3/30/2013

For the next period, we will talk about:

• The Solar Resource and its Utilization for Electric Energy • Other Resources, Just Coverage • The Smart Grid and Distribution System • Energy Economics

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Energy: Rapidly Growing, but with a Long Way to Go!

Current world-wide wind capacity is about 160 GW; total world-wide electrical capacity is about 4600 GW.

http://www.ren21.net/Resources/Publications/REN21Publications.aspx

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

1 3/30/2013

Solar Hot Water Heating: Renewables interactive map worldwide

http://map.ren21.net/

Renewables Global Futures Report (GFR). Download here

http://www.ren21.net/Portals/0/REN21_GFR_2013_print.pdf

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

The Solar Resource

• Before we can talk about , we need to talk about the source itself (the sun) – Need to know how much sunlight is available – Can predict where the sun is at any time – Insolation : incident solar radiation – Want to determine the average daily insolation at a site – Want to be able to chose effective locations and panel tilts of solar panels

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

2 3/30/2013

The Sun and Blackbody Radiation • The sun – 1.4 million km in diameter – 3.8 x 1020 MW of radiated electromagnetic energy • Black bodies – Both a perfect emitter and a perfect absorber – Perfect emitter – radiates more energy per unit of surface area than a real object of the same temperature – Perfect absorber – absorbs all radiation, none is reflected

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Plank’s Law

• Plank’s law – wavelengths emitted by a blackbody depend on temperature 3.74 108 E  (7.1) 5 14400  exp 1 T • λ = wavelength (μm) 2 • Eλ = emissive power per unit area of black body (W/m -μm) • T = absolute temperature (K)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

3 3/30/2013

Electromagnetic Spectrum Visible light has a wavelength of between 0.4 and 0.7 μm, with ultraviolet values immediately shorter, and infrared immediately longer

Source: en.wikipedia.org/wiki/Electromagnetic_radiation

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Blackbody Spectrum

Area under curve is the total radiant power emitted A black body is an The earth as a black body idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

Figure 7.1

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

4 3/30/2013

Stefan-Boltzmann Law

Total radiant power emitted is given by the Stefan –Boltzman law of radiation

EAT  4 (7.2)

E = total blackbody emission rate (W) σ = Stefan-Boltzmann constant = 5.67x10-8 W/m2-K4 T = absolute temperature (K) A = surface area of blackbody (m2)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Wien’s Displacement Rule

The wavelength at which the emissive power per unit area reaches its maximum point

2898   (7.3) max T

T = absolute temperature (K) λ = wavelength (μm)

λmax =0.5 μm for the sun , T = 5800 K λmax = 10.1 μm for the earth (as a blackbody), T = 288 K

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

5 3/30/2013

Extraterrestrial Solar Spectrum

Impact of atmosphere

Figure 7.2 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Intensity: Atmospheric Effects

Sun photosphere

Extraterrestrial sunlight (AM0)

Sunlight at sea level at 40° N Latitude at Intensity noon (AM1.5)

“AM” means “air mass”

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

6 3/30/2013

Air Mass Ratio

Figure 7.3

h 1 air mass ratio m  2 = (7.4) h1 sin  As sunlight passes through the atmosphere, less energy arrives at the earth’s surface • Air mass ratio of 1 (“AM1”) means sun is directly overhead • AM0 means no atmosphere • AM1.5 is assumed average at the earth’s surface

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Spectrum on Surface

• The air mas ratio (m) increases as the sun appears lower in the sky. • Notice there is a large loss towards the blue end for higher m, • The above is the reason why the sun appears reddish at sun rise and sun set

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

7 3/30/2013

The Earth’s Orbit

Figure 7.5

For applications, we’ll consider the characteristics of the earth’s orbit to be unchanging

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Declination

• Solar declination δ – the angle formed between the plane of the equator and the line from the center of the sun to the center of the earth • δ varies between +/- 23.45˚ • Assuming a sinusoidal relationship, a 365 day year, and n=81 is the spring equinox, the approximation of δ for any day n can be found from

360  23.45sinn 81 (7.6) 365

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

8 3/30/2013

The Sun’s Position in the Sky

Solar declination

What we need this for • Predict where the sun will be in the sky at any time • Pick the best tilt angles for photovoltaic (PV) panels

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Noon and Collector Tilt • Solar noon – sun is directly over the local line of longitude • Rule of thumb for the Northern Hemisphere - a south facing collector tilted at an angle equal to Figure 7.8 the local latitude

During solar noon, the sun’s rays are perpendicular to the collector face

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

9 3/30/2013

Altitude Angle βN at Solar Noon

• Altitude angle at solar noon βN – angle between the sun and the local horizon

N  90L  (7.7) • Zenith – perpendicular axis at a site

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Position at Any Time of Day • Described in terms of altitude angle β and azimuth

angle of the sun ϕS

• β and ϕS depend on latitude, day number, and time of day

• Azimuth angle (ϕS ) convention – positive in the morning when sun is in the east – negative in the evening when sun is in the west – reference in the Northern Hemisphere (for us) is true south • Hours are referenced to solar noon

