EE155/255 Green Electronics - PDF Free Download

EE155/255 Green Electronics Electric Motors 10/19/16 Prof. William Dally Computer Systems Laboratory Stanford University

This week is flipped Course Logistics Discussion on 10/17, Motors on 10/19, Isolated Converters on 10/21 Solar day is Monday 10/24 HW 3 was due on 10/17 HW 4 out, due next Monday 10/24 Lab 3 must be checked off this week Lab 4 out this week

AH No Date Topic HW out HW in Lab out Lab ck Lab HW 1 9/26/16 Intro (basic converters) 1 1 Intro to ST32F3 Periodic Steady State 2 9/28/16 Embedded Prog/Power Elect. 3 10/3/16 Power Electronics - 1 (switches) 2 1 2 1 AC Energy Meter Power Devices 4 10/5/16 Power Electronics - 2 (circuits) 5 10/10/16 Photovoltaics 3 2 3 2 PV MPPT PV SPICE 6 10/12/16 Feedback Control 7 10/19/16 Electric Motors 4 3 4 3 Motor control Matlab Feedback 8 10/21/16 Isolated Converters 9 10/24/16 Solar Day 5/PP 4 5 4 Motor control - Lab/ Isolated Converters 10 10/26/16 Magnetics 11 10/31/16 Soft Switching 6 5/PP 6 5 PS Magnetics and Inverters 12 11/2/16 Project Discussions 13 11/7/16 Inverters, Grid, PF, and Batteries 6 P 6 Project 14 11/9/16 Thermal & EMI 15 11/14/16 Quiz Review C1 16 11/16/16 Grounding, and Debugging Q 11/16/16 Quiz - in the evening C2 11/21/16 Thanksgiving Break 11/23/16 Thanksgiving Break 17 11/28/16 18 11/30/16 Martin Fornage, enphase C3 19 12/5/16 Colin Campbell, Tesla 20 12/7/16 Wrapup TBD Project presentations P TBD Project webpage due

Course to Date We need sustainable energy systems Voltage converters PSSA, buck and boost Real circuits: losses, dead-time, snubbers PV cells characterized by a diode-like I-V curve PV systems 1f store energy, MPPT and invert Feedback control - PID Derivative looks ahead stabilizes Integral cancels residual error Actuators have limits EE155/255 Lecture 6 - Control

Motor Operation Motor Model Agenda Steady State and Transient Response Motor control with buck/boost Types of Motors Permanent magnet (PM) (brushed) Brushless permanent magnet (BLPM) AC Induction Radial vs axial flux Poles and phases

Motors and Generators are Everywhere Electric and Hybrid Cars Windmills and Hydro-Power Windows, door locks, Camera focus Printers Anywhere you need to convert between mechanical and electrical energy

Lorentz Force F = q(b x v)

In a Wire F = i(b x L)

Force is proportional to Current F = i(b x L)

Faraday Induction V = L (B x v)

Voltage is proportional to velocity V = L (B x v) This voltage pushes back on the current

Motors Just do this in a circle

Motor Equations V = L (B x v) V = K M w F = i(b x L) t = K M i t = I M (dw/dt) Simultaneously both a motor and a generator

Power is Conserved (mostly) P = VI P = (K M w)(t/k M ) P = wt

Models Develop mathematical expressions that predict behavior of physical (electrical and mechanical systems) Discard unnecessary detail to focus on the problem at hand

Motor Model L M R M + V B i M + - V =K =K i M -

Motor Model L M R M + V B i M + - V =K =K i M - Motor is characterized by four parameters Electrical: L M, R M Mechanical: I M Electro-mechanical: K M

Electrical: t E = L M /R M Two key time constants Mechanical: t M = R M I M /K M 2

Composite Model L M R M + i M + V M V =K M - 2 C M = I M /K M R F = 1/K F i L = L K M

Composite Model Angular Momentum Friction Energy output to shaft L M R M + i M + V M V =K M - 2 C M = I M /K M R F = 1/K F i L = L K M

Composite Model Combines electrical and mechanical properties Capacitor models inertia integrates t into w Resistor models friction of motor and load L M R M + i M + V M V =K M - 2 C M = I M /K M R F = 1/K F i L = L K M

