Engineering 1 : Photovoltaic System Design
What do you need to learn about?
Gil Masters
Terman 390 … but leaving town tonight
feel free to email me anytime: gmasters@stanford.edu
I. Very quick electricity review
II. Photovoltaic systems
III. PV technology
IV. The solar resource
V. Batteries
VI. Load analysis
I’m here to help...
VII. PV Sizing
VIII. Battery Sizing
… all in one class !! ?? !!
December 2, 2003
I. BASIC ELECTRICAL QUANTITIES
Electric Charge
q (Coulombs)
1 electron = 1.602 x10-19 C
POWER
Watts =
P=
Current
ei
+
Voltage
i ( Amps) =
1 Coulomb
second
Time (sec)
dW dW dq
=
⋅
dt
dq dt
Power is a RATE !!
P=vi
charge/time = current
energy/charge =volts
ENERGY
ENERGY = POWER X TIME (watt-hrs, kilowatt-hours)
“the push”
energy W
V=
charge q
watts
dq
…is the flow of charges i =
dt
Energy (W,joules)
Watt hours = volts x amps x hours = volts x (amp-hours)
1 Joule
1 Volt =
Coulomb
Batteries !
1
II. PV SYSTEM TYPES:
1.
2.
GRID-CONNECTED PV SYSTEMS:
•
Simple, reliable, no batteries (usually),
•
≈ $ 15,000 (less tax credits), A=200 ft2 for efficient house
•
Sell electricity to the grid during the day (meter runs backwards), buy it
back at night.
*
Sizing is simple… how much can you afford?
•
But compete with “cheap” 10¢/kWh utility grid power
A FULL-BLOWN HYBRID STAND-ALONE SYSTEM WITH BACKUP
ENGINE-GENERATOR (“Gen-Set”) ….Not what you will design
DC
DC
DC loads
DC
Fuse
Box
DC
Batteries
Charge Controller
..may want all DC,
all AC,
or mix of AC/DC
DC
PVs
Generator
Charger
AC to DC
AC
Inverter
DC to AC
AC
AC loads
AC
Fuse
Box
AC
DC
Power
Conditioning
Unit
Inverter/Charger
DC-to-AC to run AC loads
some can do AC-to-DC to charge batteries
Utility
Grid
AC
PVs
Complex, expensive, requires maintenance, tricky to design
But…
competes against $10,000/mile grid extension to your house or
40¢/kWh noisy, balky, fuel-dependent on-site generator
…NOT what you are going to design
TRADE-OFF BETWEEN DC AND AC SYSTEMS:
3. SIMPLER STAND-ALONE SYSTEMS:
+
-
DC
ALL DC
Battery
3000 Wh/d
= 3530 Wh/ d
0.85
ALL AC
DC
DC
Batteries
DC
Inverter
Example:
h=0.85
DC Loads
+
Charge
Controller
DC
Batteries
DC
Inverter
AC
(including a 1200 Wh/d
AC fridge)
INVERTER FOR AC
AC
3000 Wh/d AC
AC/DC
DC
DC
Charge
Controller
Charge
Controller
DC
DC
Batteries
Batteries
DC
DC
Inverter
Inverter
AC
DC
..YOU’LL DESIGN ONE OF THESE !
CHARGE CONTROLLER TO
PROTECT BATTERIES
AC
DC
Loads
SOME AC, SOME DC (e.g. fridge)
..avoids some inverter losses
..smaller inverter saves $
..but more $ for DC fridge
..but need AC and DC wiring, $
OR…Buy a more expensive, very efficient DC refrigerator that uses say 800 Wh/d
instead of the 1200 Wh/d for an AC fridge
1800 Wh / d
+ 800 Wh/ d = 2920 Wh/d
0.85
0.85
DC
Charge
Controller
DC
Batteries
DC
Inverter
AC
DC
Cheaper PVs, battery, inverter
1800 Wh/d AC
800 Wh/d DC
More expensive fridge
More expensive wiring
2
III.
MOST SOLAR CELLS ARE MADE FROM SILICON..
PHOTOVOLTAIC TECHNOLOGY
SO, HOW DO
WE COLLECT SOLAR ENERGY?
VALENCE
valence
ELECTRONS
electrons
+4
+4
+14
+14
(a) actual
(a)
actual
QUARTZ TO SILICON…
Si is ≈ 20% of the earth’s crust, usually as SiO2
..an energy intensive process using an arc furnace
converts it to pure silicon
(b) simplified
(b)
simplified
CZOCHRALSKI METHOD OF FORMING CRYSTALLINE WAFERS..
MELT the pure Si (1400 C) in a quartz crucible..
DIP, then withdraw, a “seed crystal” turning continuously so that each
atom freezes in place in the crystal..
GET a cylindrical ingot (perhaps 1 m long, 20 cm diameter)
Rock-like hunks of
99.9999% pure silicon..