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

10 3/30/2013

Altitude Angle and Azimuth Angle

Altitude Angle

Azimuth Angle

Figure 7.10

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Altitude Angle and Azimuth Angle

• Hour angle H- the number of degrees the earth must rotate before sun will be over your line of longitude • If we consider the earth to rotate at 15˚/hr, then 15 hour angle H  hours before solar noon (7.10) hour • At 11 AM solar time, H = +15˚ (the earth needs to rotate 1 more hour) • At 2 PM solar time, H = -30˚

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

11 3/30/2013

Example 7.3 – Where is the Sun?

• Find altitude angle β and azimuth angle ϕS at 3 PM solar time in Boulder, CO (L = 40˚) on the summer solstice (when the solar declination δ ˚ = 23.45) • Hour angle H is found from (7.10) 15 H -3 h 45 h • The altitude angle is found from (7.8)

sin  cos 40cos 23.45cos 45 sin 40sin 23.45 0.7527

 sin1  0.7527 48.8

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Example 7.3 – Where is the Sun? • The sin of the azimuth angle is found from (7.9) cos 23.45 sin 45  sin  = -0.9848 S cos 48.8 • Two possible azimuth angles exist 1 S = sin -0.9848  80 1 S = 180 -sin -0.9848 260 or 100 • Apply the test (7.11)

tan tan 23.45 cosH  cos 45 0.707  0.517 tanL tan 40

S =  80 (80  west of south)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

12 3/30/2013

Sun Path Diagrams for Shading Analysis • Now we know how to locate the sun in the sky at any time • This can also help determine what sites will be in the shade at any time • Sketch the azimuth and altitude angles of trees, buildings, and other obstructions • Sections of the sun path diagram that are covered indicate times when the site will be in the shade

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Sun Path Diagram for Shading Analysis • Trees to the southeast, small building to the southwest • Can estimate the amount of energy lost to shading

Figure 7.15

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

13 3/30/2013

California Solar Shade Control Act

• The shading of solar collectors has been an area of legal and legislative concern (e.g., a neighbor’s tree is blocking a ) • has the Solar Shade Control Act (1979) to address this issue – No new trees and shrubs can be placed on neighboring property that would cast a shadow greater than 10 percent of a collector absorption area between the hours of 10 am and 2 pm. – Exceptions are made if the tree is on designated timberland, or the tree provides passive cooling with net energy savings exceeding that of the shaded collector – First people were convicted in 2008 because of their redwoods

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

The Guilty Trees were Subject to Court Ordered Pruning

Source: This was from an article in NYTimes on 4/7/08

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

14 3/30/2013

Clear Sky Direct-Beam Radiation

o Direct beam radiation IBC – passes in a straight line through the atmosphere to the receiver

o Diffuse radiation IDC – scattered by molecules in the atmosphere

 Reflected radiation IRC – bounced off a surface near the reflector

Energy Systems Research Laboratory, FIU Figure 7.18 Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Extraterrestrial Solar Insolation I0

• Starting point for clear sky radiation calculations

• I0 passes perpendicularly through an imaginary surface outside of the earth’s In one year, less thanFigure half 7.19 of atmosphere I0 reaches earth’s surface as a direct beam • Ignoring sunspots, I0 can be written as

360n 2 I0 SC 1 0.034cos (W/m ) (7.20) 365 • SC = solar constant = 1.377 kW/m2 • n = day number On a sunny, clear day, beam radiation may exceed 70%

of I0

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

15 3/30/2013

Attenuation of Incoming Radiation • Can treat attenuation as an exponential decay function

km IAeB  (7.21) • A = apparent extraterrestrial flux • IB = beam portion of the radiation that reaches the earth’s • k = optical depth surface • m = air mass ratio from (7.4)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Insolation on a Collecting Surface • Direct-beam radiation is just a function of the angle between the sun and the collecting surface (i.e., the incident angle 

IIBC B cos • Diffuse radiation is assumed to be coming from essentially all directions to the angle doesn’t matter; it is typically between 6% and 14% of the direct value. • Reflected radiation comes from a nearby surface, and depends on the surface reflectance,  ranging down from 0.8 for clean snow to 0.1 for a shingle roof.