Steady-State Response 0 Torque (Nm) max Anguar Velocity (rad/s) max

Steady-State Response t 0 = K M V B /R M 0 w max = V B /K M Torque (Nm) max t(w) = K M (V B -wk M )/R M Anguar Velocity (rad/s) max

Transient Response 70 60 50 (rad/s) 40 30 20 10 0 0 0.5 1 1.5 2 2.5 3 t (s)

Transient Response 70 60 (rad/s) 50 40 30 + V B - L M i M R M C M = I M K K E R L = K F /K V =K + - 20 Second order system 10 Time constant and damping factor depend on motor parameters 0 0 0.5 1 1.5 2 2.5 3 t (s)

Composite Model Motor is second order, but typically electrical time constant L/R << mechanical time constant (I M K F /K E ), so we can approximate it as a first-order system. L M R M + i M + V M V =K M - 2 C M = I M /K M R F = 1/K F i L = L K M

Need to Control the Motor Applying full battery voltage to a motor system with significant inertia will generally result in destructive currents R M is small milliohms Locked rotor current I LR = V B /R M is large 10 3-10 5 A Unless inertia is very low, sustained current will Destroy switching element (MOSFET or IGBT) Burn insulation off of windings Disconnect windings from brushes Fuse windings and wiring All of the above

Suppose I want to Apply 16V to the motor but all I have is a 48V battery?

What if we apply 48V 1/3 of the time and 0V 2/3 of the time? a/b L M R M + V B i M + - V =K =K i M -

What if we apply 48V 1/3 of the time and 0V 2/3 of the time? a/b i p i L i 0 t 0 t 1 t 2

How fast do we need to run to make current variation less than 10%?

How fast do we need to run to make current variation less Suppose L = 1mH than 1A

How fast do we need to run to make current variation less Suppose L = 1mH Need DI <= 1A than 1A DI = V(t/3)/L = (48V-16V)(t/3)/(1mH) = (10.7k)t = 1A T = 1A/10.7k ~ 94us

Motor Power Path i M 48V 34AH F 1 C 1 A M 2 R A M 1 CS S 1 S 2 M M 4 M 3 B B M 5 R L C Optional Load

Buck Converter Motor controller is just a buck converter Rotor winding is the inductor L Back-EMF sets the output voltage V E a V Batt + - L i L b + - V E

Regenerative Braking

Boost Converter b V E + - L i L a + - V Batt

Boost Waveforms a/b i p i L i 0 t 0 t 1 t 2

Brushed permanent magnet motors (PM) What we have been talking about so far Types of Motors PM on stator, windings on rotor switched by commutator Brushless permanent magnet motors (BLPM) Like PM but no brushes PM on rotor Use controller to commutate stator current AC voltage required on windings AC induction motors Rotor is shorted winding acts like a transformer Stator excites rotor and generates field Series and shunt wound DC motors Separate stator and rotor windings Radial and axial flux versions of all of the above

All Motors Look Like a Brushed PM Motor Inverter AC Induction Motor

All Motors Look Like a Brushed PM Motor Torque is proportional to current Velocity generates back EMF Inverter AC Induction Motor Only difference is need for inverter, electronic commutator or other power shaping electronics

Separate Motor Controller Design Brushed PM Controller + Inverter Combine redundant elements Inverter needs to estimate rotor position and/or velocity PM Controller Inverter AC Induction Motor Or Brushless PM

Brushless PM Motor 1 N 3 S 2

Consider Brushless PM as a Generator 1 Angle 0 is up (0,1) Phases at 0, 120, 240 degrees Field produced by rotor at angle q: B = (B 0 sinq, B 0 cosq) N f = BA = (B 0 Asinq, B 0 Acosq) 3 S 2 Voltage in phase i is df/dt at a i df(q)/dt = (B 0 Awcosq, -B 0 Awsinq) V(a) = df(q)/dtu(a) V(a) = -B 0 Awsin(q-a)

Back EMF 1 N V(a) = -Kwsin(q-a) Open-circuit voltage (back EMF) of each phase is a sinusoid that 3 S 2 Is proportional to w Reaches peak value when rotor is 90 degrees from phase.

