Photovoltaic System Layout for Optimized Self-Consumption637625/FULLTEXT01.pdf · PV System Layout...

ES13026

Examensarbete 30 hpJuli 2013

Photovoltaic System Layout for Optimized Self-Consumption

Rasmus Luthander

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Photovoltaic System Layout for OptimizedSelf-Consumption

Rasmus Luthander

Most of the photovoltaic (solar cell) systems in Sweden today are installed in privatehouses and connected to the public grid. Photovoltaic (PV) power can be consumeddirectly in the house, called self-consumption, or fed in to the public grid. For thehouse owner self-consumed PV energy often has a higher economic value than soldexcess PV energy, since the savings from not buying one kWh is larger than theincome of selling one kWh. The self-consumption can be expressed as an absolutevalue; amount of produced/consumed kWh, or as a relative; absoluteself-consumption divided with total PV production. The PV production andself-consumption were calculated on an hourly basis.

In this Master thesis a MATLAB tool for calculating and optimizing the production,absolute and relative self-consumption and profit for PV systems with panels in one(1DPV), two or three directions (3DPV) was developed.

The results show possibilities to increase especially the relative self-consumption with3DPV. There is however no economic gain of using 3DPV instead of south-directed1DPV for the studied case; a private house close to Västerås with a 1DPV system of3360 W and variable electricity prices based on hourly Nord Pool Spot prices. Therated power of the inverter can be decreased with 3DPV compared tosouth-oriented 1DPV and still keep minimal production losses. A smaller inverter andother peripheral equipment such as cables might compensate for the lower yearlyprofit with 3DPV when calculating the payback period. Further studies of economicaspects and how to optimize them have to be carried out for 3DPV systems, sinceeconomy is very crucial for investment decisions.

ISSN: 1650-8300, UPTEC ES13 026Examinator: Kjell Pernestål, Uppsala universitetÄmnesgranskare: Joakim Widén, Uppsala universitetHandledare: Bengt Stridh, ABB Corporate Research

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Corporate Research Rasmus Luthander

Doc. title Revision Page

PV System Layout for Optimized Self-Consumption 01 1/61

We reserve all rights in this document and in the information contained therein. Reproduction, use or disclosure to third parties

without express authority is strictly forbidden. © Copyright 2013 ABB Ltd.

EXECUTIVE SUMMARY In this Master thesis a MATLAB tool was developed to optimize the yearly photovoltaic (PV) production,

self-consumption and profit for PV systems in one (1DPV), two and three (3DPV) directions. Self-

consumption is the generated PV energy consumed in the house, in this case on an hourly basis.

The results show that the self-consumption can increase with 3DPV compared to south-oriented 1DPV

for a house in Västerås, Sweden, with a PV system of 3360 W. The yearly PV production and profit will

however decrease with 3DPV. An inverter of smaller rated power can be used with 3DPV with minimal

production losses and the lower investment cost may compensate for the lower yearly profit.

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ACKNOWLEDGEMENTS I would like to thank my supervisor Bengt Stridh, ABB Corporate Research, and reviewer Joakim Widén,

Uppsala University, for the very valuable advice and support they have given me in the working and

writing procedure of this Master thesis. Without their guidance this thesis would not have been possible.

I would also like to thank ABB Corporate Research and the Department of Engineering Sciences, Solid

State Physics at Uppsala University for letting me use workplaces at their offices in Västerås and at the

department, respectively.

STRÅNG solar radiation data used here are from the Swedish Meteorological and Hydrological Institute

(SMHI), and were produced with support from the Swedish Radiation Protection Authority and the

Swedish Environmental Agency.

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POPULÄRVETENSKAPLIG SAMMANFATTNING Intresset för solenergi och framför allt för solceller har växt snabbt i världen på senare tid. I rapporten

används det engelska ordet photovoltaics, förkortat PV, vilket innebär att en halvledare (solcell) används

för att omvandla solljus (fotoner) till elektrisk effekt. Den totala installerade solcellseffekten i början av

2013 nådde 100 GW, vilket motsvarar 69 kärnkraftverk med samma effekt som Sveriges största

(Oskarshamn 3: 1450 MW). Framför allt är solceller populärt i Tyskland – de stod för omkring en

tredjedel av all installerad effekt. Intresset i Sverige är dock betydligt svalare – endast 24 MW installerad

effekt. Dock var ökningen under 2012 omkring 22 procent jämfört med 2011. Kostnaden för kompletta

solcellsinstallationer på privathus har minskat från 32 SEK per kW till 22 SEK per kW exklusive moms

mellan 2011 och 2012, vilket har bidragit till att öka populariteten.

De flesta solcellsanläggningar i Sverige är idag (2013) installerade på privathus, framför allt på villatak

vända mot söder. Optimal lutning på dessa tak för maximal solinstrålning är omkring 40° till 50°,

beroende på var i landet huset ligger (brantare lutning i norr än i söder). Även flackare tak på omkring 30°

har hög instrålning och ger därför hög effekt från solcellerna. Dock kanske inte personerna är hemma mitt

på dagen när solen lyser som starkast och istället används energikrävande utrustning som till exempel

tvättmaskin och ugn på morgonen och kvällen. Naturligtvis finns det dagar när man gör tvärt om, till

exempel på helger. Den dåliga matchningen gör att elkonsumtionen i huset överstiger

solcellsproduktionen morgon och kväll samtidigt som det omvända förhållandet gäller på dagen beroende

på bland annat hur stor solcellsanläggningen är och elkonsumtionen i huset.

Elpriset för att köpa är oftast högre än säljpriset, speciellt om man har rörliga priser för både köp och sälj.

Det beror på att det ingår skatter och avgifter i köppriset, bland annat energiskatt och nätavgift med moms

på totalsumman, något man inte får tillbaka då solcellsanläggningen producerar ett överskott och

levererar el in på nätet. Om den elenergi som solcellsanläggningen har producerat kan användas direkt i

huset slipper el köpas in och besparingarna per producerad kWh är därför högre än intäkterna om man

skulle sälja samma mängd till en elleverantör. Den elkonsumtion som härrör från PV-produktionen kallas

egenkonsumtion och kan antingen uttryckas i absoluta tal (kWh) eller i procent av den totala

elproduktionen från solcellsanläggningen. I detta examensarbete har produktion och egenkonsumtion

beräknats på timbasis.

Det finns i huvudsak tre sätt att öka egenkonsumtionen: ”demand side management” (DSM) som innebär

att ett reglersystem flyttar vissa elektriska laster, till exempel tvättmaskin och torkskåp, till de tillfällen

när solinstrålningen och därigenom PV-produktionen är hög. Man kan även använda batterier för att lagra

överproduktion av elenergin från solcellsanläggningen mitt på dagen till ett senare tillfälle. En tredje

metod – vilken har utvärderats i detta examensarbete – är förändring i layouten av solcellssystemet, det

vill säga vilket håll solcellsmodulerna pekar.

Som tidigare nämnt är de flesta solcellsanläggningar idag södervända och samtliga solcellsmoduler pekar

i samma riktning (1DPV). Om man istället väder hela eller en del av anläggningen åt öster eller väster och

eventuellt förändrar dess lutning kan produktionstoppen inträffa tidigare eller senare på dagen jämfört

med för ett södervänt solcellssystem. Med solceller i tre riktningar – 3DPV – kan man få en jämnare

dagsproduktion, det vill säga högre produktion på morgon och kväll och lägre mitt på dagen. På så sätt

finns en potential att öka egenkonsumtionen. Om det går att öka egenkonsumtionen med 3DPV jämfört

med de södervända 1DPV-system och om detta kan öka de årliga intäkterna har undersökts i detta

exmensarbete.

Flera program för att beräkna bland annat egenkonsumtion och årliga intäkter för solcellssystem har

utvecklats i MATLAB och även ett grafiskt användargränssnitt (GUI – graphical user interface) för att

förenkla möjligheterna för användaren att ange inparametrar som systemstorlek i watt och önskad typ av

diagram för åskådliggöring av resultatet. Betydligt fler resultat (diagram) än de som visas i

examensarbetet kan simuleras då användaren kan mata in egna värden för exempelvis storlek i watt på

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PV-systemet och elpriser för köp och sälj. På så sätt blir möjligheterna i princip oändliga, vilket gör att

samtliga resultat inte kan redovisas i rapporten.

Beräkningarna av timvisa produktionsdata har gjorts i det kommersiella programmet PVsyst och bygger

på data över solinstrålning från en databas kallad STRÅNG och temperaturdata från en mätstation vid

Västerås flygplats. Parametrar för beräkningarna i PVsyst som bland annat typ av solcellsmoduler och

installerad effekt har hämtats från en solcellsanläggning på en villa i Gäddeholm utanför Västerås. Den

installerade effekten – något som sällan eller aldrig nås – på solcellsanläggningen är 3360 W tillsammans

med en växelriktare på 3000 W. De flesta simuleringar av 3DPV-anläggningar har därefter gjorts med

lastprofilen från 2011 för denna villa. Även lastprofiler från 19 andra villor (totalt 20 hus finns därmed att

välja bland i GUI) finns tillgängliga i det utvecklade MATLAB-verktyget. Det gör att ännu fler grafer kan

visas. I appendix finns resultaten för två hus redovisade, de med lägst respektive högst årlig elkonsumtion

av de 20 husen. Det är även möjligt att lägga in egna lastprofiler (som behöver vara lika långa som antalet

timmar på ett år, det vill säga 8760 värden) för att ta fram resultat för fler hus.

Programmen kan bland annat sammanställa och visa årsproduktionen från en solcellsanläggning av valfri

storlek och beräkna den absoluta och relativa egenkonsumtionen. Detta ligger till grund för bland annat

beräkningar av årliga intäkter och anläggningens återbetalningstid. Användaren kan antingen använda

standardvärdena som finns angivna i programmet eller som tidigare nämnt ange egna parametrar såsom

elpris och storlek på anläggningen.

Resultaten visar på en årsproduktion från solcellsanläggningen i Gäddeholm på 3071 kWh (den verkliga

produktionen 2011 var 2901 vilket delvis kan förklaras med skuggning morgon och kväll). Som högst blir

produktionen 3140 kWh om panelernas lutning ökas till 40°. Azimutvinkeln anger åt vilket väderstreck

panelerna är riktade, där -90° är åt öster, 0° åt söder och 90° åt väster. För att beräkna de årliga intäkterna

kan antingen fasta eller rörliga elpriser väljas i MATLAB-gränssnittet. Det röriga köppriset för el baseras

på timvisa Nordpool Spot-priser inklusive energiskatt, elcertifikat, nätavgift och moms. Säljpriset består

enbart av spotpriserna plus elcertifikat. Enbart den simulerade årliga intäkten kan redovisas eftersom den

verkliga inte finns tillgänglig.

Uppmätt elkonsumtion och simulerade resultat för PV-anläggningen i Gäddeholm (3360 W,

lutning 27° och azimut -5°) redovisas nedan. Enbart simulerade resultat redovisas här för att de ska

kunna jämföras med de optimerade resultaten som återfinns lägre ned.

Elkonsumtion: 15661 kWh

Simulerad PV-produktion: 3071 kWh

Simulerad absolut egenkonsumtion: 1674 kWh

Simulerad relativ egenkonsumtion: 54.5 %

Simulerade årliga intäkter: 2750 SEK/år

Om istället maximala resultat med en lika stor solcellsanläggning (3360 W) som i Gäddeholm används

men med 3DPV och där lutning och azimutvinkel kan ändras fritt fås resultaten redovisade här

nedanför. Samtliga bygger på simuleringar vilket gör att de kan jämföras med ovanstående resultat för

den verkliga anläggningen.

Maximal årlig PV-produktion: 3140 kWh

o 3360 W, lutning 40°, azimut 0° (söder)

Maximal absolut egenkonsumtion: 1705 kWh

o 1800 W, lutning 40°, azimut -40° (öster)


o 700 W, lutning 40°, azimut 40° (väster)

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Maximal relative egenkonsumtion: 77 %

o 1800 W, lutning 90°, azimut -90° (öster)


o 560 W, lutning 90°, azimut 90° (väster)

Maximala årliga intäkter: 2780 SEK/år


Resultaten visar att det framför allt går att öka den relativa egenkonsumtionen. Dock så sjunker

PV-produktionen kraftigt eftersom solcellsmodulerna är placerade vertikalt. Om istället intäkterna

maximeras (de blir högst med spotpriser) behövs enbart en 1DPV-anläggning, vilken antagligen även har

en billigare och mindre komplicerad installation. Därför ökar inte lönsamheten med 3DPV.

En annan intressant aspekt – som kan öka lönsamheten för 3DPV – är att det sannolikt går att minska

storleken på växelriktaren eftersom solcellsanläggningens maximala effekt kommer minska med 3DPV.

För huset i Gäddeholm kan växelriktarens märkeffekt minskas 30 procent. Om storleken på växelriktare

och därigenom kablarna kan minska sjunker anläggningens totalkostnad, särskilt som solmodulerna har

sjunkit kraftigt i pris den senaste tiden och utgör en allt mindre andel av totalkostnaden för en komplett

solcellsanläggning än för några år sedan. Då de instrålningsdata som använts ger en relativt låg högsta

elproduktion (på timbasis) jämfört med de högsta verkliga produktionsvärdena är båda storlekarna,

nämligen 2540 och 1790 W för söder respektive öst-väst-riktade system, sannolikt mindre än vad som

skulle behövas. Icke desto mindre är den relativa skillnaden antagligen mer korrekt då den bygger på

samma instrålningsdata för de två beräkningarna.

Enbart de årliga intäkterna har beräknats i detta examensarbete och för att avgöra om en installation lönar

sig eller inte behöver en fördjupad ekonomisk analys göras. Framför allt återbetalningstiden för en

solcellsanläggning är mycket viktig för investeringsbeslut. Detta skulle kunna vara en del av ett framtida

examensarbete.

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LIST OF CONTENTS NOMENCLATURE ..................................................................................................................... 11 DEFINITIONS AND EXPLANATIONS ............................................................................................. 11

1 INTRODUCTION ............................................................................................................... 13

1.1 PRESENT SITUATION FOR PHOTOVOLTAICS WORLDWIDE AND IN SWEDEN .......................... 13 1.2 PURPOSE AND AIM ......................................................................................................... 14 1.3 PREVIOUS RESEARCH .................................................................................................... 14 1.4 LIMITATIONS.................................................................................................................. 15

1.4.1 Cost of the components in a PV system ................................................................ 15 1.4.2 Net metering ......................................................................................................... 15

2 SELF-CONSUMPTION OF PV POWER ............................................................................ 17

2.1 DESCRIPTION OF SELF-CONSUMPTION OF PV POWER AND HOW TO INCREASE IT ................ 17 2.2 CALCULATING PV PRODUCTION AND OPTIMIZING SELF-CONSUMPTION .............................. 19

3 THEORY ............................................................................................................................ 21

3.1 DIFFERENT KINDS OF PV MODULES ................................................................................ 21 3.2 MPP AND MPPT ........................................................................................................... 21 3.3 EFFICIENCY AND EFFECT OF TEMPERATURE .................................................................... 22 3.4 GLOBAL, DIRECT, DIFFUSE AND GROUND-REFLECTED SOLAR RADIATION ........................... 22 3.5 EFFECT OF DIFFERENT HEATING SYSTEMS ...................................................................... 23

4 METHOD ........................................................................................................................... 24

4.1 EXISTING SYSTEM IN GÄDDEHOLM .................................................................................. 24 4.2 SOFTWARES FOR CALCULATIONS AND SIMULATIONS ........................................................ 25 4.3 INPUT PARAMETERS IN RLPV ......................................................................................... 26 4.4 CHART TYPES FROM RLPV ............................................................................................ 27 4.5 DATA SOURCES FOR CALCULATION OF PRODUCTION ....................................................... 28 4.6 YEARLY PROFIT ............................................................................................................. 29 4.7 NET PRESENT VALUE AND PAYBACK PERIOD ................................................................... 29 4.8 PEARSON PRODUCT-MOMENT CORRELATION ................................................................... 30

5 RESULTS .......................................................................................................................... 31

5.1 ACCURACY OF SIMULATED PRODUCTION AND RELATIVE SELF-CONSUMPTION ..................... 31 5.2 YEARLY ELECTRIC ENERGY CONSUMPTION IN THE 20 HOUSES .......................................... 33 5.3 SIMULATED PV PRODUCTION AND CONSUMPTION ............................................................ 33 5.4 YEARLY PRODUCTION .................................................................................................... 36 5.5 ABSOLUTE SELF-CONSUMPTION ..................................................................................... 38 5.6 RELATIVE SELF-CONSUMPTION ....................................................................................... 40 5.7 YEARLY PROFIT ............................................................................................................. 43 5.8 OPTIMIZATION OF PRODUCTION, ABSOLUTE AND RELATIVE SELF-CONSUMPTION AND PROFIT

45 5.8.1 Installed PV power: 3360 Wp, azimuth 0° or ±90°, tilt 30° ...................................... 45 5.8.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt .................................. 46

5.9 EAST-WEST ROOF WITH A SOUTH POINTING FAÇADE ........................................................ 48 5.10 PAYBACK PERIOD ....................................................................................................... 50 5.11 MATCHING INVERTER POWER ...................................................................................... 51

6 DISCUSSION .................................................................................................................... 52

