformation Systems for internal se only Soltion 1. The no- test shold be exected energising the LV winding of the transformer with nominal voltage, at nominal freqency. Therefore the spply shold be able to provide line voltage V ominal no- line crrent 0 () i0 S i ,75 6,80 A () Apparent power of the spply sorce i0 i0 0,75 S0 () 0() S ,75 kva Active component of the no- phase crrent (nominal vale) P0 P acph() 1,99 A ph (Y) eactive component of the no- phase crrent (nominal vale) 6,8 1,99 6,695 A mph () 0ph() 0acph() 0()(Y) 0acph() esistance of the magnetising branch (nominal vale) ph Fe () 177,8 Ω P0 P0 900 eactance of the magnetising branch (nominal vale) ph Xm () 4,49 Ω 6,695 mph() mph() mph (). The short-circit test shold be exected energising the HV winding of the transformer with decreased voltage, at nominal freqency, to obtain the nominal crrent the LV winding short-circited. Therefore the spply shold be able to provide line crrent S 60 10,09 A k (1) ominal no- line short circit voltage k 6 k (1) V Apparent power of the spply sorce k k 6 Sk (1) k(1) S ,80 kva Active component of the short-circit phase voltage (nominal vale) 600 kph (1) 157,5 V,09 1ph Edited by Witold Kbiak, Ph.D., M.Sc., Eng.

3 nstitte of Mechatronics and nformation Systems for internal se only eactive component of the short-circit phase voltage (nominal vale) ,5 91,8 V kxph (1) kph(1) kph(1) k(1)( ) kph(1) esistance of the branch (nominal vale) 600 k (1) 11,8 Ω,09 1ph eactance of the branch (nominal vale) X kxph(1) kxph(1) kxph(1) 91,8 69,90 Ω 1ph,09 k (1) 5. The relative vales shold be calclated as ratios to appropriate phase impedances. Therefore in case of the magnetising branch it shold be ph Z ph 0,540 Ω S ph S ominal relative vale of the magnetising branch resistance Fe() 177,8 rfe 700 r.. Z 0,54 ph ominal relative vale of the magnetising reactance Xm() 4,49 xm 15,8 r.. Z 0,54 n case of the branch the vales shold be related to 1ph Z1 ph 1181Ω S 1ph S ph ominal relative vale of the winding s resistance k(1) 11,8 rk 0,01001 r.. Z ph ominal relative vale of the leakage reactance Xk(1) 69,9 xk 0,05919 r.. Z ph 6. elative percent vale of the active component of the short-circit phase voltage (nominal vale) k(1) k S k Edited by Witold Kbiak, Ph.D., M.Sc., Eng.

4 nstitte of Mechatronics and nformation Systems for internal se only t shold be noted, that the relative percent vale of the winding resistance is eqal kph(1) 1ph rk Z 1ph 1ph 1ph 1ph S 1ph 600 k elative percent vale of the reactive component of the short-circit phase voltage (nominal vale) 6 1 5,916 kx k k 7. The voltage drop on the transformer nder indctance is given by the exact formla ( cosϕ + sin ϕ ) + 0,005 β ( cosϕ ϕ ) β k kx kx k sin where β The voltage drop on the transformer nder capacitance is given by the exact formla ( cosϕ ϕ ) + 0,005 β ( cosϕ + ϕ ) β k kx kx k sin sally it is acceptable to se a simplified eqation ( k cosϕ ± kx ϕ ) (the sign in the formla depends on the type of ). a. 0, 8 ind. ( k cos ϕ + kx ϕ ) 1 (1 0,8 + 5,916 0,6) 4, 50 4,5 1 8,6 V b. 0,5 0, 8 ind. ( k cosϕ + kx sin ϕ ) 0,5 (1 0,8 + 5,916 0,6), 175, , V c. and cosϕ 1 ( k cos ϕ + kx ϕ ) 1 (1 1+ 5,916 0) 1, ,0 V Edited by Witold Kbiak, Ph.D., M.Sc., Eng. 4

5 nstitte of Mechatronics and nformation Systems for internal se only d. 0, 6 ind. ( k cosϕ + kx ϕ ) 1 (1 0,6 + 5,916 0,8) 5, 5, 1 78,7 V e. 0, 8 cap. ( k cosϕ kx sin ϕ ) 1 (1 0,8 5,916 0,6), 750,75 410,8 V Edited by Witold Kbiak, Ph.D., M.Sc., Eng. 5