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

16 3/30/2013

Tracking Systems

• Most residential solar PV systems have a fixed mount, but sometimes tracking systems are cost effective • Tracking systems are either single axis (usually with a rotating polar mount [parallel to earth’s axis of rotation), or two axis (horizontal [altitude, up-down] and vertical [azimuth, east-west] • Ballpark figures for tracking system benefits are about 20% more for a single axis, and 25 to 30% more for a two axis

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Monthly and Annual Insolation

• For a fixed system the total annual output is somewhat insensitive to the tilt angle, but there is a substantial variation in when the most energy is generated

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

17 3/30/2013

US Annual Insolation

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Worldwide Annual Insolation

http://www.ren21.net/

In 2009 worldwide PV capacity was about 21,000 MW, with almost half (9800 MW) in Germany, 3400 MW in Spain, 2600 MW in Japan and 1200 MW in the US

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

18 3/30/2013

Concentrating Solar Power Technologies (CSP)

• Basic idea: Convert sunlight into thermal energy, use that energy to get electricity • Concentration is needed to get a hot enough temperature • Three successfully demonstrated technologies: – – Solar Central Receiver – Solar Dish/ Sterling

• This is a different topic than photovoltaic (PV) cells which we’ll cover next

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Dish/ Sterling

• Multiple mirrors that approximate a parabolic dish • Receiver – absorbs solar energy & converts to heat • Heat is delivered to Stirling engine Source: http://www.eere.energy.gov/de/csp.html • Average efficiencies >20%

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

19 3/30/2013

Parabolic Troughs Source: http://www.eere.energy.gov/de/csp.html

• Receivers are tubes - Heat collection elements (HCE) • Heat transfer fluid circulates in the tubes • Delivers collected energy to steam turbine/generator • Parabolic mirrors rotate east to west to track the sun

Source: http://www.nrel.gov/csp/troughnet/solar_field.html

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Parabolic Troughs - SEGS

• Mojave Desert, California • Aerial view of the five 30MW

Source: http://www.flagsol.com/SEGS_tech.htm parabolic trough plants • Solar Electric Generation System (SEGS) • Largest solar energy facility in the Source: http://www.flagsol.com/SEGS_tech.htm world – 354 MW http://en.wikipedia.org/wiki/Solar_Energy_Generating_Systems

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

20 3/30/2013

Solar Central Receiver

• Also called Power Towers • – computer controlled mirrors • Reflect sunlight onto receiver Source: http://www.eere.energy.gov/de/csp.html

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Solar Central Receiver – Solar Two • 10 MW • Two-tank, molten-salt thermal storage system • Barstow, CA • Demolished in November 2009 • Solar Tres is being built in Spain – will be Source: http://www.trec-uk.org.uk/csp.htm 15 MW (CSP)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

21 3/30/2013

CSP Comparisons • All use mirrored surfaces to concentrate sunlight onto a receiver to run a heat engine • All can be hybridized with auxiliary fuel sources • Higher temperature -> higher efficiency

Annual Measured Required “Suns” of Efficiency Acres/MW concentration Dish Stirling 21% 4 3000

Parabolic 14% 5 100 Troughs Solar Central 16% 8 1000 Receiver

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Photovoltaics (PV) Photovoltaic definition- a material or device that is capable of converting the energy contained in photons of light into an electrical voltage and current http://www1.eere.energy.gov/solar/pv_use.html "Sojourner" Solar House exploring Mars, 1997

Rooftop PV modules on a village health center in West Bengal, India

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

22 3/30/2013

PV History

• Edmund Becquerel (1839) • Adams and Day (1876) • Albert Einstein (1904) • Czochralski (1940s) • Vanguard I satellite (1958)

• Today…

Cost/Capacity Analysis (Wp is peak Watt)

http://www.nrel.gov/pv/pv_manufacturing/cost_capacity.html

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

PV System Overview

is a diode Shadows • Photo power converted to DC • Shadows & defects convert generating areas to loads • DC is converted to AC by an inverter • Loads are unpredictable • Storage helps match generation to load

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

23 3/30/2013

Some General Issues in PV

• The device • Efficiency, cost, manufacturability automation, testing

• Encapsulation • Cost, weight, strength, yellowing, etc.

• Accelerated lifetime testing • 30 year outdoor test is difficult • Damp heat, light soak, etc.

• Inverter & system design • Micro-inverters, blocking diodes, reliability

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

What are Solar Cells? Load • Solar cells are diodes - • Light (photons) generate free + carriers (electrons and holes) n-type p-type which are collected by the electric field of the diode junction Open-circuit voltage • The output current is a fraction of this photocurrent Voltage

• The output voltage is a Maximum

fraction of the diode built-in Current Power Point voltage

Short-circuit current

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

24 3/30/2013

Standard Equivalent Circuit Model

Where does the power go?