6.1 ACCURACY OF SIMULATIONS COMPARED TO REAL MEASUREMENTS .................................. 52 6.2 COMPARISON WITH SUN-TRACKING PV SYSTEM AND RESULTS FOR HOUSE 9 AND 20 ......... 52

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6.3 PROFIT WITH DIFFERENT INSTALLED PV POWER AND ORIENTATIONS ................................. 53 6.4 FURTHER POSSIBILITIES WITH 3DPV .............................................................................. 54 6.5 SOURCES OF ERROR ..................................................................................................... 54

7 CONCLUSIONS ................................................................................................................ 55

9 FURTHER WORK ............................................................................................................. 57

LIST OF REFERENCES .......................................................................................................... 58

JOURNALS, BOOKS AND PAPERS .............................................................................................. 58 REPORTS ............................................................................................................................... 58 PRESS RELEASES ................................................................................................................... 58 PROGRAMS, DATABASES AND USER’S MANUALS ........................................................................ 59 PERSONAL COMMUNICATION .................................................................................................... 59 WEB PAGES ............................................................................................................................ 59

ENCLOSURES ........................................................................................................................ 61

APPENDIX I – RESULTS SUN-TRACKING PV SYSTEM ................................................................. 61 APPENDIX II – RESULTS HOUSE 9 ............................................................................................ 61 APPENDIX III – RESULTS HOUSE 20 ......................................................................................... 61

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List of figures FIGURE 1. EXAMPLE OF SELF-CONSUMPTION DURING A DAY. ONLY A PART OF THE PV PRODUCTION IS CONSUMED IN THE

HOUSE AND THE RELATIVE SELF-CONSUMPTION WILL THEREFORE BE LOWER THAN 100 PER CENT. SURPLUS PV

PRODUCTION IS FED INTO THE GRID AND SURPLUS CONSUMPTION IS FED OUT FROM THE GRID (INTO THE HOUSE). .. 17 FIGURE 2. THE IV-CURVE AND MAXIMUM POWER POINT FOR A SOLAR CELL (NELSON, 2004, PP. 172-173). THE BLUE

CURVE DESCRIBES THE RELATION BETWEEN CURRENT I AND VOLTAGE V WHILE THE RED CURVE DESCRIBES THE

RESULTING POWER. TO FIND PMP A MPPT HAS TO BE USED TO FIND VMP AND IMP. .................................................... 22

FIGURE 3. SCHEME OF THE WORKING PROCEDURE FOR THE CALCULATIONS AND SIMULATIONS ....................................... 24 FIGURE 4. THE HOUSE IN GÄDDEHOLM WITH THE SOLAR MODULES ON THE ROOF AND ALSO SOLAR COLLECTORS (LEFT IN

THE FIGURE) FOR HEATING OF THE HOUSE. ........................................................................................................... 25 FIGURE 5. A SKETCH OF A 3D ONE-AXIS SOLAR TRACKING PV SYSTEM. THE ROTATION OF THE PANELS AROUND THE AXIS IS

SET IN PVSYST WHEN CALCULATING PV PRODUCTION FOR MULTIPLE ORIENTATIONS. TILT (SLOPE OF ROOF) AND

AZIMUTH (DIRECTION OF HOUSE/ROOF) FOR THE SIMULATION ARE DEFINED BY THE USER IN RLPV. ....................... 28

FIGURE 6. COMPARISON BETWEEN SIMULATED AND REAL PRODUCTION OF THE SYSTEM IN GÄDDEHOLM ......................... 31

FIGURE 7. YEARLY ELECTRICITY CONSUMPTION FOR THE 20 HOUSES AVAILABLE FOR THE SIMULATIONS. GÄDDEHOLM IS

HOUSE 1. ............................................................................................................................................................. 33

FIGURE 8. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO PV SYSTEMS DURING 2011 ON HOURLY

BASIS. ................................................................................................................................................................... 34

FIGURE 9. MONTHLY MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO PV SYSTEMS IN JANUARY

2011. ................................................................................................................................................................... 34

FIGURE 10. MONTHLY MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO PV SYSTEMS IN JUNE 2011.

............................................................................................................................................................................ 35

FIGURE 11. HOURLY PRODUCTION DURING A SUNNY DAY IN THE SUMMER (29TH

JUNE 2011). ........................................................ 35

FIGURE 12. HOURLY PRODUCTION DURING A CLOUDY DAY IN THE SUMMER (4TH

JULY 2011). ......................................................... 36

FIGURE 13. PRODUCTION FOR A 1D SYSTEM WITH 3360 WP........................................................................................... 36 FIGURE 14. PRODUCTION FOR A 3DPV SYSTEM. THE INSTALLED POWER IN ORIENTATION 1 AND 2 IS SHOWN ON THE X- AND

Y-AXIS, RESPECTIVELY. THE INSTALLED POWER IN ORIENTATION 3 IS GIVEN AS TOTAL POWER MINUS POWER IN

ORIENTATION 1 AND 2. THE COLOUR OF EACH BOX REPRESENTS THE YEARLY PV PRODUCTION FOR THE GIVEN

CONFIGURATION OF INSTALLED PV POWER. .......................................................................................................... 37

FIGURE 15. ABSOLUTE SELF-CONSUMPTION FOR A 1D SYSTEM WITH 3360 WP ................................................................ 38 FIGURE 16. ABSOLUTE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 2000 WP. ORIENTATION 1: AZIMUTH -90° AND TILT

30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 30° .................................. 39 FIGURE 17. ABSOLUTE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 3360 WP. ORIENTATION 1: AZIMUTH -90° AND TILT

30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 30° .................................. 39 FIGURE 18. ABSOLUTE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 4500 WP. ORIENTATION 1: AZIMUTH -90° AND TILT

30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 30° .................................. 40

FIGURE 19. RELATIVE SELF-CONSUMPTION FOR A 1D SYSTEM WITH 3360 WP MINIMUM: 53 %, MAXIMUM: 70 % ........... 40 FIGURE 20. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 1DPV SYSTEMS WITH LOWEST (53%

YEARLY, AZIMUTH 50°, TILT 50°, BLUE) AND HIGHEST (70% YEARLY, AZIMUTH -90°, TILT 90°, GREEN) RELATIVE SELF-

CONSUMPTION DURING A MEAN DAY IN JUNE 2011. ............................................................................................... 41 FIGURE 21. RELATIVE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 2000 WP. MINIMUM: 71 %, MAXIMUM: 81 %

ORIENTATION 1: AZIMUTH -90° AND TILT 30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH

0° AND TILT 30° ................................................................................................................................................... 42 FIGURE 22. RELATIVE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 3360 WP. MINIMUM: 54 %, MAXIMUM: 63 %


0° AND TILT 30° ................................................................................................................................................... 42

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FIGURE 23. RELATIVE SELF-CONSUMPTION FOR A 3D SYSTEM WITH 4500 WP. MINIMUM: 46 %, MAXIMUM: 54 %


0° AND TILT 30° ................................................................................................................................................... 43 FIGURE 24. YEARLY PROFIT IN SEK FOR A PV SYSTEM OF 3360 WP. BUYING PRICE: 1.18 SEK/KWH, SELLING PRICE: 0.48

SEK/KWH. ORIENTATION 1: AZIMUTH -90° AND TILT 30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION

3: AZIMUTH 0° AND TILT 30° ................................................................................................................................. 44 FIGURE 25. YEARLY PROFIT IN SEK FOR A PV SYSTEM OF 3360 WP. NORD POOL SPOT PRICES INCLUDING TAXES AND

FEES. ORIENTATION 1: AZIMUTH -90° AND TILT 30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3:

AZIMUTH 0° AND TILT 30° ..................................................................................................................................... 44 FIGURE 26. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 3DPV SYSTEMS WITH HIGHEST

PRODUCTION AND ABSOLUTE SELF-CONSUMPTION (BLUE – TABLE 9) AND HIGHEST RELATIVE SELF-CONSUMPTION

(GREEN – TABLE 10) IN JUNE 2011. ...................................................................................................................... 46 FIGURE 27. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 3DPV SYSTEMS WITH HIGHEST

PRODUCTION (BLUE –TABLE 13) AND HIGHEST RELATIVE SELF-CONSUMPTION (GREEN –TABLE 15) IN JUNE 2011. . 47 FIGURE 28. PRODUCTION FOR A 3DPV SYSTEM. INSTALLED POWER: 3360 WP. ORIENTATION 1: AZIMUTH -90° AND TILT

30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 90° .................................. 48 FIGURE 29. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM. INSTALLED POWER: 3360 WP. ORIENTATION 1:

AZIMUTH -90° AND TILT 30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 90°

............................................................................................................................................................................ 49 FIGURE 30. RELATIVE SELF-CONSUMPTION FOR A 3DPV SYSTEM. INSTALLED POWER: 3360 WP. ORIENTATION 1: AZIMUTH

-90° AND TILT 30° ORIENTATION 2: AZIMUTH 90° AND TILT 30° ORIENTATION 3: AZIMUTH 0° AND TILT 90°............ 49 FIGURE 31. HOURLY PRODUCTION IN 29

TH JUNE 2011 FOR A SYSTEM MAXIMIZING THE ABSOLUTE (SYSTEM 1, BLUE) AND

THE RELATIVE SELF-CONSUMPTION (SYSTEM 2, GREEN).......................................................................................... 50

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List of tables TABLE 1. COMPONENTS OF THE ELECTRICITY PRICE FOR BUYING AND SELLING ............................................................... 17

TABLE 2. ABSOLUTE SELF-CONSUMPTION ON AN HOURLY AND 10 MINUTE BASIS WHEN THE HOURLY PV PRODUCTION

EXCEEDS THE PV CONSUMPTION. THE MEASUREMENT PERIOD STARTS AT 12:00 AND ENDS AT 13:00 IN THIS

EXAMPLE. ............................................................................................................................................................. 18

TABLE 3. ABSOLUTE SELF-CONSUMPTION ON AN HOURLY AND 10 MINUTE BASIS WHEN THE HOURLY CONSUMPTION

EXCEEDS THE PRODUCTION. THE MEASUREMENT PERIOD STARTS AT 13:00 AND ENDS AT 14:00 IN THIS EXAMPLE. .. 18

TABLE 4. DEFAULT PARAMETERS USED FOR THE SIMULATIONS IN MATLAB .................................................................... 26

TABLE 5. CONSUMPTION AND REAL AND SIMULATED PV PRODUCTION 2011 FOR GÄDDEHOLM ....................................... 32

TABLE 6. REAL AND SIMULATED ABSOLUTE SELF-CONSUMPTION 2011 FOR GÄDDEHOLM ................................................ 32

TABLE 7. REAL AND SIMULATED RELATIVE SELF-CONSUMPTION 2011 FOR GÄDDEHOLM ................................................. 32

TABLE 8. TILT, AZIMUTH AND DISTRIBUTION FOR THE TWO SYSTEMS COMPARED. BOTH HAVE THE SAME INSTALLED POWER

(3360 WP). .......................................................................................................................................................... 33

TABLE 9. OPTIMIZING THE YEARLY PV PRODUCTION AND ABSOLUTE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° 45

TABLE 10. OPTIMIZING THE RELATIVE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° ............................................ 45

TABLE 11. OPTIMIZING THE YEARLY PV PROFIT, TILT 30°, AZIMUTH 0° OR ±90° ............................................................. 45

TABLE 12. OPTIMIZING THE YEARLY PV PROFIT, TILT 30°, AZIMUTH 0° OR ±90° ............................................................. 46

TABLE 13. OPTIMIZING THE YEARLY PV PRODUCTION FOR 3360 WP .............................................................................. 46

TABLE 12. OPTIMIZING THE ABSOLUTE SELF-CONSUMPTION FOR 3360 WP ..................................................................... 46

TABLE 13. OPTIMIZING THE RELATIVE SELF-CONSUMPTION FOR 3360 WP ...................................................................... 47

TABLE 16. OPTIMIZING THE YEARLY PV PROFIT FOR 3360 WP ........................................................................................ 47

TABLE 17. OPTIMIZING THE YEARLY PV PROFIT FOR 3360 WP ........................................................................................ 47

TABLE 18. REDUCTION OF INVERTER SIZE FOR DIFFERENT LAYOUTS WITH TILT 30° ......................................................... 51

TABLE 19. REDUCTION OF INVERTER SIZE FOR DIFFERENT LAYOUTS WITH TILT 40° ......................................................... 51

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Nomenclature PV Photovoltaics, i.e. electric power

generation with solar cells

STC Standard test conditions

(Defined below)

1DPV PV systems mounted in one direction SEK Swedish krona/kronor

3DPV PV systems mounted in multiple directions Wp Power (Watt) at STC

MPP Maximum power point Wh Energy (Power (W) ∙ time (h))

MPPT Maximum power point tracker (in inverter) kWp kilowatt peak = 1000 Wp

Pmp Power at MPP – results given in Wpeak (Wp) kWh Kilowatt hour = 1000 Wh

Vmp Voltage at MPP MWp Megawatt peak = 1000 kWp

Imp Current at MPP MWh Megawatt hour = 1000 kWh

Voc Open-circuit voltage (zero current) GWp Gigawatt peak = 1000 MWp

Isc Short-circuit current (zero voltage) GWh Gigawatt hour = 1000 MWh

Definitions and explanations 1D- and 3DPV Photovoltaic systems in either one direction (1DPV) or multiple directions

(3DPV).

Azimuth angle Angle defining the points of the compass of the PV modules, where 0° defines

a system to the south,-90° to the east and +90° to the west (in the northern

hemisphere).

Installed PV power

Peak power

DC power of the PV module or system at STC conditions given in Wpeak. Also

called Rated power. The rated power of a PV module can be found in an

information sheet attached to the module.

Inverter Converts direct current (DC) from the PV modules into alternating current

(AC) to make it possible to connect to the surrounding electric grid. The

inverter also includes a MPPT trying to find the MPP of the PV modules, see

section 3.2 in the Theory chapter.

Micro production If the installed PV (or wind/bio) power and the main fuse do not exceed 43.5

kWp and 63 A, respectively, and if the household is a net consumer of

electricity seen over a calendar year, the household is regarded as a micro

producer. For a micro producer it is both easier and cheaper to connect the PV

system to the public grid than for a producer not fulfilling the terms

(Stridh (a), no date).

Net metering Allows the customer to deduct the generated electric energy from the consumed

electric energy, often at a monthly or yearly basis. Therefore, the consumer

only has to pay for the monthly or yearly surplus consumption.

Net Present Value Sum of present value for every future income and cost.

Nord Pool Spot International power market in northern Europe where electric power and energy

can be traded.

Nominal power ratio The relationship between the maximum power of the inverter and rated power

of the PV array at STC.

Off-grid PV system installed on for example a house without any connection to the

electric grid. Therefore, an energy storage system such as batteries has to be

installed to be able to deliver energy when the consumption exceeds the

production. Other electric power sources can also be used, called a hybrid

system.

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On-grid

PV system connected to the public grid. If the system is installed on a house,

surplus production can be sold and surplus consumption can be bought from an

electricity retailer.

Photovoltaics A method of generating direct current (DC) electricity from solar radiation with

semiconductors (solar cells).

PV system Complete system including PV modules, inverters and exterior equipment such

as cables and installation equipment.

Rated power See ‘Installed PV power’.

RLPV Name of the MATLAB program developed for the simulations.

Self-consumption PV production consumed directly by the producer. Absolute self-consumption

is defined as the consumption in kWh that is produced by the PV system.

Absolute self-consumption divided with the total PV production gives the

relative self-consumption in per cent. Self-consumption replaces the need to

buy electricity from an energy supplier. More about self-consumption can be

found in section 2.

STC Standard Test Conditions: solar radiation 1000 W/m2, PV cell temperature of

25°C and AM1.5 global solar spectrum (Fraunhofer ISE, n.d.). The air mass

(AM) defines how long the light has to travel through the atmosphere and thus

its spectrum and intensity. AM 1.0 means the sun in zenith and AM 1.5 an

angle of 48.2° from the zenith angle.

Tilt angle Angle defining the slope of the PV modules, where 0° is a horizontal plane and

90° a vertical plane.

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1 INTRODUCTION The Introduction deals with the present situation of solar power, both in the world and in Sweden, and its

rapid increase in recent years. The purpose and aim of the study is described and also different methods to

increase the self-consumption. A summary of the previous research in the field of self-consumption and

especially the effect of changing the PV system layout is included. There are a few limitations for this

study, which are described in the end of the introduction.

1.1 Present situation for photovoltaics worldwide and in Sweden In recent years, solar power has been more and more popular in Sweden for electric power generation,

especially decentralized systems mounted on rooftops. According to an annual report from the IEA

Photovoltaic Power System Programme, IEA-PVPS, 8.4 MWp electric PV power was installed in Sweden

in 2012, an increase with 4.4 MWp compared to 2011. The cumulative installed production capacity in the

end of 2012 was slightly more than 24 MWp. The majority of the power installed was grid-connected,

compared to historic conditions with mostly off-grid systems (Lindahl, 2013). The Swedish market is

however by far smaller than the German one, which is the largest one in the world with 7.6 GWp installed

PV power in 2012 and a cumulative installed power of more than 32 GWp (BSW-Solar, 2013). The global

installed PV power reached 100 GWp in the beginning of 2013 (EPIA, 2013).

