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Engineering 1 : Photovoltaic System Design What do you need to learn about?

Gil Masters . Very quick review Terman 390 … but leaving town tonight feel free to email me anytime: [email protected] II. Photovoltaic systems

III. PV technology

IV. The solar resource

V. Batteries

VI. Load analysis

VII. PV Sizing I’ here to help... VIII. Battery Sizing

… all in one class !! ?? !! December 2, 2003

I. BASIC ELECTRICAL QUANTITIES (,) q () = Power is a RATE !! Time (sec) 1 = 1.602 x10-19 dW dW dq P = = ⋅ dt dq dt P = i dq watts Current …is the flow of charges i = charge/time = current dt energy/charge = - 1 i (Amps) = i + ENERGY

ENERGY = POWER X TIME (-hrs, kilowatt-) “the push” Watt hours = volts x amps x hours = volts x (amp-hours) energy W 1 V = 1 = Batteries ! charge q Coulomb

1 II. PV SYSTEM TYPES: 2. A FULL-BLOWN HYBRID STAND-ALONE SYSTEM WITH BACKUP 1. GRID-CONNECTED PV SYSTEMS: ENGINE-GENERATOR (“Gen-Set”) ….Not what you will design • Simple, reliable, no batteries (usually),

2 • ≈ $ 15,000 (less tax credits), A=200 ft for efficient house DC DC DC loads DC Batteries DC ..may want all DC, • Sell electricity to the grid during the (meter runs backwards), buy it Charge Controller Box all AC, back at night. DC or mix of AC/DC

* Sizing is simple… how much can you afford? Charger Inverter AC AC loads PVs Fuse AC AC to DC DC to AC AC • But compete with “cheap” 10¢/kWh utility grid power Generator Box

AC DC Power Utility Inverter/Charger Conditioning Grid DC-to-AC to run AC loads Unit some can do AC-to-DC to charge batteries PVs AC

Complex, expensive, requires maintenance, tricky to design

But… competes against $10,000/mile grid extension to your house or

…NOT what you are going to design 40¢/kWh noisy, balky, fuel-dependent on-site generator

TRADE-OFF BETWEEN DC AND AC SYSTEMS: 3. SIMPLER STAND-ALONE SYSTEMS: 3000 Wh/ + DC ALL AC = 3530 Wh/ d ALL DC 0.85 Example: DC Loads - - + =0.85 Battery DC DC DC AC 3000 Wh/d AC Charge Batteries Inverter Controller (including a 1200 Wh/d AC fridge) DC DC AC Batteries Inverter INVERTER FOR AC

AC/DC OR…Buy a more expensive, very efficient DC refrigerator that uses say 800 Wh/d

DC DC DC AC CHARGE CONTROLLER TO instead of the 1200 Wh/d for an AC fridge Charge Batteries Inverter Controller PROTECT BATTERIES 1800 Wh / d + 800 Wh/ d = 2920 Wh/d 0.85

0.85 DC AC DC DC DC AC SOME AC, SOME DC (e.. fridge) DC DC 1800 Wh/d AC Charge Batteries Inverter Charge Batteries Inverter Controller ..avoids some inverter losses Controller DC DC ..smaller inverter saves $ DC Loads 800 Wh/d DC ..but more $ for DC fridge ..but need AC and DC wiring, $ More expensive fridge ..YOU’LL DESIGN ONE OF THESE ! Cheaper PVs, battery, inverter More expensive wiring

2 MOST SOLAR CELLS ARE MADE FROM SILICON.. III. PHOTOVOLTAIC TECHNOLOGY

SO, HOW DO WE COLLECT SOLAR ENERGY?