Series resistance

(minimize) Load Diode (maximize) Shunt resistance Photocurrent source

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Photons

Photons are characterized by their wavelength (frequency) and their energy cv  (8.1) hc Ehv (8.2) v

Table 8.2 Band Gap and Cut-off Wavelength Above Which Electron Excitation Doesn’t Occur

Quantity Si GaAs CdTe InP Band gap (eV) 1.12 1.42 1.5 1.35 Cut-off wavelength (μm) 1.11 0.87 0.83 0.92

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

25 3/30/2013

Energy-band Diagrams

Silicon band gap energy is 1.12 eV

• Conduction band – top band, here electrons contribute to current flow, empty at absolute zero for semiconductors • An electron must acquire the band gap energy to jump across to the conduction band, measured in electron-volts eV • Electrons create holes when they jump to the conduction band • Photons with enough energy create hole-electron pairs in a semiconductor http://upload.wikimedia.org/wikipedia/commons/c/c7/Isolator-metal.svg

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Silicon Solar Cell Max Efficiency

• Upper bound on the efficiency of a silicon solar cell: – Band gap: 1.12 eV, Wavelength: 1.11 μm – This means that photons with wavelengths longer than 1.11 μm cannot send an electron to the conduction band. – Photons with a shorter wavelength but more energy than 1.12 eV dissipate the extra energy as heat

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

26 3/30/2013

Silicon Solar Cell Max Efficiency For an Air Mass Ratio of 1.5, 49.6% is the maximum possible fraction of the sun’s energy that can be collected with a silicon solar cell

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

They are Diodes

• Two regions: “n-type” which donate electrons and “p-type” which accept electrons • p-n junction- diffusion of electrons and holes, current will flow readily in one direction (forward biased) but not in the other (reverse biased), this is the diode

http://en.wikipedia.org/wiki/File:Pn-junction-equilibrium.png

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

27 3/30/2013

The p-n Junction Diode

Voltage-Current (VI) characteristics for a diode

qVd / kT IIed  0 ( -1) (8.3)

38.9Vd IIed 0 (-1) (at 25C)

Figure 8.15 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Circuit Model I I + + I + I d V SC V PV - Load Load - -

• The current going to the load is the short-circuit current minus diode current qV/ kT IISC Ie0 ( -1) (8.8) • Setting I to zero, the open circuit voltage is

kT ISC VOC ln 1 (8.9) qI0 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

28 3/30/2013

PV Equivalent Circuit

• Add impact of parallel leakage resistance RP (want RP to be high) V II(SC I d ) (8.12) RP Vd

Figure 8.22. PV Cell with parallel resistance

• Add impact of series resistance RS (want RS to be small) due to contact between cell and wires and some from resistance of semiconductor

VVIRdS  (8.14) Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Series and Shunt Resistance Effects:

Considering both Rs and Rp:

1 38.9(VIR s ) IISC I0 e  1 - VIR  S @ 25  C (8.18) RP

Series resistance drops Equivalent Circuit some voltage (reduces R output voltage) s I I (minimize) Shunt resistance drops d ISC P R

some current (reduces Load Diode output current) (maximize) Photocurrent Photocurrent source

Voltage & Current are coupled

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

29 3/30/2013

Series and Shunt Resistance Effects

• Parallel (RP) – current drops by

ΔI=V/RP Figure 8.23

• Series (RS) – voltage drops by

ΔV=IRS Figure 8.25

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Fill Factor and Cell Efficiency

Fill Factor (FF) VRIR =

Isc•Voc

“AM 1.5” Incident Solar Power ~100 mW/cm2

JSC

Imax•Vmax Cell Efficiency Isc•Voc•FF () = = Incident Incident Power Power

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

30 3/30/2013

Load Multijunction Cells

- - - - Problem: Single junction loses + + + + all of the photon energy above p-type the gap energy. n-type p-type n-type p-type n-type p-type n-type

Energy (eV) 4.0 3.0 2.5 2.0 1.7 1.5 1.3 1.1 1.0 0.9 Solution: Use a series of cells 180 of different gaps. 160

140

Each cell captures the light m)  - transmitted from above. 2 120 100

But… can’t just use a graded 80

gap. Allows electrons to 60 Cell #4 (0.6 eV gap) Intensity (mW/mIntensity

escape to low gap region. 40

20 Top Cell eV (1.9 gap) Top Cell #2 (1.4 eV gap)

Need separate cells. Cell #3 (1.0 eV gap) 0 300 500 700 900 1100 1300 1500 Wavelength (nm) Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Record laboratory thin film cell efficiencies

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

31 3/30/2013

Cells to Modules to Arrays

Rain, hail, ice, snow

Local failures, shadows

Heat, humidity, corrosive gases

Modules – A 12V module has 36 cells wired in series, each cell ~ 0.5 V, 72-cell modules are also common

Arrays – combination of modules connected in series and/or in parallel

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Interconnect Schemes Soldered (standard for Si cells)

Monolithic interconnects

Encapsulation

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

32 3/30/2013

Impact of Temperature

• “1 sun” of irradiance = 1 kW/m2 for AM = 1.5

• VOC decreases by ~0.37% per ˚C for crystalline silicon cells

• ISC increases by about 0.05% per ˚C • NOCT – Normal Operating Temperature Figure 8.36 NOCT20 C TTcell amb  S (8.24) 0.8 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Impact of Shading

• Shading causes PV to act as a resistor instead of a current source, can reduce output power by > 50%

Figure 8.38

Figure 8.37 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

33 3/30/2013

Blocking Diodes -- protection from low voltage strings

Cell arrays including a weak Two good cells One good cell, one weak cell cell; the array performs at the level of the worst cell.

