the university of the west indies - uwi st. augustine · ii statement of academic honesty the...

THE UNIVERSITY OF THE WEST INDIES

B.Sc. (Engineering)

Department of Electrical and Computer Engineering

ECNG 3020 - SPECIAL PROJECT PROGRESS REPORT

PROJECT TITLE

Solar Photovoltaic Resource Assessment Tool

Adam Khan

808000249

2nd

April, 2012.

ELECTRICAL Project Supervisor: Dr. Sanjay Bahadoorsingh

& COMPUTER Project Type: IV

ENGINEERING

DEPARTMENT

ii

Statement of Academic Honesty

THE UNIVERSITY OF THE WEST INDIES ST. AUGUSTINE, TRINIDAD & TOBAGO,

WEST INDIES FACULTY OF ENGINEERING Department of Electrical & Computer Engineering

B. Sc. in Electrical & Computer Engineering

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According to The University of the West Indies Undergraduate Regulations (2008/2009), sections

32: “Cheating, Plagiarism and Collusion are serious offences under University Regulations.

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I, ………………………………………………………, have read and understood the University’s

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I understand that my submission is subject to the electronic plagiarism checker, Turnitin.

I declare that this assignment is my own work and does not involve cheating, plagiarism or collusion.

Signature:……………………………………………. Date:………………………………

iii

Abstract

The Caribbean as an ideal place to harvest solar energy such as photovoltaic cells. This

report deals with the models at different stages in producing electrical energy from

photovoltaic cells and after justifying appropriate models implement them in a Matlab

software and test them against RETScreen to validate it.

iv

Table of Contents

Chapter 1 Introduction .................................................................................................... 12

1.1 Background ............................................................................................................ 12

1.1.1 PV Configurations .......................................................................................... 12

1.2 Justification ............................................................................................................ 15

1.3 Project Objectives .................................................................................................. 16

1.4 Scope ..................................................................................................................... 16

Chapter 2 Literature Review ........................................................................................... 17

2.1 Available Solar Data .............................................................................................. 18

2.2 Irradiation on a Tilted Surface ............................................................................... 19

2.2.1 Models to Calculate the Total Hourly Irradiation on a Horizontal Surface ... 21

2.2.2 Models to Calculate the Daily Diffuse Irradiation on a Horizontal Surface .. 22

2.2.3 Models to Calculate the Hourly Diffuse Irradiation on a Horizontal Surface 24

2.2.4 Models to Calculate the Irradiation on a Tilted Surface ................................ 25

2.3 PV Performance Models ........................................................................................ 31

2.4 Battery Models ...................................................................................................... 33

2.5 Justification ............................................................................................................ 37

Chapter 3 Methodology ................................................................................................... 39

3.1 Software Model ..................................................................................................... 39

3.2 Software Design .................................................................................................... 39

3.3 Irradiation on a Tilted Surface Module ................................................................. 40

3.3.1 Sunset Hour Angle ......................................................................................... 40

v

3.3.2 Clearness Index .............................................................................................. 42

3.3.3 Total Hourly Irradiation on a Horizontal Surface .......................................... 43

3.3.4 Diffuse Daily Irradiation on a Horizontal Surface ......................................... 45

3.3.5 Hourly Diffuse Irradiation on a Horizontal Surface....................................... 47

3.3.6 Determination of Rb for fixed Arrays ............................................................. 49

3.3.7 RB for a Azimuth Tracking Surface .............................................................. 52

3.3.8 RB for Two Axis Tracking Surface ............................................................... 52

3.3.9 RB for an Axis of Arbitrary Tilt .................................................................... 52

3.3.10 RB for a horizontal axis ............................................................................... 54

3.3.11 Irradiation on Tilted Surface Sub-Function ................................................. 55

3.3.12 Irradiation on Tilted Surface Complete Module .......................................... 55

3.4 Array Module ........................................................................................................ 56

3.5 Battery Module ...................................................................................................... 57

3.6 System Design ....................................................................................................... 57

4 Testing .......................................................................................................................... 61

5 Results .......................................................................................................................... 67

6 Discussion .................................................................................................................... 70

7 Conclusion .................................................................................................................... 71

8 References .................................................................................................................... 72

Appendix A – Progress Report........................................................................................ 74

vi

List of Abbreviations and Symbols

PV - Photovoltaic

TMY-Typical Meteorological Year

ω – Hour Angle

ωs- Sunset Hour Angle

I – Hourly Irradiation Units

H – Daily Irradiation Units

Ī – Monthly Average Hourly Irradiation Units

Ĥ- Monthly Average Daily Irradiation Units

Hd- Daily Diffuse Irradiation

Id-Hourly Diffuse Irradiation

Kt- Daily Clearness Index

tK - Daily Average Clearness Index

kt-Hourly Clearness Index

IT- Hourly Irradiation on a tilted surface

Ib-Hourly Beam Irradiation

ρg – Ground Reflectance

θ – Angle of incidence

vii

θz- Zenith Angle

β – Tilt Angle

HDKR – Hay Davies Klucher Reindl

Id,T – Diffuse irradiation on a tilted surface

Id,T,iso- Isotropic component of diffuse irradiation on a tilted surface

Id,T,cs- Circumsolar component of diffuse irradiation on a tilted surface

Ai – Anisotropy index

Io – Extraterrestrial Hourly Irradiation

F1-Circumsolar Coefficient

F2-Horizon Brightness Coefficients

Ion – Extraterrestrial normal-incident radiation

m- air mass

Tc- Average Module Temperature

Ta-Ambient Temperature

NOCT- Nominal Operating Cell Tempature

sm – optimum tilt

ηp – Array Efficiency

viii

ηr – Array Reference Efficiency

Tr-Reference Temperature

βp-Temperature Coefficient for module efficiency

Cf-Correction factor

δ – Declination

Φ – Latitude

Ho-Daily Extraterrestrial Irradiation

Ĥo- Monthly Average Daily Extraterrestrial Irradiation

Gsc-Solar Constant

γ’ – Axis Azimuth

β’ – Axis Tilt

θ’ – Axis Angle of Incidence

γs- Solar Azimuth

CPRG – Collares Pereira Rabl and Gueymard

ix

List of Figures

Figure 1: Directly Connected System(Messenger & Ventre 2004) ................................ 13

Figure 2: Off Grid with Battery Backup (Lynn 2010) .................................................... 13

Figure 3: Grid Connected Systems(Messenger & Ventre 2004)..................................... 14

Figure 4: Hybrid System(Lynn 2010) ............................................................................. 15

Figure 5: General PV System .......................................................................................... 17

Figure 6: Isoflux Plot....................................................................................................... 18

Figure 7: General Tilted Irradiation Calculation ............................................................. 20

Figure 8: Sky Model from (Duffie and Beckman 2006) ................................................. 26

Figure 9: Components Irradiation on a Tilted Surface Anisotropic Sky (Duffie and

Beckman 2006) ............................................................................................................... 28

