Post on 29-Dec-2015
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Permanent-magnet motor-generatoror 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 speed, voltage, current, torque– Predict motor-generator performance at any voltage– New, fundamental, previously-unpublished formulas
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e
t
w
E
N turns
Generating
i
vi vq
Fp
Fq
B
iChange to generator mode:Same direction, rotation, wSame sign for EMF, e Sign change of torque, t Sign change of current, i
Electromotive force, e= potential energy / charge= work / charge, (Fp / q) L= 2 N w (D/2) B L e = NDBL w ≡ k w
Torque, t = 2N (D/2) B (dx/dt) dq = 2N (D/2) B (dq/dt) dxt = NDBiL = NDBL i = k i
(+) Charge (q) with velocity, V in magnetic field of strength, B:Force vector, F = q V x B
e
tw
E
N turns
Motoring
B
i
vi vq
Fp
Fqi
L
Brushed-DC motor-generator fundamental characteristics
k =“EMF const.”k = /e w = t/iVolts/(rad/s)or N-m/Amp
Model aircraft: “Kv” RPM/Volt
= 60/(2pk)
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“Equivalent DC” machine
eb
iInverter-Rectifier
= t ki ±l
w
emg
kwR
“Equivalent-DC” brushless machine + inverter/rectifier
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
• 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
VB
VB
12
3
1
2
3-7V 15V S
N
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Brushless generator with “six-pack” inverter-rectifier
eB
12
3
• 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
Snapshote1 - e3 > eB
1
2
3
~ “DC” current
Diodes provide"free" regen!
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i
= t k i - l
w
eb
R emg = kw
Motoring
i
= t k i +l
w
eb
R emg = kw
Generating
Phil Barnes Sept 2015
4-constant “Equivalent-DC” starter/motor-generator model
1. Definitions:EMF ratio, n ≡ emg/eb
Fixed torque loss, lEMF const., k = emg/w = ( +t l)/iSystem resistance, R
2. Simple circuit model:Non-dim current, iR/eb = 1-nSystem efficiency, h = tw/(ebi)
Combine circuit model EQs:“4-const. Equiv. DC” modelmotor: n < 1 - lR/(keb):
Generator: n > 1, h = ebi /(tw):
Model accommodates motor, gen, or motor-genModel predicts M-G performance at any VoltageFixed torque loss (l) ≈ 0.8% of stall torque, keb/RTorque loss and resistance (R) degrade efficiencyNeglecting losses, motor efficiency = EMF ratioNeglecting losses, gen. efficiency = 1 / EMF ratioNext chart: 4-constant model matches test data
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System efficiency,tw/(ebi)
orebi/(tw)
n ≡ EMF ratio, emg /eb = k w /eb = speed ratio, w / (eb /k)
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
motor and battery
generator & battery
ideal motor system
ideal generator sys.
test_data
, l N-m ≈ 0.0065 k eb / R
GENERATINGLMCLTD.neteb=48V / 3,600 RPMk = 0.16 N-m/AR = 0.041 Ohm
MOTORINGVisForVoltage.org1-HP Scott motoreb=24V / 15,000 RPMk = 0.070 N-m/AR = 0.054 Ohm
4-constant EqDC model, motor 4-constant EqDC model, generator
, l N-m ≈ 0.010 k eb / R
Phil
Barn
es S
ept 2
015
4-constant “Equivalent-DC” model matches test data
Ideal motorin
g =
h
n Ideal generating = 1/h
n
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Torque group, tR/(keb) or
Current group,i R / eb
n ≡ EMF ratio, emg /eb = k w /eb = speed ratio, w / (eb /k)
"4-const. equiv.-DC" model: Starter-genor motor-gen. system efficiency & non-dim. speed, current, & torque
4-constant “Equivalent-DC” model: Torque and Current
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-nTorque & current change sign, generator mode
, l N-m ≈ 0.0065 k eb / R
GENERATINGLMCLTD.neteb=48V / 3,600 RPMk = 0.16 N-m/AR = 0.041 Ohm
MOTORINGVisForVoltage.org1-HP Scott motoreb=24V / 15,000 RPMk = 0.070 N-m/AR = 0.054 Ohm , l N-m ≈ 0.010 k eb / R
Current group, i R/eb
Torque group, t R/(keb )
Motor eff., tw/(e b
i)
Gen eff., eb i/(tw)
Lines/curves: modelsymbols: test data
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Brushless machine commutation and speed control
Commutation “accommodates” RPM, matching fields & magnets
TerminalVoltage
Battery
ground
Pulse-width modulation (PWM),superimposed on commutation, indirectly “controls” speed bychopping current, & thus torque
Whether or not the machine is “sensorless,” rotor position or phase EMF is sensed for commutation
• 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
| |
dt| t |
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DC boost architecture – increased capability and efficiency
"Evaluation of 2004 Toyota Prius,"Oakridge National Lab, U.S. Dept. of Energy
233 Vdc in
5 10 15 20 kW
Regen
M-G
Motor
PWMiGBT
CL VB
• 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
ib /Gb
tw
Gb
Rh kw
eb
Rh
ib
a
Motoring
Gm ib
tw
Gm
Rh kw
eb
Rh
ib
a
Generating
ib = [eb Gb2- Gb kw] / [Rh (1+Gb
2)] motoring
ib = [kwGm - eb] / [Rh (1+Gm2)] regeneration
G ≡ DCBC voltage gain
• 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)
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Summary: PM Motor-generator Review & Renew
• 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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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.
About the Author