Monolithically-interconnected Cell Array Diodes can be used to Front contact prevent current from strong Cell 1 Cell 2 Back contact arrays flowing through weak array segments. However, they reduce output voltage. For a full discussion, see H.S. Rauschenbach, Solar Cell Array Design Handbook (Van Nostrand Reinhold, New York, 1980)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Bypass Diodes -- protection from low current strings • Bypass diodes are used in modules to route current around shadowed or defective strings (series connected strings must maintain constant current throughout) • Used typically every 15-20 cells

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

34 3/30/2013

Silicon Solar Modules • Crystalline silicon – Single crystals – Cast polycrystals • Well understood • Cost analysis easy • Source material is expensive • Material sensitive to impurities & defects • The major limitation to Si technology is the availability of electronic- grade Si … most manufactured technology

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Silicon Solar Modules • Steps to make a Si module: • Growth of the Si bulk crystal (ingot) • Cutting of the wafers from the grown ingot • Diffusion of dopants to form the junction • Interconnection • Packaging

EnergyFigure Systems courtesy Research R. Birkmire, Laboratory, Univ. of Delaware FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

35 3/30/2013

Czochralsky Si

• Bulk single crystal boules grown by this method.

Growth rate 0.5-3 mm/min

Typical PV boule diameter: 100-150 mm length: 40-150 cm

Some issues: • Low throughput • High energy use • Requires skilled operator Photographs courtesy MEMC Electronic Materials Inc, St. Peters MO.

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Cast Monocrystalline Silicon

Figures Courtesy:

Seed crystal

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

36 3/30/2013

Crystalline Si by Casting

• Bulk Polycrystals grown by this method

Wire Saw Mold

Cast Slow cooling Polycrystal Features: • Large grains possible • Batch process is fast • Low technology, cost • Relatively fast • Lower quality crystals

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Crystalline Si: Ribbon methods

String-ribbon growth (STR) method: Large grain multicrystals close to {110}. Throughput: 160 kW/furnace/year @ 15% efficiency, 90% yield

Cells: 15-16% best

Developed and used by Evergreen solar

Image courtesy: Evergreen solar, www.evergreen.com used with permission

In ribbon growth, the casting produces a ribbon without much cutting.

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Cast Monocrystalline Silicon

After doping/passivation

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

PV Systems – Four configurations

1. Grid-connected systems

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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PV Systems – Four Configurations

2. Stand-alone systems with directly-connected loads

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

PV Powered Water Pumping

http://www.rajkuntwar.com/html/Solar.html

http://www.oksolar.com/pumps/

http://solar-investment.us/solar-pv-surface-and-bore-water-pumping/

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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DC Motor I-V Curve

• DC motors have an I-V curve similar to a resistor

• e = kω is back emf, Ra is armature resistance VIRka  (9.3)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

DC Motor I-V Curve Linear Current Booster (LCB) helps the motor be able to start in low sunlight

Figure 9.10

Figure 9.9 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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PV Systems – Four Configurations

3. Stand-alone systems which charge batteries

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

PV Systems – Four Configurations Microgrids • A small electric grid with several generation sources – The microgrid can be configured to operate either connected to the main grid or standalone • The military is a key proponent of microgrids, since they would like the ability to operate bases independent of any grid system for long periods of time • Renewable generation by be quite attractive because it decreases the need to store large amounts of fossil fuel – Time magazine reported in Nov 2009 that average US solider in Afghanistan requires 22 gallons of fuel per day at an average costs of $45 per gallon

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Load I-V Curves

• PV panels have I-V curves and so do loads • Use a combination of the two curves to tell where the system is actually operating • Operating point – the intersection point at which the PV and the load I-V curves are satisfied

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Resistive Load I-V Curve

1 VIR IV  (9.1) R • Straight line with slope 1/R • As R increases, operating point moves to the right • Can use a potentiometer to plot the PV module’s IV curve • Resistance value that results in maximum power

Vm Rm  (9.2) Im Figure 9.5 Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Maximum power transfer

• Maximum power point (MPP) should occur when the load resistance

R = VR/IR under 1-sun 25˚C, AM 1.5 conditions

• A MPP tracker maintains PV system’s highest efficiency as the amount of insolation changes.

