EE155/255 Green Electronics
Power CircuitsPhotovoltaics
10/5/16
Prof. William DallyComputer Systems Laboratory
Stanford University
Course Logistics• HW2 due Monday 10/10• Lab1 signed off this week• Lab2 out
EE155/255 Lecture 4 - Power Circuits
Course to Date• We need sustainable energy systems• At the core they are voltage converters• Periodic steady-state analysis, buck and boost• Intelligent control + power path• Intelligent control done with event-driven embedded software• Real devices have switching and conduction loss
EE155/255 Lecture 4 - Power Circuits
Last Time• DC and AC characteristics of MOSFETs, Diodes, and IGBTs• Switches in pairs• One switch does the work• Turn on transient• Diode reverse recovery• Parasitics• Gate drive and Miller capacitance• “Dead time” and “shoot through”
EE155/255 Lecture 4 - Power Circuits
Review - Turn-On Loss
EE155/255 Lecture 4 - Power Circuits
IP
ILQRR QD
ID
VDS
s
t1 t2 t3
Review - Effect of Miller Cap on Rise Time
M1
iG
CDG
dVDdt
=iGCDG
Δt = ΔVDCDG
iG
Example: iG = 0.5A, C = 100pF, DV = 400V
EE155/255 Lecture 4 - Power Circuits
Snubbers
EE155/255 Lecture 4 - Power Circuits
LD
G 50V
+-
40A
RS
CS
D
Cj
M
Dampen Ringing Nodes
LD and Cj resonate when M is on
Parallel RS dampens tank
Series CS limits dissipation
EE155/255 Lecture 4 - Power Circuits
Inductance on Drain
8uJ turn-on
42uJ turn-off
EE155/255 Lecture 4 - Power Circuits
With Snubber (1nF, 5W)
8uJ turn-on
2uJ in snubber
42uJ turn-off
EE155/255 Lecture 4 - Power Circuits
LD
G 50V
+-
40A
RS
CS
D
Cj
M
Design Procedure
Pick RS ~ 1/wCj
Pick CS so t >= p/w
OrEs = CSV2/2
EE155/255 Lecture 4 - Power Circuits
G 50V+-
40A
RS
CS
D
M
DS
Move Turn-Off Dissipation to Passive Device
CS slows rise time of drain
CSV2/2RS dissipated in RS when CS discharges
Rarely used today
Other forms slow fall time and rising/falling currentEE155/255 Lecture 4 - Power Circuits
Critical Loop
EE155/255 Lecture 4 - Power Circuits
Critical Loop
EE155/255 Lecture 4 - Power Circuits
M1G1
ii
M2
V1
+-
G2
(a)
M1G1
M2G2
V1
+-
(b)
Lab Half-Bridge Module
EE155/255 Lecture 4 - Power Circuits
The Half-Bridge Module
1
2
Hin
IRS21834
ComVss
LO
S
HO
COM
Out
VDVB
M1
M2
R14.7
R24.7
U1
����
VCC
3
DT
GND
4
Hin
����
V12
C14.7 F
2.2 F200V
D356V5W
D1
R3 1
C21 F
VBCSupply
VDCFilter
D215V
C3
7
6
5
13
12
11
EE155/255 Lecture 4 - Power Circuits
Bootstrap Supply
1
2
Hin
IRS21834
ComVss
LO
S
HO
COM
Out
VDVB
M1
M2
R14.7
R24.7
U1
����
VCC
3
DT
GND
4
Hin
����
V12
C14.7 F
2.2 F200V
D356V5W
D1
R3 1
C21 F
VBCSupply
VDCFilter
D215V
C3
7
6
5
13
12
11
EE155/255 Lecture 4 - Power Circuits
Bootstrap Supply
EE155/255 Lecture 4 - Power Circuits
Drain Voltage Filter
1
2
Hin
IRS21834
ComVss
LO
S
HO
COM
Out
VDVB
M1
M2
R14.7
R24.7
U1
����
VCC
3
DT
GND
4
Hin
����
V12
C14.7 F
2.2 F200V
D356V5W
D1
R3 1
C21 F
VBCSupply
VDCFilter
D215V
C3
7
6
5
13
12
11
EE155/255 Lecture 4 - Power Circuits
Drain Voltage Filter300nH Input Inductance
EE155/255 Lecture 4 - Power Circuits
SPICE
EE155/255 Lecture 4 - Power Circuits
SPICE Example – A Voltage Doubler
EE155/255 Lecture 4 - Power Circuits
A Voltage Doubler* Simple voltage "doubler".include "gel.lib".param td=100n tr=100n tf=100n tw=2.5u tcy=5u ncy=2.param l1=22uH c1=10uF r1=10
* call half-bridge subcircuitxhb vd mid g g 0 v12 gel_hb
* circuitl1 vin mid {l1}c1 vd 0 {c1}r1 vd 0 {r1}
* suppliesv12 v12 0 12vin vin 0 24
* stimulusVG g 0 PULSE(0 5 {td} {tr} {tf} {tw} {tcy} {ncy})
.ic i(l1)=9.2
.ic v(vd)=42.8
.tran {ncy*tcy}
EE155/255 Lecture 4 - Power Circuits
Turn-On Transient
EE155/255 Lecture 4 - Power Circuits
Steady State
EE155/255 Lecture 4 - Power Circuits
Close up of Drain Current
EE155/255 Lecture 4 - Power Circuits