Figure 10: Single Diode PV Model (Desoto 2004) ......................................................... 31

Figure 11: Fraction of Load Met Determined by SLR and ALR (NRCan 2005) ........... 36

Figure 12: Iterative Software model................................................................................ 39

Figure 13: Clearness Index Sub Module ......................................................................... 43

Figure 14: Total Hourly Irradiation on a Horizontal Surface Module ............................ 43

Figure 15: CPRG Flow Chart .......................................................................................... 44

Figure 16: Erbs et al Diffuse Daily Irradiation Module .................................................. 45

Figure 17: Erbs et. al Flow Chart .................................................................................... 46

Figure 18: Diffuse Hourly Irradiation ............................................................................. 47

Figure 19: Flow Chart of Liu and Jordan Model ............................................................ 48

Figure 20: RB Fixed Array Module ................................................................................ 50

Figure 21: RB for a Fixed Array Flow Chart .................................................................. 51

x

Figure 22: General Input Output Relation for Tilted Irradiation Calculation ................. 55

Figure 23: Tilted Irradiation Module .............................................................................. 56

Figure 24: Array Module Inputs/Outputs ........................................................................ 56

Figure 25: Solar Resource Assessment Tool Main Screen ............................................. 57

Figure 26: Resource Assessment Screenshot .................................................................. 58

Figure 27: Module Information Screenshot .................................................................... 59

Figure 28: Off Grid/On Grid Screenshot......................................................................... 60

xi

List of Tables

Table 1: Brightness Coefficients for Perez Anisotropic Sky (Duffie and Beckman 2006)

......................................................................................................................................... 30

Table 2: Justification of Models chosen .......................................................................... 37

Table 3: Recommended Average Days for Months and Declination (Duffie and

Beckman 2006) ............................................................................................................... 41

Table 4: Test Data ........................................................................................................... 61

Table 5: Fixed and Isotropic Model ................................................................................ 63

Table 6: Fixed Array and HDKR model ......................................................................... 63

Table 7: Fixed Axis and Perez Model ............................................................................. 64

Table 8: Two Axis Tracking and Isotropic model .......................................................... 64

Table 9: Two axis and HDKR model .............................................................................. 65

Table 10: Two Axis and Perez ........................................................................................ 65

Table 11: Case Study Results Isotropic........................................................................... 68

Table 12: Case Study Results HDKR ............................................................................. 68

Table 13: Case Study Results Perez ................................................................................ 69

12

Chapter 1 Introduction

1.1 Background

The amount of solar energy incident on the earth per day exceeds the requirements for

the entire population of the earth for an entire year (Lynn 2010).

One type of technology that utilizes solar energy is photovoltaic cells. In the Caribbean,

there are potential projects that utilize solar energy and photovoltaic cells such as the

solar powered equipment that are to be installed at the newly established Police

Surveillance Bays along the Uriah Butler and Solomon Hochoy Highways from Caroni

to Golconda in Trinidad and Tobago (Dowlat 2011).

In order to determine if projects are feasible a programme is required to perform

analyses on several factors to determine if a project is feasible. Some of the factors are

the available solar energy at a site, output of a photovoltaic array, shading and a

financial analysis of the entire project.

1.1.1 PV Configurations

Directly Connected

The simplest kind of PV configuration is an off grid, directly connected system where

the PV array supplies the load directly; a diagram of this configuration is given in figure

1 below, where the module is connected to a fan.

13

Figure 1: Directly Connected System(Messenger & Ventre 2004)

Off-Grid with Battery Back-Up

Some systems require a continuous supply of electricity so a battery is used. One of the

configurations is shown in figure 2 below with a charge controller and an inverter so that

the system can supply AC and DC loads.

Figure 2: Off Grid with Battery Backup (Lynn 2010)

14

Grid Connected

A grid connected system is a system which is connected to the electricity power grid by

some means. Three possible configurations are given in figure 3 below.

Figure 3: Grid Connected Systems(Messenger & Ventre 2004)

15

Hybrid

Hybrid systems are systems that are supplied by two different technologies such as a PV

array and a diesel generator or a PV array and a wind turbine. A diagram of a standalone

system supplied by a wind turbine and a PV array is shown figure 4 below.

1.2 Justification

The need for a software tool in the Caribbean to perform feasibility studies on PV

arrays.

Figure 4: Hybrid System(Lynn 2010)

16

1.3 Project Objectives

1. Literature review of models identifying critical factors to produce electrical

energy yields from (historical) solar data set.

2. Assessment of the goodness of fit of the solar data set to PV conversion models.

3. Justifying suitable model(s) and recommended approach(es), develop using

MATLAB a user friendly GUI solar photovoltaic resource assessment tool

(complete with user manual) modeling the production of electrical energy.

4. Determine the annual net average electrical energy production and capacity

factor that would be expected from a particular PV unit at a given site.

5. Validate software using existing available open source data.

6. Appropriate case study.

1.4 Scope

The project deals with the development of a MATLAB based tool to determine the

amount of solar energy available to photovoltaic arrays. Using the energy available at a

particular location and temperature information determine the efficiency of the arrays

and the net energy available from the PV arrays.

17

Chapter 2 Literature Review

In order to quantify the net electrical energy output of a PV array system, models at each

intermediate step need to be looked at and accessed. The general steps involved are

shown in figure 5 below.

As shown in figure 5 above, the first step is the type of solar radiation and climate

information available. Critical information would be the solar irradiation and irradiance

on a titled array. Usually the solar radiation data available are for horizontal surfaces

(Duffie and Beckman 2006) therefore models would be required to determine the solar

radiation a collector would be exposed to.

After determining the type of climate and solar radiation data available that would be

used as inputs to the PV array a model for the array would be required to determine the

energy output of the array.

Then models for components that can be connected to the PV array need to be

determined such as the inverter, battery, charge controller and maximum power point

tracker. The models and available data will be discussed below.

Figure 5: General PV System

18

2.1 Available Solar Data

Different types of solar data are available such as typical mean year data for a

particular location, average daily, monthly or yearly solar insolation, global isoflux

contours, sunshine hours data, solar insolation based on satellite cloud-cover data

and calculations of solar radiation (Bowden).

TMY is hourly solar data that is averaged over a certain number of years. TMY1

data was collected during the period 1948 and 1980(NASA), TMY2 data is averaged

during the time period 1961 to 1990 and TMY3 averaged over 1991 to 2005 (NREL)

. TMY data sets feature information such as the day, hour, irradiation for a particular

hour, air temperature for a particular hour and wind speed. However TMY data is

not suitable for the Caribbean because they do not contain data for Caribbean

countries.

Global isoflux contours are plots that show the variation of solar energy on the globe

as shown below in figure 6.

