Post on 04-Jun-2018
transcript
1Challenge the future
Overview Electrical Machines and
Drives
• 7-9 1: Introduction, Maxwell’s equations, magnetic circuits
• 11-9 1.2-3: Magnetic circuits, Principles
• 14-9 3-4.2: Principles, DC machines
• 18-9 4.3-4.7: DC machines and drives
• 21-9 5.2-5.6: IM introduction, IM principles
• 25-9 Guest lecture Emile Brink
• 28-9 5.8-5.10: IM equivalent circuits and characteristics
• 2-10 5.13-6.3: IM drives, SM
• 5-10 6.4-6.13: SM, PMACM
• 12-10 6.14-8.3: PMACM, other machines
• 19-10: rest, questions
• 9-11: exam
2Challenge the future
Organisation 3
• Laboratory work:
• 3 half days between 17 September and 3 November
• DC machines, IM and SM
• In groups of up to 8 students
• Register via blackboard
• 17 (morning), 17 (afternoon), 20 (afternoon) Sept for DCM
• 24 (morning), 24 (afternoon), 27 (afternoon) Sept for DCM
• 1 (morning), 1 (afternoon), 4 (afternoon) Oct for IM
• 8 (morning), 8 (afternoon), 11 (afternoon) Oct for IM
• 15 (morning), 15 (afternoon), 18 (afternoon) Oct for SM
• 22 (morning), 22 (afternoon), 25 (afternoon) Oct for SM
3Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
4Challenge the future
Electromagnetic energy conversion
(4.1)
5Challenge the future
Induced voltage
BlvE =
6Challenge the future
Lorentz force
BliF =
FvBlviEiP ===Power balance holds:
)( BvEqF����
×+=
7Challenge the future
Lorentz force
8Challenge the future
Lorenz force, induced voltage
• Generally not valid when iron is present
• Sometimes dangerous, only valid if flux linkage changes
• Safe way of calculating voltage: from flux linkage
• Safe way of calculating forces: power or energy balance
tNRi
tRiu
d
d
d
d Φ+≈+= λ
9Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
10Challenge the future
Energy or power balance
Electrical energy input
Mechanical energy output
Increase stored energy
Energylosses
= + +
11Challenge the future
Energy balance
eWd
fWd
Electrical energy input
- resistance losses
Mechanical energy output
+ friction, windage losses
Increase stored energy+ core losses
= +
mechWdis the electrical energy input during dtis the mechanical energy output during dtis the change in stored field energy (core loss neglected)
2 2dd ( )d (( ) )d d
deW ui Ri t Ri i Ri t it
λ λ= − = + − =
d dmech mechW f x=
d d de mech fW W W= +
d d dmech fi f x Wλ = +
12Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
13Challenge the future
Magnetic field energy
14Challenge the future
Calculation of magnetic field energy
Movable part is kept stationary
d d df eW W i λ= = dfW iλ
λ= ∫
15Challenge the future
Example calculation of magnetic
energy
d dm mC S
H s J n Aτ⋅ = ⋅∫ ∫∫� �� �
� c c g gH l H l Ni+ =
NBAλ =
d d d dB B B
g g c cf g g c c
H l H lW i NA B Al H B Al H B
N
λ
λ+
= = = +∫ ∫ ∫ ∫
Using
and
In case of linear core material 0c r cB Hµ µ=2 2
0 0
0.199 0.002J2 2f g c
r
B BW Al Al
µ µ µ= + = +
Energy mainly in air gap !
B = 1 T
μr = 5000
μ0 = 4π10-7 H/m
lc = 0.2 m
lg = 5 mm
Ac = 1 cm2
lg is total air gap lengthlc is total core length
16Challenge the future
Coenergy
dfW iλ
λ= ∫ di
fW iλ′ = ∫ f fW W iλ′+ =
17Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
18Challenge the future
Calculation of force from (co)energy
d d d d d( ) d dmech f f ff x i W i i W W iλ λ λ λ′ ′= − = − − = −
constant
fmech
i
Wf
x =
′∂=
∂ constant
fmech
Wf
x λ=
∂= −
∂
19Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
20Challenge the future
Calculation of reluctance force
dd d
d d dfe mech
WW W
t t t= +
2 2 2d d d ( ) d ( ) d d( ) ( )
d d d d d deW L x i L x x i
ui Ri i Ri Ri i i iL xt t t x t t
λ= − = + − = = +
d d
d dmech
mech mech
W xP f
t t= =
2122
d d ( ) d 1 d ( ) d( )
d d d 2 d dfW L x i i L x x
iL x it t t x t
= = +
21 d ( )
2 dmech
L xf i
x=
Power balance:
Conclusion:
ixL )(=λ
21Challenge the future
Reluctance force from (co)energy
2 2
constant
1 1 d ( )( )
2 2 df
mech
i
W L xf L x i i
x x x=
′∂ ∂ = = = ∂ ∂
2 2
2
constant
d ( )
2 ( ) 2 ( ) df
mech
W L xf
x x L x L x xλ
λ λ
=
∂ ∂= − = = − ∂ ∂
Force �tries to increase inductance�tries to close the gap
22Challenge the future
Reluctance force, magnetic pressure
21 d ( )
2 dmech
L gf i
g=
20( )2
gA NL g
g
µ=
2 20
24g
mech
i A Nf
g
µ= −
0
2 2 gg
BNi gH g
µ= =
2
0
22mech g
Bf A
µ= −Using gives
What is a realistic value of the force density?
