EE155/255 Green Electronicsweb.stanford.edu/class/ee152/lecture_slides/... · 3 10/3/16 Power...
Transcript of EE155/255 Green Electronicsweb.stanford.edu/class/ee152/lecture_slides/... · 3 10/3/16 Power...
EE155/255 Green Electronics
PhotovoltaicsFeedback Control
10/10/16
Prof. William DallyComputer Systems Laboratory
Stanford University
Course Logistics• Next week schedule is ‘flipped’
– Lectures on Wed/Fri, Discussion on Monday• HW2 due Today (In box outside Sue’s office by 10AM tomorrow)• HW3 out – SPICE simulation – Due Monday 10/17• Lab2 signed off this week• Lab3 out – PV MPPT
EE155/255 Lecture 5 - Photovoltaics
No Date Topic HWout HWin Labout Labck Lab HW1 9/26/16 Intro(basicconverters) 1 1 IntrotoST32F3 PeriodicSteadyState2 9/28/16 EmbeddedProg/PowerElect.3 10/3/16 PowerElectronics-1(switches) 2 1 2 1 ACEnergyMeter PowerDevices4 10/5/16 PowerElectronics-2(circuits)5 10/10/16 Photovoltaics 3 2 3 2 PVMPPT PVSPICE6 10/12/16 FeedbackControl7 10/19/16 ElectricMotors 4 3 4 3 MotorcontrolMatlab Feedback8 10/21/16 IsolatedConverters9 10/24/16 SolarDay 5/PP 4 5 4 Motorcontrol-Lab/ IsolatedConverters10 10/26/16 Magnetics11 10/31/16 SoftSwitching 6 5/PP 6 5 PS MagneticsandInverters12 11/2/16 ProjectDiscussions13 11/7/16 Inverters,Grid,PF,andBatteries 6 P 6 Project14 11/9/16 Thermal&EMI15 11/14/16 QuizReview C116 11/16/16 Grounding,andDebuggingQ 11/16/16 Quiz-intheevening C2
11/21/16 ThanksgivingBreak11/23/16 ThanksgivingBreak
17 11/28/1618 11/30/16 MartinFornage,enPhase C319 12/5/16 ColinCampbell,Tesla20 12/7/16 Wrapup
TBD Projectpresentations PTBD Projectwebpagedue
Course to Date• We need sustainable energy systems• At the core they are voltage converters• Periodic steady-state analysis, buck and boost• Intelligent control (embedded uC) + power path• Real devices have switching and conduction loss• Half-bridges, dead-time, and snubbers• PV cells characterized by a diode-like I-V curve
– With a maximum power point
EE155/255 Lecture 5 - Photovoltaics
PV Module Review
EE155/255 Lecture 5 - Photovoltaics
Simple Equvalent Circuit
EE155/255 Lecture 5 - Photovoltaics
Current proportional to irradiance (ISC)
VOC = VDiode(ISC)
Typical PV Module
… … …
EE155/255 Lecture 5 - Photovoltaics
Typical 250W module:
• 3 strings of 20 cells
• “Bypass” diodes between strings• Diodes turn on when voltage
across string becomes negative• When Imodule > Istring
IV Curve from SPICE ModelISC
VOC
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
MPPT is a boost converter that regulates its INPUT voltage
EE155/255 Lecture 5 - Photovoltaics
PV Systems
EE155/255 Lecture 5 - Photovoltaics
Microinverter
Panel InverterAC Line240 Vrms~1Arms
30-40V0-10A
EE155/255 Lecture 5 - Photovoltaics
Store Energy During AC Null
EE155/255 Lecture 5 - Photovoltaics
Approach 1 – DC Link
Boost
30-40V0-10A
340-600V0-1A
Buck Unfold
Rectified AC240V, 1A rms
EE155/255 Lecture 5 - Photovoltaics
Approach 2 – Single Stage
30-40V0-10A
Convert Unfold
Rectified AC240V, 1A rms
EE155/255 Lecture 5 - Photovoltaics
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 5 - Photovoltaics
3-Phase
String ofPanels
Inverter
AC Line480 V20 A3 phase
600-1000V10A
No need for energy storage
EE155/255 Lecture 5 - Photovoltaics
48V34AH
RCSF1
C1
A
A
B
B
C
C
A B C
3-F Inverter Power Path
EE155/255 Lecture 5 - Photovoltaics
Transformerless
EE155/255 Lecture 5 - Photovoltaics
Typical Utility-Scale PV System
EE155/255 Lecture 5 - Photovoltaics
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 5 - Photovoltaics
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 5 - Photovoltaics