Figure 6: Isoflux Plot

19

Sometimes sunshine hour and cloud cover data is simpler to obtain than measured

irradiation data and sunshine hours can be used to estimate the solar irradiation

2.2 Irradiation on a Tilted Surface

The most easily accessible solar irradiation data in the Caribbean is monthly average

daily irradiation data on a horizontal surface available on NASA’s website (NASA)

calculated from satellite data. Therefore the irradiation models used to calculate the

irradiation on a titled surface were based on daily irradiation data. Solar irradiation is

made up of two components beam and diffuse. The component that reaches the

surface without being scattered is called the beam component and the component

that reaches the surface after being scattered is called the diffuse component. The

general flow of the calculation is shown in figure 7 below where not all the variables

are highlighted. First the total daily horizontal irradiation data is split up into its

hourly values, occurring in parallel using the daily horizontal irradiation data the

daily diffuse irradiation on a horizontal surface is calculated and from that the hourly

diffuse irradiation on a tilted surface is calculated. Using the total hourly irradiation

and the hourly diffuse irradiation the beam irradiation is calculated. The hourly beam

and diffuse irradiation are used to calculate the irradiation on a titled surface. In this

section, models for the individual blocks in figure 7 will be explored.

20

Figure 7: General Tilted Irradiation Calculation

21

2.2.1 Models to Calculate the Total Hourly Irradiation on a Horizontal Surface

In order to compute the irradiation on a tilted surface the hourly values of the total

irradiation on a horizontal surface must be calculated or measured. Models available to

calculate the hourly irradiation from daily irradiation are:

Collares-Pereira and Rabl as cited by (Alam, Garg and Kaushik 2007)

Liu and Jordan as cited by (Alam, Garg and Kaushik 2007)

Gopinathan and Soler (Alam, Garg and Kaushik 2007)

Jain as cited by (Koussa, Malek, and Haddadi 2009)

Collares-Pereira and Rabl modified by Gueymard as cited by (Ahmad and Tiwari

2008)

Newell Model as cited by (Ahmad and Tiwari 2008)

Baig et. Al Model cited by (Ahmad and Tiwari 2008)

According to (Alam, Garg and Kaushik 2007) the Collares-Pereira and Rabl model is

the universally accepted model. However in a study performed by (Ahmad and Tiwari

2008) the Collares-Pereira and Rabl as modified by Gueymard performs better than the

Collares-Pereira and Rabl model as the study performed by (Alam, Gard and Kaushik

2007) did not consider the Gueymard model.

The Collares-Pereira and Rabl model (Duffie and Beckman 2006) is given as:

22

(2.1)

/tr I H (2.2)

That is the fraction of irradiation allocated to a particular hour.

0.409 0.5016sin( 60)sa (2.3)

And

0.6609 0.4767sin( 60)sb (2.4)

All angles are in degrees and ω is the hour angle. The hour angle is given by:

15*Hour (2.5)

Where Hour is the hours from solar noon, and ωs is the hour angle at sunset or sunrise

assuming they are symmetrical.

For the Collares Pereira and Rabl model as modified by Gueymard (Ahmad and Tiwari

2008) equation 2.1 is multiplied by:

0.5 ( sin cos ) / (sin /180cos )s s s s s sa b (2.6)

2.2.2 Models to Calculate the Daily Diffuse Irradiation on a Horizontal Surface

Models to calculate the daily diffuse irradiation on a horizontal surface are based on

sunshine hours, atmospheric water content and clearness index (Koussa, Malek, and

Haddadi 2009)

Models based on sunshine hours are:

/ 24( cos )cos cos / (sin /180cos )t s s s sr a b

23

Iqbal’s Model (Koussa, Malek, and Haddadi 2009)

Hay’s Model (Koussa, Malek, and Haddadi 2009)

Models based on sunshine hours and atmospheric water content

Hussain’s Model (Koussa, Malek, and Haddadi 2009)

Models based on clearness index

Liu and Jordan Model (Koussa, Malek, and Haddadi 2009)

Page’s Model (Koussa, Malek, and Haddadi 2009)

Collares Pereira and Rabl (Koussa, Malek, and Haddadi 2009)

Iqbal’s Relation(Koussa, Malek, and Haddadi 2009)

Erbs et. al Model (Koussa, Malek, and Haddadi 2009)

Now since the available data does not include sunshine hours only the models based on

clearness index were considered. The clearness index is a ratio of the measured

irradiation to the extraterrestrial irradiation.

The study conducted by (Koussa, Malek, and Haddadi 2009) gave the results of the

models with respect to Algerian climates however the universal applicability of the Erbs

et. Al Model (Duffie and Beckman 2006) was mentioned.

The Erbs et al model (Duffie and Beckman 2006) is:

For sunset hour angle less than or equal to 81.4 degrees and clearness index between 0.3

and 0.8 equation 2.7 is used

24

2 3/ 1.391 3.560 4.189 2.137d T T TH H K K K (2.7)

For sunset hour angle greater than 81.4 degrees and clearness index between 0.3 and 0.8

Equation 2.8 is used

2 3/ 1.311 3.022 4.427 1.821d T T TH H K K K (2.8)

2.2.3 Models to Calculate the Hourly Diffuse Irradiation on a Horizontal

Surface

After calculating the daily diffuse irradiation on a horizontal surface the hourly diffuse

irradiation has to be determined. Models available to determine the hourly diffuse

irradiation on a horizontal surface are:

Model of Jain cited by (Koussa, Malek, and Haddadi 2009)

Liu and Jordan Model cited by (Koussa, Malek, and Haddadi 2009)

According to (Koussa, Malek, and Haddadi 2009) the Liu and Jordan model is superior

to model of Jain.

The Liu and Jordan model is given as:

/ 24cos cos / (sin cos ) /d s s s s d dr I H (2.9)

Where rd is the ratio of the hourly diffuse irradiation to the daily diffuse irradiation.

25

2.2.4 Models to Calculate the Irradiation on a Tilted Surface

Three models to calculate the irradiation on a tilted surface will be considered. An

isotropic model and two anisotropic models.

Isotropic – Liu and Jordan cited by (Duffie and Beckman 2006)

Anisotropic – HDKR cited by (Duffie and Beckman 2006)

– Perez et. al cited by (Duffie and Beckman 2006)

– The Circumsolar model cited (Notton et al. 2006)

– The Bugler Model cited by (Notton et al. 2006)

– The Temps and Coulson model cited by (Notton et al. 2006)

– Ma and Iqbal model cited by (Notton et al. 2006)

– Skartveit and Olseth model cited by (Notton et al. 2006)

– The Gueymard model cited by (Notton et al. 2006)

– The Muneer model cited by (Notton et al. 2006)

The differences with the models is the way they threat with the diffuse components.

Figure 8 below illustrates the components of the diffuse model; it also includes the beam

irradiation.

26

Figure 8: Sky Model from (Duffie and Beckman 2006)

The sky model shown in figure 8 shows irradiation of being made up of the diffuse

isotropic irradiation, circumsolar diffuse and horizon brightening (Duffie and Beckman

2006). The isotropic diffuse irradiation is the radiation received uniformly from the sky

dome (Duffie and Beckman 2006). The circumsolar diffuse is the radiation received due

to the forward scattering of solar radiation and that concentrated in the part of the sky

around the sun (Duffie and Beckman 2006). Horizon brightening is the radiation that is

concentrated around the horizon (Duffie and Beckman 2006). Lastly figure 8 includes

the beam radiation which is the radiation that passes through the sky dome directly

without being scattered.