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Maximum Power Point Trackers

• Maximum Power Point Trackers (MPPTs) are often a standard part of PV systems, especially grid- connected • Idea is to keep the operating point near the knee of the PV system’s I-V curve • Buck-boost converter – DC to DC converter, can either “buck” (lower) or “boost” (raise) the voltage • Varying the duty cycle of a buck-boost converter can be done such that the PV system will deliver the maximum power to the load

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Hourly I-V Curves

• Current at any voltage is proportional to insolation

• VOC drops as insolation decreases • Can just adjust the 1-sun I-V curve by shifting it up or down

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Grid-Connected Systems

• Can have a combiner box and a single inverter or small inverters for each panel • Individual inverters make the system modular • Inverter sends AC power to utility service panel • Power conditioning unit (PCU) may include – MPPT – Ground-fault circuit interrupter (GFCI) – Circuitry to disconnect from grid if utility loses power – Battery bank to provide back-up power

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Components of Grid-Connected PV

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Individual Inverter Concept

• Easily allow expansion • Connections to house distribution panel are simple • Less need for expensive DC cabling

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Interfacing with the Utility • – customer only pays for the amount of energy that the PV system is unable to supply • In the event of an outage, the PV system must quickly and automatically disconnect from the grid • A battery backup system can help provide power to the system’s owners during an outage • Good grid-connect inverters have efficiencies above 90%

http://www.pasolar.ncat.org/lesson05.php

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Losses from Mismatched Modules • Illustrates the impact of slight variations in module I-V curves • Only 330 W is possible instead of 360 W

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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“Peak-Hours” Approach • 1-sun is 1 kW/m2 • We can say that 5.6 kWh/(m2-day) is 5.6 hours of “peak sun” • PVUSA test conditions (PTC) – 1-sun, 20˚C ambient temperature, wind-speed of 1 m/s

• Pac(PTC) = AC output of an array under PTC

• If we know Pac, computed for 1-sun, just multiply by hours of peak sun to get kWh • If we assume the average PV system efficiency over a day is the same as the efficiency at 1-sun, then

Energy (kWh/day)Pac kW h/day of "peak sun" (9.14)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Capacity Factor of PV

Energy kWh/yr Pac kWCF 8760 h/yr (9.15) h/day of "peak sun" CF (9.16) 24 h/day

Figure 9.28 PV Capacity Factors for US cities

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Stand-Alone PV Systems • When the grid is not nearby, the extra cost and complexity of a stand-alone power system can be worth the benefits • System may include batteries and a backup generator

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Stand-Alone PV - Considerations

• PV System design begins with an estimate of the loads that need to be served by the PV system • Tradeoffs between more expensive, efficient appliances and size of PVs and battery system needed • Should you use more DC loads to avoid inverter inefficiencies or use more AC loads for convenience? • What fraction of the full load should the backup generator supply? • Power consumed while devices are off • Inrush current used to start major appliances

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Batteries and PV Systems • Batteries in PV systems provide storage, help meet surge current requirements, and provide a constant output voltage. • Lots of interest in battery research, primarily driven by the potential of pluggable hybrid electric vehicles – $2.4 billion awarded in August 2009 • There are many different types of batteries, and which one is best is very much dependent on the situation – Cost, weight, number and depth of discharges, efficiency, temperature performance, discharge rate, recharging rates

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Battery I-V Curves

• Energy is stored in batteries for most off-grid applications

• An ideal battery is a voltage source VB

• A real battery has internal resistance Ri

VVBi RI (9.4) Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Battery I-V Curves

• Charging– I-V line tilts right with a slope of 1/Ri, applied voltage must be greater than VB • Discharging battery- I-V line tilts to the left with slope

1/Ri, terminal voltage is less than VB

Figure 9.12

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Lead Acid Batteries • Most common battery for larger-scale storage applications • Invented in 1859 • There are three main types: 1) SLI (Starting, Lighting and Ignition) : optimized for starting cars in which they are practically always close to fully charged, 2) golf cart : used for running golf carts with fuller discharge, and 3) deep-cycle, allow much more repeated charge/discharge such as in a solar application

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Basics of Lead-Acid Batteries

+2 Positive Plate: PbO24 + 4H + SO + 2e  PbSO 42 2H O (9.21) 2 Negative Plate: PbO24 + SO PbSO 4 2e (9.22)

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Basics of Lead-Acid Batteries

• During discharge, voltage drops and specific gravity drop • Sulfate adheres to the plates during discharge and comes back off when charging, but some of it becomes permanently attached

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Battery Storage • Battery capacity has tended to be specified in amp- hours (Ah) as opposed to an energy value; multiply by average voltage to get watt-hours – Value tells how many amps battery can deliver over a specified period of time. – Amount of Ah a battery can delivery depends on its discharge rate; slower is better

Figure shows how capacity degrades with temperature and rate

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Battery Technologies

Type Density, Cost Cycles Charge Power Wh/kG $/kWh time, W/kg hours Lead-acid, 35 50-100 1000 12 180 deep cycle Nickel-metal 50 350 800 3 625 hydride Lithium Ion 170 500-100 2000 2 2500

