PV Energy Utilization

Energy Systems Research Laboratory, FIU

PV Energy Utilization

Professor Osama A. Mohammed

Department of Electrical and Computer Engineering

EEL5285 & EEL 4930All Sections (Spring 2017)

Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017


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

Rooftop PV

modules on a

village health

center in West

Bengal, India

http://www1.eere.energy.gov/solar/pv_use.html

"Sojourner"

exploring Mars,

1997

Solar House


Energy Systems Research Laboratory, FIUProfessor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017

Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017


Loads- Household Consumption

Source: EIA 2008

Annual Energy

Review



Example: Daily Variation

for CA



Example: Weekly Variation



Example: Annual System

Load

0

5000

10000

15000

20000

250001

518

1035

1552

2069

2586

3103

3620

4137

4654

5171

5688

6205

6722

7239

7756

8273

Hour of Year

MW

Lo

ad



Load Duration CurveA very common way of representing the annual load is to sort the one hour

values, from highest to lowest. This representation is known as a “load

duration curve.”

6000

5000

4000

3000

2000

1000

0DE

MA

ND

(M

W)

0 1000 HRS 7000 8760

Load duration curve tells how much generation is needed



Ball park Energy Costs

Source: http://www.oe.energy.gov/DocumentsandMedia/adequacy_report_01-09-09.pdf



Support for Renewable Energy

• The White House issued report about how the

stimulus is going. Renewable energy projects

were very much included. For example the

largest solar PV installation in US, 579 MW

Solo Star Site in California.

• Cost of residential solar is projected to decrease

from $0.21 per kWh in 2009 to $0.10 in 2015

and $0.06 by 2030; wholesale parity is $0.05.

http://www.whitehouse.gov/sites/default/files/uploads/Recovery_Act_Innovation.pdf


Energy Systems Research Laboratory, FIU Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017

Solar Star (I and II) United States 34°49′50″N

118°23′53″W

579 2015

Topaz Solar Farm United States35°23′N 120°4′W

550 2017

Desert Sunlight Solar

FarmUnited States 33°49′33″N

115°24′08″W

550 2015

Copper Mountain

Solar FacilityUnited States

35°47′N 114°59′W458 2015

Largest Solar Plants in the US

https://en.wikipedia.org/wiki/Solar_Star

https://en.wikipedia.org/wiki/United_States

https://tools.wmflabs.org/geohack/geohack.php?pagename=List_of_photovoltaic_power_stations&params=34_49_50_N_118_23_53_W_&title=Solar+Star

https://en.wikipedia.org/wiki/Topaz_Solar_Farm


https://tools.wmflabs.org/geohack/geohack.php?pagename=List_of_photovoltaic_power_stations&params=35_23_N_120_4_W_&title=Topaz+Solar+Farm

https://en.wikipedia.org/wiki/Desert_Sunlight_Solar_Farm


https://tools.wmflabs.org/geohack/geohack.php?pagename=List_of_photovoltaic_power_stations&params=33_49_33_N_115_24_08_W_&title=Desert+Sunlight+Solar+Farm

https://en.wikipedia.org/wiki/Copper_Mountain_Solar_Facility


https://tools.wmflabs.org/geohack/geohack.php?pagename=List_of_photovoltaic_power_stations&params=35_47_N_114_59_W_&title=Copper+Mountain+Solar+Facility


Efficiency and Home Energy Use

• Whole-house energy efficiency approach – find out

which parts consume the most energy

http://www1.eere.energy.gov/consumer/tips/home_energy.html



PV History

• Edmund Becquerel (1839)

• Adams and Day (1876)

• Albert Einstein (1904)

• Czochralski (1940s)

• Vanguard I satellite (1958)

• Today…

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

Cost/Capacity Analysis(Wp is peak Watt)



PV System Overview

Shadows• Solar cell is a diode

• Photopower 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



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



What are Solar Cells?

Cu

rre

nt

Voltage

Open-

circuit

voltage

Short-circuit

current

Maximum

Power

Point

n-t

ype

p-t

ype

-+

Load

• Solar cells are diodes

• Light (photons) generate

free carriers (electrons and

holes) which are collected

by the electric field of the

diode junction

• The output current is a

fraction of this

photocurrent

• The output voltage is a

fraction of the diode built-

in voltage



Standard Equivalent Circuit Model

Photo

curr

ent

sourc

e

Dio

de

Shunt

resis

tance

Load

Series resistance

Where does the power go?