The growing popularity is partly based on the decreasing system costs of solar power systems. Different

economic supporting systems such as decreased feed-in tariffs have also had an influence on the

increasing popularity. The national IEA-PVPS report states that the cost of the PV systems in Sweden

2012 had dropped to about a half of the price compared to two years earlier. Two major reasons behind

this are the price decrease of the solar modules and the fact that the number of installation companies in

Sweden has increased in recent years (Lindahl, 2013). The competition between the companies has

increased and thus lowered the prices. The cost for installation and other components besides the modules

now make up the majority of the cost of a complete PV system seen from an American point of view

(Chandler, 2012), but the same trend is probably distinguishable in Sweden. According to the IEA-PVPS

report the system cost in the end of 2012 in Sweden was approximately 22 SEK per Wp exclusive value

added tax (VAT) for a typical residential roof mounted PV system of up to a few kWp. This is a rapid

decrease in system price from 32 SEK per Wp exclusive VAT in 2011. The majority of all PV systems

today are mounted on roofs on residential houses or at commercial buildings. The alternative –

centralized systems exclusively for generation to the public grid – made up a very small share of the

market in Sweden in 2012 (Lindahl, 2013).

The majority of all installations in Sweden are roof-mounted on private houses. This means that it is of a

large interest to increase the self-consumption, i.e. the share of the PV power production that is consumed

in the house, from the house owner’s perspective. The savings from self-consumed PV-generated electric

energy are much higher than the profit from selling it to spot prices. For the self-consumed energy neither

taxes nor fees, such as energy tax and grid fee, have to be paid. It may also be of interest for the

distribution grid operator to increase the self-consumption and to make the production profiles smoother

of the PV systems connected to the grid. The fluctuations of the fed in PV power due to (rapid) varying

solar irradiance will then have a smaller influence on the grid.

The highest yearly electric power production is achieved with a south-oriented system with a tilt of

approximately 40° to 50° at the latitudes of Sweden, which can be calculated through the sun-path. The

further north the system is placed, the larger is the optimal tilt. This is calculated and presented in the

Results section. The highest self-consumption can however occur for other azimuth and tilt angles.

In recent time, there have been discussions about the potential of smart grids and small-scale power

production in residential areas. One of the main parts of the small-scale power production is the PV

systems. Possible drawbacks of increasing the on-grid micro production from PV systems are their

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production profiles and the hosting capacity for solar power in the distribution grids. The hosting capacity

can however be large; it was 70 per cent in a city grid in Sweden when considering overload limitations

according to a study from Walla et al. (2012). Around noon at sunny days, the PV generation can be

considerable if many systems are connected to the same distribution grid. In the morning and evening the

electric power consumption in residential areas might be higher than at noon depending on the habits of

the people living there (many of them might not be at home during daytime). This could be a problem if

the distribution grid is designed only for consumption purposes. With a lower electric power production

in the middle of the day and increased production in the morning and in the evening, the fluctuations in

electric power fed in from or out to the grid can be lowered.

1.2 Purpose and aim The purpose of this thesis is to investigate how the self-consumption of a residential photovoltaic system

will change by placing the solar modules in different directions other than the one optimized for the best

yearly PV production. Self-consumption is defined as the share of the photovoltaic power production

consumed by the producer, either as absolute in kWh per year or as relative in per cent of the PV

production. A further description of self-consumption of PV generated power is presented in section 2.1.

Questions to be answered:

How does the yearly production change when the orientation of the PV modules changes?

Is it possible to increase the self-consumption if the solar modules are placed in one or

several different directions (1D- and 3DPV)?

How does the profit change for different configurations of installed PV power in up to three

directions?

Are there any further possibilities with 3DPV systems, i.e. also regarding other components

besides the PV modules?

The aim is to develop a MATLAB tool (RLPV) to optimize the installation, i.e. the azimuth and tilt

angles of the modules on private houses as well as the configuration of the modules between the different

directions. The optimization can be performed both with respect to the self-consumption, yearly

production and from an economic point of view. It is important that the accuracy of the MATLAB

simulations are high and therefore a comparison with an existing system will be carried out. In RLPV

there should be default values needed for the calculations, such as consumption profiles from several

houses, installed PV power and different costs, but the user should also be able to define new values. This

makes it possible to evaluate how the different parameters influence the results.

1.3 Previous research The research within the field of increasing the self-consumption through changing the layout has so far

been very limited. According to Bernardi et al. (2012, pp. 6880-6884) there is a lack of research of the

benefits of 3DPV and study of the effects of weather conditions, locations and seasons. The fact that the

PV modules earlier made up the majority of the system costs has limited the research on 3DPV as an

alternative to the dominating 1D installation.

Depending on the location, weather and consumption pattern, the advantage of 3DPV will vary.

According to research from MIT the largest improvements for use of 3DPV are at high latitudes, where

the sun often is close to the horizon (Chandler, 2012). Also the production during cloudy days could even

be higher with 3DPV than a one-direction installation (Bernardi et. al, 2012, pp. 6880-6884). The

orientation of the PV systems will also affect the time of highest production of the solar cells. According

to a conference paper, a shift in azimuth angle from 0° south to ±35° would shift the top production with

two hours and the yearly production loss of less than five per cent in Germany (Erban, 2011).

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There exist only a few non-residential (centralized) PV systems with modules pointing in directions other

than due south, mainly in Germany. Close to Kassel in Germany, an east-west oriented free-standing PV

system of 800 kWp was installed in 2012 aiming to stabilizing the PV generated fluctuations in the grid

(Städtische Werke, 2012).

If the panels are placed in other directions than due south, a smaller rated power of the inverter in

comparison with the rated power of the PV modules can be used. The relation between the rated power of

the inverter and the modules is called the nominal power ratio. If 50 per cent of the panels are facing due

east and the rest due west, all of them with a tilt of 30°, the nominal power ratio can according to a

conference paper be decreased to 68 per cent with a revenue loss of 0.2 per cent when using fixed

electricity prices for the PV production in Germany (Straub et. al, 2012).

1.4 Limitations The results will be based on the solar radiation during 2011. The solar radiation pattern and the resulting

production profile can change from one year to another and the following years might have different solar

radiation pattern. According to measurements by SMHI the yearly solar radiation can vary with

±10 per cent (SMHI, 2007, p. 6).Therefore, the results most probably vary depending on the year used for

the study. The reason for choosing 2011 is the comprehensive PV production and consumption data from

the system in Gäddeholm which were used to verify the simulated production.

Off-grid houses could also benefit from increased self-consumption due to a change in the layout. This

could make the need for batteries lower, since the production would better match the consumption.

However, the number of solar panels needed would increase. This would make it necessary to evaluate

the best and cheapest alternative; either a lower number of batteries and a higher number of solar panels

or vice versa. Until 2006 off-grid PV systems were the most common application in Sweden. Thereafter,

grid-connected systems became more popular and today make up the largest share. In the rest of the

world on-grid system is also the dominant application type (PV Grid, 2013).

Since the main topic of the thesis is to evaluate different PV systems from a consumer point of view,

possible advantages and drawbacks in the distribution grid and for the grid operator when increasing the

self-consumption for a residential PV system will not be investigated. Nevertheless it is expected that

increased self-consumption would be a benefit for the grid operator as the amount of electric power fed in

to and out from the grid will be more even during the day.

1.4.1 Cost of the components in a PV system

The individual variations in cost of the different components required for a PV system, such as panels,

inverter, support structure, cables and additional installation equipment will not be included in this thesis.

The total costs are assumed to be linearly scalable, which is a simplification. However, it is difficult to

predict the development of the individual costs of the components. It can be assumed that the prices will

decrease if the worldwide as well as the Swedish market of small-scale solar power will increase, but the

different components might undergo different price drops. It is also difficult to predict the changes in the

energy prices, especially since the warranties of many PV modules are around 25 years. Some of the parts

in a PV system such as the inverter have a shorter useful life today and therefore have to be replaced more

often (Parker, 2011). No extra costs are supposed to be needed during the useful life of the PV system and

no degradation of the PV efficiency is considered. In the simulations fixed system costs per kWp set by

the user will be used for the calculations.

1.4.2 Net metering

Net metering for residential PV power installations has been discussed in Sweden in the recent time. With

net metering the consumer can deduct the PV production from the consumption, often on a monthly or

yearly basis. This would make it more profitable to install larger facilities than with hourly metering,

since the value of the total production will increase. It is also most profitable to point every module to the

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south, since the hourly self-consumption is not important. In this thesis only hourly metering will be

considered.

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2 SELF-CONSUMPTION OF PV POWER The Self-consumption of PV power chapter deals with different ways of increasing the self-consumption.

Today there exist three methods to achieve this, namely demand side management, battery storage and

change of the layout. Thereafter, the calculations of the PV electric energy production are described and

how this should be done to optimize the self-consumption.

2.1 Description of self-consumption of PV power and how to increase it The electric power from the residential PV system can either be used directly in the house, i.e. self-

consumption, or fed in to the public grid. An example of self-consumption, surplus PV production and

electricity consumption in the house is shown in Figure 1. The house owner could profit up to two to three

times more from self-consumption of the produced PV power than from selling the surplus production to

fixed or hourly Nord Pool Spot tariffs. This is due to the taxes and other fees added to the buying price

which make the savings for a self-consumed kWh larger than the income from a sold kWh (see Table 1).

The prices are found in section 4.3.

Figure 1. Example of self-consumption during a day. Only a part of the PV production is

consumed in the house and the relative self-consumption will therefore be lower than 100

per cent. Surplus PV production is fed into the grid and surplus consumption is fed out

from the grid (into the house).

Table 1. Components of the electricity price for buying and selling

Savings (self-consumed PV energy)

Income (sold PV energy)

Spot price Spot price

Energy certificate Energy certificate

Energy tax -

Grid fee -

Value added tax -

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The self-consumption can be calculated for different periods of time, for example instantaneously, hourly,

monthly or yearly self-consumption. When measuring the electricity consumption, PV production and

self-consumption, electricity meters with two or four registers are used; one measuring the amount of

energy fed in to the grid when there is a surplus production and one measuring the energy fed out of the

grid when there is a surplus consumption. The meters can be read on different time intervals.

The longer the billing period is the larger facilities would be profitable (Molin et. al, 2010). Depending on

measurement period, both the absolute and also the relative self-consumption will be different. Generally,

the shorter the time period is, the lower is the self-consumption. Examples of the mismatch when

calculating the self-consumption with different time steps are presented in Table 2 and Table 3. Both when

the consumption exceeds the PV production and when the production exceeds the consumption on an

hourly basis (in this case, also other time steps can be used), the self-consumption will be lower for a

shorter measurement period.

Table 2. Absolute self-consumption on an hourly and 10 minute basis when the

hourly PV production exceeds the PV consumption. The measurement period starts

at 12:00 and ends at 13:00 in this example.

Time

(10 minute step)

Production

(units)

Consumption

(units)

Absolute self-

consumption (units)

12:00-12:10 30 10 10

12:10-12:20 40 20 20

12:20-12:30 50 70 50

12:30-12:40 60 70 60

12:40-12:50 50 50 50

12:50-13:00 40 20 20

SUM (1 hour) 270 units 240 units 210 units

Absolute self-

consumption

240 units

(1 hour basis)

210 units

(10 minute basis)

Relative self-

consumption

Table 3. Absolute self-consumption on an hourly and 10 minute basis when the

hourly consumption exceeds the production. The measurement period starts at

13:00 and ends at 14:00 in this example.

Time

(10 minute step)

Production

(units)

Consumption

(units)

Absolute Self-

consumption (units)

13:00-13:10 30 20 20

13:10-13:20 40 60 40

13:20-13:30 50 80 50

13:30-13:40 60 80 60

13:40-13:50 50 50 50

13:50-14:00 40 30 30

SUM 270 units 320 units 250 units

Absolute self-

consumption

270 units

(1 hour basis)

250 units

(10 minute basis)

Relative self-

consumption

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The total absolute self-consumption for the two hours in Table 2 and Table 3 is 510 units (240+270) and

the total PV power production is 540 units (270+270). The relative self-consumption is defined as the

absolute self-consumption divided with the total PV power production for a given period of time. This

means that the total relative self-consumption for the two hours in the tables is 94.4 per cent (510/540).

The formula for calculating the relative self-consumption for n number of time steps is presented in

Equation 1.

∑

∑

Equation 1

The self-consumption is dependent on the system size; the more PV power installed the more often the

production exceeds the consumption. Therefore, the self-consumption is not linearly scalable with

installed power.

There are mainly three different methods to increase the self-consumption of a photovoltaic system;

demand side management (DSM), battery storage and PV module orientation and configuration. Only the

latter one will be studied in this report. With the demand side management strategy the electric loads in

the households are actively shifted to better match the power profile generated by the PV panels (Widén,

Wäckelgård and Lund, 2009). Batteries can be used to extend the period of the day with PV generated

energy; they cut of the surplus production and store the energy to the evening or next morning when the

electric power consumption exceeds the PV production.

Increased self-consumption will lead to less electric power delivered to the grid for a given peak

production capacity and therefore the problems arising from PV generated fluctuations may decrease.

Especially when the rate of installed PV power in a distribution grid is high, problems with overvoltage in

the grid can occur (IEA, 2009). The distribution grid may also not be designed for distributed production

such as residential solar power and therefore might have to be modified to be able to handle the voltage

variations. This means that also the grid operator might profit from higher self-consumption and a more

even PV production profile during the day.

One of the advantages with PV systems in multiple directions is a more even production during the day,

since modules facing east and west will increase the production during the morning and afternoon. The

number of hours with high PV power generation (relative to maximum PV power) can therefore be

increased. An arrangement of a PV system in three directions – 3DPV – requires more PV area per unit

energy than a south-oriented one but will not necessary prevent the use of 3DPV (Bernardi et. al, 2012,

pp. 6880-6884).

2.2 Calculating PV production and optimizing self-consumption The orientation of the photovoltaic panels, in terms of azimuth and tilt angle, affects the instantaneously

as well as the yearly production. With different orientation than the optimal, the peak power output may

be shifted towards the peak consumption (Widén, Wäckelgård and Lund, 2009). A program which

handles all these prerequisites has to be developed to attain the desired results.

The location is important when calculating the production and therefore also the self-consumption, since

it determines how the solar radiation will change both during the day and year. The solar radiation due to

location can be calculated when knowing the sun path and will be the same for every year, if the effect of

clouds and atmospheric humidity is neglected. To calculate the hourly production it is important to know

the instant weather conditions. The weather at the location will have a large impact on the instant solar

radiation, and it is therefore difficult to predict how this will evolve in the future when using the results

from the production simulations for several years.

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Simulations for multiple orientations are needed to be able to optimize the self-consumption from several

points of views. The same solar radiation data are used for all simulations of the production and to

calculate the effect of changing the orientation of the modules, trigonometric functions are used. This is

handled by the commercial program PVsyst (2012), which is described in the Method chapter, and the

user only has to define the system parameters such as type of solar modules, inverter and power.

Optional, solar radiation data for a horizontal plane and ambient temperature data can be uploaded. If no

such data is uploaded, the program will use own data. More about meteorological data can be found in

PVsyst’s user’s manual (2012, pp.120-121).

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3 THEORY The Theory chapter deals with the existing PV technology and contains also a summary of the theory of

photovoltaics, i.e. how the voltage and current and thus the power are correlated, and how the temperature

affects the efficiency of a solar cell. The different types of solar radiation are described and finally the

effect of the heating system in the house on the self-consumption is described.

3.1 Different kinds of PV modules The main photovoltaic techniques are mono- and polycrystalline silicon and thin film. Silicon-based solar

modules are the most widespread technique in the world today and thin film solar cells only make up a

small share.

The monocrystalline silicon solar cell has the highest efficiency, since the silicon is arranged in a

continuous single-crystal lattice. The monocrystalline material is manufactured in cylinders and the

resulting wafers are therefore round. To fit in more wafers on the surface of a module, the wafers are

often cut into more quadratic shapes. However, the more material that is cut away the more expensive is

the manufacturing.

Polycrystalline solar cells, the other common technique, are cheaper than the monocrystalline technique

but have a slightly lower efficiency. They are manufactured from large blocks of molten silicon which are

carefully cooled and cut into square wafers.

There are also thin film solar cells, which is an umbrella term for several different techniques. Thin film

coating is put directly on for example a glass plate. There are for example cadmium-telluride (CdTe),

copper indium gallium selenide (CIGS) and amorphous silicon. The efficiency of thin film solar cells is

lower than for crystalline silicon cells. To be able to compete with crystalline silicon, they must therefore

be cheaper to manufacture. Because of the lower efficiency, film panels cover a larger area for the same

installed PV power and this might be a disadvantage when installing on places with a limited surface,

such as on roofs, and will also increase the installation cost. Therefore, it is important not only to focus on

the price per power unit (Wp) for a PV module.

3.2 MPP and MPPT The voltage and current generated by a solar cell can be described by a diode equation and the result can

be presented in an IV-curve (current versus voltage) as seen in Figure 2. The equation is mainly used to

describe a semi-conductor in darkness but can also be used for light conditions, which is the case for solar

cells. The IV characteristic, which has the shape of an exponential function, can be seen in Figure 2.

The current from a solar cell is linearly proportional to the solar radiation whereas the voltage increases or

decreases logarithmically with increased or decreased solar radiation, respectively (Nelson, 2004, pp.

172-173). The electric power is the product of voltage and current generated and it is possible to find a

combination which gives the maximum power output (Pmp). To find the maximum power point (MPP), a

maximum power point tracker (MPPT) is used, which continuously varies the voltage to find the

maximum power. The MPPT is often included in the inverter box.

