Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
TRANSFORMERS Ideal transformer voltage and current relations E1 N1 a 1 n E2 N2 I1 N2 1 n a I2 N1 Transformer modelling - impedance relations secondary winding impedance reflected to primary 2 Z 2 N 1 Z 2 a 2 Z 2 N2 primary winding impedance reflected to secondary 2 Z 1 N 2 Z 1 n 2 Z 1 N1 equivalent impedance seen at primary Z in Z 1 a 2 Z 2 a 2 Z load Impedance Diagram Representation 2 V2 V 22,B 2 V 1,B and Z n Z 1,B S1,B 2,B S S B B B Efficiency P out 100% 1 P losses 100% P in P in Voltage Regulation V 1,serving rated load at rated voltage 1 100% VR V 1,rated LINE PARAMETERS Line inductance per phase and unit length L o ln GMD 2 GMR b if transposed GMD 3 D ab D bc D ac if bundled GMR b b r d 12 d 13 d 1b r re r /4 o 2 10 7 henrys/meter 2 Line capacitance per phase and unit length o C 2 GMD ln GMR c b GMR cb b rd 12 d 13 d 1b o 8. 854 10 12 farads/meter Series impedance per phase and unit length z jL R Shunt admittance per phase and unit length y jC CIRCUIT MODELS Admittance parameters regulating (off-nominal) transformer I1 I2 Y eq /a V1 Y eq /a Y eq /|a| 2 V2 Y eq Line Characteristics Zc z y yz Long transmission line sinh l Z zl Z c sinh l l Y yl tanh l 2 l 2 2 tanh Zc l 2 Medium line Z zl and Y yl Short line Z zl and Y 0 POWER CAPABILITY OF LINES Power flow on lossless line for medium line and short line B jX so P V 1 V 2 sin X P max V 1 V 2 X POWER FLOW Admittance Matrix Y bus G jB Y ij Y ij ij Y ii y ij Sum of admittances connected to bus i Y ij y ij Admittance between bus i and j Power flow equations n S i S Gi S Di V i V j Y ij i j ij j1 or n S i V i Y ij V j j1 or n P i P Gi P Di V i V j G ij cos i j B ij sin i j f i V, j1 n Q i Q Gi Q Di V i V j G ij sin i j B ij cos i j g i V, j1