Transcript Permanent-magnet motor-generator

Permanent-magnet motor-generator
or starter-generator Review & Renew
J. Philip Barnes 14 Sept 2015
• Any electric motor is a generator and vice versa
• “Motor-generator” applications: electric vehicles
• “Starter-gen.” applications: aircraft APUs/engines
• Assumed herein: “permanent magnet” behavior
– Classical brushed-DC, or typical 3-phase brushless
• Introduced herein: “4-constant equivalent DC” model
– Efficiency Vs. non-dim. speed, voltage, current, torque
– Predict motor-generator performance at any voltage
– New, fundamental, previously-unpublished formulas
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Brushed-DC motor-generator fundamental characteristics
(+) Charge (q) with velocity, V
in magnetic field of strength, B:
Force vector, F = q V x B
w
L
B
Fq
e
i
E
i
vi v
q
Fp
Motoring
Electromotive force, e
= potential energy / charge
= work / charge, (Fp / q) L
= 2 N w (D/2) B L
e = NDBL w ≡ k w
t
k =“EMF const.”
k = e/w = t/i
Volts/(rad/s)
or N-m/Amp
Torque, t
= 2N (D/2) B (dx/dt) dq
= 2N (D/2) B (dq/dt) dx
t = NDBiL = NDBL i = k i
Model aircraft:
“Kv” RPM/Volt
= 60/(2pk)
t
w
Fq
e
Change to generator mode:
Same direction, rotation, w
Same sign for EMF, e
Sign change of torque, t
Sign change of current, i
i
E
i
vi v
q
Fp
B
Generating
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“Equivalent-DC” brushless machine + inverter/rectifier
emg
R kw
i
InverterRectifier
eb
t = ki ±l
w
BLDC system has same characteristics of classic brushed-DC:
• 2-wire interface with the battery (or power source)
• Motor-generator EMF proportional to rotation speed, (w)
• Torque (t), +/- fixed loss (l), is proportional to current (i)
• System resistance (R) incl. batt., cables, & M-G windings
• “Battery” can be supercap., other gen., or power supply
• “Chopping loss” not included (Inverter at 100% duty cycle)
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Brushless motor with “six-pack” inverter-rectifier
VB
1
VB
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•
2
1
2
-7V 15V
3
3
Inverter converts 2-wire DC to 3-wire "AC“
Alternating transistor “diagonal pairs”
Commutation toggles each phase 0-to-VB
Relatively low frequency, 100% duty cycle
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Brushless generator with “six-pack” inverter-rectifier
Snapshot
e1 - e3 > eB
1
1
eB
Diodes provide
"free" regen!
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2
3
3
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M-G max delta EMF exceeds battery EMF
Six-pack rectifies 3-wire AC into 2-wire DC
Battery recharged through flyback diodes
IGBTs unidirectional: commutation ignored
~ “DC” current
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4-constant “Equivalent-DC” starter/motor-generator model
Phil Barnes Sept 2015
i
R
emg = kw
w
Motoring
eb
t=ki-l
i
R
emg = kw
w
eb
Generating
t = k i +l
Model accommodates motor, gen, or motor-gen
Model predicts M-G performance at any Voltage
Fixed torque loss (l) ≈ 0.8% of stall torque, keb/R
Torque loss and resistance (R) degrade efficiency
Neglecting losses, motor efficiency = EMF ratio
Neglecting losses, gen. efficiency = 1 / EMF ratio
Next chart: 4-constant model matches test data
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1. Definitions:
EMF ratio, n ≡ emg/eb
Fixed torque loss, l
EMF const., k = emg/w = (t+l)/i
System resistance, R
2. Simple circuit model:
Non-dim current, iR/eb = 1-n
System efficiency, h = tw/(ebi)
Combine circuit model EQs:
“4-const. Equiv. DC” model
motor: n < 1 - lR/(keb):
Generator: n > 1, h = ebi /(tw):
4-constant “Equivalent-DC” model matches test data
Starter/motor-generator system efficiency (h)
Brushed-DC or Brushless with inverter/rectifier Sys.
"4-const. EqDC" model, sys. resistance (R) & fixed torque loss (l)
eb = battery EMF, k = EMF constant, t = torque, w = rotation speed
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System efficiency,
tw/(ebi)
or
ebi/(tw)
0.9
0.8
0.7
GENERATING
LMCLTD.net
eb=48V / 3,600 RPM
k = 0.16 N-m/A
R = 0.041 Ohm
l, N-m ≈ 0.010 k eb / R
motor and battery
0.6
MOTORING
VisForVoltage.org
1-HP Scott motor
eb=24V / 15,000 RPM
k = 0.070 N-m/A
R = 0.054 Ohm
l, N-m ≈ 0.0065 k eb / R
generator & battery
ideal motor system
0.5
ideal generator sys.
