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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 speed, voltage, current, torque– Predict motor-generator performance at any voltage– New, fundamental, previously-unpublished formulas

www.HowFliesTheAlbatross.com2

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)


“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)


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


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!


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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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

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


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 |


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


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)


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


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

www.howfliesthealbatross.com permanent-magnet motor-generator or starter-generator review &...

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