SLICE the cylinder into wafers….
(same as integrated circuits)
3
IF A PHOTON HAS “ENOUGH” ENERGY, IT CAN BUMP AN
ELECTRON INTO THE CONDUCTION BAND..leaving a positively
charged “hole” behind
CRYSTALLINE SILICON FORMS A TETRAHEDRAL
STRUCTURE…
Hole
+
silicon
nucleus
+4
+4
+4
+4
+4
+4
Free
electron
shared
valence
electrons
tetrahedral
a) (a)
Tetrahedral
Photon
+4
Si
(b) 2-D version
b) 2-D version
Max efficiency ≈ 50%
Photons with TOO MUCH energy (l < 1.11 mm) waste 30.2%
Photons with TOO LITTLE energy (l > 1.11 mm) lose another 20.2%
SEPARATE HOLES AND ELECTRONS USING
THE ELECTRIC FIELD CREATED IN A p-n JUNCTION
Produces Direct Current (dc)
Electrical contacts
on top
p-n junction
creates an E
electric field
CELLS, MODULES AND ARRAYS...
ARRAY wired in series and
parallel for voltage and power
Single CELL ≈ 0.5 V
electrons
- - - -
n-type
V
+ + + +
p-type
Load
5” - 8” diameter
+
MODULE, typically “12-V or 24V”
Rated by peakwatts (e.g. 53 W)
(≈ 1 m x 0.5 m) 36 cells wired in series
Bottom contact
Current I
Trim edges
4
LOTS OF PHOTOVOLTAIC TECHNOLOGIES….
Thick Si
200 - 500 mm
Multicrystalline Si
30%
Homojunction
CdTe
CIS
Example: AstroPower 7105: PR = 75W, IR =4.4A, VR = 17.0V, Isc = 4.8A, Voc = 21.0V
Polycrystalline thin-film Si
Amorphous Si 20%
Ribbon
Flat-plate
50%
Short circuit current, Isc
Open circuit voltage, Voc
Current at “rated conditions” IR
Voltage at maximum power point (rated voltage) VR
Rated power (@1 kW/m2 solar insolation, 25oC cell temperature, at max pwr pt) PR
Thin films
1 - 10 mm
Heterojunction
Single-crystal Si
Czochralski
CZ
Manufacturer specification of photovoltaic module:
PHOTOVOLTAICS
Concentrator
4
GaAs
InP
1 kW/m2 insolation (“1-sun”)
4.8A
Maximum power point
4.4A x 17V = 75W
4.4A
3
Multijunction,
Tandem cells
I (amps)
2
2.4A
0.5 kW/m2 insolation 1/2 sun
1
12.7%
6.3%
0
0
IV. THE SOLAR RESOURCE…. kWh/ m2-day of insOlation
*
*
*
*
Location
Orientation of modules (due south generally best for U.S.)
Tilt angle
Fixed orientation vs 1-axis tracking vs 2-axis tracking
10
V (volts)
17.0
20
21.0
V
THE KEY TRICK TO INTERPRETING INSOLATION DATA…
“mid-day, clear day, normal to rays”
“1-SUN” OF INSOLATION IS DEFINED TO BE 1 kW/m2
Summer
Spring, Fall
Winter
tilt
south
AVERAGE DAILY INSOLATION EXPRESSED IN (KWh/m2-day)
CAN BE INTERPRETED TO MEAN HOURS OF FULL SUN
e.g. Boulder, CO in June, collector tilt = latitude sees 6.1 kWh/m2 of insolation
“that’s like 6.1 hours/day of 1 kW/m2 “full sun”
Tilt = Latitude gives perpendicular angle to sun at equinoxes at noon
5
GOOD SOURCE OF REAL DATA…
SINGLE-AXIS TRACKER (East to West)
kWh/m2 -day
1-axis tracker, tilt = lat
Zomeworks: Passive single-axis tracker… on the roof since 1977
… IS IT WORTH THE EXTRA COST?
INSOLATION IN BOULDER, CO..
9
1-Axis Tracking
(Annual 7.2 kWh/m2-d)
INSOLATION (kWh/m2-day)
8
Lat - 15 (5.4 kWh)
7
6
Lat (5.5 kWh)
5
Lat + 15 (5.3 kWh)
4
3
2
1
0
JAN
2-AXIS TRACKER….. Not much better than 1-axis
FEB
MAR
APR
MAY
JUN
JLY
AUG
SEP
OCT
NOV
DEC
30% extra insolation with 1-axis tracker (annual)
6
V. ENERGY STORAGE…
Basic lead-acid battery...
BATTERIES
COMPRESSED AIR
HYDROGEN
FLYWHEELS, etc
One Cell ≈ nominal 2 V
6-cells, “12-V battery”
+
CHARGED
-
+
H+
Pb
PbSO4
FOR NOW.. BATTERIES ARE IT..