According to (Duffie and Beckman 2006) the isotropic model tends to underestimate the

solar irradiation on a tilted surface where as the HDKR and Perez et. al gives a better

performance. Skartveit and Olseth, HDKR and Perez et. al models perform the best

according to a study done by (Noorian, Moradi, and Kamali 2008) for south facing

27

surfaces in Kara and the Perez et. al models performs the best for north facing surfaces

also noted is that the Perez et. al model gives the best overall performance. A study done

by (Notton et al. 2006) using data from a French Mediterranean site suggests that the

Perez et. al model, Ma and Iqbal model, Skartveit and Olseth model and previous

versions of the HDKR model gives the best performance. The complexity and the good

performance of the Perez et. al models is noted in a study conducted by (Posadillo and

López Luque 2009) although the model was not tested. The models tested were the

HDRK model, previous version of it and the Liu and Jordan isotropic model. The results

of the study indicated that the HDRK model performed the best among the three as well

as the simple application of it.

Only three models were considered and implemented, the isotropic model because that

is the model that RETScreen uses, the software that is used to test the MATLAB

software and two anisotropic models, that is the HDKR model for its simplicity and

accuracy and the Perez model for its accuracy. The three models are presented in the

remainder of this section.

The Isotropic model as presented by (Duffie and Beckman 2006) is shown below:

(1 cos ) / 2 (1 cos ) / 2T b b d gI I R I I (2.10)

Where cos / cosb zR (2.11)

The total radiation on a tilted surface according to this model consists of three

components the beam component, the diffuse component and the ground albedo

component.

28

Figure 9 below shows the components of radiation incident on a tilted surface. The

HDRK model makes use of this sky model.

Figure 9: Components Irradiation on a Tilted Surface Anisotropic Sky (Duffie and Beckman 2006)

The general diffuse components as presented by (Duffie and Beckman 2006) is shown

below:

, , , , ,d t T d iso T d csI I I (2.12)

Equation 2.12 says that the diffuse irradiation is made up of two components the

isotropic component and the circumsolar component.

The HDKR model (Duffie and Beckman 2006) is shown below:

29

3( ) (1 )(1 cos ) / 2[1 sin ( / 2)]

(1 cos ) / 2

T b d i b d i

g

I I I A R I A f

I

(2.13)

Where /i b oA I I (2.14)

Ai is the anisotropy index which determines the portion of the horizontal diffuse

irradiation which is to be treated as forward scattered (Duffie and Beckman 2006).

And f is a correction factor given by:

/bf I I (2.15)

According to (Duffie and Beckman 2006) the Perez model is based a more detailed

analysis of the three components that make up the diffuse radiation.

The diffuse radiation on a tilted surface calculation as cited by (Duffie and Beckman

2006) is shown below:

, 1 1 2[(1 )(1 cos ) / 2 / sin )]d T dI I F F a b F (2.16)

Where F1 and F2 are circumsolar and horizon brightness coefficients and are given by

(Duffie and Beckman 2006):

1 11 12 13max[0,( ( /180) )]zF f f f (2.17)

2 21 22 23( ( /180) )zF f f f (2.18)

Where f11, f12, f13, f21, f22, f23 are determined from a variable ε which is used to get the

brightness coefficients from a table which is shown below in table 1.

30

6 3,

6 3

( ) 5.535 10

1 5.535 10

d b nz

d

z

I I xI

x

(2.19)

Table 1: Brightness Coefficients for Perez Anisotropic Sky (Duffie and Beckman 2006)

Range of ε f11 f12 f13 f21 f22 f23

1.000-1.065 -0.008 0.588 -0.062 -0.060 0.072 -0.022

1.065-1.230 0.130 0.683 -0.151 -0.019 0.066 -0.029

1.230-1.500 0.330 0.487 -0.221 0.055 -0.064 -0.026

1.500-1.950 0.568 0.187 -0.295 0.109 0.152 0.014

1.950-2.800 0.873 -0.392 0.362 0.226 -0.462 0.001

2.800-4.500 1.132 -1.237 -0.412 0.288 -0.823 0.056

4.500-6.200 1.060 -1.600 -0.359 0.264 -1.127 0.131

6.200-∞ 0.678 -0.327 -0.250 0.156 -1.377 0.251

And the brightness parameter Δ is given by (Duffie and Beckman 2006):

/d onmI I (2.20)

31

2.3 PV Performance Models

Four PV array performance models were considered:

Sandia PV Array Performance Model (Klise and Stein 2009)

5 Parameter Model (Desoto 2004)

4 Parameter Model (Desoto 2004)

Evans and Facinelli as cited by (NRCan 2005)

The Sandia PV Array Performance model requires additional testing of the PV array to

successfully used the model and cannot be used with the datasheet values only.

The 5 Parameter model is based on the single diode model as shown in figure 10 below.

The 4 Parameter model is based on the single diode model as well but the shunt

resistance, Rsh would tend to infinity (Desoto 2004) that is removing it from the circuit.

The 5- parameter model and 4 – parameter model requires the solution of highly non

linear and implicit system of equations.

Figure 10: Single Diode PV Model (Desoto 2004)

32

The Evans and Facinelli model is the simplest to implement and most suitable for

feasibility studies as it only finds the efficiency at the maximum operating point and

only requires information from the manufacturer’s data sheet.

The array’s efficiency based on the Evans and Facinelli model is shown in the following

(NRCan 2005):

The average module temperature, Tc, is calculated first, it is given by:

20

(219 832 )800

c a tNOCT

T T K

(2.21)

If the array’s tilt is not optimal the right hand side of 2.21 is multiplied by a corrector

factor given below (NRCan 2005):

4 21 1.17 10 ( )f mC x s (2.22)

The efficiency is given by:

[1 ( )]p r p c rT T (2.23)

33

2.4 Battery Models

For off-grid applications the need for energy storage is important. Battery models used

for solar applications are:

KiBaM (Klise and Stein 2009)

Riso (Klise and Stein 2009)

RETScreen (NRCan 2005)

The KiBaM and Riso model (Klilse and Stein 2009) requires inputs that the Evans and

Facinelli PV Array does not provide such as voltage and current, they are geared toward

simulation software.

The RETScreen model uses the utilizability concept from (Duffie and Beckman 2006) to

calculate the energy supplied directly to the continuous load and the matched load. After

calculating the energy met directly by the array, the fraction of the load that is supplied

by the battery is found (NRCan 2005)

The mathematics for the RETSCreen model is given below.

