INTRODUCTION TO ELECTRIC MACHINES - STS Proyectosstsproyectos.com/U/M/MAQ_01.pdf · INTRODUCTION TO...
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INTRODUCTION TO ELECTRIC MACHINES
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Magnetic circuits theory
Transformers
Most pictures come from Jesús Fraile Mora “Máquinas Eléctricas” 5ª ed. 2003, McGraw Hill
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MAGNETIC CIRCUITS THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
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• Magnetic field
• Magnetized materials
• H : magnetic field intensity (A/m)
• B : magnetic induction (T Tesla)
• μ : Magnetic permeability (H/m)
Remember:
• Diamagnetic μr ≈1
• Paramagnetic μr ≈1000
• Ferromagnetic μr ≫1000
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Magnetization curves of different ferromagnetic materials
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Magnetic hysteresis
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MAGNETIC CIRCUITS THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
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Ampere’s law:
Circulation of magnetic field H along a curve
[A· v]
ii
i
S
ii
i
H
iγ
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Ampere’s law:
Magnetomotive force (mmf)
ii
iii
B
i
S
γ
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Magnetic flux through S:
Number of magnetic force lines through any perpendicular surface S
Weber
Magnetic flux along a ferromagnetic core
Hopkinson’s coefficient:
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[A· v]
Combining equations:
Magnetic reluctance
Hopkinson’s law
Permeability
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Electric circuit Magnetic circuit
e : e.m.f. F : m.m.f.
j : current density (A/m) B : induction (T)
σ : conductivity (S/m) μ : permeability (H/m)
i : electric current (A) : magnetic flux (Wb)
V : electric potential (V) U : magnetic potential (AT)
E : electric field (V/m) H : magnetic field (AT/m)
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Electric circuit Magnetic circuit
H : intensidad de campo magnético A/m
Φ : flujo magnético o número de líneas de fuerza que atraviesan cada unidad
de superficie perpendicular a ellas
Φ = B S cosWeber Wb
μ : permeabilidad magnética H/m = (Wb/A) / m
B : inducción magnética o densidad de flujo magnético
B = μ HTesla T = H/m· A/m =
= (Wb/A)/m· A/m = Wb/m2
1 T = 10 000 Gauss
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Faraday’s law:
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MAGNETIC CIRCUITS THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
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Energy:
Steady state ( no movement)
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Energy:
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Energy:
Self inductance
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Hysteresys:
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Other core losses:
eddy currents (Foucault)
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Eddy current looses:
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Eddy current looses:
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MAGNETIC CIRCUITS THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current & magnetism
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v
i
R L
Self-inductance:
Magnetic flux:
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v
i
R LAlternative voltage:
c.a.
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Core with losses:
V
I
Iμ
IFe
Φ
ϕ
exc
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