L#6 Per Unit Calculations

# L#6 Per Unit Calculations - Per Unit Calculations Masoud...

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Per Unit Calculations Masoud Fathizadeh, PhD, PE Department of Engineering Technology Purdue Calumet Hammond, Indiana 46323

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Transformers Overview Power systems are characterized by many different voltage levels, ranging from 765 kV down to 220/110 volts. Transformers are used to transfer power between different voltage levels. The ability to inexpensively change voltage levels is a key advantage of ac systems over dc systems. In this section we’ll development models for the transformer and discuss various ways of connecting three phase transformers.
Ideal Transformer First we review the voltage/current relationships for an ideal transformer no real power losses magnetic core has infinite permeability no leakage flux We’ll define the “primary” side of the transformer as the side that usually receives power from a line etc, and the secondary as the side that usually delivers power to a load etc: primary is usually the side with the higher voltage, but may be the low voltage side on a generator step-up transformer.

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Ideal Transformer Relationships 1 1 1 2 2 12 1 1 2 2 1 2 1 1 1 2 2 2 Assume we have flux in magnetic material. Then flux linking coil 1 having turns is: , and similarly , = turns ratio m mm m N NN dd v N v N dt dt dt dt d v v V N a dt N N V N    Note that I 2 and I 2 are in opposite directions
Current Relationships ' 1 1 2 2 ' 1 1 2 2 ' 1 1 2 2 To get the current relationships use ampere's law with path around core having total length : mmf Assuming uniform flux density in the core having area , L d N i N i H L N i N i BL N i N i A        HL ' 1 1 2 2 then BA L N i N i A 

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Current/Voltage Relationships ' 1 1 2 2 ' 1 2 1 2 22 ' 1 2 1 2 1 2 12 If is infinite then 0 . Hence 1 or , where 1 Then: and: 0 1 0 N i N i i N i N ii N i N a i I Ia a VV II a        
Impedance Transformation Example Example: Calculate the primary voltage and current for an impedance load Z on the secondary 2 1 2 1 22 / and substituting: 0 1 0 a V V V I Z a I V Z    2 1 2 1 2 1 1 1 primary referred value of secondary load impedance

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## This note was uploaded on 10/01/2011 for the course ECET 331 taught by Professor Tim during the Summer '11 term at Purdue University-West Lafayette.

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L#6 Per Unit Calculations - Per Unit Calculations Masoud...

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