Firstly the total DC load is given by:

,dc equ matched continuous batteryD D D D (2.24)

where Dmatched is the load that is supplied by the PV array

Dcontinuous is the load that is constant through the day

Dbattery is that load that is supplied only by the battery

34

The critical absorption level is then calculated:

24

continuouscrit

DP W (2.25)

According to (NRCan 2005) a critical radiation level is the radiation level that must be

exceeded so that the array can produce more energy that can be used by the constant

load and it is given by:

2/

critTc

A

PI W m

S (2.26)

The monthly average critical radiation level is given by (NRCan 2005):

,

Tcc

t n n

IX

r R H (2.27)

The monthly average utilisability is given by (NRCan 2005):

2( )( )n

c cR

a b X cXRe

(2.28)

where

22.943 9.271 4.031T Ta K K (2.29)

24.345 8.853 3.602T Tb K K (2.30)

and 20.170 0.306 2.936T Tc K K (2.31)

35

R is the ratio of the monthly average daily radiation to that on a horizontal plane. It is

given as:

tH

RH

(2.32)

and Rn is the ratio of the irradiation for a particular hour to that on a horizontal surface

for that day.

The energy delivered to the continuous load is given by (NRCan 2005):

(1 )continuous AE E (2.33)

Where EA is the energy from the array

The energy delivered to the matched load is given by (NRCan 2005):

min( , )matched matched A continuousE D E E (2.34)

The energy delivered directly to the load is given by (NRCan 2005):

D continuous matchedE E E (2.35)

and the energy delivered to the battery is the differences between the array energy and

ED

In order to find the amount of energy passing through the battery a number of

simulations were run on WATSUN and the fraction of the load met was determined.

From these simulations it was determined what fraction of the load was met given a

36

particular ALR and SLR and a surface was generated as shown in figure 11 below

(NRCan 2005).

Figure 11: Fraction of Load Met Determined by SLR and ALR (NRCan 2005)

37

2.5 Justification

This section summarizes the justification for the use of each model and data type used.

Table 2: Justification of Models chosen

Model/Data Type

Used

Justification

Solar Data Monthly Average

Daily Total

Irradiation

Availability

Hourly Irradiation on a

Horizontal Plane

Collares Pereira

Rabl and

Gueymard

Accuracy

Daily Diffuse Irradiation on

a Horizontal Plane

Erbs et. al Universal acceptance

Hourly Diffuse Irradiation

on a Horizontal Plane

Liu and Jordan Universal acceptance

Irradiation on a tilted

surface

Isotropic

HDKR

Perez et. al

Isotropic used to test with

RETScreen. HDKR used because

of its accuracy and ease of use.

Perez et. al used because of its

accuracy

38

PV Performance Model Evans and Facinelli Simple and accurate for feasibility

studies

Battery Hybrid Model Some of the RETScreen model is

used the tabulated version of the

SLR and ALR surface is not

available

39

Chapter 3 Methodology

3.1 Software Model

The software model chosen was the iterative model as shown in figure 12.

This model was chosen as the need to go back and refine implementation of code to

achieve an optimal implementation of the chosen solar models. The programming

language chosen was MATLAB.

3.2 Software Design

The requirements of the software led to the decoupling of the system into modules. The

modules were further broken down into its constituent functions in the following

sections. The different modules are:

Figure 12: Iterative Software model

40

Irradiation on a Tilted Surface Module

PV Array Module

On Grid and Off Grid Module

3.3 Irradiation on a Tilted Surface Module

Firstly all the functions that are necessary for the operation of this module will be

discussed first.

3.3.1 Sunset Hour Angle

The sunset hour angle is used to determine the clearness index so its implementation

will be discussed here. The sunset hour angle is the angle the sun is displaced at sunset

or sunrise, it operates on the assumption that they are symmetrical. The formula to

calculate the sunset hour angle stated in (Duffie and Beckman 2006) is shown below:

tan tans (3.1)

The implementation of this function is using the declination for the average day numbers

of each month and the declination at each of these months as stated in (Duffie and

Beckman 2006).The average day of a month is defined as the day in which the average

irradiation for a month is equal to the irradiation for that day (Duffie and Beckman

2006). Table 3 shows the day numbers and the corresponding declination which was

adapter from (Duffie and Beckman 2006). The declination is defined as the angular

position of the sun at solar noon with respect to the equator (Duffie and Beckman 2006).

41

Table 3: Recommended Average Days for Months and Declination (Duffie and Beckman 2006)

Month Day Number Declination

January 17 -20.9

February 47 -13.0

March 75 -2.4

April 105 9.4

May 135 18.8

June 162 23.1

July 198 21.2

August 228 13.5

September 258 2.2

October 288 -9.6

November 318 -18.9

December 344 -23.0

42

3.3.2 Clearness Index

All of the models use clearness index so a function is required to compute the clearness

index. The monthly average clearness index is give by the equation as shown below:

/t oK H H (3.2)

That is the ratio of the monthly average daily horizontal irradiation to the monthly

average daily extraterrestrial irradiation.

The monthly average daily extraterrestrial irradiation is given by the equation shown

below where the average day numbers are used (Duffie and Beckman 2006):

24 3600 360(1 0.033cos )(cos cos sin

365

sin sin )180

sco s

s

x G nH

(3.3)

A pictorial representation of the clearness index sub-module is given below in figure 13

illustrating the inputs and output. Where H is a 1x12 matrix containing the monthly

average daily irradiation for each month, declination is a 1x12 matrix containing the

declination for the average days of each month, n is a 1x12 matrix containing the day

numbers for the average days, w is a 1x24 matrix containing the hour angles at the mid

point of each hour in a day and the output is a 1x12 matrix containing the clearness

index for the average day of each month.

43

Figure 13: Clearness Index Sub Module

3.3.3 Total Hourly Irradiation on a Horizontal Surface

The equation to calculate the total hourly irradiation on a horizontal surface is given by

equation 2.1 as modified by equation 2.6. Figure 14 below shows the inputs and outputs

of the module. H and Hour angle is the same as the previous section and the Sunset

Hour Angle is a 1x24 matrix which gives the hour angles at the mid point of each hour

in a day. The output is a 12x24 matrix where the ith

row represents the month and the jth

column represents the hour and that gives the irradiation for that hour and month.

Figure 14: Total Hourly Irradiation on a Horizontal Surface Module

A flow diagram of the logic of the module is shown in figure 15 below.

44

Figure 15: CPRG Flow Chart

45

3.3.4 Diffuse Daily Irradiation on a Horizontal Surface

The equations to calculate the daily diffuse irradiation on a horizontal surface is given

by equations 2.7 and 2.8, the Erbs et. al equation. Figure 16 below shows the inputs and

outputs of the calculation. The sunset hour angle is the same as before, the clearness

index is a 1x12 matrix representing the average daily clearness index for the average

days of each month as calculated in the previous section and H is the same as before.

The output is a 1x12 matrix containing the diffuse daily irradiation for the average day

of each month.

Figure 16: Erbs et al Diffuse Daily Irradiation Module

A flow chart of the internal working of the module is shown below in figure 16.