The above values are just approximate; battery technology is rapidly changing, and there are many different types within each category. For stationary applications lead-acid is hard to beat because of its low cost. It has about a 75% efficiency. For electric cars lithium ion batteries appear to be the current front runner

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Estimating Storage Needs

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

Stand-Alone PV Systems – Design Summary • Battery Sizing – How many days of storage needed? • Generator Sizing • System Costs

http://www.ecosolarenergy.com.au/How_a_Standalone_System_Works-28.htm Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2013

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Modeling a Practical PV System

DC AC Cable TL PV Array G DC DC Grid Transformer Boost Converter VSI

To filter the ripple on the output voltage of the PV arrays • Reactive power compensation is Maximum Power Point needed to connect to the grid Tracking is implemented here • PV supplies active power

• To convert the voltage from DC to AC • The AC voltage has to be synchronized with the grid voltage Energy Systems Research Laboratory, FIU

Why we need Power Conditioning in PV Systems?

1. The output voltage of PV systems is DC, while most of the loads are AC

2. The characteristics of PV arrays are non- linear hence power conditioning units are needed to track their maximum power point

Energy Systems Research Laboratory, FIU

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grid-connected PV systems without battery storage— Two Conditioning Units

Phase‐locked loop has to be used to synchronize the power with the grid MPPT

MPPT is implemented in the boos converter controller Note: During power deficiency (e.g. at night), the power is received from the grid

Energy Systems Research Laboratory, FIU

grid-connected PV systems without battery storage— Single Conditioning Unit

Phase‐locked loop has to be used to synchronize the power with the grid

MPPT

MPPT is implemented within the inverter controller Energy Systems Research Laboratory, FIU

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grid-connected PV systems with battery storage

MPPT

• In this system, there are two options for covering power deficiencies: the grid and the battery.

• This can be used for energy management.

Energy Systems Research Laboratory, FIU

Stand-Alone PV Systems

This system is applicable for rural residential areas

Optional

The capacity of the battery is an essential parameter in stand‐alone systems.

Energy Systems Research Laboratory, FIU

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Modeling the PV Array

• Modeling a PV array is achieved by implementing the equations relating the PV output voltage and power the its parameters:

photo-generated current IL, diode saturation current ID, parallel resistance RSH and series resistance Rs

Example

Energy Systems Research Laboratory, FIU

Boost Converter Modeling

From SimPowerSystems Library Control and Signal Processing

Energy Systems Research Laboratory, FIU

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Inverter

DC Input

IGBT or MOSFET switches

Energy Systems Research Laboratory, FIU

Modeling a Practical PV System

260 V/ 25 kV DC AC 25 kV Grid Cable TL PV Array G DC DC Grid Transformer Boost Converter VSI

100 kW PV Array 10 kVar Maximum Power Point Tracking achieved by the Incremental Conductance Technique • A 3-level VCS is used to convert DC to AC • 33*60 Hz, 500 V

Energy Systems Research Laboratory, FIU

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A modeling example

• PVarray_Grid_IncCondReg_det.mdl is a detailed model of a 100-kW array connected to a 25- kV grid via a DC-DC boost converter and a three-phase three-level Voltage Source Converter (VSC). • Maximum Power Point Tracking (MPPT) is implemented in the boost converter by means of a Simulink model using the “Incremental Conductance + Integral Regulator” technique.

Energy Systems Research Laboratory, FIU

Energy Systems Research Laboratory, FIU

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Detailed Model Description The detailed model contains: • PV array delivering a maximum of 100 kW at 1000 W/m2 sun irradiance. • 5-kHz boost converter (orange blocks) increasing voltage from PV natural voltage (272 V DC at maximum power) to 500 V DC. Switching duty cycle is optimized by the MPPT controller that uses the “Incremental Conductance + Integral Regulator” technique. • 1980-Hz (33*60) 3-level 3-phase VSC (blue blocks). The VSC converts the 500 V DC to 260 V AC and keeps unity power factor. • 10-kvar capacitor bank filtering harmonics produced by VSC. 100-kVA 260V/25kV three-phase coupling transformer. • Utility grid model (25-kV distribution feeder + 120 kV equivalent transmission system). • For this detailed model, the electrical circuit is discretized at 1 µs sample time, whereas sample time used for the control systems is Energy100 Systems µs. Research Laboratory, FIU

PV Array Modeling

• The 100-kW PV array of the detailed model uses 330 SunPower modules (SPR-305). The array consists of 66 strings of 5 series-connected modules connected in parallel (66*5*305.2 W= 100.7 kW). • Open the PV-array block menu and look at model parameters. • Manufacturer specifications for one module are: Number of series-connected cells : 96 Open-circuit voltage: Voc= 64.2 V Short-circuit current: Isc = 5.96 A Voltage and current at maximum power : Vmp =54.7 V, Imp= 5.58 A

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PV Characteristics

• The PV array block menu allows you to plot the I-V and P-V characteristics for one module and for the whole array. The characteristics of the SunPower-SPR305 array are reproduced below.

