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EEE471Ch3 - Transformers and Per unit Chapter 3 1 2 Ideal...

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1 Transformers and Per unit Chapter 3
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2
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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
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4 Ideal Single Phase Transformer and Polarity Marking E E Reversed Polarity Marks
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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 =
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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
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7 Complete Transformer Equivalent Circuit V E V E X1 Gc - jBm X2 R2 R1 n1 n2
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8 Transformer Equivalent Circuit for Power System Analysis V E V E R1 +a 2 R2 X1+a 2 X2
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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.
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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
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11 Constant MVA Per Unit System for Single Phase Selection of base quantities : MVA Arbitrary 3 1 1 1 10 x kV MVA I B B B = 1 2 1 1 ) ( B B B MVA kV Z =
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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 =
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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 = = = = =
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