VALENCEvalence ELECTRONSelectrons

+14+14 +4+4

(a) actualactual ()(b) simplified

QUARTZ TO SILICON… CZOCHRALSKI METHOD OF FORMING CRYSTALLINE WAFERS.. Si is ≈ 20% of the earth’ crust, usually as SiO 2 MELT the pure Si (1400 C) in a quartz crucible.. ..an energy intensive process using an arc furnace DIP, then withdraw, a “seed crystal” turning continuously so that each converts it to pure silicon 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 CRYSTALLINE SILICON FORMS A TETRAHEDRAL ELECTRON INTO THE CONDUCTION BAND..leaving a positively STRUCTURE… charged “hole” behind Hole Photon silicon nucleus + +4 +4 +4 Free shared valence electron +4 +4 +4 +4 Si

(a) tetrahedral a) Tetrahedral (b) 2-D version b) 2-D version Max efficiency ≈ 50%

Photons with TOO MUCH energy ( < 1.11 mm) waste 30.2% Photons with TOO LITTLE energy (l > 1.11 mm) lose another 20.2%

SEPARATE HOLES AND ELECTRONS USING CELLS, MODULES AND ARRAYS... THE CREATED IN A p- JUNCTION ARRAY wired in series and parallel for voltage and power Produces (dc) Single CELL ≈ 0.5 V Electrical contacts electrons on top

- - - - - p-n junction n-type creates an E V Load electric field 5” - 8” diameter p-type + + + + +

MODULE, typically “12-V or 24V” Bottom contact Rated by peakwatts (e.g. 53 W) (≈ 1 m x 0.5 m) 36 cells wired in series Current I Trim edges

4 LOTS OF PHOTOVOLTAIC TECHNOLOGIES…. Manufacturer specification of photovoltaic module: Short circuit current, Isc Thick Si Thin films Open circuit voltage, Voc 200 - 500 mm 1 - 10 mm Current at “rated conditions” IR Voltage at maximum power point (rated voltage) VR Heterojunction Homojunction Rated power (@1 kW/m2 solar insolation, 25oC cell temperature, at max pwr pt) P Single-crystal Si

Multicrystalline Si CdTe Example: AstroPower 7105: P = 75W, I =4.4A, V = 17.0V, Isc = 4.8A, Voc = 21.0V Czochralski CIS R R R CZ 30% Polycrystalline thin-film Si 4 Ribbon 1 kW/m2 insolation (“1-sun”) Amorphous Si 20% GaAs 4.8A InP Maximum power point Flat-plate 3 Concentrator 4.4A 4.4A x 17V = 75W 50% Multijunction,

Tandem cells 2 0.5 kW/m2 insolation 1/2 sun 2.4A I (amps)

1 12.7%

6.3% 0 0 10 17.0 21.020 V V (volts)

IV. THE SOLAR RESOURCE…. kWh/ m2-day of insOlation THE KEY TRICK TO INTERPRETING INSOLATION DATA…

* Location * Orientation of modules (due south generally best for .S.) “mid-day, clear day, normal to rays” * Tilt angle * Fixed orientation vs 1-axis tracking vs 2-axis tracking

“1-SUN” OF INSOLATION IS DEFINED TO BE 1 kW/m2

Summer AVERAGE DAILY INSOLATION EXPRESSED IN (KWh/m2-day) Spring, Fall CAN BE INTERPRETED TO MEAN HOURS OF FULL SUN

Winter e.g. Boulder, CO in June, collector tilt = latitude sees 6.1 kWh/m2 of insolation

tilt south “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 8 (Annual 7.2 kWh/m2-d)

7 Lat - 15 (5.4 kWh)

6 Lat (5.5 kWh) 5 Lat + 15 (5.3 kWh)

4

3

INSOLATION (kWh/m2-day) 2

1

0 JAN FEB MAR APR MAY JUN JLY AUG SEP OCT NOV DEC

30% extra insolation with 1-axis tracker (annual) 2-AXIS TRACKER….. Not much better than 1-axis

6 V. ENERGY STORAGE… Basic lead-acid battery... One Cell ≈ nominal 2 V BATTERIES COMPRESSED AIR 6-cells, “12-V battery” HYDROGEN FLYWHEELS, etc + CHARGED - + DISCHARGED - FOR NOW.. BATTERIES ARE IT..