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Figure 2. The IV-curve and maximum power point for a solar cell

(Nelson, 2004, pp. 172-173). The blue curve describes the relation

between current I and voltage V while the red curve describes the

resulting power. To find Pmp a MPPT has to be used to find Vmp

and Imp.

3.3 Efficiency and effect of temperature The efficiency of a solar cell can be calculated when knowing the maximum power Pmp and the solar

radiation power, as can be seen in Equation 2.

Equation 2

When the temperature rises, as it does for a cell in sunlight, the open-circuit voltage decreases and short-

circuit increases. Since the decrease of the voltage is larger than the increase of the current, the efficiency

and hence the power output decrease (PVEducation.org, n.d.). The temperature coefficient, which

describes the rate of decrease with increasing temperature, is always stated in the solar panel

specifications but is not taken into consideration in the power calculations in PVsyst (for further details of

the program PVsyst, see section 4.2). Instead an energy balance between ambient temperature and the

heating of the cell due to solar radiation is used (PVsyst, 2012, pp. 84-85).

3.4 Global, direct, diffuse and ground-reflected solar radiation For PV applications, there are three different parts of solar radiation measured – direct, diffuse and

ground-reflected. They are summed up to the global solar radiation. The solar radiation are often given in

energy per second (watt) and square meter ⁄ or energy per square meter and

year ⁄ . The global solar radiation is the total solar radiation measured on a horizontal

surface and includes direct, diffuse and reflected solar radiation. The direct solar radiation passes directly

through the atmosphere without being scattered on the way to the surface of the earth. The diffuse solar

radiation has been scattered from the direct beam and hit the surface of the earth from all directions. The

ground-reflected solar radiation has been reflected on non-atmospheric objects such as the ground. The

reflection varies with the albedo of the object, e.g. high albedo and thus high reflection for snow and low

albedo and reflection for asphalt.

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There are different methods to measure the radiation depending on the type of solar radiation. According

to the National Renewable Energy Laboratory (NREL), global and diffuse radiation is often measured

with a pyranometer, which measures almost the whole sun spectra, and the results are given for a

horizontal area. When measuring the diffuse component, a tracking ball shades the direct beam. Direct

solar radiation is either calculated when both the global and the diffuse components are known or

measured with a sun-tracking pyrheliometer (Stoffel and Wilcox, 2004). In this project only global solar

radiation is used (see more in section4.5). To calculate the reflected solar radiation, the objects

surrounding the measurement point have to be known and also their albedo.

3.5 Effect of different heating systems The electric consumption in a private house is dependent on season and its heating system. If the house

has a direct-acting electric heating system, the consumption will be high especially during the winter. For

a district heated house, the daily and monthly electric power consumption is more similar seen over the

whole year. Also, the consumption can be lowered with other types of heating systems, most of them

waterborne, such as geothermal heating and solar collectors. When there is no waterborne heating system

installed in a house, an air heat pump can be used to decrease the electric power consumption compared

to the direct-acting heating.

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4 METHOD The Method chapter first describes the existing system in Gäddeholm, a village close to the city of

Västerås, Sweden. This residential PV system is used as a reference for the calculations and simulations.

How to perform the calculations and simulations is thereafter described. A scheme of the complete

procedure can be seen in Figure 3. Two softwares – PVsyst and MATLAB – are used for the calculations.

Thereafter, the parameters needed for the MATLAB tool (named RLPV) and the output chart types from

the simulations are described. Data sources for solar radiation and temperature are described in the

section thereafter and finally methods of how to calculate the payback period and the correlation between

two data series are presented.

Figure 3. Scheme of the working procedure for the calculations and simulations

4.1 Existing system in Gäddeholm The modelling is based on the PV system on a house in Gäddeholm, as can be seen in Figure 4. The

installed PV system size is 3.36 kWp and consists of 14 Sanyo HIT-240HDE4 monocrystalline modules

of 240 Wp each. The modules are connected in two strings with seven modules in each string (Stridh (b),

n.d.). The more modules in one string, the higher the voltage. Increasing the number of strings will

instead increase the current. The system size and type of module and inverter are the same in the

simulations as for the real system to be able to validate the accuracy of the simulations.

The inverter used, which includes one MPPT, is a Sunny Boy 3000TL from SMA of 3.0 kW (Stridh (b),

n.d.) The maximum power of the inverter can normally be slightly lower than the peak power of the PV

modules, since they rarely deliver the STC power. At 1000 W/m2 the temperature of the cells are often

higher than 25°C, even if the ambient temperature is lower. The efficiency decreases with increasing cell

temperature and thus the power output also decreases. Also, the incoming radiation should be close to

normal to the modules to reach STC conditions, which only occurs during a short time of the day and

only if the tilt is optimal. The optimal tilt also varies during the year.

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Figure 4. The house in Gäddeholm with the solar

modules on the roof and also solar collectors (left in the

figure) for heating of the house1.

The PV panels are roof mounted with a tilt of 27° and azimuth of -5°. In the mornings and evenings there

is a partial shadowing which gives a yearly production loss of around 20 per cent compared to a similar

un-shadowed PV installation (Stridh (b), n.d.). In the calculations in PVsyst no shadowing will be

considered while the calculations also are used for a general system and not only for the one in

Gäddeholm.

The heating system is important for the yearly electric power consumption as well as for the daily

consumption profile. The tap water and floor heating system in Gäddeholm is based on solar collectors

during spring to fall and mainly on an electric immersion heater in a hot water storage tank in winter

when less solar energy is available. There is also a fireplace with water jacket contributing to the heating

system.

4.2 Softwares for calculations and simulations There are several softwares available to calculate the hourly production from a PV system. One of them,

which will be used in this project, is the commercial program PVsyst (version 5.64). In the program a

number of variables need to be set, such as type of solar modules and converter, installed power of the

system and tilt and azimuth angle. Based on for example location, solar radiation and temperature data the

hourly production of the total PV system will be calculated.

The output from PVsyst is in this report given as hourly production for different tilt and azimuth angles

with total 19 times 10 cells (azimuth angles -90° to +90° and tilt 0° to 90°, both with a length of step of

10°) for the fixed plane and 13 times 10 cells (azimuth step 15° and tilt step 10°) for the tracking plane,

since it is not the main topic of this thesis. These data are used for the calculations in the MATLAB

models, e.g. self-consumption and economy of the system. PV production data from PVsyst with exactly

the same orientation as the system in Gäddeholm are compiled to calculate the correlation between

simulated and measured production data.

The MATLAB model is presented in a Graphical User Interface (GUI), where input parameters and chart

types can be chosen2. The available alternatives are given in the following two sections.

Consumption data for several houses, similar to the ones from Gäddeholm, are available from the

Swedish Energy Agency1. Consumption profiles for 19 houses in Sweden are used, in total 20 houses

1 Accessed 31 May 2013 from Bengts villablogg, http://bengts.blogg.viivilla.se/vara-solceller/

2 The MATLAB GUI and code will only be presented in the report for ABB.

http://bengts.blogg.viivilla.se/vara-solceller/

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including Gäddeholm. More consumption profiles from the Swedish Energy Agency were available but

20 alternatives were assumed to be a reasonable number, since the simulation possibilities already are

very comprehensive. The locations of these houses as well as the year of measurement are however not

known. These data can be used to investigate how the results depend on the consumption profile of the

house. To be able to compare the results for the different houses, the same solar radiation data will be

used for every house.

4.3 Input parameters in RLPV There are a few input parameters required for the simulations in RLPV. Every input parameter is not

necessarily used for every calculation.

Table 4. Default parameters used for the simulations in MATLAB

Default parameter Unit User modifiable

Installed power (existing

PV system)

3360 Wp No

Installed power (PV

systems to be simulated)

3360

(5 possibilities)

Wp Yes

House (consumption

profile)

Gäddeholm - Yes (20

alternatives)

Fixed electricity price

(buy), including VAT

1.182 SEK/kWh Yes

Fixed electricity price

(sell), no VAT

0.483 SEK/kWh Yes

Energy tax (no VAT) 0.293 SEK/kWh (Vattenfall

(a), 2013)

No

Electricity certificate fee

(no VAT)

0.04 SEK/kWh (Vattenfall

(b), 2013)

No

Grid fee (including

VAT)

0.225 SEK/kWh (Stridh (c),

2012)

No

Value added tax 25 % No

Investment cost incl.

VAT

(fixed plane)

20,000 SEK/kWp Yes

Investment cost incl.

VAT

(tracking plane)

30,000 SEK/kWp Yes

Mean inflation 2000-

2012 in Sweden (SCB,

n.d.).

1.53 % / year Yes

Nominal rate of return4 3 % / year Yes

1 License from the Swedish Energy Agency (Energimyndigheten) is required for these data.

2 Hourly mean price 2011. Spot price including energy tax, energy certificate, grid fee and VAT.

3 Mean hourly price 2011. Spot price and energy certificate, excusive VAT.

4 The rate of return has a very important effect on the payback period of the PV system and is difficult to define in

advance. This is one of the reasons why results of the payback periods are not presented in this report.

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Simulated production from PVsyst is calculated with the components and size of the system in

Gäddeholm. The production is thereafter normalized as watt-hour per watt peak (Wh/Wp) to be able

to set the system size. Up to five different system sizes can be set for every simulation.

Hourly consumption profiles for 20 houses are available.

Electricity prices, either fixed or variable prices for buying and selling. The future energy prices are

assumed to increase with the yearly mean inflation 2000-2012. New rates of inflation can be set by

the user. How the spot prices will evolve during coming 25 years, which often is the guaranteed

useful life of a PV module (Parker, 2012) are however almost impossible to forecast.

If variable prices are chosen, Nord Pool Spot prices from 2011 are used (Nord Pool Spot, n.d.).

Surplus production is sold for spot prices and surplus consumption is bought for spot prices plus taxes

and fees (see Table 4).

The investment cost per kWp is assumed to be linearly scalable with the installed power.

Desired nominal rate of return, for example when the PV system is financed by a bank loan with a

specific interest. The desired rate of return can be changed to meet the requirements of the user.

It is possible to put in new consumption profiles into the program and the calculations if the

MATLAB code is slightly modified. Instructions about how to this can be found in the

‘input_parameters.m’-file in RLPV1.

4.4 Chart types from RLPV

Hourly electric power consumption for 2011 will be displayed for every house available in the

simulations, in total 20 houses, which can be compared to the hourly PV production of the chosen

system. A monthly and yearly mean production and consumption are also presented for every hour

for one average day. The production profiles for two 3DPV systems of the same size but different

orientations, i.e. azimuth and tilt, are displayed in every figure.

Comparison (only available for Gäddeholm) of the simulated and real production is displayed to

evaluate the accuracy in the simulated production data.

Bar chart showing the total yearly consumption for the 20 houses is also displayed.

Yearly production for a PV system for different tilt and azimuth angles. Four alternatives.

o Modules installed on a fixed surface, for example a roof. All the modules can either point in

the same direction (1D) or in three different directions (3D).

o Modules installed on a one-axis solar tracking plane (1D or 3D). The frame can rotate

between -30° and +30°around the axis, defined as rotation 0° when the plane is facing the

axis azimuth, see Figure 5. This is calculated in PVsyst and cannot be set by the user. All the

modules can either be 1D or 3D. A maximum rotation angle of ±30° was assumed to be an

adequate value for installations on private houses.

Yearly self-consumption for a PV system of different tilt and azimuth. Eight alternatives.

o Either absolute (in kWh/year) or relative (in per cent of production for every direction) self-

consumption can be calculated.

o Either fixed (1D or 3D) or tracking (1D or 3D) can be simulated.

Yearly profit for a PV system for different tilt and azimuth angles and configurations. The calculation

of the profit can be found in section 4.6 and is calculated with the parameters given in Table 4. Four

alternatives.

1 The files will only be enclosed to the report for ABB

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o Only 3D systems can be simulated, both for a fixed and a one-axis solar-tracking PV system.

o Fixed or variable electricity prices.

Payback period for a PV system for different tilt and azimuth and configurations. The payback period

is based on the yearly profit. The formulas for calculating the payback period are presented in

Equation 6 and Equation 7 in section 4.7. Four alternatives.

o Only 3D systems can be simulated, both for a fixed and a one-axis solar-tracking PV system.

o Fixed or variable electricity prices.

Figure 5. A sketch of a 3D one-axis solar tracking PV system. The rotation of the

panels around the axis is set in PVsyst when calculating PV production for

multiple orientations. Tilt (slope of roof) and azimuth (direction of house/roof)

for the simulation are defined by the user in RLPV.

4.5 Data Sources for Calculation of Production The two most important data types needed when calculating the production of a PV system are hourly

solar irradiation and ambient temperature data. The temperature of the cells can be calculated when

knowing the ambient temperature, solar irradiation and mounting, e.g. integrated in a building, mounted

on a roof or façade with an air-gap in between, as in this case, or free-standing. Also the wind contributes

to the cell temperature. However, since the wind can vary between the measurement point and location of

the PV system, wind data will not be used.

For solar irradiation data three different sources for the region of Västerås have been found. The Swedish

Meteorological and Hydrological Institute (SMHI) together with two other Swedish authorities have

developed a database for solar irradiation data called STRÅNG (n.d.). Based on irradiance measurements

from a number of locations in Sweden, a model for a specific location can be interpolated. The second

data source is measurements of the global solar radiation from a cogeneration plant (CHP – combined

heat and power) in Västerås1. The plant is run by the power company Mälarenergi. The third data source

is global solar radiation measurements from LantMet for research purposes (LantMet, n.d). The

measurements are made in Brunnby near Västerås and another sensor than the pyranometer, called a PAR

sensor, is used to measure the radiation. With this sensor, a smaller spectrum is measured, since the

research is focused on vegetation and agriculture. Because of this, the measuring equipment in Brunnby

will constantly measure lower values than the other two.

1 Retrieved via e-mail from Mälarenergi

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One important advantage with data from STRÅNG is the possibility to generate data for any location in

Sweden. The two others can only be used for locations near Västerås. If calculations for PV systems in

other locations would be made, other solar radiation data have to be found. For this reason, data from

STRÅNG will be used in this project. However, a disadvantage is the accuracy of the STRÅNG data,

especially for locations relatively far from the measurements such as Västerås. The nearest solar radiation

measurements are made in Stockholm, Norrköping, Karlstad and Borlänge (SMHI, n.d.). The margin of

error for hourly data when comparing the model data with point observations is approximately 30 % for

global solar radiation and 60 % for direct solar radiation (STRÅNG, n.d.). Therefore, only global solar

radiation is used in the calculations in PVsyst. However, PVsyst needs the diffuse and direct solar

radiation for the calculations and therefore uses a mathematical model to calculate these components from

the global solar radiation (PVsyst, 2012, p. 137). This means that also the calculations in PVsyst have a

margin of error in the direct and diffuse solar radiation but this value is not known.

The temperature data comes from the measurements from Västerås Airport and are compiled by Robert

Larsson (2013). The distance between Gäddeholm and the airport is around five kilometres. Since the

efficiency of the solar cells, and thus the power, is dependent on the cell temperature and therefore also

the ambient temperature, temperature data has to be uploaded in PVsyst.1

4.6 Yearly profit The yearly profit is calculated for every hour of the year, in total 8760 hours, since both the spot price, PV

production and consumption will change. The calculations are shown in Equation 3 to Equation 5.

∑( )

Equation 3

{

Equation 4

{

Equation 5

4.7 Net Present Value and payback period The payback period of the PV system is the time until the costs of the PV systems are compensated by the

savings and profits. In this study, the net present value (NPV) is used for the calculations of the payback

period, see Equation 6 and Equation 7. The results for the payback period can be found in section 5.10.

∑

Equation 6

Equation 7

NPV Net present value (SEK)

1 It is possible to run simulations in PVsyst with neither external solar radiation nor temperature data, i.e. the user

does not have to upload own data. If no external data are uploaded, PVsyst uses data from Meteonorm

(http://meteonorm.com/). This is however not as accurate as external input data, since the hourly values is generated

by a stochastic model (PVsyst, 2012, p.126).

http://meteonorm.com/

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t Year (between t=0 and t=n) n N b r y r NPV P Yearly profit (SEK/year) i Yearly inflation (%) RoR Rate of return (%) I Investment cost

4.8 Pearson product-moment correlation The simulated PV production data from PVsyst are compared to the real production data from the PV

system in Gäddeholm. The comparison can be found in the Results chapter in section 5.1. To make it

possible to evaluate the accuracy of the simulated production data, the Pearson product-moment

correlation coefficient is used, which can be seen in Equation 8. It measures the linear correlation between

two data series. The better linearity the closer the coefficient r is to +1, or -1 if the series are negatively

correlated (de Smith, n.d.). A value of 0 indicates that there is no correlation.

Pearson Product-Moment Correlation Coefficient (de Smith, n.d.)

∑

√∑ √∑

Equation 8

x First series of measurements

y Second series of measurements

Mean of measurements x

Mean of measurements y

i Sample number

n Number of samples

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5 RESULTS The results are presented in charts for the chosen input parameters, such as installed PV power,

consumption profile, costs and gains. It is possible to retrieve 14 charts1, each with different result, for

every house with one system size, i.e. installed PV power, and fixed input parameters and orientations.

Since consumption profiles for 20 houses are available for the simulations, this would result in 280 charts,

plus two extra charts shown in Figure 6 and Figure 7, all results cannot be presented in this report. When

varying the installed power, other input parameters and orientations of the modules, even many more

diagrams can be created. Therefore, only the simulated results for the PV system in Gäddeholm are

presented in the main report. In Appendix II and III similar results for two other houses, one with the

lowest yearly consumption and one with the highest, are presented to make comparisons possible. The

results for the one-axis sun tracking system can be found in Appendix I.