Torque 1 N Current in winding i produces a field at angle a i Torque is effect of this field on the rotor at angle q t = -(Ki)sin(q-a i ) 3 S 2 Power is conserved tw = -w(ki)sin(q-a i ) = -(i)kwsin(q-a i ) = iv

Torque t = -(Ki)sin(q-a i ) 1 Torque is proportional to current N Torque is maximum when rotor is 90 degrees behind phase 3 S 2 Torque from each phase is sinusoidal

Rotating Stator Field 1 N Stator field is superposition of fields from each phase To generate a field at angle y apply current I i = cos(y-a i ) 3 S 2 To phase i Note currents sum to zero with evenly spaced phases

Sense rotor position Hall effect sensors Measure phase current and voltage Estimate position by fitting model Brushless PM Motors Stator creates rotating magnetic field Set angle at 90-degrees ahead of rotor to maximize torque May be effective 90 degrees in multi-pole arrangements Stator field rotates at same rate as rotor w s = w r Leads rotor by 90 degrees Q s = Q r + 90

Angle of Magnetic Fields Stator Field Rotor Field

3-F Inverter Power Path A B C 48V 34AH F 1 C 1 R CS A A B B C C

3-F Inverter Power Path Duty factor applied to phase i D i = D V x D i (q) Bipolar, D in [-1,1] -1 is 0%, 0 is 50%, 1 is 100% Level shift to make min 0% A B C 48V 34AH F 1 C 1 R CS A A B B C C

Brushless PM Motors

Example Stator from fan

Stator Outside

Animations of BLPM http://ironmaiden.awardspace.com/elektronik_files/4-pole-bldc-motor031102[1].swf http://www.ece.umn.edu/users/riaz/animations/brushlessdc.html

AC Induction Motor 3' 2 1 1' 2' 3 EE 155/255 Lecture 8 - Isolated Converters

Phase of Currents and Voltages V S I S V R I R I M EE 155/255 Lecture 8 - Isolated Converters

Equivalent Circuit L S R S L R + i S i R R R V S i M L M - stator rotor 1- R R Air Gap EE 155/255 Lecture 8 - Isolated Converters

Torque Calculations Developed power L S R S L R P = (1-s/s)I 2 R r + i M R R Torque V M L M 1-s s R R t = P/w = (1-s/s)I 2 R r /w r - Starting Torque t 0 = I 2 R r /w s 1 3 2

Torque and Efficiency 10 1 8 0.8 6 0.6 τ (Nm) ν 4 0.4 2 0.2 0 0 5 10 15 20 25 0 30 ω s (rad/s) EE 155/255 Lecture 8 - Isolated Converters

AC Induction Animation http://www.ece.umn.edu/users/riaz/animations/sqmoviemotgen.html http://www.ece.umn.edu/users/riaz/animations/sqmovies.html

Inverters BLPM and Induction motors both need 3-phase inverters 3-channel PWM half-bridge Control to synthesize desired phase angle BLPM sense (and estimate) rotor position set field to equal this position AC sense rotor velocity generate rotating field with desired slip

3-F Inverter Power Path A B C 48V 34AH F 1 C 1 R CS A A B B C C

3-F Inverter Power Path Duty factor applied to phase i D i = D V x D i (q) Bipolar, D in [-1,1] -1 is 0%, 0 is 50%, 1 is 100% Level shift to make min 0% A B C 48V 34AH F 1 C 1 R CS A A B B C C

Axial Flux and Radial Flux Motor Geometry

Poles and Phases A stator can be described as having P phases and N=kP poles. Rotating phases Q degrees rotates field Q/k degrees w s = kw m Number or rotor poles may differ to reduce camming

Summary + V B L M R M i M + - V =K =K i M Motors and generators ubiquitous Voltage is velocity, current is torque V = K M w, t = K M i = I M (dw/dt) Load curve and transient response Control motor with PWM Buck converter during drive Boost during braking (gen) BLPM requires rotating field Determine rotor angle Apply stator current for perpendicular fields In rotor reference field looks just like a brushed motor AC Induction motors Torque is function of slip Equivalent circuit Multiple poles w s = kw m 48V 34AH s = ω s ω r ω s F1 C1 RCS A A + V B - L M A B C B B C C + VM - - LS i M R M Torque (Nm) 0 max Stator Field im RS LM C M = I M K K E R L = K F /K Anguar Velocity Rotor Field LR RR RR 1-s s (rad/s) + V =K - max