Lead-Acid car batteries (SLI =Starter, Lighting, Ignition system)_ H + PbO Pb PbSO PbSO4 2 + 4 Designed for high current (400-600A), shallow discharge (20%), not so good for PV H H Lead-Acid “golf-cart” deep-cycle batteries… often used due to low cost, satisfactory performance = 2 SO 4 True Deep-Cycle Lead-Acid batteries… very good, but expensive

Nickel- batteries… very expensive, great for very cold, harsh conditions, can take abuse Figure 9.40 A lead-acid battery in its charged and discharged states.

Max Depth Energy Density Cycle life Calendar life Efficiencies Cost Battery Discharge Wh/kg cycles years Ah % Wh % $/kWh As battery discharges: Lead-acid, SLI 20% 50 500 1-2 90 75 50 Lead-acid, golf cart 80% 45 1000 3-5 90 75 60 * Specific gravity of electrolyte drops (gives indication of state-of-charge) Lead-acid, deep-cycle 80% 35 2000 7-10 90 75 100

Nickel-cadmium 100% 20 1000-2000 10-15 70 60 1000 o o Nickel-metal hydride 100% 50 1000-2000 8-10 70 65 1200 * More vulnerable to freezing…(charged freeze at -57 C; discharged at -8 C)

Rough comparison of battery characteristics * 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 BATTERY RATINGS…. bottom) * Voltage… for lead-acid about 2 V per cell. Typical “nominal Voltage can be used… (but battery needs to have been “at rest” for several hours to be voltage” for battery is 6 V or 12 V (3 or 6 cells per battery) accurate)

13.0 1.30 * Voltage depends on state of charge and whether you are charging the 12.8 1.28 battery or discharging it. Voltage can range from about 11 to 15 V 12.6 1.26 SPECIFIC 12.4 1.24 V * Energy stored = Volts x Amps x Hours = Watt-hours 12.2 1.22

12.0 1.20 GRAVITY SG 11.8 1.18 * With voltage varying all over the map, how do you describe the energy

VOLTAGE (V) 11.6 1.16 stored in a battery? 11.4 1.14 11.2 1.12 Ans. Use “Amp-hours” @ nominal battery voltage as the measure of energy 11.0 1.10 stored in battery ! 100 80 60 40 20 0 STATE OF CHARGE (%)

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) 120

Example: A 12-volt golf-cart battery rated at 100 Amp-hours (Ah) 110 o when discharged over a 20- period of time (C/20) at 25 C … 100 C/72 C/48 90 C/20 Nominal C/20 Means it can deliver 5 Amps for 20 hours (5A x 20h = 100 Ah) 80 And 25oC C/10 Energy stored ≈ Volts x Amps x Hours = 12 V x 100 A-hr =1.2 kWhr 70 C/5 60

BATTERIES IN PARALLEL (Ah adds, V same); IN SERIES (Ah same, V adds) 50

Capacity / (Rated Capacity) 40 24V, 200Ah 24V, 100Ah 30 + + + + + 20 12V -30 -20 -10 0 10 20 30 40 12V, 200Ah 100Ah Battery Temperature (oC) - - - + DISCHARGE FASTER… less storage capacity + + + + + 12V 12V 12V Example: A 100 Ah, C/20 battery discharged at C/10 (10A), 25o has ≈ 90 Ah of capacity 100Ah 100Ah 100Ah ------COLDER TEMPERATURE… less storage capacity Example: 100 Ah, C/20 battery when discharged at -20oC and C/10 has ≈ 55 Ah of capacity (a) Parallel, Amp-Hrs add (b) Series, add (c) Series/Parallel 2.4 kWh 2.4 kWh 4.8 kWh