(minimize)

(maxim

ize)



Photons

• Photons are characterized by their wavelength

(frequency) and their energy

(8.1)c v

(8.2)hc

E hvv

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

Table 8.2 Band Gap and Cut-off Wavelength Above Which Electron

Excitation Doesn’t Occur



Energy-band Diagrams

• 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/co

mmons/c/c7/Isolator-metal.svg

Silicon band gap

energy is 1.12 eV



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



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



Review of 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



The p-n Junction Diode

Voltage-Current (VI) characteristics for a diode/

0( -1) (8.3)dqV kT

dI I e

38.9

0( -1) (at 25 C)dV

dI I e

Figure 8.15Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017


Circuit Model

• The current going to the load is the short-circuit

current minus diode current

• Setting I to zero, the open circuit voltage is

/

0( -1) (8.8)qV kT

SCI I I e

0

ln 1 (8.9)SCOC

IkTV

q I

ISC

Id

I

VLoad

+

-

I

VLoad

+

-

+

-PV



PV Equivalent Circuit

• Add impact of parallel leakage resistance RP (want

RP to be high)

• Add impact of series resistance RS (want RS to be

small) due to contact between cell and wires and

some from resistance of semiconductor

( ) (8.12)SC d

P

VI I I

R

(8.14)d SV V I R

Figure 8.22. PV Cell with parallel resistance

Vd



Series and Shunt Resistance Effects:

Considering both Rs and Rp:

Series resistance drops

some voltage (reduces

output voltage)

Shunt resistance drops

some current (reduces

output current)

Voltage & Current are coupled

Ph

oto

cu

rre

nt

so

urc

e

Dio

de

RP

Load

Rs

(minimize)

(ma

xim

ize

)

Equivalent Circuit

38.9( )

0

1e 1 - @ 25 C (8.18)sV IR

SC S

P

I I I V I RR

Id

I

ISC



Series and Shunt Resistance Effects

• Parallel (RP) –

current drops by

ΔI=V/RP

• Series (RS) –

voltage drops by

ΔV=IRS

Figure 8.23

Figure 8.25



Fill Factor and Cell

Efficiency

Fill Factor (FF)

=

VRIR

Isc•Voc

Cell Efficiency

(h) =

Isc•Voc•FF

Incident

Power

Imax•Vmax

Incident

Power

=

“AM 1.5” Incident Solar

Power ~100 mW/cm2

JSC



Multijunction Cells

Problem: Single junction loses

all of the photon energy above

the gap energy.

Energy (eV)

0

20

40

60

80

100

120

140

160

180

300 500 700 900 1100 1300 1500

4.0 3.0 2.5 2.0 1.7 1.5 1.3 1.1 1.0 0.9

Inte

nsity (

mW

/m2-m

m)

Wavelength (nm)

To

p C

ell

(1.9

eV

ga

p)

Ce

ll #

2

(1.4

eV

ga

p)

Ce

ll #

3

(1.0

eV

ga

p) Ce

ll #

4

(0.6

eV

gap)

Solution: Use a series of cells

of different gaps.

Each cell captures the light

transmitted from above.

But… can’t just use a graded

gap. Allows electrons to

escape to low gap region.

Need separate cells.

n-t

ype

p-t

ype

n-t

ype

p-t

ype

n-t

ype

p-t

ype

n-t

ype

p-t

ype

-+

-+

-+

-+

Load



Record laboratory thin film

cell efficiencies



Cells to Modules to Arrays

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

Heat, humidity, corrosive

gases

Rain, hail, ice, snow

Local failures, shadows



Interconnect SchemesSoldered (standard for Si cells)

Monolithic interconnects

Encapsulation



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 Temperature20

S (8.24)0.8

cell amb

NOCT CT T

Figure 8.36



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



Blocking Diodes -- protection from low voltage strings

Cell arrays including a weak

cell; the array performs at

the level of the worst cell.

Cell 1 Cell 2

Back contact

Front contact

Monolithically-interconnected Cell Array

Two good cells

One good cell, one weak cell

Diodes can be used to

prevent current from strong

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)



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



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



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

Figure courtesy R. Birkmire, Univ. of Delaware Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring 2017


• Bulk single crystal boules grown by this method.

Czochralsky Si

Growth rate

0.5-3 mm/min

Photographs courtesy MEMC Electronic Materials Inc, St. Peters MO.

Some issues:

• Low throughput

• High energy use

• Requires skilled

operator

Typical PV boule

diameter:

100-150 mm

length:

40-150 cm



Cast Monocrystalline Silicon

Seed crystal

Figures Courtesy:



• Bulk Polycrystals grown by this method

Crystalline Si by Casting

Mold

Cast

Polycrystal

Wire

Saw

Slow cooling

Features:

