Overview Electrical Machines and
Drives
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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
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1
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)
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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
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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
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Flux density
∫ H ⋅τ d s = ∫∫ J ⋅ n d A
Cm
Sm
2H g lg = 2 N f I f
Bg =
µ0 N f I f
lg
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Flux density
• Sketch flux linkage of a
turn on the rotor
• Calculate the maximum
voltage induced in turn
from Faraday’s law
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Armature turn
voltage
At θ=0, the flux linkage is
minimum
dλ d
et =
= ∫∫ B ⋅ n d A
d t d t Se
d
= −l
dt
θ +π
∫θ B(θ )r dθ
dθ
dθ
− lrB(θ + π )
dt
dt
= 2lrB (θ )ω = 2lB(θ )v
= lrB (θ )
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Commutator as
rectifier
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Commutation
Commutating coil in
interpolar region: no
induced voltage
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Armature windings
• English: turn, coil, winding
• Dutch: winding, spoel, wikkeling
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Mechanical and electrical angles
p
θe = θm
2
p
ωe = ωm
2
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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)
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Armature voltage
An armature winding has N turns
with a parallel paths
and therefore N/a series-connected turns
For the turn voltage, we found
et = 2lrωm B(θ )
The average is lower:
Flux per pole
et = 2lrωm B (θ )
Φ = ∫∫ B ⋅ n d A = l
2π / p
∫ B(θ )r d θ =
0
Using this, the turn voltage is given by
Therefore
et =
p
π
2π
rlB (θ )
p
Φω m
N
Np
Ea = et =
Φω m = K a Φω m
a
πa
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Voltage and torque from power
balance
d Ia
U = RI a + L
+ K a Φ ωm
dt
d Ia
2
P = UI a = RI a + I a L
+ I a K a Φωm
dt
Power balance:
P = P Cu + Pf + Pmech
Therefore
T=
Pmech
ωm
= K a ΦI a
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Electromagnetic torque from Lorenz
Ia
Fc = B(θ )lI c = B(θ )l
a
Ia
Tc = rFc = B(θ )rl
a
Ia
p
Tc = B (θ )rl =
ΦI a
a 2πa
Np
T = 2 NTc =
ΦI a = K a ΦI a
πa
P = ωmT = ωm K a ΦI a = Ea I a
Lorenz force gives the same result as power balance.
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Magnetic circuit
Which part saturates first?
Why?
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Magnetization curve
Why is this not a straight line?
Why does it not start from zero?
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DC Machines
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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)
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Armature reaction
• Section 4.3 (Sen) has the title “DC generators”
• DC machines are hardly used as generators
• The operating principles are the same in motoring and
generating
• Therefore, we only look at constructional aspects of DC
machines discussed in 4.3, which are present in DC motors as
well as in DC generators:
• compensating winding (Dutch: compensatiewikkeling)
• interpoles (Dutch: hulppolen)
• Both are related to armature reaction
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Armature reaction
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Consequences
armature
reaction
• Saturation
• Commutation problems
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Compensation winding
• Saturation problem reduced
• Expensive; only applied in machines that are often heavily loaded.
Why in these machines?
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Interpoles
Armature reaction
produces a flux
density in the
interpolar region, so
that a voltage is
induced in the
commutating coil.
This voltage opposes
commutation.
Interpoles reverse the
direction of this flux
density to induce a
voltage that
accelerates
commutation.
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DC Machines
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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)
• Connections of DC machines
• Separately excited DC machine
• Series connected DC machine
• DC machine drives (4.5)
• PMDC machines / PCB machines (4.6, 4.7)
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Connections of DC machines
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Separately excited DC machines
Pole flux does not depend on
armature voltage and load
T = K a ΦI a
Ea = ω m K a Φ
U t = Ra I a + Ea
Ra I a
RaT
U
U
ωm =
−
=
−
K a Φ K a Φ K a Φ ( K a Φ) 2
How to control speed?
Calculate no-load speed and stall torque.
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Torque speed characteristic
• Where are motor, generator and plugging operation?
• Speed control by means of
• Voltage control: what happens if the voltage is increased?
• Field control: what happens if the current is increased?
• Resistance control: old-fashioned
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Voltage control
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Field control
Are the
characteristics
of (c) parallel?
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Series DC machine (universal motor)
Φ = K1 I a
T = K a ΦI a = K a K1 I a2
Neglecting saturation!
What happens to the speed when the torque is zero?
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Series DC motor
Φ = K1 I a
T = K a ΦI a = K a K1 I a2
U t = Ra I a + Ea = Ra I a + K a Φωm = Ra I a + K a K1 I aωm
Ut
Ia =
Ra + K a K1ωm
2
U
t
T = K a ΦI a = K a K1 I a2 = K a K1
( Ra + K a K1ωm ) 2
Ut
Ra
ωm = ±
−
K a K1T K a K1
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DC machines
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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)
• Ward-Leonard system
• Power electronics (Rectifier, Chopper)
• Closed loop control
• PMDC machines / PCB machines (4.6, 4.7)
Challenge the future
32
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
Challenge the future
33