VI. LOAD ANALYSIS: How much energy do you “need?” BUT YOU DON’T GET TO USE THE FULL AMP-HR STORAGE…

Appliance Power (W) Hours Watt-hrs/day Percentage * For reasonable battery life, don’t discharge a car SLI battery more than about 20% Refrigerator, 19 cu. ft. 1,140 39% Lights (6 @ 30 W) 180 5 900 30% TV, 19-in., Active mode 68 3 204 7% * You should use deep-cycle batteries, and discharge them no more than 80 % TV, 19-in., Standby mode 5.1 21 107 4% Satellite, Active mode 17 3 51 2% Satellite, Standby mode 16 21 336 11% Usable Ah = 0.80 x nominal battery rated Ah of storage Cordless phone 4 24 96 3% Well pump, 100 ft, 1.6 gpm 100 1.25 125 4% Total 2,959 100%

2/3rds of TV is standby!

EXPRESS THE LOAD IN AMP-HOURS @ SYSTEM VOLTAGE (12V good for ≈ 1200 W)

2959 volts x amps x hours Batteries need to deliver = = 245 Ah/day 12 volts

8 LOAD ANALYSIS: How do you know how much power/energy an appliance uses? VII. BASIC PV SIZING..

kWh/m2 day * Read the nameplate on a device (Watts) (hrs/d @ 1-sun) “adjusted” …is maximum power device uses so it is on the high side PV output V Battery Ah/day Output AC DC Inverter * EPA appliance labels (kWh/yr) DeRating + - AC h ≈ 85% … refrigerators rated in 90oF kitchen (overestimate) h ≈ 90% Ah/day LOAD Dirt..etc Coulomb Ah/d @V Efficiency * Tables in Real Goods, on the web, and other places.. IR Amps @ 1-sun per module h ≈ 90% DC * Measure it yourself ! n modules in parallel LOAD (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

Coulomb System Rated power Inverter 2 dirt voltage kWh/m -d of module insolation

VIII. HOW SIZE THE BATTERIES? 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? n modules “adjusted” * Is there a backup generator? PV output 12 V Battery Ah/day Output AC 16 DC Inverter kWh/m2 day DeRating + - AC 14 (hrs/d @ 1-sun) h ≈ 90% 84 Ah/day h ≈ 85% LOAD 12 Dirt..etc Coulomb 850 Wh/d 10 Efficiency IR Amps @ 1-sun 99% Availability h ≈ 90% 71 Ah/d@12V 8 per module

6 * Convert AC Wh/d load to Ah/d @ system voltage V Days of Usable Storage 4 * Divide by inverter efficiency to get Ah/d from batteries 2 95% Availability * Multiply by days of storage wanted 0 * Divide Ah by maximum discharge depth allowed 2 3 4 5 6 7 8 Peak Sun Hours Example: •850 Wh/d AC load, 12-V system = 850/12 = 71 Ah/d Example: With 3.1 “peak sun hours” in December •85% efficient inverter -- 71/0.85 = 84 Ah/d from batteries 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.. •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 2.0 * Wire batteries in parallel to get Ah needed 2-modules

+ + I 1.0 1-module + - - - 0.0 EXAMPLE: 0 10 20 VB •850 Wh/d AC load, 12-V system = 850/12 = 71 Ah/d A COMPLETE SYSTEM: PV •85% efficient inverter -- 71/0.85 = 84 Ah/d from batteries DC AC + disconnect Fuse Charge Inverter •2 days of storage -- 84 Ah/d x 2d = 168 Ah Controller Box 12V, 200Ah •80% maximum discharge -- 168 Ah/0.8 = 210 Ah + + + + - Battery 6V, 6V, disconnect •6V 100 Ah batteries -- 2 batteries in series for 12V 100 Ah 100 Ah + + switch LOADS - - Astro - •2 strings would give 200 Ah… close enough 7105 + + 6V, 6V, - - 100 Ah 100 Ah + + - - 6V, - 100 Ah - -

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