46

Figure 17: Erbs et. al Flow Chart

47

3.3.5 Hourly Diffuse Irradiation on a Horizontal Surface

The equation to calculate the diffuse hourly irradiation on a horizontal surface is given

by equation 2.9. Figure 18 below shows the inputs and outputs of the module. Hd is the

diffuse daily irradiation as calculated in the previous section. Hour angle and the Sunset

Hour Angle is the same as section 3.3.3. The output is a 12x24 matrix where the ith

row

represents the month and the jth

column represents the hour and that gives the hourly

diffuse irradiation for that hour and month.

Figure 18: Diffuse Hourly Irradiation

A flow diagram of the logic is shown below in figure 19.Note the output is initialized to

a zero matrix that is why when the if condition is not true the module does nothing.

48

Figure 19: Flow Chart of Liu and Jordan Model

49

3.3.6 Determination of Rb for fixed Arrays

In order to calculate the irradiation on a tilted surface the ratio of the beam radiation on a

tilted surface to that on a horizontal surface must be computed. According to (Duffie and

Beckman 2006) this is calculated as:

cos / cosb zR (3.4)

Where θ is the angle of incidence of the beam radiation on a titled surface and θz the

angle of incidence of the beam radiation on a horizontal surface also known as the zenith

angle.

The general formula for cosθ is given below (Duffie and Beckman 2006):

cos sin sin cos sin cos sin cos cos cos cos cos

cos sin sin cos cos

(3.5)

The formula for cosθz is given below (Duffie and Beckman 2006):

cos cos cos cos sin sinz (3.6)

Figure 20 below identifies the inputs and outputs of the Rb module where the array is

fixed. The declination is as before a 1x12 matrix containing the declination for the

average day of each month, the latitude, the surface azimuth, the surface tilt, the hour

angle a 1x24 matrix as before and the sunset hour angle a 1x12 matrix. The outputs are

12x24 matrices of RB, zenith angle and the angle of incidence.

50

Figure 20: RB Fixed Array Module

Figure 21 below shows the flow chart for calculating RB for a fixed surface. Note the

outputs are initialized as zeros matrices.

51

Figure 21: RB for a Fixed Array Flow Chart

52

3.3.7 RB for a Azimuth Tracking Surface

For an azimuth tracking surface the formula to calculate the angle of incidence is given

by (Duffie and Beckman 2006):

cos cos cos sin sinz z (3.7)

Figures 20 and 21 from the previous section are still applicable here except that the

formula to calculate the angle of incidence, equation 3.7 is used instead and there is no

need to specify the azimuth.

3.3.8 RB for Two Axis Tracking Surface

For two axis tracking the angle of incidence is given by (Duffie and Beckman 2006):

cos 1 (3.8)

Figures 20 and 21 from section 3.3.6 are still applicable here except that the formula to

calculate the angle of incidence, equation 3.8 is used instead and there is no need to

specify the tilt and azimuth.

3.3.9 RB for an Axis of Arbitrary Tilt

In order to calculate RB for this type of array the solar azimuth had to be calculated

because it is used in the calculation of the azimuth of the array, the solar azimuth is

given by the formula (Duffie and Beckman 2006):

1 cos sin sin

( ) | cos ( ) |sin cos

zs

z

sign

(3.9)

The azimuth of the array is calculated from a formula in (Braun and Mitchell 1983):

53

1 2180o (3.10)

where

1 sin sin( ')

' tan [ ]cos 'sin '

z so

(3.11)

1

0 if ( ')( ') 0

1 if otherwise

o s

(3.12)

2

1 if ( ') 0

1 if otherwise

s

(3.13)

The surface slope is given by (Braun and Mitchell 1983):

' ' 180o (3.14)

where

1 tan '' tan [ ]

cos( ')o

(3.15)

o0 if ' 0

'1 otherwise

(3.16)

Then the angle of incidence can be calculated using equation 3.5.

Figures 20 and 21 from section 3.3.6 are still applicable except the equations in this

section are used and the array tilt and azimuth are replaced by the axis tilt and azimuth.

54

3.3.10 RB for a horizontal axis

In order to calculate RB for this type of array the solar azimuth had to be calculated

because it is used in the calculation of the azimuth of the array. The solar azimuth is

calculated using equation 3.9.

The azimuth of the array is calculated from a formula in (Braun and Mitchell 1983):

s

s

' 90 if - ' 0

' 90 if - '<0

(3.17)

The surface slope is given by (Braun and Mitchell 1983):

180o (3.18)

where

1tan (tan cos( ))o z s (3.19)

and

00 if 0

1 otherwise

(3.20)

Then the angle of incidence can be calculated using equation 3.5.

Figures 20 and 21 from section 3.3.6 are still applicable except the equations in this

section are used and the array tilt and azimuth are removed and the axis azimuth is used.

55

3.3.11 Irradiation on Tilted Surface Sub-Function

Three different models were used the isotropic model, HDKR and Perez et. a model.

The equations used are the equations outlined in section 2.

The inputs to all the models were the same; figure 22 below illustrates the inputs and

outputs of the function.

3.3.12 Irradiation on Tilted Surface Complete Module

The complete module for calculating the tilted irradiation on a tilted surface is shown in

figure 23 below. The inputs shown here are the inputs the user will choose. Some of the

inputs in the previous section do not appear here because they are internal to the module.

Figure 22: General Input Output Relation for Tilted Irradiation Calculation

56

Figure 23: Tilted Irradiation Module

3.4 Array Module

The array module is based on equations 2.21 to 2.23; figure 24 below shows the inputs

and outputs required for the array module.

Figure 24: Array Module Inputs/Outputs

57

3.5 Battery Module

The battery module employed is a hybrid model. It uses equations 2.21 to 2.23 to

determine the energy available to the battery from the array. It divides the energy into

hourly average values depending on the amount of hours of sunlight for a particular

month and energy available. Then an hourly balance of the energy available to the

battery taking into account the maximum depth of discharge and capacity of the battery.

Then a balance is done on the demand of the load that needs to be met for that day.

3.6 System Design

Figure 25 below shows a screenshot of the main screen of the MATLAB software.

Figure 25: Solar Resource Assessment Tool Main Screen

58

When ‘Site and Solar’ is clicked another screen pops up to enter the solar and site

information, figure 26 is a screenshot of that screen.

Figure 26: Resource Assessment Screenshot

The Solar irradiance Plot and difference plot plots the irradiation of the different models

and the difference between the models with respect to the isotropic model respectively.

The Module Information button brings up a GUI to input the PV module information. A

screenshot of that screen is shown below in figure 27

59

Figure 27: Module Information Screenshot

The Off Grid/On grid button brings up a screen that gives the energy output of off grid

and on grid systems. A screenshot of that screen is shown in figure 28 below.

60

Figure 28: Off Grid/On Grid Screenshot

61

4 Testing

The software was tested and benchmarked against RETScreen. Blackbox testing was

used because of the ability to get data to verify with that is the data from RETSCreen.

The input data used to test was obtained from RETScreen. The values of irradiance and

temperature are shown in the table 4 below.