23Challenge the future
Error in form of force
• Do you see the error in the form
of the force?
24Challenge the future
Rotating machines with saliency
(3.4)
0=ri
2 d1
2 dss
mech s
LT i
θ=
Torque �tries to increase self-inductance�tries to close the gap
25Challenge the future
Cylindrical rotating machines (3.5)
d d
d dsr
mech s r s r
L MT i i i i
θ θ= =
Torque �tries to increase mutual inductance�tries to align the fields of stator and rotor
26Challenge the future
Principles of electromechanics (3)
• Lorentz force, induced voltage (4.1)
• Energy or power balance (3.1)
• Energy and coenergy (3.2)
• Calculation of force from (co)energy (3.3)
• Application to actuators and rotating machines (3.4, 3.5)
27Challenge the future
Overview Electrical Machines and
Drives
• 7-9 1: Introduction, Maxwell’s equations, magnetic circuits
• 11-9 1.2-3: Magnetic circuits, Principles
• 14-9 3-4.2: Principles, DC machines
• 18-9 4.3-4.7: DC machines and drives
• 21-9 5.2-5.6: IM introduction, IM principles
• 25-9 Guest lecture Emile Brink
• 28-9 5.8-5.10: IM equivalent circuits and characteristics
• 2-10 5.13-6.3: IM drives, SM
• 5-10 6.4-6.13: SM, PMACM
• 12-10 6.14-8.3: PMACM, other machines
• 19-10: rest, questions
• 9-11: exam
28Challenge the future
DC machines
• Introduction, construction (4.2)
• Principle of operation and basic calculations (4.2)
• Armature reaction, interpoles, compensating winding (4.3)
• Characteristics, means to control speed (4.4)
• DC machine drives (4.5)
• PMDC machines / PCB machines (4.6, 4.7)
29Challenge the future
Basic construction elements
• slots• cylindrical rotor
• salient pole rotor
• stator• rotor• teeth
30Challenge the future
Stator and rotor laminations
31Challenge the future
DC machine introduction
• history: loader for accumulators, moving coil in magnetic field
• generates DC voltage in generating operation
• operates on a DC voltage in motoring operation
• has many applications in controlled drives and traction
• reason: easy to control
• importance decreasing because induction machines with VSI are
cheaper and more robust
32Challenge the future
DC machine construction
• stator: yoke, pole, field winding• rotor / armature: teeth, slots, armature winding• commutator
33Challenge the future
Cutaway views of
DC machines
34Challenge the future
DC machine characteristics
• rotor is cylindrical with slots (except at very small power)
• stator has salient poles with field windings or permanent
magnets
• the number of poles may be larger than two (but even)
• the rotor is laminated
• the excitation current is a dc current, resulting in a constant
excitation field
• the excitation current is provided by
• a separate source (separately excited dc machine)
• the armature voltage (shunt dc machine)
• the armature current (series dc machine)
35Challenge the future
DC machines
• Introduction, construction (4.2)
• Principle of operation and basic calculations (4.2)
• air gap flux density (1.1)
• armature turn voltage and commutation (4.2.2)
• armature windings (4.2.3)
• total armature voltage (4.2.4)
• torque (4.2.5)
• magnetisation curve (4.2.6)
• Armature reaction, interpoles, compensating winding (4.3)
• Characteristics, means to control speed (4.4)
• DC machine drives (4.5)
• PMDC machines / PCB machines (4.6, 4.7)
36Challenge the future
Assumptions for calculations
• steady state (mechanical and electrical)
• the air gap is so small that the flux density does not change in
radial direction
• the air gap is so small that the flux density crosses the air gap
perpendicular
• iron losses are negligible
• the magnetic permeability of iron is infinite
37Challenge the future
Air gap flux density
• The field winding around one pole has Nf turns and carries a
current If
• Calculate the air gap flux density between the poles and the rotor
38Challenge the future
Flux density
d dm mC S
H s J n Aτ⋅ = ⋅∫ ∫∫� �� �
�
2 2g g f fH l N I=
0 f fg
g
N IB
l
µ=
39Challenge the future
Armature turn voltage
• Sketch flux linkage of a turn on the rotor
• Calculate the maximum voltage induced in turn from Faraday
40Challenge the future
DC Machines
• Introduction, construction (4.2)
• Principle of operation and basic calculations (4.2)
• air gap flux density (1.1)
• armature turn voltage and commutation (4.2.2)
• armature windings (4.2.3)
• total armature voltage (4.2.4)
• torque (4.2.5)
• magnetisation curve (4.2.6)
• Armature reaction, interpoles, compensating winding (4.3)
• Characteristics, means to control speed (4.4)
• DC machine drives (4.5)
• PMDC machines / PCB machines (4.6, 4.7)
41Challenge the future
Overview Electrical Machines and
Drives
• 7-9 1: Introduction, Maxwell’s equations, magnetic circuits
• 11-9 1.2-3: Magnetic circuits, Principles
• 14-9 3-4.2: Principles, DC machines
• 18-9 4.3-4.7: DC machines and drives
• 21-9 5.2-5.6: IM introduction, IM principles
• 25-9 Guest lecture Emile Brink
• 28-9 5.8-5.10: IM equivalent circuits and characteristics
• 2-10 5.13-6.3: IM drives, SM
• 5-10 6.4-6.13: SM, PMACM
• 12-10 6.14-8.3: PMACM, other machines
• 19-10: rest, questions
• 9-11: exam