Lead-Acid car batteries (SLI =Starter, Lighting, Ignition system)_
Designed for high current (400-600A), shallow discharge (20%), not so good for PV
PbO 2
Lead-Acid “golf-cart” deep-cycle batteries… often used due to low cost, satisfactory performance
H
+
=
SO
4
DISCHARGED
-
PbSO4
H 2O
True Deep-Cycle Lead-Acid batteries… very good, but expensive
Nickel-Cadmium batteries… very expensive, great for very cold, harsh conditions, can take abuse
Battery
Lead-acid, SLI
Lead-acid, golf cart
Lead-acid, deep-cycle
Nickel-cadmium
Nickel-metal hydride
Max Depth
Discharge
20%
80%
80%
100%
100%
Energy Density
Wh/kg
50
45
35
20
50
Cycle life Calendar life
cycles
years
500
1-2
1000
3-5
2000
7-10
1000-2000
10-15
1000-2000
8-10
Efficiencies
Ah %
Wh %
90
75
90
75
90
75
70
60
70
65
Cost
$/kWh
50
60
100
1000
1200
Rough comparison of battery characteristics
Voltage can be used… (but battery needs to have been “at rest” for several hours to be
accurate)
13.0
1.30
12.8
1.28
VOLTAGE (V)
1.22
12.0
1.20
SG
1.18
11.6
1.16
11.4
1.14
11.2
1.12
11.0
1.10
80
60
40
STATE OF CHARGE (%)
20
SPECIFIC GRAVITY
1.24
V
12.2
100
* Specific gravity of electrolyte drops (gives indication of state-of-charge)
* More vulnerable to freezing…(charged freeze at -57oC; discharged at -8oC)
BATTERY RATINGS….
* Voltage… for lead-acid about 2 V per cell. Typical “nominal
voltage” for battery is 6 V or 12 V (3 or 6 cells per battery)
* Voltage depends on state of charge and whether you are charging the
battery or discharging it. Voltage can range from about 11 to 15 V
1.26
12.6
11.8
As battery discharges:
* Plates coated with PbSO4 yields higher internal resistance, cell voltage drops
STATE OF CHARGE (SOC)
Hydrometer to measure specific gravity (but electrolyte may stratify with H2SO4 on
bottom)
12.4
Figure 9.40 A lead-acid battery in its charged and discharged states.
0
* Energy stored = Volts x Amps x Hours = Watt-hours
* With voltage varying all over the map, how do you describe the energy
stored in a battery?
Ans. Use “Amp-hours” @ nominal battery voltage as the measure of energy
stored in battery !
A 12-V battery that reads only 12 V (at rest) is almost completely discharged…
7
BATTERY STORAGE IS DESCRIBED USING A NOMINAL VOLTAGE (2-V/cell) AND..
BUT… AMP-HOURS DEPENDS ON DISCHARGE RATE AND TEMPERATURE
AMP-HOURS AT A CERTAIN DISCHARGE RATE C/T (…at a certain temperature)
Means it can deliver 5 Amps for 20 hours (5A x 20h = 100 Ah)
Energy stored ≈ Volts x Amps x Hours = 12 V x 100 A-hr =1.2 kWhr
BATTERIES IN PARALLEL (Ah adds, V same); IN SERIES (Ah same, V adds)
24V, 200Ah
24V, 100Ah
+
12V, 200Ah
12V
100Ah
+
+
-
-
+
12V
100Ah
-
(a) Parallel, Amp-Hrs add
2.4 kWh
+
-
+
12V
100Ah
12V
100Ah
-
(b) Series, Voltages add
+
+
-
-
+
+
-
-
+
100
C/72
C/48
90
Nominal C/20
And 25oC
C/20
80
C/10
70
C/5
60
50
40
30
20
-30
-20
-10
0
10
Battery Temperature (oC)
20
30
40
Example: A 100 Ah, C/20 battery discharged at C/10 (10A), 25o has ≈ 90 Ah of capacity
-
COLDER TEMPERATURE… less storage capacity
Example: 100 Ah, C/20 battery when discharged at -20o C and C/10 has ≈ 55 Ah of capacity
4.8 kWh
BUT YOU DON’T GET TO USE THE FULL AMP-HR STORAGE…
* For reasonable battery life, don’t discharge a car SLI battery more than about 20%
* You should use deep-cycle batteries, and discharge them no more than 80 %
Usable Ah = 0.80 x nominal battery rated Ah of storage
110
DISCHARGE FASTER… less storage capacity
(c) Series/Parallel
2.4 kWh
120
Capacity / (Rated Capacity)
Example: A 12-volt golf-cart battery rated at 100 Amp-hours (Ah)
when discharged over a 20-hour period of time (C/20) at 25oC …
VI. LOAD ANALYSIS: How much energy do you “need?”
Appliance
Refrigerator, 19 cu. ft.