Table 4: Test Data

Month Irradiation kWh/m2/day Temperature degrees celcius

January 4.69 26

February 5.28 26

March 5.64 26.6

April 5.69 27.4

May 6.03 27.9

June 5.44 27.5

July 5.89 27.3

August 5.89 27.6

September 5.44 27.7

October 5.44 27.5

November 5.03 26.8

62

December 4.53 26.3

The location is Crown Point, Tobago

Latitude – 11.2 degrees north

The energy demand for each type of load is 7.5kWh both AC and DC aswell.

Battery Capacity of 500Ah and maximum depth of discharge of 90%.

Each Solar radiation model was tested as follows:

Fixed array – 45 degree tilt, 0 degree azimuth

Two Axis Tracking

Module Information :

Reference Efficiency – 13%

Collector Area – 46.2m2

NOCT – 45 degrees celcius

Temperature coefficient – 0.40%

Capacity – 6kW

63

Table 5: Fixed and Isotropic Model

Solar Resource

Assessment Tool

RETScreen

Annual Tilted Irradiation

MWh

1.7417 1.74

Annual Energy Supplied

to Load MWh

7.4734 7.3

% Load Supplied 100 95.3

Capacity Factor % 18.31 18.2

Table 6: Fixed Array and HDKR model

Solar Resource

Assessment Tool

RETScreen


MWh

1.7593 1.74


to Load MWh

7.4734 7.3



64

Table 7: Fixed Axis and Perez Model

Solar Resource

Assessment Tool

RETScreen


MWh

1.7599 1.74


to Load MWh

7.4734 7.3



Table 8: Two Axis Tracking and Isotropic model

Solar Resource

Assessment Tool

RETScreen


MWh

2.534 2.53


to Load MWh

7.4734 7.3



65

Table 9: Two axis and HDKR model

Solar Resource

Assessment Tool

RETScreen


MWh

2.7099 2.53


to Load MWh

7.4734 7.3



Table 10: Two Axis and Perez

Solar Resource

Assessment Tool

RETScreen


MWh

2.78 2.53


to Load MWh

7.4734 7.3



66

The results show that the isotropic model behaves just as the isotropic model in

RETScreen however the battery model used in the solar resource assessment tool yields

better results than RETSCreen. The other two solar models, HDKR and Perez model

produces higher yields of solar energy on a tilted surface as expected. The values are

very close to the values in RETScreen so the software is validated and working.

67

5 Results

The information for the case study is as follows:

Location – Syrian Arab Republic Latitude – 36.3 degrees north

The energy for a battery based load – 8.4kWh

Battery Capacity of 1101Ah and maximum depth of discharge of 80%.

Battery efficiency – 85% Charge Controller Efficiency 95%

Each Solar radiation model was tested as follows:

Fixed array – 45 degree tilt, 0 degree azimuth

Module Information :

Reference Efficiency – 11.4%

Collector Area – 31.5m2

NOCT – 45 degrees celcius

Temperature coefficient – 0.40%

Capacity – 3.6kW

68

Table 11: Case Study Results Isotropic

Solar Resource

Assessment Tool

RETScreen


MWh

1.937 1.70


to Load MWh

2.7594 3.34

% Load Supplied 100 108.9%


Table 12: Case Study Results HDKR

Solar Resource

Assessment Tool

RETScreen


MWh

2.01 1.70


to Load MWh

2.7594 3.34



69

Table 13: Case Study Results Perez

Solar Resource

Assessment Tool

RETScreen


MWh

2.06 1.70


to Load MWh

7.4734 3.34



From the results it can be seen that the RETScreen implementation of the models

underestimate the solar irradiation on a tilted surface however it manages to supply the

load with 108.9% of the required energy.

70

6 Discussion

The report dealt with the models required to determine the net annual energy production

produced by a PV panel and what percent of that energy that can be supplied to a load or

to the grid and to develop a tool geared to be used in the Caribbean.

From the results it can be seen that the energy incident on a collector is underestimated

when using the isotropic model and the other two anisotropic models produce better

results, also the battery model was investigated and the battery model in the solar

resource assessment tool performed better than the one in RETScreen.

71

7 Conclusion

The project had six objectives and the six objectives were met. A Matlab tool was

developed that can determine the net annual electrical energy from a PV unit at a given

site based on minimal amount of information.

The Software was tested, validated and benchmarked against RETScreen and the results

were very close in most cases except for the anistropic models that generally produce

higher irradiance values.

72

8 References

Ahmad, Firoz, and S. A. Husain. 1986. "Computation of monthly average hourly and daily solar radiation incident on a flat tilted surface at Karachi, Pakistan." Solar & Wind Technology no. 3 (4):329-333. doi: 10.1016/0741-983x(86)90014-7.

Alam, S, Sn Garg, and Sc Kaushik. 2007. Computation of Monthly Mean Hourly Global Solar Radiation from Daily Total. Journal of Energy and Environment 6, no. May: 10-17. http://www.buet.ac.bd/ces/shah-alam.doc

Bekker, Bernard, and Trevor Gaunt. 2008. Simulating The Impact of Design-Stage Uncertainties on PV Array Energy Output Estimation. In 16th PSCC.

Glasgow,Scotland Bowden, Christiana Honsberg and Stuart. Available from

http://pvcdrom.pveducation.org/SUNLIGHT/RADDATA.HTM Braun, J. E., and J. C. Mitchell. 1983. "Solar geometry for fixed and tracking surfaces." Solar

Energy no. 31 (5):439-444. doi: 10.1016/0038-092x(83)90046-4. De Soto, W.L. (2004). Improvement and Validation of a Model for Photovoltaic Array

Performance. Master's Thesis, University of Wisconsin-Madison. Dowlat, Rhondor. 2011. "Solar Power for Surveillance Bays." Newsday, August 27th, 2011,

18. Duffie, J.A, and W.A Beckman. 2006. Solar Engineering of Thermal Processes. 3rd Edition ed.

Hoboken, New Jersey: John Wiley & Sons. Farret, F., and M. Simões. 2006. Integration of Alternative Sources of Energy. New Jersey:

John Wiley & Sons. Klise, Geoffrey T, and Joshua S Stein. 2009. Models Used to Assess the Performance of

Photovoltaic Systems. Contract, no. December. http://www.osti.gov/bridge/servlets/purl/974415-t6N0f7/.

Koussa, M., A. Malek, and M. Haddadi. 2009. "Statistical comparison of monthly mean hourly and daily diffuse and global solar irradiation models and a Simulink program development for various Algerian climates." Energy Conversion and Management no. 50 (5):1227-1235. doi: 10.1016/j.enconman.2009.01.035.

Lynn, Paul A. 2010. Electricity from Sunlight: An Introduction to Photovoltaics. United Kingdom: John Wiley & Sons.

Messenger, R.A, and J Ventre. 2004. Photovoltaic Systems Engineering. 2nd Ed. ed. Washington D.C: CRC Press.