With PID Control
EE155/255 Lecture 4 - Power Circuits
A Warning• SPICE (or any simulator) is a Verification tool, not a Design tool• Design your circuit first
– Use Excel, Matlab, a calculator etc… to calculate component values• Then simulate your circuit to check operation and fine-tune parameters• Don’t try to design your circuit using SPICE
• Simulation is not a substitute for thinking
EE155/255 Lecture 4 - Power Circuits
Summary of Power Circuits• Real switches have limitations
– Conduction losses (RON for FETs, VCE for IGBTs, Diode drop)– Switching losses (finite ton, toff, trr)
• With current source load, current ramps, then voltage falls • And voltage rises before current falls• May be dominated by reverse recovery time• Complicated by inductance
– Parasitic L and C• Power MOSFETs
– Switch quickly, have linear I-V, integral diode• IGBTs
– Diode-like I-V, slower switching• Diodes
– Have reverse recovery time• Switches operate in pairs
– For one-way converters, one switch may be a diode– Synchronous rectification – make both switches FETs to reduce loss– Need “dead time” to avoid “shoot through” current
• Gate-drive circuits control rise and fall times– Supply Miller capacitance
• Bootstrap supply needed for high-side driver• Snubbers dampen voltage and current transients• Use SPICE as a verification tool, not a design tool
Photovoltaics
EE155/255 Lecture 4 - Power Circuits
Energy Conversion
EE155/255 Lecture 4 - Power Circuits
EE155/255 Lecture 4 - Power Circuits
Photovoltaic System
Solar Panel
Solar Panel
Solar Panel
Solar Panel
Solar Panel
Solar Panel
Photovoltaic Array
PV Controller and Inverter
Batteries
400V DC 240V AC60 Hz
48V DC
To Grid
EE155/255 Lecture 4 - Power Circuits
EE155/255 Lecture 4 - Power Circuits
M
215 Installation and Operation
C
opyright � 2012 Enphase Energy
141-00012 Rev 04
29
Sam
ple Wiring D
iagram – M
215, 240 VA
C
EE155/255 Lecture 4 - Power Circuits
Electrons absorb energy from photons
EE155/255 Lecture 4 - Power Circuits
Equivalent Circuit
RSHISC
RS
D1 VC
+
_
D2
EE155/255 Lecture 4 - Power Circuits
IV-Curve
EE155/255 Lecture 4 - Power Circuits
Typical Module CS6P60 cells in series
~0.5V per cell
3 strings of 20 with bypass diode on each string
EE155/255 Lecture 4 - Power Circuits
Typical Module
… … …EE155/255 Lecture 4 - Power Circuits
IV Curve from SPICE Model
EE155/255 Lecture 4 - Power Circuits
Peak-Power Tracking• Find point on IV curve where power is maximized.
Start at any point (v(0),i(0))“Dither” v, v(i+1) = v(i) + DvCheck result: if(p(i+1) < p(i)) v(i+1) = v(i)Try both directions: Dv = -Dv
EE155/255 Lecture 4 - Power Circuits
MPP Tracking – The Movie
EE155/255 Lecture 4 - Power Circuits
Start at (35 V, 5.5A) P=192.5
EE155/255 Lecture 4 - Power Circuits
Dither by DV = 0.5V to V = 35.5V(35.5V, 4.7A) P=166.9 < 192.5
EE155/255 Lecture 4 - Power Circuits
(35.5V, 4.7A) P=166.9 < 192.5Bad Move – Go Back to (35, 5.5)
EE155/255 Lecture 4 - Power Circuits
Dither by -0.5V to 34.5V(34.5, 6.2) P=213.9 > 192.5
EE155/255 Lecture 4 - Power Circuits
(34.5, 6.2) P=213.9 > 192.5Keep move and keep going
EE155/255 Lecture 4 - Power Circuits
Move to 34.0(34.0, 6.7) P=227.8 > 213.9
EE155/255 Lecture 4 - Power Circuits
(34.0, 6.7) P=227.8 > 213.9Keep move and keep going
EE155/255 Lecture 4 - Power Circuits
(33.5, 7.0) P=234.5> 227.8 Keep move and keep going
EE155/255 Lecture 4 - Power Circuits
(33.0, 7.3) P=240.9 > 234.5Keep move and keep going
EE155/255 Lecture 4 - Power Circuits
(32.5, 7.5) P=243.75 > 240.9 Keep move and keep going
EE155/255 Lecture 4 - Power Circuits
(32.0, 7.6) P=243.2 < 243.75 Abandon Move and Go Back!