5.1 Accuracy of simulated production and relative self-consumption The simulated production from PVsyst for a PV system with the same PV modules and inverter as the one

in Gäddeholm is compared to the real production, based on hourly production data for 2011. The result is

shown in Figure 6.

Only data points where at least one of the production values (real or simulated) is positive are used for the

calculation. The ideal correlation is shown in Figure 6 as a red line with slope +1. The correlation

coefficient r = 0.86 indicates a relatively high linearity. The formula for calculating the coefficient can be

found in section 4.8. As seen in the figure, the simulated production is often higher than the real one for

the lower power interval, up to approximately 1500 Wh/h. For power exceeding 1500 Wh/h, the real

power exceeds the simulated. Shadowing in the mornings and evenings, as mentioned in section 4.1,

might be one of the explanations for the low PV power data for the lower interval (since the PV power is

highest in the middle of the day). There are at least three sources of error for the simulated PV production

data; varying unreliability in the solar radiation data from STRÅNG, in the estimation of direct and

diffuse solar radiation in PVsyst and in the modelling of the PV system. The calculation of the solar

radiation components in PVsyst can be found in section 4.5.

Figure 6. Comparison between simulated and real

production of the system in Gäddeholm

1 It is possible to display the results of the simulations in two different chart types, namely pseudocolour (also

called checkerboard) and surface charts. This results in 23 graphs per house (a few graphs are not surface or

pseudocolour plots). A surface plot is displayed in 3D whereas a pseudocolour plot presents the results in 2D.

Only the pseudocolour charts will be presented in the report, as can be seen in Figure 14 and forward, as they

sometimes are easier to read and to understand. Some parts of a surface plot can be hidden, which makes it

impossible to evaluate the whole result of the simulation.

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A comparison of the relative self-consumption of the real system and the simulated system is presented in

Table 5 to Table 7. The simulated relative self-consumption is higher than the real one which partly may

depend on the two different measurement periods as described in section 2.1. The real PV production and

absolute self-consumption are measured instantaneously and the simulated production and self-

consumption are measured hourly, which can affect the results as shown in the examples in Table 2 and

Table 3 (section 2.1). The relative self-consumption depends on both absolute self-consumption and PV

production as shown in Equation 1 (section 2.1). Electric consumption and real and simulated values for

yearly PV production, absolute and relative self-consumption 2011 for Gäddeholm are found in Table 5 to

Table 7. The margin of errors can also be found.

Table 5. Consumption and real and simulated PV

production 2011 for Gäddeholm

Electric consumption 15661 kWh

Real PV production 2901 kWh

Simulated PV production 3071 kWh

Absolute margin of error 170 kWh

Relative margin of error 5.8 %

Table 6. Real and simulated absolute self-consumption 2011

for Gäddeholm

Real absolute self-

consumption 1375 kWh

Simulated absolute self-

consumption 1674 kWh

Absolute margin of error 299 kWh


Table 7. Real and simulated relative self-consumption 2011

for Gäddeholm

Real relative self-

consumption 47.4 %

Simulated relative self-

consumption 54.5 %

Absolute margin of error 7.1 %


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5.2 Yearly electric energy consumption in the 20 houses Data for the hourly electricity consumption comes from Gäddeholm (house 1) and the Swedish Energy

Agency (house 2-20). Total consumption 2011 for every house is shown in Figure 7. Results for the

houses with the highest and lowest consumption, i.e. house 9 and 20, respectively, can be found in

Appendix II and III. The houses may have different heating systems, which can affect the results to a high

extent, as described in section 3.5. The heating system of the houses and the year for the consumption

data, except the one in Gäddeholm which is described in section 4.1, are however not known.

Figure 7. Yearly electricity consumption for the 20 houses

available for the simulations. Gäddeholm is house 1.

5.3 Simulated PV production and consumption The hourly electric power consumption and simulated PV production can be presented for two PV

systems with same installed power but with different orientations and distribution between the

orientations. In the following charts the systems defined in Table 8 will be compared. In the first system

all panels are pointing south. In the second system they are divided into 50 per cent west and 50 per cent

east. Both systems have the same tilt of 30°, which is a realistic tilt for a roof of a private house.

Table 8. Tilt, azimuth and distribution for the two systems

compared. Both have the same installed power (3360 Wp).

The mean consumption and production for the full year of 2011 on hourly basis is presented in Figure 8. It

can be noted that the highest consumption occurs in the morning and evening. High consumption in the

early morning is due to the immersion heater in the hot water storage tank, which is most active during

this period of time. At noon and early afternoon when the production is at its highest, the consumption is

lower.

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Figure 8. Mean electric power consumption and production of

the two PV systems during 2011 on hourly basis.

The consumption is significantly higher in January than in June, which can be seen in Figure 9 and Figure

10. The monthly PV production has an opposite pattern, i.e. considerably higher in the summer than in the

winter. The mismatch between the monthly production and consumption for one year negatively affects

the self-consumption, since the production is low when the demand is high and vice versa.

Figure 9. Monthly mean electric power consumption and

production of the two PV systems in January 2011.

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Figure 10. Monthly mean electric power consumption and

production of the two PV systems in June 2011.

The difference in hourly production between a cloudy and a clear day in the summer is shown in Figure 11

and Figure 12. It can be seen that the difference between the two systems are significantly larger during

clear days than during cloudy days, both in the morning, at noon and in the evening. During the cloudy

day presented, the two production profiles are almost identical. The latter case is expected since the solar

radiation only, or almost only, consists of diffuse solar radiation in case of cloudy weather, since the solar

radiation has a more undetermined course.

Figure 11. Hourly production during a sunny day in the summer

(29th

June 2011).

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Figure 12. Hourly production during a cloudy day in the summer

(4th

July 2011).

5.4 Yearly production The yearly PV production can either be simulated for a system where every panel points in the same

direction or divided into several directions. A system with all the modules in the same direction and

azimuth of 0° and tilt of 40° gives the highest yearly production of 3140 kWh, which can be seen in

Figure 13. The lowest yearly production is 1700 kWh for azimuth -90° and tilt 90°. The production from

the simulations in PVsyst is slightly higher for west-mounted systems than for east-mounted and therefore

the top production seems shifted towards the west but occurs at 40° tilt and 0° south, which can be seen

when the numbers are shown.

Figure 13. Production for a 1D system with 3360 Wp

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For simulations of 3D systems, three orientations have to be set. Default values are tilt 30° in every

direction and azimuth -90°, 0° and 90°, which are used for the simulation presented in Figure 14 and in the

rest of the 3DPV charts.

Figure 14. Production for a 3DPV system. The installed power in orientation 1

and 2 is shown on the x- and y-axis, respectively. The installed power in

orientation 3 is given as total power minus power in orientation 1 and 2. The

colour of each box represents the yearly PV production for the given

configuration of installed PV power.

Orientation 1: azimuth -90° and tilt 30°

Orientation 2: azimuth 90° and tilt 30°


The lower right corner in Figure 14 (as well as in all other charts displaying PV systems divided into

three directions) represents a system only directed in orientation 1 (azimuth -90° and tilt 30°). The upper

left corner represents a system with all the modules in orientation 2 (azimuth 90° and tilt 30°) and the

lower left a system only in orientation 3 (azimuth 0° and tilt 30°). The azimuth and tilt angles for every

direction can be set individually by the user. The colour in each box describes the yearly production for

the actual configuration of installed PV power in the different orientations (tilt and azimuth angles).

It was expected that panels pointing east would give a higher yearly production, in contrast to the results

from these simulations. This is partly because of lower temperatures and possibly clearer weather in the

morning than in the evening. However, simulations for a 1D system with STRÅNG solar radiation data

from 2012 resulted in a higher production for a PV system pointing east with a tilt of 90° than for a west-

mounted system with the same tilt, namely 1687 and 1610 kWh per year, respectively. These simulations

were only executed to investigate if data from different years gave different results or if there was a

yearly production pattern and they will therefore not be presented in charts.

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5.5 Absolute self-consumption The self-consumption is calculated both for systems pointing in one and several directions. Charts for

solar tracking systems and house 9 and 20 can be found in Appendix I, II and III, respectively. The

maximum absolute self-consumption for the 1DPV system is slightly shifted towards east compared to

the production of the same system (Figure 13). This indicates higher electric power consumption in the

morning than in the evening, as shown in Figure 8.

Absolute self-consumption for 3DPV of three different sizes, 2000 Wp, 3360 Wp and 4500 Wp, are

presented in Figure 16 to Figure 18. Mind the different production scales when comparing the figures.

The absolute self-consumption is highest for the south-mounted system but the difference when installing

a small share directed towards the east is marginal. The same trend is observable for all three systems

presented. The absolute self-consumption does not increase linearly with the installed power. Furthermore

is the difference between a south-oriented system and a system divided with panels to the east and west

not very high; around 100 kWh per year.

Figure 15. Absolute self-consumption for a 1D system with 3360 Wp

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Figure 16. Absolute self-consumption for a 3D system with 2000 Wp. Orientation 1: azimuth -90° and tilt 30°






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5.6 Relative self-consumption Even though the absolute self-consumption in kWh is lower for some orientations, the relative self-

consumption can be higher due to a lower production in the actual orientation. The highest relative self-

consumption (70 per cent) for 1DPV occurs for an east-mounted system with a tilt of 90°, as presented in

Figure 19. The azimuth and tilt angles of the peak absolute and peak relative self-consumption are not the

same. This can be explained by the varying production profile for different orientations, as seen in Figure

15.

Figure 19. Relative self-consumption for a 1D system with

3360 Wp Minimum: 53 %, maximum: 70 %

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The minimum relative self-consumption for a 1DPV system occurs for a tilt of 50° and azimuth 50° and

the highest for a 1DPV system for a tilt of 90° and azimuth -90°. An example of the mean electric power

consumption and PV production in June 2011 for the two PV systems is presented in Figure 20. As seen in

the figure, the production profile of the vertical system oriented east follows the consumption profile in

June 2011 better than the production profile of the other system, which results in a higher relative self-

consumption. The total production is also lower for the first system, which contributes to a higher relative

self-consumption.

Figure 20. Mean electric power consumption and production of the two

1DPV systems with lowest (53% yearly, azimuth 50°, tilt 50°, blue) and

highest (70% yearly, azimuth -90°, tilt 90°, green) relative self-

consumption during a mean day in June 2011.

Relative self-consumption charts for 3DPV are presented in Figure 21 to Figure 23. The colour bars, i.e.

the scale interval, are the same for all three simulations. The self-consumption varies between 71 and 81

per cent of the production for the system with 2000 Wp installed power, between 54 and 63 per cent for

3360 Wp and between 46 to 54 per cent for 4500 Wp. The difference between the highest and lowest

relative self-consumption is 10 percentage units for 2000 Wp, 9 percentage units for 3360 Wp and 8

percentage units for 4500 Wp. The decreasing trend of the relative self-consumption when increasing the

installed PV power is highly expected. This is due to that the PV production more often exceeds the

consumption when the system power is increased and thus lowering the relative self-consumption.

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Figure 21. Relative self-consumption for a 3D system with 2000 Wp.

Minimum: 71 %, maximum: 81 %




Figure 22. Relative self-consumption for a 3D system with 3360 Wp.





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Figure 23. Relative self-consumption for a 3D system with

4500 Wp.





5.7 Yearly profit The yearly profit is calculated with the absolute self-consumption, production and selling and buying

price of electricity as shown in Equation 3 to Equation 5 (section 4.6). The profit in the main report is

calculated for a 3DPV system of 3360 Wp with the consumption data from Gäddeholm. Profit charts for

house 9 and 20, i.e. the ones with the lowest and highest yearly electric power consumption, can be found

in Appendix II and III. If the tilt is set to 30°, i.e. similar to the tilt of the roof in Gäddeholm, and the

directions are set to east, west and south, the profit from fixed buying and selling prices is presented in

Figure 24 and the profit from variable prices (Nord Pool Spot) is presented in Figure 25.

When calculating the yearly profit the possibility to be assigned and sell electricity certificates for the

produced PV energy has not been taken into account, since very few residential houses with PV systems

have applied for electricity certificates so far. In addition the electricity certificates only give an extra

income for the excess electricity and not the self-consumed one. If the house owner wants to be assigned

electricity certificates for the whole PV production, a too expensive fee is applied which cannot be

compensated by the extra income.

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Figure 24. Yearly profit in SEK for a PV system of 3360 Wp.

Buying price: 1.18 SEK/kWh, selling price: 0.48 SEK/kWh.




If the same layout and installed power is used but variable prices are used, based on hourly Nord Pool

Spot prices, the chart will change, which can be seen in Figure 25.

Figure 25. Yearly profit in SEK for a PV system of 3360 Wp.

Nord Pool Spot prices including taxes and fees.




The maximum profit when using variable prices (Nord Pool Spot) is slightly higher when using fixed

prices based on the yearly mean of the variable, 2750 and 2660 SEK respectively. The profit loss for a PV

system of 3360 Wp with azimuth 0° and tilt 30° relative to a profit-optimized east-west PV system with

azimuth ±90° and tilt 30° are seen in Equation 9 (fixed prices) and Equation 10 (spot prices). The optimal

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configuration for an east-west-pointing system consists of 1780 Wp to the east and 1580 Wp to the west

when both variable and fixed prices are used.

Fixed prices

= -13% Equation 9

Variable prices

= -14% Equation 10

5.8 Optimization of production, absolute and relative self-consumption and profit

5.8.1 Installed PV power: 3360 Wp, azimuth 0° or ±90°, tilt 30°

With the defined conditions of 30° tilt, azimuth 0° or ±90° and 3360 Wp installed power, which are used

for the most of the simulations, the maximum yearly PV production and absolute and relative self-

consumption are 3100 kWh, 1670 kWh and 63 per cent, respectively. The configuration between the three

orientations can be seen in Table 9 and Table 10.The yearly PV production loss is 630 kWh per year

when changing layout from south to east-west, which is a production loss of about 20 per cent. The loss in

absolute self-consumption is however smaller; 100 kWh per year, a reduction of approximately 6 per

cent. The relative self-consumption is increasing with 9 percentage units, from 54 to 63 per cent of the PV

production. Electric power consumption data from Gäddeholm are used for the calculations. The yearly

profit with either variable electricity prices (Nord Pool Spot including taxes and fees) and fixed prices

(yearly mean of the variable prices) are shown in Table 11 and Table 12. Fees to/from the energy supplier,

if any, are not included. For the different taxes and fees used for the simulations, see section 4.4.

Table 9. Optimizing the yearly PV production and absolute self-consumption, tilt 30°, azimuth 0° or ±90°

Power

(Wp) Azimuth (°) Tilt (°)

Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)

Orientation 1 0 -90 30

3100 1670 54 Orientation 2 0 90 30

Orientation 3 3360 0 30

Table 10. Optimizing the relative self-consumption, tilt 30°, azimuth 0° or ±90°

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


2480 1570 63 Orientation 2 1080 90 30


Table 11. Optimizing the yearly PV profit, tilt 30°, azimuth 0° or ±90°

Buying price: 1.18 SEK/kWh1, selling price: 0.48 SEK/kWh.

Power


Profit

(SEK/year)


2660 Orientation 2 0 90 30


1 The fixed prices are based on the yearly mean of the variable buying and selling prices.

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Table 12. Optimizing the yearly PV profit, tilt 30°, azimuth 0° or ±90°


Power


Profit

(SEK/year)





3DPV systems with highest production and absolute self-consumption

(blue – Table 9) and highest relative self-consumption (green – Table

10) in June 2011.

5.8.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt

If it is possible to vary tilt and azimuth angles within the boundaries, that is between 0° and 90° tilt and

between -90° and 90° azimuth, the optimized configurations and orientations of the modules will change

in respect to the results in section 5.8.1. The optimal configurations for optimization of the yearly

production, absolute and relative self-consumption are presented in Table 13 to Table 15. Electric power

consumption data from Gäddeholm are used for the calculations.

Table 13. Optimizing the yearly PV production for 3360 Wp

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3140 1680 54 Orientation 2 0 90 40


Table 14. Optimizing the absolute self-consumption for 3360 Wp

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3040 1705 56 Orientation 2 700 40 40


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Table 15. Optimizing the relative self-consumption for 3360 Wp

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


1810 1390 77 Orientation 2 1000 90 90


Table 16. Optimizing the yearly PV profit for 3360 Wp

Buying price: 1.18 SEK/kWh1, selling price: 0.48 SEK/kWh.

Power


Profit

(SEK/year)




Table 17. Optimizing the yearly PV profit for 3360 Wp


Power


Profit

(SEK/year)





3DPV systems with highest production (blue –Table 13) and highest relative

self-consumption (green –Table 15) in June 2011.

1 The fixed prices are based on the yearly mean spot price for 2011, including taxes and fees (spot price plus

energy tax, grid fee, energy certificate and VAT for buying and spot price plus energy certificate (with VAT) for

selling. Fees to/from the energy retailer, if any, are not included. For the costs used for the simulations, see

section 4.4.