Lights (6 @ 30 W)
TV, 19-in., Active mode
TV, 19-in., Standby mode
Satellite, Active mode
Satellite, Standby mode
Cordless phone
Well pump, 100 ft, 1.6 gpm
Total
Power (W)
Hours
180
68
5.1
17
16
4
100
5
3
21
3
21
24
1.25
Watt-hrs/day
1,140
900
204
107
51
336
96
125
2,959
Percentage
39%
30%
7%
4%
2%
11%
3%
4%
100%
2/3rds of TV is standby!
EXPRESS THE LOAD IN AMP-HOURS @ SYSTEM VOLTAGE (12V good for ≈ 1200 W)
Batteries need to deliver =
2959 volts x amps x hours
= 245 Ah/day
12 volts
8
LOAD ANALYSIS: How do you know how much power/energy an appliance uses?
* Read the nameplate on a device (Watts)
…is maximum power device uses so it is on the high side
VII. BASIC PV SIZING..
kWh/m2 day
(hrs/d @ 1-sun)
DC
* EPA appliance labels (kWh/yr)
… refrigerators rated in 90oF kitchen (overestimate)
DeRating
“adjusted”
PV output
Ah/day
* Measure it yourself !
-
Battery
Output
Ah/day
h ≈ 90%
AC
Inverter
h ≈ 85%
AC
LOAD
Ah/d @V
Coulomb
Efficiency
h ≈ 90%
Dirt..etc
IR Amps @ 1-sun
per module
* Tables in Real Goods, on the web, and other places..
V
+
DC
LOAD
n modules in parallel
(Ah/d)
COULOMB EFFICIENCY = (AMP-HOURS OUT) / (AMP-HOURS IN) ≈ 0.90
(Hrs/d @ 1-sun) x IR (A/module) x n (modules) x 0.90 x 0.90 x 0.85 x V = Wh/day to load
Rated power
of module
kWh/m2-d
insolation
VIII. HOW SIZE THE BATTERIES?
16
Days of Usable Storage
n modules
DC
kWh/m2 day
(hrs/d @ 1-sun)
14
DeRating
Dirt..etc
IR Amps @ 1-sun
per module
10
99% Availability
8
6
*
*
*
*
4
95% Availability
0
3
4
5
Peak Sun Hours
6
7
8
Example: With 3.1 “peak sun hours” in December
To be 99% sure of having enough battery storage, provide about 12 days of
storage, for 95% availability provide about 4.5 days of storage..
Example:
“adjusted”
PV output
Ah/day
12 V
+
-
h ≈ 90%
12
2
Inverter
System
voltage
VII. BASIC BATTERY SIZING..
* How many days without sun do you want to provide for?
* How important is it to be sure you have enough storage for those days?
* Is there a backup generator?
2
Coulomb
dirt
Battery
Output
Inverter
84 Ah/day h ≈ 85%
Coulomb
Efficiency
h ≈ 90%
AC
AC
LOAD
850 Wh/d
71 Ah/d@12V
Convert AC Wh/d load to Ah/d @ system voltage V
Divide by inverter efficiency to get Ah/d from batteries
Multiply by days of storage wanted
Divide Ah by maximum discharge depth allowed
•850 Wh/d AC load, 12-V system = 850/12 = 71 Ah/d
•85% efficient inverter -- 71/0.85 = 84 Ah/d from batteries
•2 days of storage
-- 84 Ah/d x 2d = 168 Ah
•80% maximum discharge -- 168 Ah/0.8 = 210 Ah
Sandia: Standalone PV systems
9
BATTERY SIZING PROCEDURE (continued):
Need more current or power?… add PV modules in parallel (currents add):
* Wire batteries in series to get voltage
* Wire batteries in parallel to get Ah needed
+
+
I
-
-
-
EXAMPLE:
•850 Wh/d AC load, 12-V system = 850/12 = 71 Ah/d
2-modules
1.0
1-module
0.0
0
+
PV
disconnect
20
AC
DC
Charge
Controller
-- 84 Ah/d x 2d = 168 Ah
Inverter
Fuse
Box
12V, 200Ah
•80% maximum discharge -- 168 Ah/0.8 = 210 Ah
•6V 100 Ah batteries -- 2 batteries in series for 12V
VB
10
A COMPLETE SYSTEM:
•85% efficient inverter -- 71/0.85 = 84 Ah/d from batteries
•2 days of storage
+
2.0
6V,
100 Ah
•2 strings would give 200 Ah… close enough
6V,
100 Ah
+
+
-
-
+
+
-
-
+
+
6V,
100 Ah
Astro
7105
+
-
6V,
100 Ah
-
6V,
100 Ah
+
-
-
+
+
-
-
-
Battery
disconnect
switch
LOADS
10