ELECTRIC CIRCUITS THEORY 1 These lecture slides have been compiled by Mohammed LECTURE 9 SalahUdDin Ayubi. Transformers 24 August 2005
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Outline • Ideal Transformers • Transformer Equations – Voltage Transform – Current Transform – Resistance Transform
• Transformer Ratings • Real Transformers • Transformers and the Power Grid 24 August 2005
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Physical Configuration
+
i1(t)
φ
V1(t)
+
V2(t)
-
-
n2 turns
n1 turns
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i2(t)
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Transformer Symbol i1(t)
i2(t)
+
+
V1(t)
V2(t)
-
-
n1:n2
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Outline • Ideal Transformers • Transformer Equations – Voltage Transform – Current Transform – Resistance Transform
• Transformer Ratings • Real Transformers • Transformers and the Power Grid 24 August 2005
Engineer M S Ayubi
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Transformer Equations di1 (t ) v1 (t ) = L1 dt di1 (t ) di2 (t ) v1 (t ) = L1 +M dt dt di1 (t ) di2 (t ) v2 (t ) = M + L2 dt dt
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Transformer Equations v2 n2 = v1 n1 i2 n1 =− i1 n2
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Transformer Equations i1(t)
i2(t)
+
+
V1(t)
Req
V2(t)
-
-
n1:n2
v2 n2 = v1 n1 i2 n =− 1 i1 n2
2
n1 R Reqeq = ? R n2 24 August 2005
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Example 1 • Find turns ratio for maximum power (i.e., match the impedances)
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n1 =5 n2
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Example 2 • Find V2
i1(t)
i2(t)
+
+
V1(t)
V2(t)
-
-
2:1 V2 = 0 V 24 August 2005
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Example 3 • Find V2
i1(t)
i2(t)
+
+
V1(t)
V2(t)
-
-
2:1 V2 = 5 sin2t V 24 August 2005
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Example 4 • Find the magnitude of the secondary voltage, the primary current, and the secondary current • Find power delivered by the source
60∠ 0° Vrms
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Example 4 • Magnitude of secondary voltage: vˆ1 = 60∠0° v1 = 60
60∠ 0° Vrms
v2 n2 = v1 n1 v2 =
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n2 1 v1 = 60 = 20Vrms n1 3
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Example 4 • Magnitude of primary current: 60∠ 0° Vrms
v1 i1 = Zˆ
eq 2
2
n1 3 Z eq = Z 2 = 2.2 2 + 12 = 21.75Ω 1 n2 60V i1 = = 2.76A rms 21.75Ω 24 August 2005
Engineer M S Ayubi
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Example 4 • Magnitude of secondary current:
60∠ 0° Vrms
n1 3 i2 = − i1 = − 2.76 = −8.28A rms n2 1
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Example 4 • Power delivered by source:
60∠ 0° Vrms
Ps = PR = I 2 R = (8.28 A)(2.2Ω) = 151W
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Outline • Ideal Transformers • Transformer Equations – Voltage Transform – Current Transform – Resistance Transform
• Transformer Ratings • Real Transformers • Transformers and the Power Grid 24 August 2005
Engineer M S Ayubi
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Transformer Ratings 0.125 KVA; 230/115 VAC; 50/60 HZ
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Outline • Ideal Transformers • Transformer Equations – Voltage Transform – Current Transform – Resistance Transform
• Transformer Ratings • Real Transformers • Transformers and the Power Grid 24 August 2005
Engineer M S Ayubi
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Real Transformers • Internal power loss due to: – – – –
core loss core reluctance uncontained flux lines winding resistance
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Outline • Ideal Transformers • Transformer Equations – Voltage Transform – Current Transform – Resistance Transform
• Transformer Ratings • Real Transformers • Transformers and the Power Grid 24 August 2005
Engineer M S Ayubi
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The Power Grid
Diagram courtesy howstuffworks.com
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Power Grid
3-phase industrial
Intertie Power Plants Generator 0.5 – 5kV
Step-up Transformer
Generator 0.5 – 5kV
Step-up Transformer
Step-down Transformer
Substation Step-down Transformer 100-750 kV
Step-down Transformer
35-70 kV
4-15 kV
Step-down Transformer 120/240V residential
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Transmission Tower
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Incoming Power at Substation
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Incoming Power Conditioning
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Step-Down Transformers
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Transformer
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Outgoing Switch Banks
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Outgoing 3-Phase Power
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Utility Pole Carrying Three Phase
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Three Phase Transformers
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