I-V and P-V characteristics of PV array

Red dots on blue curves indicate module manufacturer specifications (Voc, Isc, Vmp, Imp) under standard test conditions (25 degrees Celsius, 1000 W/m2).

Energy Systems Research Laboratory, FIU

Array Type

• Using the “Module type” pop-up menu, you can choose among various array types for your simulation. Ten different types are proposed. The module characteristics were extracted from NREL System Advisor Model (https://sam.nrel.gov/).

• The average model uses two 100-kW PV arrays. PV1 uses SunPower-SPR305 modules and PV2 uses Kyocera-DD205GX-LP modules.

Energy Systems Research Laboratory, FIU

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Boost Converter Modeling

• In the detailed model, the boost converter (orange blocks) boosts DC voltage from 273.5 V to 500V. • This converter uses a MPPT system which automatically varies the duty cycle in order to generate the required voltage to extract maximum power.

Energy Systems Research Laboratory, FIU

Boost Converter Modeling

• Look under the mask of the “Boost Converter Control” block to see how the MPPT algorithm is implemented. • For details on various MPPT techniques, refer to the following paper: Moacyr A. G. de Brito, Leonardo P. Sampaio, Luigi G. Jr., Guilherme A. e Melo, Carlos A. Canesin “Comparative Analysis of MPPT Techniques for PV Applications”, 2011 International Conference on Clean Electrical Power (ICCEP).

Energy Systems Research Laboratory, FIU

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VSC Modeling

• The three-level VSC (blue blocks) regulates DC bus voltage at 500 V and keeps unity power factor.

• The control system uses two control loops: an external control loop which regulates DC link voltage to +/- 250 V and an internal control loop which regulates Id and Iq grid currents (active and reactive current components).

• Id current reference is the output of the DC voltage external controller.

Energy Systems Research Laboratory, FIU

VSC Modeling

• Iq current reference is set to zero in order to maintain unity power factor. Vd and Vq voltage outputs of the current controller are converted to three modulating signals Uref_abc used by the PWM three-level pulse generator. • The control system uses a sample time of 100 µs for voltage and current controllers as well as for the PLL synchronization unit. In the detailed model, pulse generators of Boost and VSC converters use a fast sample time of 1µs in order to get an appropriate resolution of PWM waveforms.

Energy Systems Research Laboratory, FIU

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Demo 1—Running the detailed model

• 1. Run the PVarray_Grid_IncCondReg_det model for 3 seconds and observe the following sequence of events on Scopes. • Note: In order to speed up simulation, select the “Accelerator” mode before starting simulation. Using the Accelerator with this demo provides a performance gain of approximately 7X.

Energy Systems Research Laboratory, FIU

• From t=0 sec to t= 0.05 sec, pulses to Boost and VSC converters are blocked. PV voltage corresponds to open-circuit voltage (Nser*Voc=5*64.2=321 V, see V trace on Scope Boost). • The three-level bridge operates as a diode rectifier and DC link capacitors are charged above 500 V (see Vdc_meas trace on Scope VSC).

Energy Systems Research Laboratory, FIU

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• At t=0.05 sec, Boost and VSC converters are de- blocked. DC link voltage is regulated at Vdc=500V. Duty cycle of boost converter is fixed (D= 0.5 as shown on Scope Boost) and sun irradiance is set to 1000 W/m2. Steady state is reached at t=0.25 sec. • Resulting PV voltage is therefore V_PV = (1-D)*Vdc= (1-0.5)*500=250 V (see V trace on Scope Boost). The PV array output power is 96 kW (see Pmean trace on Scope Boost) whereas maximum power with a 1000 W/m2 irradiance is 100.7 kW. • Observe on Scope Grid that phase A voltage and current at 25 kV bus are in phase (unity power factor).

Energy Systems Research Laboratory, FIU

• At t=0.4 sec MPPT is enabled. The MPPT regulator starts regulating PV voltage by varying duty cycle in order to extract maximum power.

• Maximum power (100.7 kW) is obtained when duty cycle is D=0.453. At t=0.6 sec, PV mean voltage =274 V as expected from PV module specifications (Nser*Vmp=5*54.7= 273.5 V).

Energy Systems Research Laboratory, FIU

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• From t=0.7 sec to t=1.2 sec, sun irradiance is ramped down from 1000 W/m2 to 250 W/m2. MPPT continues tracking maximum power. • At t=1.2 sec when irradiance has decreased to 250 W/m2, duty cycle is D=0.485. • Corresponding PV voltage and power are Vmean= 255 V and Pmean=22.6 kW. Note that the MMPT continues tracking maximum power during this fast irradiance change.

Energy Systems Research Laboratory, FIU

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