EE155/255 Lecture 4 - Power Circuits
Operate at (32.5, 7.5) P=243.8With occasional forays to 32.0 and 33.0
EE155/255 Lecture 4 - Power Circuits
“Hillclimbing” On the Power Curve
EE155/255 Lecture 4 - Power Circuits
Compound Power Curve
EE155/255 Lecture 4 - Power Circuits
Compound Power Curve (2 Panels)
Not convexHow do you find maximum power point?
EE155/255 Lecture 4 - Power Circuits
Three Panels
EE155/255 Lecture 4 - Power Circuits
Typical String of 10 PV Panels
EE155/255 Lecture 4 - Power Circuits
Search Strategies for Non-Convex MPPT• Exhaustion
– Try every operating point• Random
– Randomly pick new points – keep if better• Hierarchical
– Try every point – with coarse spacing– Try every point near best point with finer spacing– Repeat
• Acquire and Track– One of the above to acquire MPPT (e.g., hierarchical)– Then gradient search to track– Periodically revisit (devote some fraction of string time to this)
• Optimal method depends on – Shape of curve– How fast the curve changes– How the curve changes
EE155/255 Lecture 4 - Power Circuits
Good Optimization Depends on Understanding The Problem
• Collect lots of data– Time series of IV curves from typical strings
• Understand the data• What causes “dips”
– Bad panels • Static offset in current
– Fixed shading – trees, buildings, etc… • Periodic offset – same time each day
– Variable shading – clouds, etc… • Unpredictable shading – but shifts across panels in one direction
• Develop algorithms• Test on data
EE155/255 Lecture 4 - Power Circuits
An Example of Optimization• Trade-off parameters against one another to maximize a figure of merit.
• In this case, parameters are panel voltage and current.
• Figure of merit is power.
• Optimization is done real-time because temperature and irradiance change.– Sometimes optimization is done at design time, or calibration time.
EE155/255 Lecture 4 - Power Circuits
MPPT Power Path(Boost Converter with Energy Meter)
Ci
VPV
PV Panel
RS
M1G
CO
L1
Load
M2G
VL
IPV
EE155/255 Lecture 4 - Power Circuits
MPPT Power Path(Boost Converter with Energy Meter)
Ci
VPV
PV Panel
RS
M1G
CO
L1
Load
M2G
VL
IPV
MPPT is a boost converter that regulates its INPUT voltage
EE155/255 Lecture 4 - Power Circuits
Cycle Waveforms
350 355 360 365 370 375 3802
4
6
8
il(A)
350 355 360 365 370 375 38034.5
35
35.5
v in (V
)
350 355 360 365 370 375 38043
43.5
44
44.5
v out (V
)
t (µs)
Size input cap Ci for acceptable ripple
Size output cap Co for acceptable ripple
Size inductor L to set ripple
EE155/255 Lecture 4 - Power Circuits
SPICE
EE155/255 Lecture 4 - Power Circuits
Longer Simulation
0 2 4 6 8 10 12 14 1610
20
30
40
v in(V
)
0 2 4 6 8 10 12 14 160
5
10
i pv(A
)
0 2 4 6 8 10 12 14 1620
40
60
v out(V
)
0 2 4 6 8 10 12 14 160
0.2
0.4
D
0 2 4 6 8 10 12 14 1650
100150200250
P (W
)
t (ms)
EE155/255 Lecture 4 - Power Circuits
PV Systems
EE155/255 Lecture 4 - Power Circuits
Microinverter
Panel InverterAC Line240 Vrms~1Arms
30-40V0-10A
EE155/255 Lecture 4 - Power Circuits
Store Energy During AC Null
EE155/255 Lecture 4 - Power Circuits
Approach 1 – DC Link
Boost
30-40V0-10A
340-600V0-1A
Buck Unfold
Rectified AC240V, 1A rms
EE155/255 Lecture 4 - Power Circuits
Approach 2 – Single Stage
30-40V0-10A
Convert Unfold
Rectified AC240V, 1A rms
EE155/255 Lecture 4 - Power Circuits
Buck
Boost
400VDC Unfold
400-600V120Hz Buck
240V 120Hz rectified sine240V AC 60Hz
2/3 of power through main pathLower path levels input current