test_data
0.4
0.2
4-constant EqDC model, generator
4-constant EqDC model, motor
0.1
Phil Barnes Sept 2015
0.3
0
0
0.2
0.4
0.6
0.8
1
1.2
n ≡ EMF ratio, emg /eb = k w /eb = speed ratio, w / (eb /k)
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1.4
1.6
4-constant “Equivalent-DC” model: Torque and Current
"4-const. equiv.-DC" model: Starter-gen
or motor-gen. system efficiency &
non-dim. speed, current, & torque
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0.9
0.8
0.7
0.6
Torque group,
tR/(keb) or
Current group,
i R / eb
0.5
0.4
0.3
Lines/curves: model
symbols: test data
0.2
0.1
GENERATING
LMCLTD.net
eb=48V / 3,600 RPM
k = 0.16 N-m/A
R = 0.041 Ohm
l, N-m ≈ 0.010 k eb / R
MOTORING
VisForVoltage.org
1-HP Scott motor
eb=24V / 15,000 RPM
k = 0.070 N-m/A
R = 0.054 Ohm
l, N-m ≈ 0.0065 k eb / R
Non-dimensional rotation speed: n = w / (eb
/k)
Non-dim. torque: t R / (k eb ) ≈ 1-n- l R/(keb )
Non-dim. current:
i R/eb = 1-n
Torque & current change sign, generator mode
n ≡ EMF ratio, emg /eb = k w /eb = speed ratio, w / (eb /k)
0
-0.1
-0.2
-0.3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
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0.9
1
1.1
1.2
1.3
Brushless machine commutation and speed control
Battery
Commutation “accommodates”
RPM, matching fields & magnets
Terminal
Voltage
ground
Whether or not the machine is “sensorless,” rotor
position or phase EMF is sensed for commutation
Pulse-width modulation (PWM),
superimposed on commutation,
indirectly “controls” speed by
chopping current, & thus torque
| t | | | dt
• Commutation “accommodates” the existing RPM
• Relatively low frequency, order ~100-1000 Hz
• PWM reduces speed via chopping at duty cycle (d)
• PWM is applied only to “upper” 6-pack IGBTs
• Relatively high frequency, order ~20 kHz
• Switching loss prompts alternate architectures
• Also, PWM is not well suited for regeneration
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DC boost architecture – increased capability and efficiency
Regen
233 Vdc in
Motor
VB
L
PWM
C
M-G
iGBT
5
10
15
20 kW
"Evaluation of 2004 Toyota Prius,"
Oakridge National Lab, U.S. Dept. of Energy
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DC boost architecture enables efficient bi-directional power
Age-old regen problem: reduced motor-gen RPM & EMF < battery
DC boost converter (DCBC) amplifies either battery or MG Voltage
Low-Voltage PWM duty cycle at IGBT gate sets DCBC Voltage gain
Highest system efficiency, with or without interest in regeneration
For starter-gen, DCBC is well suited to adjust torque-speed profile
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System efficiency and current with DC boost converter
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Get sys. efficiency & battery current for DC boost architecture
With the DCBC, current “gain” is inverse of Voltage gain (G)
Boost battery Voltage to motor ; otherwise boost MG Voltage
Say “half resistance (Rh)” resides up & downstream of DCBC
Solve for Voltage at node “a” to get battery current by mode
Efficiency has trends shown earlier, but Vs. ne ≡ Gmkw/(Gbeb)
ib = [eb Gb2- Gb kw] / [Rh (1+Gb2)] motoring
G ≡ DCBC voltage gain
Rh
ib
eb
a
Rh
Gb
ib = [kwGm - eb] / [Rh (1+Gm2)]
kw
ib /Gb
tw
Motoring
Rh
ib
eb
a
regeneration
Rh
Gm
kw
Gm ib
tw
Generating
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Summary: PM Motor-generator Review & Renew
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Assumed: “permanent-magnet-type” behavior
Review: Classic brushed-DC machine principles
Renew: Brushless + inverter/rectifier “Equiv. DC”
Review: “Six-pack” inverter & rectifier operation
Renew: New formulas for system efficiency
Renew: Non-dimensional speed, torque, current
Renew: New methods validated by test data
Review: “Chop” Vs. “DC boost” speed control
Renew: System efficiency & current with DCBC
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About the Author
Phil Barnes has a Master’s Degree in
Aero Engineering from Cal Poly Pomona
and BSME from the University of
Arizona. He is a 35-year veteran of air
vehicle, propulsion, and subsystems
performance analysis at Northrop
Grumman. Phil authored a “landmark”
study of dynamic soaring, and he is
pioneering the science of regenerative
electric flight. Author of numerous SAE,
AIAA, and other technical papers, he is
often invited to present travel-paid
lectures at various universities. The
charter of his free website is to apply
“green aero engineering” to help
prevent or delay extinction of the
wandering albatross.
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