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5.9 East-west roof with a south pointing façade Interesting results are given for a house with a roof in east-west direction and a vertical façade pointing

south, as can be seen in Figure 28 and Figure 30. The best orientation from a yearly production point of

view, presented in Figure 28, is to have only west-directed modules but the production differs only

slightly with a change in the layout. For south-directed modules only the yearly PV production is

approximately 2350 kWh per year, for only east-directed approximately 2450 kWh per year and for only

west directed approximately 2470 kWh per year. This means that the difference between the highest and

lowest PV production is approximately 120 kWh per year, around 5 per cent difference compared to the

total production.

The calculations do not take possible production losses due to dirtying or snow covering of the PV

modules into consideration. The albedo of the ground will also be more important when the tilt of the

modules increases. For example has snow a higher albedo than grass or asphalt, which is not taken into

consideration in the calculations in PVsyst. If these aspects were considered the production of the PV

modules with high tilt would most probably be higher in the winter due to the change in albedo and lower

for PV modules with low tilt due to snow covering and increased dirtying.

Figure 28. Production for a 3DPV system. Installed power: 3360 Wp.




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Figure 29. Absolute self-consumption for a 3DPV system.

Installed power: 3360 Wp.




Figure 30. Relative self-consumption for a 3DPV

system. Installed power: 3360 Wp.




The lower left corner in Figure 29 and Figure 30 represents a PV system only directed in orientation 3

(azimuth 0° and tilt 90°). The lower right corner is a vertical system where all the modules are facing east

with a tilt of 30° and the upper left where all the modules face west with a tilt of 30°. The highest and

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lowest relative self-consumptions shown are 66 and 57 per cent, respectively. The chosen orientations are

valid for a house with an east-west roof and a façade facing south.

The self-consumption, both the absolute and the relative, is at highest when dividing the panels into three

directions, as seen in Figure 29 and Figure 30. The configuration with the highest absolute self-

consumption – 1587 kWh per year – is 1500 Wp east, 800 Wp west and thus approximately 1060 Wp

south. The highest relative self-consumption is obtained with 1100 Wp east, 400 Wp west and thus 1900

Wp south. As mentioned before is the self-consumption not direct correlated with the installed power and

new simulations therefore have to be made for every PV system power. The production profiles during a

clear day – 29th June 2011 – for the two systems are shown in Figure 31.

Figure 31. Hourly production in 29th

June 2011 for a system maximizing

the absolute (system 1, blue) and the relative self-consumption (system 2,

green).

5.10 Payback period The theory of the payback period and the net present value (NPV) can be found in section 4.7 and the

default input parameters in section 4.3. The NPV is based on the profit calculated in section 5.7. The

payback period is very important for an investment and it is therefore of high interest to calculate it.

However, there are many parameters heavily affecting the payback period, such as investment cost and

rate of return besides the yearly profit. Therefore, it is difficult to generalize the parameters to be valid for

every system. There is still a possibility to calculate the payback period for a system with RLPV. When

knowing the specific parameters such as investment costs and rate of return, the result will most likely

have a higher accuracy. Here, some aspects affecting the payback are presented:

Yearly profit

PV system price

Desired rate of return

Future energy price

Degradation of solar cells

Service life of components

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5.11 Matching inverter power Depending on how the PV panels are directed, the top power output can be lowered or augmented. The

highest simulated hourly production during 2011 – 2999 Wh per hour – occurred 19 March at 11:00 for a

PV system with an azimuth of -30° and a tilt of 60°. The highest production from the system in

Gäddeholm was 2910 Wh per hour whereas the maximum production for the simulated PV system with

the same azimuth and tilt, i.e. -5° and 27°, was 2741 Wh per hour.

Since the panels never deliver the rated power – 3360 Wp – on an hourly basis in neither the simulations

nor the reality, the inverter power can be decreased compared to the rated power of the PV panels with

without any loss of production. If all the panels are directed to the south, i.e. an azimuth of 0°, and a tilt of

30°, a maximum hourly production of 2762 Wh per hour in the simulations is reached. However, if a

yearly PV production loss of maximum 0.2 per cent is accepted, as in the conference paper from Straub

et. al (2012), the inverter power can be further decreased as presented in Table 18 and Table 19 (in the

study profit losses of 0.2 per cent was considered, but due to the data available for the calculations only

PV production losses can be calculated). With different layouts, even more reductions are possible, still

with a maximum yearly production loss of 0.2 per cent. This is presented in Table 18. Similar results, but

for systems with tilt 40°, are presented in Table 19. These power ratios are only valid for the solar

radiation data used in this project and might change if other data is used, for example for another year.

These values of the inverter power can be compared with the results from Straub et. al (2012). Their

results are shortly described in section 1.3. An important difference is the comparison; in these

simulations the inverter power needed for a south-pointing system is used as a reference whereas Straub

et. al uses the rated power of the system (modules) as reference power.

Table 18. Reduction of inverter size for different layouts with tilt 30°

Orientation (tilt 30°) Inverter power (W) with

a production loss of 0.2 %

Rated inverter power reduction (%)

compared to tilt 30°, azimuth 0°

Azimuth 0° 2541 -

Azimuth 50% -90°, 50% +90° 1785 30

Azimuth -90° 2247 12

Azimuth +90° 2184 14

Table 19. Reduction of inverter size for different layouts with tilt 40°

Orientation (tilt 40°) Inverter power (W) with

a production loss of 0.2%

Rated inverter power reduction (%)

compared to tilt 40°, azimuth 0°

Azimuth 0° 2619 -

Azimuth 50% -90°, 50% +90° 1602 39

Azimuth -90° 2334 11

Azimuth +90° 2247 14

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6 DISCUSSION The Discussion chapter handles the results presented in the main report and a few comparisons with the

results of other systems presented in the enclosures. The accuracy of the simulations, the results presented

in the main report and in the enclosures are discussed. Thereafter, the interesting result with decreased

rated power of the inverters with 3DPV strings is discussed. There are also a few sources of error which

may affect the results.

6.1 Accuracy of simulations compared to real measurements The accuracy of the simulations is not ideal but is acceptable in this study, since the thesis can be seen as

a feasibility study of the possibilities with 3DPV. A possible explanation why the hourly PV power

production in the lower power interval of the simulated system often exceeds the real one – as seen in

Figure 6 in section 5.1– is the partial shadowing in the mornings and evenings of the system in

Gäddeholm. Since the simulated production should be general and not only valid for the system in

Gäddeholm, this result is desired. It would however be desirable that the high production had a better

correlation. The mismatch is due to the relatively low solar irradiance for the high power interval from the

STRÅNG database, which in turn may partly be explained by the distances to the solar radiation

measurement stations.

The PV production is lower for east-pointing panels than for west-pointing ones as seen in Figure 13 in

section 5.4. Intuitive this should be reverse, since the sun rises in the east and sets in the west. The

efficiency of solar cells increases with decreasing temperature and usually it is colder in the mornings

than in the evenings. It is also possible that the weather usually is clearer in the morning than in the

evenings. However, the results from solar irradiation in 2012 show a higher production in the east than in

the west and therefore the production results for 2011 may not be representative for a longer time period.

The margin of errors for the real and calculated self-consumptions for Gäddeholm can partly be explained

by the different time steps of the measurements. The self-consumption decreases with shorter

measurement periods as presented in section 2.1. The real value of the self-consumption – 47.4 per cent –

is based on instantaneous measurements of the feed into and out from the public grid. This was not

possible for the production data from PVsyst; only hourly values were calculated, and therefore the self-

consumption will be higher. Together with the influence of the distances to the irradiance measurement

stations the simulated production data are considered to have an acceptable accuracy.

6.2 Comparison with sun-tracking PV system and results for house 9 and 20 For a one-axis sun-tracking PV system the hourly PV production during a mean day, both on monthly and

yearly basis, will almost always be higher for a south-oriented PV system compared to an east-west-

oriented system, as seen in Figure 2 to Figure 4 in Appendix I. This means that there probably is no

advantage of using 3DPV with sun-tracking one-axis systems. In the simulations a rotation of ±30°

around the axis has been set when calculating the production in PVsyst. With other rotation limits the PV

production changes but most probably the trend of decreasing production of 3DPV compared to south-

oriented 1DPV will continue with increasing rotation limits. If the rotation is for example ±90° a PV

system with an axis directed to the south will follow the sun path from east to west (morning to evening).

If the PV system axis is oriented to the east, rotation limits of ±90° (north to south) mean that the sun path

followed by the PV system will be shorter, since the system cannot follow the sun in the afternoon (west).

A sketch of a 3DPV one-axis sun-tracking system can be seen in Figure 5 in section 4.4.

For both house 9 and 20, with the highest and lowest yearly power consumption, both the maximal

absolute and relative self-consumption occurs when more panels are directed to the west than to the east.

This indicates that the electric consumption in the afternoon is higher than in the morning, which also can

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be seen in the power consumption profiles in Appendix II and III. The results are presented in

Appendix II (house 9) and Appendix III (house 20).

As expected both the absolute and relative self-consumption will increase for a house with high yearly

electric power consumption of electric power and decrease for a house with a low consumption, as seen in

Appendix II and III. However, since the PV system only delivers electric power during daytime, the

power consumption profile of the house is as important for the absolute self-consumption as the total

yearly consumption. In a house with electric direct heating, the heater may be most active during the night

when the ambient temperature and the solar irradiance are lower. During the day the electric heaters may

not be needed as much as during the night, which decreases the absolute self-consumption (if the PV

power exceeds the electric consumption during the day). The possible mismatch between electric

consumption and PV production therefore makes it more difficult to find a direct relationship between

yearly electric consumption and self-consumption, although high yearly electric consumption often leads

to high self-consumption. Also the outcome of changing from 1DPV to 3DPV needs to be calculated for

every house, i.e. consumption profile.

6.3 Profit with different installed PV power and orientations

3DPV gives lower PV production and profit than south-directed 1DPV, as shown in section 5.4 and 5.5,

which makes it more difficult to justify from an economic point of view with the studied electricity

prices. Lower yearly production for 3DPV cannot be compensated with possible increased absolute or

relative self-consumption in the studied cases. However, for east-west oriented PV systems the layout can

be maximized to give a 13 and 14 per cent reduction in profit when using fixed and variable electricity

prices, respectively, compared to the profit for a south-oriented 1DPV system (all with a tilt of 30°). The

calculations can be found in section 5.7. If the profit losses are possible to compensate, for example with

a smaller inverter as discussed in next section, the payback period for the south and east-west systems

may be similar. This is not calculated but would be an interesting topic for further studies.

The highest profit for the system simulated in section 5.7 occurred for variable electricity prices based on

hourly Nord Pool Spot (compared to fixed prices calculated as the yearly mean of the variable prices).

This indicates that the spot prices were higher during the day – when the PV system generates power –

than during the night. If this pattern is occurs every year (or most of them) of the useful life of the PV

system, it can be more profitable to choose variable electricity prices than fixed. This depends of course

on the conditions of the electricity agreement with the energy supplier.

The profit per installed power unit (Wp) is important when deciding the installed PV power, since it will

decrease when the installed power increases. This is due to the relative self-consumption, which decreases

the larger the PV system is since the PV production increases linearly with the installed power whereas

the absolute self-consumption increases with a lower rate of speed. For a large PV system the production

will more often exceed the consumption than for a smaller system and therefore the relative self-

consumption will decrease. The profit is dependent on the relative self-consumption and will therefore not

increase as fast as the yearly production when the installed power increases. The cost per installed power

unit may however be higher the smaller the system is. This means that it is possible to optimize the

installed power to give as short payback period as possible. To calculate this, all the variables listed in

section 5.10 have to be known.

For existing houses, tilt and azimuth angles are not variable if the PV panels are installed directly on the

roof. If a house owner plans to build a PV system on an existing house the RLPV program is useful for

simulating the self-consumption and the profit for different PV systems. If the house has an east-west

oriented roof, a PV system may still be a profitable investment compared to a system on a south-pointing

roof while the production losses are not very large (13 and 14 per cent as discussed above).

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6.4 Further possibilities with 3DPV As seen in Figure 8 in section 5.3 the PV power production is slightly higher in the morning and evening

for an east-west oriented 3DPV system than for a south-oriented 1DPV system. The difference in PV

power in the mornings and evenings is however marginal on a yearly basis but the difference in top

production is more noticeable.

Since the price of PV modules has decreased more rapidly than the price of other components and the

installation, a lower nominal power ratio and a larger area of a 3DPV system compared to the ratio for a

1DPV system pointing south could be profitable. A larger number of PV modules are needed for the

3DPV system to reach the same maximum production as for the south-directed 1DPV, but the other

components such as inverter and cables could have the same rated power for the both systems as

described in section 5.11. A reduction of the inverter power of 30 per cent, and thus also a lower cost, for

the simulated east-west PV system may compensate for the lower production. Besides increasing number

and thus higher costs for the PV panels, the installation costs per installed PV power will determine if this

is profitable or not.

It can be noted that on houses with a roof pointing east and west, there are twice as much area available

than on a house with a roof pointing south (if neglecting the part of the roof pointing north as its yearly

PV production is low).

6.5 Sources of error For the electric power consumption data from Swedish Energy Agency, neither the locations nor the year

of measurements for the houses from Swedish Energy Agency are known. Especially if the house has

direct-acting electric heating, changes in the ambient temperature will not correlate with the consumption

as good as for the system in Gäddeholm, since the electricity consumption often is higher the lower the

ambient temperature is. However, seen over a whole year, the seasons should cancel out the most of the

differences since they are rather similar from one year to another. If the house has district heating, the

effect of ambient temperature is most probably not that large.

As mentioned before, there are at least three sources of error that will affect the PV power production:

uncertainty in the STRÅNG solar radiation data and the calculations in PVsyst as well as possible errors

in the calculations in MATLAB. Moreover, the simulations are only based on solar radiation data from

2011 and might be different for other years.

The economic simulation results and especially the payback period may not have the highest accuracy

because of uncertainty in the economic variables such as future electricity price changes. Therefore, an

evaluation of the results with different input parameters has to be made. The effect of decreasing or

increasing investment costs for example have to be evaluated. Moreover, the cost per kWp will most

probably decrease with increasing installed PV power due to for example non-linear installation costs as

discussed in section 5.7.

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7 CONCLUSIONS

Simulated values for the 1DPV system of 3360 Wp (3360 Wp, tilt 27°, azimuth 5° east) for the

house in Gäddeholm, Sweden, 2011. The real (measured) values can be found in the brackets.

o PV production: 3071 kWh/year (real value: 2901 kWh/year)

o Absolute self-consumption: 1674 kWh/year (real value: 1375 kWh/year)

o Relative self-consumption: 54.5 % (real value: 47.4 %)

o Profit: 2750 SEK/year (simulated for tilt 30°, azimuth 0°)

Optimized PV systems of totally 3360 Wp for the house in Gäddeholm, Sweden, 2011:

o Maximum PV production: 3140 kWh/year

3360 W, tilt 40°, azimuth 0° (south)

o Maximum absolute self-consumption: 1705 kWh/year

1800 W, tilt 40°, azimuth -40° (east)


700 W, tilt 40°, azimuth 40° (west)

o Maximum relative self-consumption: 77 %

1800 W, tilt 90°, azimuth -90° (east)


560 W, tilt 90°, azimuth 90° (west)

o Maximum profit: 2780 SEK/year


The orientations for optimized absolute self-consumption changes with different consumption

profiles and are not always the south-oriented 1DPV. The differences between 3DPV optimized

for absolute self-consumption and 1DPV are however not very large.

The relative self-consumption increases with 3DPV compared to south-oriented 1DPV. The PV

production increases in the morning and evening and decreases at noon, especially during sunny

days in the summer. Therefore, the surplus PV production in the middle of the day decreases and

a larger share of the PV power will then be consumed in the house. A lower yearly PV production

with 3DPV than with 1DPV also increases the relative self-consumption, since the absolute self-

consumption does not decrease with the same rate as the production.

For one-axis sun-tracking PV systems there is no gain to change azimuth angle, since the hourly

electric power production of PV systems with other azimuth angles almost never exceeded the

south-directed one. On a yearly basis the PV production, absolute self-consumption and profit are

highest for the south-oriented sun-tracking PV system.

The yearly profit is highest for a south-oriented 1DPV system for all studied cases (Gäddeholm,

house 9, house 20 and Gäddeholm with a one-axis sun-tracking PV system). This is valid for both

variable electricity prices based on hourly Nord Pool Spot prices including taxes and fees as well

as fixed prices based on the yearly mean of the variable prices. Therefore, 3DPV is not profitable

with the studied economic conditions seen from a yearly point of view (for payback period, see

the last bullet).

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For a PV system in Gäddeholm the yearly profit maximum occurs with variable electricity prices

(hourly Nord Pool Spot including taxes and fees). With fixed prices based on yearly mean of the

variable prices, the yearly profit is slightly lower due to higher spot prices in the day than in the

night.

The yearly profit for an east-west PV-system will always be lower than for a south-oriented

1DPV system with the same tilt. The profit of the east-west PV system can be maximum

87 per cent of the south-oriented 1DPV system, both with a tilt of 30° and variable electricity

prices based on Nord Pool Spot. There are however other possibilities with an east-west PV

system:

It is possible to decrease the inverter power with 3DPV. With a 50/50 per cent east-west oriented

PV system the rated power of the inverter can be decreased with 30 per cent compared to a south-

oriented 1DPV system, both in Gäddeholm and with a tilt of 30°. In both cases a maximum

yearly PV production loss of 0.2 per cent is accepted. When increasing the tilt to 40°, a reduction

in rated power of the inverter of 39 per cent is possible. Lower investment costs for inverter,

cables etc. might compensate for the yearly profit loss when calculating the payback period of the

PV system. This has to be further investigated.

