EE2191 – Electrical Machines
Transformers
Chamali Gamage
Department of Electrical and Electronic Engineering
University of Sri Jayewardenepura
Real Transformers
• Magnetization current
• Flux leakage from windings
• Losses in the core
• Resistance in the winding
Equivalent circuit for a real transformer
Simplification of the equivalent circuit
Simplified equivalent circuit
Voltage Regulation
Quantity that describes the degree of constancy of the output
voltage
𝐸𝑁𝐿 − 𝐸𝐹𝐿
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 =
𝑋 100
𝐸𝐹𝐿
Where,
𝐸𝑁𝐿 = Secondary voltage at no-load (V)
𝐸𝐹𝐿 = Secondary voltage at full load (V)
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Efficiency of a transformer
PO = Output real power
PI = Iron losses (Fixed losses)
PC = Copper losses
𝑃𝑂
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 η =
𝑃𝑂 + 𝑃𝑖 + 𝑃𝐶
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All Day Efficiency of a Transformer
𝑂𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝑘𝑊ℎ 𝑑𝑢𝑟𝑖𝑛𝑔 𝑎 𝑑𝑎𝑦
% 𝐴𝑙𝑙 𝑑𝑎𝑦 η =
𝑥 100
𝐼𝑛𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝑘𝑊ℎ 𝑑𝑢𝑟𝑖𝑛𝑔 𝑎 𝑑𝑎𝑦
𝑂𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦 𝑖𝑛 𝑘𝑊ℎ 𝑑𝑢𝑟𝑖𝑛𝑔 𝑎 𝑑𝑎𝑦
= 𝑂𝑢𝑡𝑝𝑢𝑡 𝑒𝑛𝑒𝑟𝑔𝑦+𝐸𝑛𝑒𝑟𝑔𝑦 𝑠𝑝𝑒𝑛𝑡 𝑓𝑜𝑟 𝑡𝑜𝑡𝑎𝑙 𝑙𝑜𝑠𝑠𝑒𝑠 𝑥
100
Energy spent on iron core loss =𝑃𝑖 x total time transformer is energized
Energy spend on copper losses =
𝐿𝑜𝑎𝑑 𝐾𝑉𝐴 2
(
) 𝑃𝐶𝑢 𝐹𝐿 x
𝐾𝑉𝐴 𝑟𝑎𝑡𝑖𝑛𝑔
(total time of consumption)
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Autotransformers
𝑁2
𝐸2 =
𝐸1
𝑁1
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Autotransformer under load
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Current across BC = 𝐼1
Current across AC =𝐼2 − 𝐼1
mmf produced by 𝐼1 must be equal and opposite to the mmf produced by 𝐼2 − 𝐼1
Therefore
𝐼1 (𝑁1 − 𝑁2 ) = (𝐼2 − 𝐼1 ) 𝑁2
𝐼1 𝑁1 = 𝐼2 𝑁2
Assumptions
Both transformer losses and exciting current are negligible
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑝𝑜𝑤𝑒𝑟 𝑑𝑟𝑎𝑤𝑛 𝑏𝑦 𝑡ℎ𝑒 𝑙𝑜𝑎𝑑
= 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑝𝑜𝑤𝑒𝑟 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑠𝑜𝑢𝑟𝑐𝑒
𝐸1 𝐼1 = 𝐸2 𝐼2
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