PV Economics 2• Module is only 40% of cost (20% for residential)• Real issue is balance-of-system (installation labor)
EE155/255 Lecture 5 - Photovoltaics
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 5 - Photovoltaics
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 5 - Photovoltaics
Individual MPPT with per-module buck
EE155/255 Lecture 5 - Photovoltaics
Module
Buck
Individual MPPT with incremental harvesting
EE155/255 Lecture 5 - Photovoltaics
Module
Flyback
Smart PV Systems
EE155/255 Lecture 5 - Photovoltaics
Inverter…
Conv
……
Conv
Smart PV Systems• Smart inverter provides central control over panels• Turns off some substrings
– Voc clipping– Smart bypass– Converter (if present) incrementally harvests mismatch
• Without adding connections
EE155/255 Lecture 5 - Photovoltaics
Faults and Failures• Cell open/short• Diode open/short• Arc fault
EE155/255 Lecture 5 - Photovoltaics
PV Monitoring• https://enlighten.enphaseenergy.com/systems/153078/graphs?range=last
7Days&view=power_production• https://enlighten.enphaseenergy.com/systems/153078/arrays?range=last
7Days&view=power_production
EE155/255 Lecture 5 - Photovoltaics
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 • Single phase systems must store energy during AC cycle• PV economics dominated by “balance of system”• Opportunities for “intelligent” PV systems
EE155/255 Lecture 5 - Photovoltaics
No Date Topic HWout HWin Labout Labck Lab HW1 9/26/16 Intro(basicconverters) 1 1 IntrotoST32F3 PeriodicSteadyState2 9/28/16 EmbeddedProg/PowerElect.3 10/3/16 PowerElectronics-1(switches) 2 1 2 1 ACEnergyMeter PowerDevices4 10/5/16 PowerElectronics-2(circuits)5 10/10/16 Photovoltaics 3 2 3 2 PVMPPT PVSPICE6 10/12/16 FeedbackControl7 10/19/16 ElectricMotors 4 3 4 3 MotorcontrolMatlab Feedback8 10/21/16 IsolatedConverters9 10/24/16 SolarDay 5/PP 4 5 4 Motorcontrol-Lab/ IsolatedConverters10 10/26/16 Magnetics11 10/31/16 SoftSwitching 6 5/PP 6 5 PS MagneticsandInverters12 11/2/16 ProjectDiscussions13 11/7/16 Inverters,Grid,PF,andBatteries 6 P 6 Project14 11/9/16 Thermal&EMI15 11/14/16 QuizReview C116 11/16/16 Grounding,andDebuggingQ 11/16/16 Quiz-intheevening C2
11/21/16 ThanksgivingBreak11/23/16 ThanksgivingBreak
17 11/28/1618 11/30/16 MartinFornage,enPhase C319 12/5/16 ColinCampbell,Tesla20 12/7/16 Wrapup
TBD Projectpresentations PTBD Projectwebpagedue
Feedback Control
EE155/255 Lecture 5 - Photovoltaics
Control• Most dynamic systems require control• Some are inherently unstable • Humans often close the control loop (bicycle, car)• Most Green-Electronic systems require a controller• Most use layered control
– Each level of control presents simpler interface to higher levels• Feedback control
– Feedback output or error signal to produce input• Model-based control
– Explore possible input sequences with model and pick the best
Feedback Control in a Nutshell• The Plant (system being controlled) is described by ODEs.
– Linearize and describe as P(s)• Controller applies input(s) to Plant to get desired output
– Linearize and describe as C(s)• Apply “error signal” as controller input
• Verify stability by checking unity-gain phase– Across operating conditions
G(s) = C(s)P(s)1+C(s)P(s)
=H (s)1+H (s)
System with Feedback
Controller Plantx e a y
+
_
System with Feedback
Controller Plantx e a y
+
_
Can also have feed-forward control
Linearize and Model with Laplace Xform
C(s) P(s)X(s) E(s) A(s) Y(s)+
_
G(s) = C(s)P(s)1+C(s)P(s)
=H (s)1+H (s)
E(s) = X(s)−Y (s)E(s) = X(s)−H (s)E(s)(1+H (s))E(s) = X(s)
E(s) = X(s)1+H (s)
Y (s) = E(s)H (s)
Y (s) = X(s) H (s)1+H (s)