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9 FURTHER WORK

There are several fields of this thesis that could be further investigated. A few of them are shortly

discussed here.

There is a need of a more detailed economic evaluation of 3DPV systems for different condition, for

example for different houses/consumption profiles, electricity prices and investment costs etc. There

might be a combination of these variables when 3DPV systems are more profitable than 1DPV. Aspects

such as payback period are often very important for investment decisions. It would also be interesting to

know if it is profitable to increase the number of modules and keep the same size of the remaining

components, i.e. lower the nominal power ratio, as discussed in section 6.4. For this, prices for every

component of the PV system have to be known.

Short- and long-term studies of a real 3DPV system to verify, reject or modify the results of this thesis

could also be carried out. Either a small-scale system with for example solar cell charger or a more

comprehensive system with larger modules, inverters and peripheral equipment could be investigated. Of

course the more advanced the system is, the more accurate the results will be, but a simpler system could

possibly give a hint of the performance of a 3DPV system.

As described in section 3.2 the current of a PV cell is linearly proportional to the solar radiation whereas

the voltage only changes logarithmically when the solar radiation increases or decreases. This is an

interesting behaviour for 3DPV applications. When the PV modules are placed in different directions,

they will not be exposed to the same radiation strength, especially during sunny days. If the PV strings are

of the same length, i.e. same number of modules connected in series, but placed in different directions,

the current and voltage will differ during the day. The voltage will however not differ as much as the

current. When connecting the strings in parallel, the voltage over every string will be the same and the

currents will be added. This could make it possible to connect multiple strings to the same MPPT and thus

decrease the costs. If the lower cost of the inverter can compensate for a production loss due to mismatch

of the voltages of the different strings would be interesting to investigate.

Technical Report






LIST OF REFERENCES

Journals, books and papers

Bernardi, Marco; Ferralis, Nicola; Wan, Jin; Villalon, Rachelle; Grossman, Jeffery (2012), Solar energy

generation in three dimensions, Energy Environmental Science, 2012, vol. 5, pp. 6880-6884

Erban, Christof (2011), kWh output is not the main objective of photovoltaic, 26th European Photovoltaic

Solar Energy Conference and Exhibition, Hamburg, Germany, September 2011

Nelson, Jenny (2004), The Physics of Solar Cells, Imperial College Press, pp. 172-173

Straub, Thomas; Laschinski, Joachim; Hartmann, Matthias; Merz, Christhoper; Umland, Andreas, Walter,

Matthias, (2012) Auslegung von PV-Anlagen im Polystring-Betrieb – Eigenverbrauchsoptimierung vs.

Mismatch-Verlust, 27th Symposium Photovoltaische Solarenergie, Bad Staffelstein, Germany, March

2012

Walla, Tobias; Widén, Joakim; Johansson, Joar; Bergerland, Christer (2012) Determining and increasing

the hosting capacity for photovoltaics in Swedish distribution grids, 27th European Photovoltaic Energy

Conference (EU-PVSEC), Frankfurt, Germany, September 24-28, 2012

Widén, Joakim; Wäckelgård, Ewa; Lund, Peter (2009), Options for improving the load matching

capability of distributed photovoltaics: Methodology and application to high-latitude data, Solar Energy,

vol. 83, pp. 1953-1966, August 2009

Reports

BSW-solar (2012), Statistic data on the German Solar power (photovoltaic) industry, German Solar

Industry Association

EPIA – European Photovoltaic Industry Association (2013), World’s solar photovoltaic capacity passes

100-gigawatt landmark after strong year, Brussels, 11 February 2013

IEA, (2009) Overcoming PV grid issues in the urban areas, International Energy Agency Photovoltaic

Power Systems Programme (IEA-PVPS), October 2009

Lindahl, Johan (2013), National Survey Report of PV Power Applications in Sweden 2012, IEA

Photovoltaic Power Systems Programme (IEA-PVPS), Uppsala 14 May 2012

Molin, Andreas; Widén, Joakim; Stridh, Bengt; Karlsson, Björn (2010) Konsekvenser av

avräkningsperiodens längd vid nettodebitering av solel, Elforsk rapport 10:93, December 2010

Press releases

Chandler, David (2012), A new dimension for solar energy, MIT News Office, Accessed 16 January

2013, http://web.mit.edu/newsoffice/2012/three-dimensional-solar-energy-0327.html, 27 march 2012

Klipp & Zonen (2010) Briefing on pyranometers and Pyrheliometers, Renewable Energy World,

Retrieved 26 April 2013, http://www.renewableenergyworld.com/rea/partner/kipp-

zonen/news/article/2010/02/briefing-on-pyranometers-and-pyrheliometers, 24 February 2010

http://web.mit.edu/newsoffice/2012/three-dimensional-solar-energy-0327.html

http://www.renewableenergyworld.com/rea/partner/kipp-zonen/news/article/2010/02/briefing-on-pyranometers-and-pyrheliometers

http://www.renewableenergyworld.com/rea/partner/kipp-zonen/news/article/2010/02/briefing-on-pyranometers-and-pyrheliometers

Technical Report






Parker, Paul (2011) PV Inverter Reliability, Solar Novus Today, Accessed 22 April 2013,

http://www.solarnovus.com/index.php?option=com_content&view=article&id=2252:pv-inverter-

reliability&catid=38:application-tech-features&Itemid=246, 17 February 2011

Städtische Werke AG (2012), Solarpark fängt Sonne am Morgen und Abend ein, Accessed 2013-01-24,

https://www.sw-kassel.de/privatkunden/unternehmen/aktuelles/detail/solarpark-faengt-sonne-am-morgen-

und-abend-ein.html, Niestetal/Kassel, 15 November 2012

Programs, databases and user’s manuals

LantMet (no date), LANTMET vid SLU/Fältforsk, Retrieved 30 January 2013.

http://www.ffe.slu.se/lm/LMHome.cfm?LMSUB=0&ADM=0

Nord Pool Spot (no date) Historical market data for 2011, Accessed 6 February 2013,

http://www.nordpoolspot.com/Market-data1/Downloads/Historical-Data-Download1/Data-Download-

Page/

PVsyst (2012), program for calculating PV production, http://www.pvsyst.com/en/

PVsyst (2012), User's Guide – PVsyst Contextual Help, Accessed 4 February 2013,

http://files.pvsyst.com/pvsyst5.pdf

SCB (no date), Konsumentprisindex (KPI) – Inflation I Sverige 1831-2012, Statistiska

centralbyrån/Statistics Sweden, Accessed 8 May 2013,

http://www.scb.se/Pages/PricesCrib____258649.aspx

STRÅNG (no date), STRÅNG - a mesoscale model for solar radiation, Accessed 12 February 2013,

http://strang.smhi.se/

Personal communication

Larsson, Robert (2013), Historical temperature data from Västerås Airport, http://rl.se/vadret/, E-mail

conversation, 20 February 2013

Web pages

de Smith, Michael J (no date) Pearson (Product Moment) Correlation, Accessed 16 May 2013,

STATSREF: Statistical Analysis Handbook,

http://www.statsref.com/HTML/index.html?pearson_product_moment_correla.html

Fraunhofer ISE (no date) STC Measurements, Fraunhofer – Institut für Solare Energiesysteme, Accessed

8 May 2013, http://www.ise.fraunhofer.de/en/service-units/callab-pv-cells-callab-pv-modules/callab-pv-

modules/stc-measurements

Lee, Cheng-Few and Lee, Alice C. (2006) Net Present value, Encyclopedia of finance, Accessed 15 May

2013, http://link.springer.com/content/pdf/10.1007%2F0-387-26336-5_1390.pdf, p 189

PVEducation.org (Photovoltaic Education Network) (no date), Effect of temperature, Accessed 25 March

2013, http://pveducation.org/pvcdrom/solar-cell-operation/effect-of-temperature

http://www.solarnovus.com/index.php?option=com_content&view=article&id=2252:pv-inverter-reliability&catid=38:application-tech-features&Itemid=246

http://www.solarnovus.com/index.php?option=com_content&view=article&id=2252:pv-inverter-reliability&catid=38:application-tech-features&Itemid=246

https://www.sw-kassel.de/privatkunden/unternehmen/aktuelles/detail/solarpark-faengt-sonne-am-morgen-und-abend-ein.html

https://www.sw-kassel.de/privatkunden/unternehmen/aktuelles/detail/solarpark-faengt-sonne-am-morgen-und-abend-ein.html

http://www.ffe.slu.se/lm/LMHome.cfm?LMSUB=0&ADM=0

http://www.nordpoolspot.com/Market-data1/Downloads/Historical-Data-Download1/Data-Download-Page/

http://www.nordpoolspot.com/Market-data1/Downloads/Historical-Data-Download1/Data-Download-Page/

http://www.pvsyst.com/en/

http://files.pvsyst.com/pvsyst5.pdf

http://www.scb.se/Pages/PricesCrib____258649.aspx

http://strang.smhi.se/

http://rl.se/vadret/

http://www.statsref.com/HTML/index.html?pearson_product_moment_correla.html

http://www.ise.fraunhofer.de/en/service-units/callab-pv-cells-callab-pv-modules/callab-pv-modules/stc-measurements

http://www.ise.fraunhofer.de/en/service-units/callab-pv-cells-callab-pv-modules/callab-pv-modules/stc-measurements

http://link.springer.com/content/pdf/10.1007%2F0-387-26336-5_1390.pdf

http://pveducation.org/pvcdrom/solar-cell-operation/effect-of-temperature

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PV Grid (2013) Residential systems in Sweden, Accessed 26 March 2013,

http://www.pvgrid.eu/database/pvgrid/sweden/national-profile-10/residential-systems/2767/residential-

1/grid-connection-permit-4.html, last updated 11 January 2013

SMHI (2007), Solstrålning, Faktablad nr 31, Accessed 11 June 2013,

http://www.smhi.se/polopoly_fs/1.6403!faktablad_solstralning%5B1%5D.pdf, p. 6

SMHI (no date), Karta, strålningsstationer, Accessed 11 June 2013,

http://www.smhi.se/polopoly_fs/1.3260!sol_dec-2009.pdf

Stoffel, Tom; Wilcox; Steve (2004) Solar Radiation Measurements, National renewable Energy

Laboratory (NREL), U.S. Department of Energy, Accessed 8 May 2013,

http://www.nrel.gov/docs/gen/fy04/36831p.pdf

Stridh, Bengt (a) (no date) Köpare solel, Bengts villablogg, Accessed 20 May 2013,

http://bengts.blogg.viivilla.se/kopare-solel/

Stridh, Bengt (b) (no date) Vår Solcellsanläggning, Bengts villablogg, Retrieved 20 March 2013,


Stridh, Bengt (c) (2012) Vattenfall höjer nätavgifterna, Bengts villablogg, Accessed 21 May 2013,

http://bengts.blogg.viivilla.se/2012/05/21/vattenfall-hojer-natavgifterna/, posted on 21 May 2012

Vattenfall (a) (2013) Energiskatter, Vattenfall, Accessed 21 May 2013,

http://www.vattenfall.se/sv/energiskatter.htm, updated 17 May 2013

Vattenfall (b) (2013) Elcertifikatshistoria, Vattenfall, Accessed 21 May 2013,

http://www.vattenfall.se/sv/elcertifikatshistorik.htm, updated 2 May 2013

http://www.pvgrid.eu/database/pvgrid/sweden/national-profile-10/residential-systems/2767/residential-1/grid-connection-permit-4.html

http://www.pvgrid.eu/database/pvgrid/sweden/national-profile-10/residential-systems/2767/residential-1/grid-connection-permit-4.html

http://www.smhi.se/polopoly_fs/1.6403!faktablad_solstralning%5B1%5D.pdf

http://www.smhi.se/polopoly_fs/1.3260!sol_dec-2009.pdf

http://www.nrel.gov/docs/gen/fy04/36831p.pdf

http://bengts.blogg.viivilla.se/kopare-solel/


http://bengts.blogg.viivilla.se/2012/05/21/vattenfall-hojer-natavgifterna/

http://www.vattenfall.se/sv/energiskatter.htm

http://www.vattenfall.se/sv/elcertifikatshistorik.htm

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ENCLOSURES The appendixes are presenting charts, similar to the ones presented in the report, for a sun-tracking PV

system, for house 9 and for house 20. The latter two have the highest and lowest yearly electric power

consumption, respectively, and use a fixed PV system in the simulations. The charts can be compared to

the results for the fixed PV system in Gäddeholm presented in the main report and interesting similarities

and differences are discussed in section 6.2. The appendixes are attached as individual documents in the

end of the report.

Appendix I – Results Sun-Tracking PV System

Appendix II – Results House 9

Appendix III – Results House 20

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Appendix I – Results Sun-Tracking PV System 01 1/11



APPENDIX I – RESULTS SUN-TRACKING PV SYSTEM In this Appendix simulations for a sun-tracking PV system are presented. The consumption profile comes

from Gäddeholm. Interesting differences will be discussed in the Discussion chapter in the report.

List of Contents

APPENDIX I – RESULTS SUN-TRACKING PV SYSTEM ...........................................................................1

1.1 SIMULATED PV PRODUCTION AND CONSUMPTION ................................................................................2 1.2 PRODUCTION ....................................................................................................................................4 1.3 ABSOLUTE SELF-CONSUMPTION .........................................................................................................5 1.4 RELATIVE SELF-CONSUMPTION ...........................................................................................................7 1.5 OPTIMIZATION OF PRODUCTION, ABSOLUTE AND RELATIVE SELF-CONSUMPTION ....................................9

1.5.1 Installed PV power: 3360 Wp, azimuth 0° or ±90°, tilt 30° ......................................................9 1.5.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt ................................................ 10

1.6 YEARLY PROFIT .............................................................................................................................. 11

List of Figures FIGURE 1. A SKETCH OF A 3D ONE-AXIS SOLAR TRACKING PV SYSTEM. THE ROTATION OF THE PANELS AROUND THE AXIS IS SET IN PVSYST

WHEN CALCULATING PV PRODUCTION FOR MULTIPLE ORIENTATIONS. TILT (SLOPE OF ROOF) AND AZIMUTH (DIRECTION OF

HOUSE/ROOF) FOR THE SIMULATION ARE DEFINED BY THE USER IN THE MATLAB PROGRAM RLPV ............................................ 2 FIGURE 2. SAME LAYOUT AND DISTRIBUTION AS IN THE MAIN THE REPORT ..................................................................................... 2 FIGURE 3. MEAN CONSUMPTION AND PRODUCTION DURING 2011 ............................................................................................. 3 FIGURE 4. MEAN PRODUCTION AND CONSUMPTION IN JANUARY 2011 ........................................................................................ 3 FIGURE 5. MEAN PRODUCTION AND CONSUMPTION IN JUNE 2011 .............................................................................................. 4 FIGURE 6. YEARLY ELECTRIC ENERGY PRODUCTION FOR A 1D SUN-TRACKING PV SYSTEM .................................................................. 4 FIGURE 7. YEARLY ELECTRIC ENERGY PRODUCTION FOR A 3D SUN-TRACKING PV SYSTEM .................................................................. 5 FIGURE 8. ABSOLUTE SELF-CONSUMPTION FOR A 1DPV SUN-TRACKING SYSTEM ............................................................................ 5 FIGURE 9. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 2000 WP. ..................................................... 6 FIGURE 10. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 3360 WP. ................................................... 6 FIGURE 11. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 4500 WP. ................................................... 7 FIGURE 12. RELATIVE SELF-CONSUMPTION FOR A 1DPV SUN-TRACKING SYSTEM ............................................................................ 7 FIGURE 13. RELATIVE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 2000 WP. MINIMUM: 62 %, MAXIMUM: 75 % .. 8 FIGURE 14. RELATIVE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 3360 WP. MINIMUM: 45 %, MAXIMUM: 56 % .. 8 FIGURE 15. RELATIVE SELF-CONSUMPTION FOR A 3DPV SUN-TRACKING SYSTEM WITH 4500 WP. MINIMUM: 36 %, MAXIMUM: 46 % .. 9 FIGURE 16. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 3DPV SYSTEMS WITH HIGHEST PRODUCTION AND

ABSOLUTE (BLUE – TABLE 1) AND RELATIVE (GREEN – TABLE 2) SELF-CONSUMPTION IN JUNE 2011. ........................................ 10 FIGURE 17. YEARLY PROFIT FOR A 3DPV SUN-TRACKING SYSTEM WITH 3360 WP WITH FIXED PRICES .............................................. 11 FIGURE 18. YEARLY PROFIT FOR A 3DPV SUN-TRACKING SYSTEM WITH 3360 WP WITH SPOT PRICES ............................................... 11

List of Tables TABLE 1. OPTIMIZING THE YEARLY PV PRODUCTION AND ABSOLUTE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° . 9 TABLE 2. OPTIMIZING THE RELATIVE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° ................................................ 9 TABLE 3. OPTIMIZING THE YEARLY PV PRODUCTION AND ABSOLUTE SELF-CONSUMPTION FOR 3360 WP .......................... 10 TABLE 4. OPTIMIZING THE RELATIVE SELF-CONSUMPTION FOR 3360 WP ......................................................................... 10

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In a one-axis sun-tracking PV system the modules rotate around an axis, which is mounted on the roof, see Figure 1.

