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Unformatted text preview: 1 Transformers and Per unit Chapter 3 2 3 Ideal Single Phase Transformer and Polarity Marking rated E rated E N N a t 2 1 2 1 = = 2 1 E a E t = 2 2 1 1 I N I N = t a I I 2 1 = * * * * 2 2 2 2 1 1 1 I E a I E a I E S t t = = = Constant MVA E E 4 Ideal Single Phase Transformer and Polarity Marking E E Reversed Polarity Marks 5 Accounting for Transformer in a Circuit 2 1 E a E = E E Z 2 2 2 2 2 I Z V E + = 1 2 I a I = 1 2 2 1 I a aZ V a E + = V 2 1 N N a = 6 Accounting for Transformer in a Circuit aV V a 2 Z 2 1 2 2 2 1 I Z a V a E + = E 7 Complete Transformer Equivalent Circuit V E V E X1 Gc jBm X2 R2 R1 n1 n2 8 Transformer Equivalent Circuit for Power System Analysis V E V E R1 +a 2 R2 X1+a 2 X2 9 Constant MVA Per Unit System Major advantages: Do not need to deal with transformers turns ratio in circuit analysis Per Unit values of similar types of equipment fall in a fairly narrow range. 10 Constant MVA Per Unit System Basic principles: Per Unit (pu) quantity= Actual quantity Base quantity Selection of study MVA base is arbitrary Selection of study kV base is arbitrary for one point in the system 11 Constant MVA Per Unit System for Single Phase Selection of base quantities : MVA Arbitrary 3 1 1 1 10 x kV M V A I B B B = 1 2 1 1 ) ( B B B MVA kV Z = 12 Constant MVA Per Unit System for Three Phase Selection of base quantities MVA Arbitrary 3 3 3 3 10 3 x kV MVA I B B B = 3 2 3 3 ) ( B B B MVA kV Z = 13 kV BASES Z1 n1 n2 Z2 n2 Z3 Z4 n2 n3 n4 Z5 Z6 n3 n3 n5 n5 n5 n6 6 5 4 3 2 1 6 5 4 3 2 1 n KV n KV n KV n KV n KV n KV B B B B B B = = = = = 14 Constant MVA Per Unit System Changing Bases Derivation...
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This note was uploaded on 02/21/2010 for the course EEE ??? taught by Professor Farmer during the Spring '10 term at ASU.
 Spring '10
 FARMER

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