Example, driving a car• x – position of car in lane• q – angle of car on road• f – angle of wheels
• dq/dt = f• dx/dt = q
• How do you stay on the road?– Need a control law
x(s) = aφ(s)s2
Feedback Control
Controller Plantx e a y
+
_
P(s) = 1s2
C(s)
Y (s) = X(s)−Y (s)( )C(s)P(s)
Y (s) = X(s) C(s)P(s)1+C(s)P(s)"
#$
%
&'
Consider Proportional Control
C(s) = p
H (s) =C(s)P(s) = ps2
G(s) = Y (s)X(s)
=H (s)1+H (s)
=p
s2 + p
Three Ways to See this is Unstable
C(s) = p
H (s) =C(s)P(s) = ps2
G(s) = Y (s)X(s)
=H (s)1+H (s)
=p
s2 + p
1. Unity-gain phase of open loop response H(s)2. Damping factor of closed loop response3. Simulation
10−1 100 101 102 10310−4
10−2
100
102
104
|H(s
)|
10−1 100 101 102 103−200
−150
−100
−50
0
∠H
(s) (
degr
ees)
ω (rad/s)
Open Loop ResponseH (s) =C(s)P(s) = p
s2
Damping Factor
G(s) = Y (s)X(s)
=H (s)1+H (s)
=p
s2 + p=
ks2 + 2ζω0s+ω
20
ζ = 0,
ω0 = p
Damping Factor
G(s) = Y (s)X(s)
=H (s)1+H (s)
=p
s2 + p=
ks2 + 2ζω0s+ω
20
ζ = 0,
ω0 = p
Frequency scales with sqrt of proportional gain
Simulation
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
Time (s)
x (m
), θ
(rad) x
q
PD ControlProportional feedback oscillatesAdd derivative term to “look ahead” Td
C(s) = p+ rs
H (s) =C(s)P(s) = p+ rss2
G(s) = Y (s)X(s)
=H (s)1+H (s)
=p+ rs
s2 + rs+ p
ω0 = p
ζ =r2ω0
=r
2 pWith p=100, pick r=20
Zero at s = p/r
PD is Predictive
10−1 100 101 102 10310−4
10−2
100
102
104
|H(s
)|
10−1 100 101 102 103−200
−150
−100
−50
0
∠H
(s) (
degr
ees)
ω (rad/s)
ω1 = 20.5116
θ1 = −103.699
PD Open LoopH (s) =C(s)P(s) = p+ rs
s2
Zero at w=5
10−1 100 101 102 10310−4
10−2
100
102
104
|H(s
)|
10−1 100 101 102 103−200
−150
−100
−50
0
∠H
(s) (
degr
ees)
ω (rad/s)
ω1 = 20.5116
θ1 = −103.699
What happens if zero is moved left or right?H (s) =C(s)P(s) = p+ rs
s2
Zero at w=5
PD Simulation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.04
−0.03
−0.02
−0.01
0
0.01
0.02
0.03
0.04
Time (s)
x (m
), θ
(rad)
q
x
Effect of damping factor
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.01
−0.008
−0.006
−0.004
−0.002
0
0.002
0.004
0.006
0.008
0.01
Time (s)
x (m
), θ
(rad) 1
.5
.25
.125
Summary• Plant is described by ODEs (possibly non-linear)• Controller drives plant input(s) to achieve goal• Feedback control, input is function of “error”• Stable if
– z >= 1– H(s) has phase margin at unity gain
• PD and PI controllers– Derivative feedback stabilizes 2nd order system– Integral feedback cancels residual error (but avoid wind up)
• Motor control with current limit• Analog and digital implementations• Can also implement “model-based” control
G(s) = C(s)P(s)1+C(s)P(s)
=H (s)1+H (s)
No Date Topic HWout HWin Labout Labck Lab HW1 9/26/16 Intro(basicconverters) 1 1 IntrotoST32F3 PeriodicSteadyState2 9/28/16 EmbeddedProg/PowerElect.3 10/3/16 PowerElectronics-1(switches) 2 1 2 1 ACEnergyMeter PowerDevices4 10/5/16 PowerElectronics-2(circuits)5 10/10/16 Photovoltaics 3 2 3 2 PVMPPT PVSPICE6 10/12/16 FeedbackControl7 10/19/16 ElectricMotors 4 3 4 3 MotorcontrolMatlab Feedback8 10/21/16 IsolatedConverters9 10/24/16 SolarDay 5/PP 4 5 4 Motorcontrol-Lab/ IsolatedConverters10 10/26/16 Magnetics11 10/31/16 SoftSwitching 6 5/PP 6 5 PS MagneticsandInverters12 11/2/16 ProjectDiscussions13 11/7/16 Inverters,Grid,PF,andBatteries 6 P 6 Project14 11/9/16 Thermal&EMI15 11/14/16 QuizReview C116 11/16/16 Grounding,andDebuggingQ 11/16/16 Quiz-intheevening C2
11/21/16 ThanksgivingBreak11/23/16 ThanksgivingBreak
17 11/28/1618 11/30/16 MartinFornage,enPhase C319 12/5/16 ColinCampbell,Tesla20 12/7/16 Wrapup
TBD Projectpresentations PTBD Projectwebpagedue