The tilt is the gradient of the roof and the azimuth is the direction of the roof. The frame/PV modules follow the path

of the sun during the day as far as possible. Depending on for example the distance between roof and axis as well as

the width of the PV modules/frame, there is a maximum angle of rotation which has to be set in PVsyst when

calculating the production. (If the PV modules would rotate further, the edge/long side would hit the roof). In the

calculations a maximum rotation angle of ±30° around the axis was set, defined as 0° when the plane is parallel to

the roof. A maximum rotation angle of ±30° was assumed to be an adequate value for installations on private

houses.

Figure 1. A sketch of a 3D one-axis solar tracking PV system. The rotation of

the panels around the axis is set in PVsyst when calculating PV production for

multiple orientations. Tilt (slope of roof) and azimuth (direction of house/roof) for

the simulation are defined by the user in the MATLAB program RLPV

1.1 Simulated PV production and consumption

Figure 2. Same layout and distribution as in

the main the report

The consumption of electric energy is the same as presented in the report. The production from a sun-

tracking PV system with the axis oriented south has always a higher production than the system divided

into two orientations, seen over both the whole year of 2011 as well as January and June in 2011. The

only exceptions seen in the figures are the first and last two hours in June but the difference in production

is very small, see Figure 5.

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Figure 3. Mean consumption and production during 2011

Figure 4. Mean production and consumption in January 2011

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Figure 5. Mean production and consumption in June 2011

1.2 Production

The main advantage with sun-tracking compared to fixed PV system is the higher production. The production will

be higher the more the modules can rotate around the axis. For these simulations a rotation of ±30° is used. The

production for both 1DPV and 3DPV is presented in Figure 6 and Figure 7.

Figure 6. Yearly electric energy production for a 1D sun-tracking PV

system

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Figure 7. Yearly electric energy production for a 3D sun-

tracking PV system

1.3 Absolute self-consumption

The highest absolute self-consumption for a 1DPV sun-tracking system, presented in Figure 8, is the

same as for the highest yearly production, i.e. a 1DPV system with azimuth 0° and tilt 40°. For 3DPV

sun-tracking systems the absolute self-consumption is highest when every module is oriented towards the

south.

Figure 8. Absolute self-consumption for a 1DPV sun-tracking system

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Figure 9. Absolute self-consumption for a 3DPV sun-tracking

system with 2000 Wp.



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1.4 Relative self-consumption

The relative self-consumption is higher for a 1DPV sun-tracking system oriented towards the east, as seen

in Figure 12. For 3D systems, it is best to have slightly more power installed towards the east than

towards the west seen from a relative self-consumption point of view.

Figure 12. Relative self-consumption for a 1DPV sun-tracking

system

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1.5 Optimization of production, absolute and relative self-consumption


With the defined conditions, which are used for the most of the simulations, the maximum yearly PV power

production and absolute and relative self-consumption are 3800 kWh, 1870 kWh and 57 per cent, respectively. The

configuration between the three orientations can be seen in Table 1 to Table 2 .The yearly PV production loss is

730 kWh per year when changing layout from due south to east-west, which is a production loss of about 19

per cent. The loss in absolute is smaller; 120 kWh per year, a reduction of approximately 6 per cent. The relative

self-consumption is increasing with 8 percentage units, from 49 to 57 per cent of the PV production. Electric power

consumption data from Gäddeholm are used for the calculations.



Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3800 1870 49 Orientation 2 0 90 30


Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3070 1750 57 Orientation 2 1380 90 30


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1.5.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt If only the installed power is fixed and it is possible to vary tilt and azimuth angles within the boundaries, that is 0°

and 90° tilt and -90° to 90° azimuth, the optimized configurations and orientations of the modules will change in

respect to the results in previous section. The optimal configurations for optimization of the yearly production,

absolute and relative self-consumption are presented in

Table 3 to

Table 4. Electric power consumption data from Gäddeholm are used for the calculations.

Table 3. Optimizing the yearly PV production and absolute self-consumption for 3360 Wp


Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


1350 1100 81 Orientation 2 1380 90 90



3DPV systems with highest production and absolute (blue – Table 1)

and relative (green – Table 2) self-consumption in June 2011.

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3830 1880 49 Orientation 2 0 30 30


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1.6 Yearly profit

The highest profit is gained from south-directed systems, both with fixed and variable prices. The profit

span is rather large, about 800 SEK per year as can be seen in Figure 17.

Figure 17. Yearly profit for a 3DPV sun-tracking system with 3360

Wp with fixed prices

Figure 18. Yearly profit for a 3DPV sun-tracking system with 3360

Wp with spot prices

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Appendix II – Results House 9 01 1/10



APPENDIX II – RESULTS HOUSE 9 In this Appendix simulations for house 9 are presented, i.e. the house with the highest yearly electric

consumption, around 22,500 kWh per year. The production charts are the same as the ones which can be

found in the report. Interesting differences will be discussed in the Discussion chapter in the report.

List of Contents

APPENDIX II – RESULTS HOUSE 9 ...........................................................................................................1

LIST OF CONTENTS .......................................................................................................................................1 LIST OF FIGURES ..........................................................................................................................................1 LIST OF TABLES ...........................................................................................................................................1 1.1 SIMULATED PV PRODUCTION AND CONSUMPTION ................................................................................2 1.2 ABSOLUTE SELF-CONSUMPTION .........................................................................................................4 1.3 RELATIVE SELF-CONSUMPTION ...........................................................................................................6 1.4 OPTIMIZATION OF PRODUCTION, ABSOLUTE AND RELATIVE SELF-CONSUMPTION ....................................8

1.4.1 Installed PV power: 3360 Wp, azimuth 0° or ±90°, tilt 30° ......................................................8 1.4.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt ...................................................8

1.5 YEARLY PROFIT .............................................................................................................................. 10

List of Figures FIGURE 1. SAME LAYOUT AND DISTRIBUTION AS IN THE MAIN REPORT ........................................................................................... 2

FIGURE 2. MEAN CONSUMPTION AND PRODUCTION DURING 2011 ............................................................................................. 2

FIGURE 3. MEAN PRODUCTION AND CONSUMPTION IN JANUARY 2011 ........................................................................................ 3

FIGURE 4. MEAN PRODUCTION AND CONSUMPTION IN JUNE 2011 .............................................................................................. 3

FIGURE 5. ABSOLUTE SELF-CONSUMPTION FOR A 1DPV SYSTEM ................................................................................................. 4

FIGURE 6. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 2000 WP........................................................................... 4

FIGURE 7. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 3360 WP. .......................................................................... 5

FIGURE 8. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 4500 WP. .......................................................................... 5

FIGURE 9. RELATIVE SELF-CONSUMPTION FOR A 1DPV SYSTEM ................................................................................................... 6

FIGURE 10. RELATIVE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 2000 WP. MINIMUM: 93 %, MAXIMUM: 97 % ....................... 6



FIGURE 13. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 3DPV SYSTEMS WITH HIGHEST PRODUCTION AND

ABSOLUTE (BLUE – TABLE 1) AND RELATIVE (GREEN – TABLE 2) SELF-CONSUMPTION IN JUNE 2011. ......................................... 8

FIGURE 14. YEARLY PROFIT FOR A 3DPV SYSTEM WITH 3360 WP WITH FIXED PRICES ................................................................... 10

FIGURE 15. YEARLY PROFIT FOR A 3DPV SYSTEM WITH 3360 WP WITH SPOT PRICES .................................................................... 10

List of Tables

TABLE 1. OPTIMIZING THE YEARLY PV PRODUCTION AND ABSOLUTE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° . 8

TABLE 2. OPTIMIZING THE RELATIVE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° ................................................ 8

TABLE 3. OPTIMIZING THE YEARLY PV PRODUCTION FOR 3360 WP ................................................................................... 9

TABLE 4. OPTIMIZING THE ABSOLUTE SELF-CONSUMPTION FOR 3360 WP .......................................................................... 9

TABLE 5. OPTIMIZING THE RELATIVE SELF-CONSUMPTION FOR 3360 WP ........................................................................... 9

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the main report

The consumption of electric energy is rather similar during the day on a yearly basis, as seen in Figure 2.

The mean production profile in June 2011presented in Figure 4 is only slightly higher than the

consumption, which indicates a high self-consumption since the production mostly exceeds the

consumption during the summer.


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The highest absolute self-consumption for a 1DPV system, presented in Figure 5, is shifted towards the

west compared to the orientation with the highest yearly production, i.e. a 1DPV system with azimuth 0°

and tilt 40°. For 3DPV systems the self-consumption is highest for a fully south-oriented system and

slightly higher for west-mounted systems than for east-mounded, as seen in Figure 6 to Figure 8.

Figure 5. Absolute self-consumption for a 1DPV system

Figure 6. Absolute self-consumption for a 3DPV system with

2000 Wp.

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Figure 7. Absolute self-consumption for a 3DPV system with 3360 Wp.

Figure 8. Absolute self-consumption for a 3DPV system with 4500

Wp.

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1.3 Relative self-consumption

The relative self-consumption is highest for systems oriented towards the west, as seen in Figure 9. With

a system size of 2000 Wp, it is possible to reach 97 per cent self-consumption.

Figure 9. Relative self-consumption for a 1DPV system

Figure 10. Relative self-consumption for a 3DPV system with 2000 Wp.


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configuration between the three orientations can be seen in Table 1 and Table 2.The yearly PV production loss is

630 kWh per year when changing layout from due south to east-west, which is a production loss of about 20 per

cent. The loss in absolute is smaller; 300 kWh per year, a reduction of approximately 12 per cent. The relative self-

consumption is increasing with 8 percentage units, from 82 to 90 per cent of the PV production. Electric power

consumption data from house 9 are used for the calculations.




3DPV systems with highest production and absolute (blue – Table 1) and

relative (green – Table 2) self-consumption in June 2011.



respect to the results in previous section. The optimal configurations for optimization of the yearly production,

absolute and relative self-consumption are presented in Table 3 to Table 5. Electric power consumption data from

house 9 are used for the calculations.

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3100 2530 82 Orientation 2 0 90 30


Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


2470 2230 90 Orientation 2 1980 90 30


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Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3130 2555 82 Orientation 2 1000 20 40



Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


1800 1750 97 Orientation 2 1700 90 90


Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3140 2550 81 Orientation 2 0 90 30


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1.5 Yearly profit

Since the price for buying electric energy is higher than the selling price in the simulations in Figure 14

and Figure 15, the owner profit from the high self-consumption rate.

Figure 14. Yearly profit for a 3DPV system with 3360 Wp with fixed prices

Figure 15. Yearly profit for a 3DPV system with 3360 Wp with spot prices

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Appendix III – Results House 20 01 1/10



APPENDIX III – RESULTS HOUSE 20 In this Appendix simulations for house 20 can be found, i.e. the house with the lowest yearly electric

consumption, around 5,700 kWh per year. The production charts are the same as the ones which can be

found in the report. Interesting differences will be discussed in the Discussion chapter in the report.

List of Contents

APPENDIX III – RESULTS HOUSE 20 ........................................................................................................1

LIST OF CONTENTS .......................................................................................................................................1 LIST OF FIGURES ..........................................................................................................................................1 LIST OF TABLES ...........................................................................................................................................1 1.1 SIMULATED PV PRODUCTION AND CONSUMPTION ................................................................................2 1.2 ABSOLUTE SELF-CONSUMPTION .........................................................................................................3 1.3 RELATIVE SELF-CONSUMPTION ...........................................................................................................5 1.4 OPTIMIZATION OF PRODUCTION, ABSOLUTE AND RELATIVE SELF-CONSUMPTION ....................................8

1.4.1 Installed PV power: 3360 Wp, azimuth 0° or ±90°, tilt 30° ......................................................8 1.4.2 Installed PV power: 3360 Wp, variable azimuth, variable tilt ...................................................9

1.5 YEARLY PROFIT .............................................................................................................................. 10

List of Figures FIGURE 1. SAME LAYOUT AND DISTRIBUTION AS IN THE MAIN REPORT ........................................................................................... 2 FIGURE 2. MEAN CONSUMPTION AND PRODUCTION DURING 2011 ............................................................................................. 2 FIGURE 3. MEAN PRODUCTION AND CONSUMPTION IN JANUARY 2011 ........................................................................................ 3 FIGURE 4. MEAN PRODUCTION AND CONSUMPTION IN JUNE 2011 .............................................................................................. 3 FIGURE 5. ABSOLUTE SELF-CONSUMPTION FOR A 1DPV SYSTEM ................................................................................................. 4 FIGURE 6. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 2000 WP........................................................................... 4 FIGURE 7. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 3360 WP. .......................................................................... 5 FIGURE 8. ABSOLUTE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 4500 WP. .......................................................................... 5 FIGURE 9. RELATIVE SELF-CONSUMPTION FOR A 1DPV SYSTEM ................................................................................................... 6 FIGURE 10. RELATIVE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 2000 WP. MINIMUM: 62 %, MAXIMUM: 75 % ....................... 6 FIGURE 11. RELATIVE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 3360 WP. MINIMUM: 45 %, MAXIMUM: 56 % ....................... 7 FIGURE 12. RELATIVE SELF-CONSUMPTION FOR A 3DPV SYSTEM WITH 4500 WP. MINIMUM: 36 %, MAXIMUM: 46 % ....................... 7 FIGURE 13. MEAN ELECTRIC POWER CONSUMPTION AND PRODUCTION OF THE TWO 3DPV SYSTEMS WITH HIGHEST PRODUCTION (BLUE –

TABLE 1) AND RELATIVE SELF-CONSUMPTION (GREEN – TABLE 3) IN JUNE 2011. .................................................................. 9 FIGURE 14. YEARLY PROFIT FOR A 3DPV SYSTEM WITH 3360 WP WITH FIXED PRICES ................................................................... 10 FIGURE 15. YEARLY PROFIT FOR A 3DPV SYSTEM WITH 3360 WP WITH SPOT PRICES .................................................................... 10

List of Tables

TABLE 1. OPTIMIZING THE YEARLY PV PRODUCTION AND ABSOLUTE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° . 8 TABLE 2. OPTIMIZING THE ABSOLUTE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° ............................................... 8 TABLE 3. OPTIMIZING THE RELATIVE SELF-CONSUMPTION, TILT 30°, AZIMUTH 0° OR ±90° ................................................ 8 TABLE 4. OPTIMIZING THE YEARLY PV PRODUCTION FOR 3360 WP ................................................................................... 9 TABLE 5. OPTIMIZING THE ABSOLUTE SELF-CONSUMPTION FOR 3360 WP .......................................................................... 9 TABLE 6. OPTIMIZING THE RELATIVE SELF-CONSUMPTION FOR 3360 WP ........................................................................... 9

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the main report

The consumption of electric energy is at its highest in the evening on a yearly basis, as seen in Figure 2.

The production curves exceeds the consumption during noon both seen over the whole year and

especially during the summer, presented in Figure 4. This indicates a low self-consumption.


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The highest absolute self-consumption for a 1DPV system, presented in Figure 5, is shifted towards the

west compared to the orientation with the highest yearly production, i.e. a 1DPV system with azimuth 0°

and tilt 40°. For 3DPV systems the absolute self-consumption is highest for PV system in every direction,

mostly towards the west. The lager the system is, the larger share of the modules should be directed

towards the east to get the highest absolute self-consumption.

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Figure 5. Absolute self-consumption for a 1DPV system


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1.3 Relative self-consumption The relative self-consumption is almost the same for 1DPV systems oriented towards the east and towards

the west, as seen in Figure 9. The self-consumption is rather low because of the low consumption.

However, the 3D relative self-consumption charts have not the same shape as the ones for the absolute

self-consumption – the highest relative self-consumption occurs for east-west oriented systems.

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Figure 9. Relative self-consumption for a 1DPV system



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configuration between the three orientations can be seen in Table 1 to Table 3. The yearly PV production loss is

670 kWh per year when changing layout from due south to east-west, which is a production loss of about 21

per cent. The loss in absolute is smaller; 15 kWh per year, a reduction of approximately 12 per cent. The relative

self-consumption is increasing with 8 percentage units, from 82 to 90 per cent of the PV production. Electric power

consumption data from house 20 are used for the calculations.


Table 2. Optimizing the absolute self-consumption, tilt 30°, azimuth 0° or ±90°


Power (Wp) Azimuth (°) Tilt (°)

Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3100 1395 45 Orientation 2 0 40 30



Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


2750 1400 45 Orientation 2 1500 90 30



Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


2470 1380 56 Orientation 2 2380 90 30


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Figure 13. Mean electric power consumption and

production of the two 3DPV systems with highest

production (blue – Table 1) and relative self-consumption

(green – Table 3) in June 2011.



respect to the results in the previous section. The optimal configurations for optimization of the yearly production,

absolute and relative self-consumption are presented in Table 4 to Table 6. Electric power consumption data from

house 20 are used for the calculations.



Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


2810 1420 51 Orientation 2 2100 60 40



Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)

Orientation 1

Orientation 2

Orientation 3

1280

2080

0

-90

90

90

90

90

90 1720 1200 70

Power


Yearly

production

(kWh)

Absolute self-

consumption

(kWh)

Relative self-

consumption

(%)


3140 1380 44 Orientation 2 0 90 30


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1.5 Yearly profit

Since the price for buying electric energy is higher than the selling price in the simulations in Figure 14

and Figure 15, a lower self-consumption will lead to a lower profit.

Figure 14. Yearly profit for a 3DPV system with 3360 Wp with fixed prices

Figure 15. Yearly profit for a 3DPV system with 3360 Wp with spot prices

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