Two-Path
EE155/255 Lecture 4 - Power Circuits
3-Phase
String ofPanels
Inverter
AC Line480 V20 A3 phase
600-1000V10A
No need for energy storage
EE155/255 Lecture 4 - Power Circuits
48V34AH
RCSF1
C1
A
A
B
B
C
C
A B C
3-F Inverter Power Path
EE155/255 Lecture 4 - Power Circuits
Transformerless
EE155/255 Lecture 4 - Power Circuits
Typical Utility-Scale PV System
EE155/255 Lecture 4 - Power Circuits
Typical Utility-Scale PV System• 8,000 Modules – 400 strings of 20 modules each
– 325W/module – 2.6MW DC total• Central 2MW inverter• Central 2MW step-up transformer to 34.5kv• Single axis tracking• This 2MW “block” is repeated for larger systems
EE155/255 Lecture 4 - Power Circuits
PV Economics 1• Utility scale costs
– PV Module $0.60/W– Inverter $0.10/W– Mounting $0.15/W– Balance $0.65/W– TOTAL $1.50/W
• Return– Hours/year 2,200– Wholesale $0.05/kWh– TOTAL $0.11/Wyear– 7.3% ROI
• Residential costs– PV Module $0.60– Microinverter $0.50– Mounting $0.20– Balance $1.70– TOTAL $3.00
• Return– Hours/year 2,200– Retail $0.15-$0.35/kWh– TOTAL $0.33-0.77/Wyear– 11% - 26% ROI
EE155/255 Lecture 4 - Power Circuits
PV Economics 2• Module is only 40% of cost (20% for residential)• Real issue is balance-of-system (installation labor)
EE155/255 Lecture 4 - Power Circuits
VOC Limiting• Typical module (Trina TSM-310-PD14)
– Vmp = 36V, Voc = 46V (worst-case cold temperature)• Inverter input limited to 1kV
– Limits strings to 21 modules– At Vmp could have 27 modules – 29% increase– Reduces string cost by ~30%.
EE155/255 Lecture 4 - Power Circuits
Module (and Cell) Mismatch• String current limited to current from weakest cell• Module current mismatch s = 5%• Worse for residential installations (partial shading)
• Two questions:– What is the typical mismatch profile of a 10-module string?– What power reduction does a X % current mismatch result in?
EE155/255 Lecture 4 - Power Circuits
Faults and Failures• Cell open/short• Diode open/short• Arc fault
EE155/255 Lecture 4 - Power Circuits
Summary of PV• PV cells/strings are voltage-dependent current sources (Diode in parallel
with current source)• PV controllers regulate their input voltage/current to maximize power
– Maximum power-point tracking• Can apply almost any converter topology
– Boost used for illustration– Regulate input rather than output
• Gradient search for convex optimization• More sophisticated search needed for multi cell/panel string
EE155/255 Lecture 4 - Power Circuits
In Upcoming LecturesNo Date Topic HWout HWin Labout Labck Lab HW
1 9/26/16Intro(basicconverters) 1 1 IntrotoST32F3 PeriodicSteadyState2 9/28/16EmbeddedProg/PowerElect.3 10/3/16PowerElectronics- 1(switches) 2 1 2 1 ACEnergyMeter PowerDevices4 10/5/16PowerElectronics- 2(circuits)5 10/10/16Photovoltaics 3 2 3 2 PVMPPT PVSPICE6 10/12/16FeedbackControl7 10/17/16ElectricMotors 4 3 4 3 MotorcontrolMatlab Feedback8 10/19/16IsolatedConverters9 10/24/16SolarDay 5/PP 4 5 4 Motorcontrol- Lab/ IsolatedConverters
10 10/26/16Magnetics11 10/31/16SoftSwitching 6 5/PP 6 5 PS MagneticsandInverters12 11/2/16ProjectDiscussions13 11/7/16Inverters,Grid,PF,andBatteries 6 P 6 Project14 11/9/16Thermal&EMI15 11/14/16QuizReview C116 11/16/16Grounding,andDebuggingQ 11/16/16Quiz- intheevening C2
11/21/16ThanksgivingBreak11/23/16ThanksgivingBreak
17 11/28/1618 11/30/16 C319 12/5/1620 12/7/16Wrapup
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