NASA. [cited 30-03-12. Available from http://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?#s02. Noorian, Ali Mohammad, Isaac Moradi, and Gholam Ali Kamali. 2008. "Evaluation of 12 models

to estimate hourly diffuse irradiation on inclined surfaces." Renewable Energy no. 33 (6):1406-1412. doi: 10.1016/j.renene.2007.06.027.

Notton, G., C. Cristofari, M. Muselli, P. Poggi, and N. Heraud. 2006. Hourly Solar Irradiations Estimation : From Horizontal Measurements to Inclined Data. Paper read at Environment Identities and Mediterranean Area, 2006. ISEIMA '06. First international Symposium on, 9-12 July 2006.

NRCan. 2005. Clean Energy Project Analysis: RETScreen Engineering & Cases Textbook. Varennes, Québec, Canada: RETScreen International.

NREL. [cited 30-03-12. Available from http://rredc.nrel.gov/solar/old_data/nsrdb/.

http://pvcdrom.pveducation.org/SUNLIGHT/RADDATA.HTM

http://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?#s02

http://rredc.nrel.gov/solar/old_data/nsrdb/

73

Posadillo, R., and R. López Luque. 2009. "Evaluation of the performance of three diffuse hourly irradiation models on tilted surfaces according to the utilizability concept." Energy Conversion and Management no. 50 (9):2324-2330. doi: 10.1016/j.enconman.2009.05.014.

Ransome, Steve. 2007. 4EP.1.1 How Well Do PV Modelling Algorithms Really Predict Performance. Milan 22nd European PVSEC

74

Appendix A – Progress Report

Objectives

7. Literature review of models identifying critical factors to produce electrical

energy yields from (historical) solar data set.

8. Assessment of the goodness of fit of the solar data set to PV conversion models.

9. Justifying suitable model(s) and recommended approach(es), develop using

MATLAB a user friendly GUI solar photovoltaic resource assessment tool

(complete with user manual) modeling the production of electrical energy.

10. Determine the annual net average electrical energy production and capacity

factor that would be expected from a particular PV unit at a given site.

11. Validate software using existing available open source data.

12. Appropriate case study.

75

Background and Scope

The amount of solar energy incident on the earth per day exceeds the requirements for

the entire population of the earth for an entire year (Lynn 2010).

One type of technology that utilizes solar energy is photovoltaic cells. In the Caribbean,

there are potential projects that utilize solar energy and photovoltaic cells such as the

solar powered equipment that are to be installed at the newly established Police

Surveillance Bays along the Uriah Butler and Solomon Hochoy Highways from Caroni

to Golconda in Trinidad and Tobago (Dowlat 2011).

In order to determine if the projects are feasible a programme is required to perform

analyses on several factors to determine if a project is feasible. Some of the factors are

the available solar energy at a site, output of a photovoltaic array, shading and a

financial analysis of the entire project.

76

PV Configurations

Directly Connected

The simplest kind of PV configuration is an off grid, directly connected system where

the PV array supplies the load directly; a diagram of this configuration is given below,

where the module is connected to a fan.

Figure 29: Directly Connected System(Messenger & Ventre 2004)

77

Off-Grid with Battery Back-Up

Some systems require a continuous supply of electricity so a battery is used. One of the

configurations is shown below with a charge controller and an inverter so that the

system can supply AC and DC loads.

Grid Connected

A grid connected system is a system which is connected to the electricity power grid by

some means. Three possible configurations are given below.

Figure 30: Off Grid with Battery Backup(Lynn 2010)

78

Figure 31: Grid Connected Systems(Messenger & Ventre 2004)

Hybrid

Hybrid systems are systems that are supplied by two different technologies such as a PV

array and a diesel generator or a PV array and a wind turbine. A diagram of a standalone

system supplied by a wind turbine and a PV array is shown below.

Solutions Proposed and Implemented by Others

Figure 32: Hybrid System(Lynn 2010)

79

The general methodology used by most software is given in the figure below.

What varies among the software are the methods used to quantify the output irradiation

incident on the PV array, the PV algorithm, battery models and all other components

involved.

Currently an algorithm to calculate the titled irradiation incident on a PV array is being

investigated given monthly average daily irradiation.

Two software which are currently being looked at and uses monthly average daily

irradiation are RETScreen and Homer. RETScreen performs its calculations differently

Figure 33: General Procedure for PV Feasibility Studies (Ransome 2007)

80

than Homer, it calculates the titled monthly average daily irradiation incident on a PV

array and performs its calculations based on that (NRCan 2005), whereas Homer

calculates 8760 hourly values for each hour of the year using a more complicated

algorithm by Graham and Hollands(1990) as cited by (Farret & Simões 2006).

(NRCan 2005) compares the results using a particular case study and shows the

difference between the two algorithms shown below

Inspecting the column of incident solar radiation, it can be seen that Homer gives a

monthly average daily irradiation output higher than RETScreen.

A possibility for RETScreen yielding lower results than Homer can be accounted for by

its use of an isotropic model to determine the total irradiation incident on a titled surface

A study conducted by (Bekker & Bernard 2008) suggests replacing RETScreen’s

isotropic model with an anistropic model.

Table 14: Comparison of Homer and RETScreen(NRCan 2005)

81

Details on how the problem is being addressed

Replacing RETScreen’s isotropic model with an anistropic model

Conduct research for an optimal anistropic model

Implement anistropic model

Test complete solar resource evaluation module with measured data

82

Plans for the Completion of the Solution

Complete solar module

Research PV algorithms taking into consideration available data

Research algorithms for components of the system for various configurations

Implement suitable PV algorithm and components algorithms

Implement financial analysis module

Test Completed software with a case study

83

Problems Encountered

No study found evaluating statistical models in the Caribbean

Gantt Chart

Figure 34: Gantt Chart

84

References

Bekker, Bernard, and Trevor Gaunt. 2008. Simulating The Impact of Design-Stage

Uncertainties on PV Array Energy Output Estimation. In 16th PSCC.

Glasgow,Scotland.

Dowlat, Rhondor. 2011. "Solar Power for Surveillance Bays." Newsday, August 27th,

2011, 18.

Duffie, J.A, and W.A Beckman. 2006. Solar Engineering of Thermal Processes. 3rd

Edition ed. Hoboken, New Jersey: John Wiley & Sons.

Farret, F., and M. Simões. 2006. Integration of Alternative Sources of Energy. New

Jersey: John Wiley & Sons.

Lynn, Paul A. 2010. Electricity from Sunlight: An Introduction to Photovoltaics. United

Kingdom: John Wiley & Sons.

Messenger, R.A, and J Ventre. 2004. Photovoltaic Systems Engineering. 2nd Ed. ed.

Washington D.C: CRC Press.

NRCan. 2005. Clean Energy Project Analysis: RETScreen Engineering & Cases

Textbook. Varennes, Québec, Canada: RETScreen International.

Ransome, Steve. 2007. 4EP.1.1 How Well Do PV Modelling Algorithms Really Predict

Performance. Milan 22nd European PVSEC

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