INTRODUCTION TO ELECTRIC MACHINES
1 Magnetic circuits theory
Most pictures come from Jesús Fraile Mora “Máquinas Eléctricas” 5ª ed. 2003, McGraw Hill
1
MAGNETIC CIRCUITS 1 THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
2 MAGNETIC MATERIALS Remember: • Magnetic field • Magnetized materials • H : magnetic field intensity (A/m) • B : magnetic induction (T Tesla) • µ : Magnetic permeability (H/m)
• Diamagnetic 0 ≤ µr < 1
• Paramagnetic µr ≈1000
• Ferromagnetic µr ≫1000
3 MAGNETIC MATERIALS
Magnetization curves of different ferromagnetic materials
4 MAGNETIC MATERIALS
Magnetic hysteresis
5
MAGNETIC CIRCUITS 1 THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
6 MAGNETIC CIRCUITS
Ampere’s law:
Every electric current I creates a magnetic field B
7 MAGNETIC CIRCUITS Ampere’s law:
Magnetic field created by a loop wired current
8 MAGNETIC CIRCUITS Ampere’s law:
S H N
Magnetic field created by a solenoid (coil)
9 MAGNETIC CIRCUITS
Ampere’s law: i H
[A· v] i i γ Circulation of magnetic field S H along a curve
10 MAGNETIC CIRCUITS
Ampere’s law: i B
i i
γ Magnetomotive force (mmf) S
11 MAGNETIC CIRCUITS Magnetic flux through S: Number of magnetic force lines through any perpendicular surface S Weber
Hopkinson’s coefficient:
Magnetic flux along a ferromagnetic core
12 MAGNETIC CIRCUITS Combining equations: [A· v]
Magnetic reluctance Permeability
Hopkinson’s law
13 MAGNETIC CIRCUITS
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) R : electric resistance (Ω) R : magnetic reluctance (H-1) E : electric field (V/m) H : magnetic field (A/m)
14 MAGNETIC CIRCUITS Magnitude Units
H : intensidad de campo magnético A/m
Φ : flujo magnético o número de líneas Φ = B S cos de fuerza que atraviesan cada unidad Weber Wb de superficie perpendicular a ellas
µ : permeabilidad magnética H/m = (Wb/A) / m
B = µ H B : inducción magnética o densidad de Tesla T = H/m· A/m = flujo magnético = (Wb/A)/m· A/m = Wb/m2 1 T = 10 000 Gauss
15 MAGNETIC CIRCUITS
16 MAGNETIC CIRCUITS
Faraday’s law:
17 MAGNETIC CIRCUITS
Faraday’s law:
18 MAGNETIC CIRCUITS
Faraday’s law:
19
MAGNETIC CIRCUITS 1 THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current and magnetism
20 MAGNETIC ENERGY
Energy:
Steady state ( no movement)
21 MAGNETIC ENERGY Hysteresys:
22 MAGNETIC ENERGY Other core losses: eddy currents (Foucault)
23 MAGNETIC ENERGY Eddy current looses:
24 MAGNETIC ENERGY
Eddy current looses:
25
MAGNETIC CIRCUITS 1 THEORY
• Magnetic materials
• Magnetic circuits
• Magnetic energy
• Alternative current & magnetism
26 AC & MAGNETISM
R L
i
v
Self-inductance:
Magnetic flux:
27 AC & MAGNETISM Alternative voltage: R L
i
v
2 V N i = Φ R ; N i = R m m m N ω
c.a.
28 AC & MAGNETISM Core with losses:
IFe ϕ V
Iµ
Iexc
Φ
29