• Large grains possible

• Batch process is fast

• Low technology, cost

• Relatively fast

• Lower quality crystals



PV Systems – Four configurations

1. Grid-connected systems



PV Systems – Four Configurations

2. Stand-alone systems with directly-connected loads



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/

Professor O. A. Mohammed, EEL5285 Lecture Notes, Spring

2017


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(9.3)aV IR k



DC Motor I-V Curve

Linear Current

Booster (LCB) helps

the motor be able to

start in low sunlight

Figure 9.9

Figure 9.10




3. Stand-alone systems which charge batteries




• 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

4. Microgrids



1- Practical PV System component

• Grid-connected PV systems without battery

storage

• Grid-connected PV systems with battery

storage

• Grid-connected PV systems with battery

storage

2- Modeling the PV Array

• PV equivalent Circuit

• PV Simulink Model

• Impact of changing irradiance on Voc & load

current

3- Simulation of PV VI & VP characteristics

• Modeling Variable Load

• Study the VI & VP characteristics of the PV

panel

4- Maximum Power Point Tracking

• Modeling MPPT algorithm

• Modeling DC-DC boost converter

• Case study for MPPT performance

PV Implementation, Examples and Assignments

5- Modeling Grid Connected PV systems

• Model Description

• Voltage source Inverter (VSC) Model

• Voltage source inverter (VSC) control

• Case Study



Practical PV System component

DC

DC

VSI

To filter the ripple on the output

voltage of the PV arrays

PV Array

DC

AC

G

Boost Converter

TL

TransformerGrid

Cable

Maximum Power Point

Tracking is implemented here

• To convert the voltage from DC to

AC

• The AC voltage has to be

synchronized with the grid

voltage

• Reactive power compensation is

needed to connect to the grid

• PV supplies active power


Irradiance W/m^2


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



Grid-connected PV systems without battery storage

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

MPPT is implemented in the boos converter controller

MPPT

Note: During power deficiency (e.g. at night), the power is received from the grid



Grid-connected PV systems with

battery storage

Inverter

Distribution

Panel

AC Loads Utility Grid

PV Array

Battery

Charger

Battery

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

• This can be used for energy management.

MPPT



Stand alone PV systems with battery

storage

PV Array

Backup

Generation

Inverter

Battery

Charger

Battery

AC Loads

Optional

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

This system is applicable for rural residential areas



Modeling the PV Array

• Objective

1. Building simulation model that represent the relation between the PV output( voltage, current) and environmental parameters.

2. Utilizing the simulation model to study the impact of changing irradiance on the PV output voltage and current.

3. Simulating the performance of different PV modules consisting of series and parallel connected cells.



Modeling the PV Array

• Objective

Building mathematical models for PV array to

represent the PV voltage and current output as a

function of irradiance input.

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



PV equivalent Circuit



PV Simulink Model

Irradiance Pattern

Isc

Vt

Irradiance

Irradiance /Voc

Characteristic



Model Setting



Impact of changing irradiance on Voc

Ou

tpu

tV

olt

ag

eIr

rad

ian

ceD

iod

e cu

rren

tO

utp

ut

curr

ent

Irradiance

Ou

tpu

tV

olt

ag

e



Simulation Example Assignment #1

• Modify the Irradiance pattern in the Simulink Model “EX_IR_CHAR” to represent actual summer and winter Day In Miami Area.

• Change the number of series Module to two modules and observe the effect of the irradiance change.

• Change the number of Parallel Module to two modules and observe the effect of the irradiance change.



Impact of changing irradiance on Load

current• Connect 20 Ohm resistive

Load to the PV Model.

• Apply variable Irradiance

pattern from 0 to 1000

W/m2

• Observe the effect of the

Irradiance change at the

load current



Simulation Result

Ou

tpu

tV

olt

ag

eIr

rad

ian

ceD

iod

e cu

rren

tO

utp

ut

curr

ent

Time

Irradiance

Load

cu

rren

t



Homework Assignment #2

• Modify the Irradiance pattern in the Simulink Model “EX_IR_I_CHAR” to represent actual summer and winter Day In Miami Area.

• Modify the model to calculate the output power and efficacy

• Change the number of series Module to two modules and observe the change in the load current .

• Change the number of Parallel Module to two the change in the load current .



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



Resistive Load I-V Curve

• Straight line with slope 1/R

• As R increases, operating point moves to the right

V IR1

(9.1)I VR

• Can use a potentiometer to

plot the PV module’s IV

curve

• Resistance value that results

in maximum power

(9.2)mm

m

VR

I

Figure 9.5



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.



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



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



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



Components of Grid-Connected PV


Principal components in a grid connected PV system using a single inverter


Individual Inverter Concept

• Easily allow expansion

• Connections to house distribution panel are

simple

• Less need for expensive DC cabling



Interfacing with the Utility

• Net metering – 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



Losses from Mismatched Modules

• Illustrates the impact of slight variations in module I-V curves

• Only 330 W is possible instead of 360 W



“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) kW h/day of "peak sun" (9.14)acP



Capacity Factor of PV

Energy kWh/yr kW CF 8760 h/yr (9.15)acP

h/day of "peak sun"CF (9.16)

24 h/day

Figure 9.28

PV Capacity

Factors for

US cities



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



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



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



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

(9.4)B iV V R I



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



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



Basics of Lead-Acid Batteries

+ 2

2 4 4 2Positive Plate: PbO + 4H + SO + 2 PbSO 2H O (9.21)e

2

2 4 4Negative Plate: PbO + SO PbSO 2e (9.22)



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



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



Battery Technologies

Type Density,

Wh/kG

Cost

$/kWh

Cycles Charge

time,

hours

Power

W/kg

Lead-acid,

deep cycle

35 50-100 1000 12 180

Nickel-metal

hydride

50 350 800 3 625

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



Estimating Storage Needs



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
