Modelling extensive solar power production in urban and rural areas

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UPTEC E17 003

Examensarbete 30 hp Juni 2017

Modelling extensive solar power production in urban and rural areas

Emil Jansson

Gustav Elfving

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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

Modelling extensive solar power production in urban and rural areas

Emil Jansson & Gustav Elfving

Renewable energy sources, in form of solar power, is a growing source of energy.

Not only at an industry level but also at a commercial level. Grid-connected, building-applied solar power has increased rapidly and as the implementation of solar energy grows, so does the importance of being able to evaluate locations that are of interest of installations with respect to its potential production and its impact on the electrical grid.

In this thesis the energy production for different future scenarios is modelled for BAPV (Building Applied Photovoltaics) in Uppsala and Herrljunga.

This is done by using calculation and simulation programs called MATLAB and ArcGIS.

The results regarding Uppsala, are used in a report by BEESG (Built Environment Energy Systems Group) at Uppsala University to the Swedish energy agency.

The grid impact of installing extensive solar power as concentrated and dispersed in Herrljunga are simulated and evaluated.

Both authors has during the process been equally involved in all parts of the thesis in order to get a thorough understanding of the project as a whole. This due to the fact that the different parts of the thesis were dependent of each other (the second part could not be finished until the first were completed etc).

ISSN: 1654-7616, UPTEC E17 003 Examinator: Mikael Bergkvist

Ämnesgranskare: Joakim Munkhammar Handledare: Joakim Widén

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Summary

A growing market for renewable energy sources has during the past decade emerged, where solar energy, during the later part of the decade, has made a technological leap in terms of improved performance and reduced costs. This has made it possible to produce solar panels cheaper. Solar power and are now, together with wind power, for the first time generating energy at a lower cost than gas and oil. This, in combination with EU:s renewable energy directive and Swedens parliamentary energy commission goal to achieve 100% renewable en- ergy by year 2040, makes modelling of energy production for future planned PV-installations of great interest. How these extensive installations of renewable energy sources are aﬀecting the stability of the electrical grid is something that would be interesting to study further.

A model which uses LiDAR data, along with irradiation data obtained from a tool called

"STRÅNG", has been created in this thesis. Scenarios for reaching Uppsala municipality goals of having 30MW and 100MW installed power before 2020 and 2030 respectively, has been created. These scenarios are thoroughly evaluated by taking all rooftops in Uppsala into consideration. From there, a study is performed that determines which of these rooftops are most eﬃcient to install PV-systems on. Scenarios of scattered and dispersed placement of PV-systems is evaluated in Herrljunga with the purpose of study its impact on the LV-grid.

Herrljunga was chosen since it, unlike Uppsala, had available electrical consumption data.

The scenarios for Herrljunga is created as scaled-down versions of the Uppsala scenarios, with respect to the installed power. The evaluation is done by performing power flow analysis of the electrical system.

The results of the thesis can be utilised by urban planners as a tool in order to demonstrate how cities/settlements can accommodate more solar electricity production in the most eﬃcient way without causing problems in the electricity grid. It can also be utilised by network owners as the basis for e.g. future network design. Both the main objectives of the thesis and its milestones can be used by several diﬀerent actors in the industry that have an interest in evaluations of arbitrary chosen locations that is of interest for future plans of extensive on-site PV-generation.

Models which can be used to characterise power productions on diﬀerent time scales and

study the aﬀect of installations of PV-systems in urban and rural electrical grids, are concluded

to be of great interest. However, the models created in the thesis were found to have a

limitation regarding its precision and accuracy. This limitation were bound to the quality

of irradiation data that was used, in this case data from STRÅNG. The results were used

in BEESG:s report (Characterisation of extensive city-scale solar power generation) to the

Swedish energy agency.

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Acknowledgements

First of all we would like to express our gratitude towards our thesis-advisor Joakim Widén who, with his great enthusiasm and knowledge within the subject, guided us through this period.

We would also like to give a special thanks to David Lingfors who introduced and helped us with the program ArcGIS and the LiDAR data. Also, our thanks goes to all the people working with the Uppscale project and the people in BEESG at the department of solid state physics at Uppsala University, for giving us the opportunity to work with a project that we find very interesting. Furthermore, the experience and knowledge all these people possesses have been very inspiring and helped us to steer our work in the right direction.

STRÅNG data used in this thesis 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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Nomenclature

Symbol Description Value Units

A

_i

Anisotropy index - ms

¹

C

0

Parameter defining the cur- vature of the relationship be- tween AC output power and DC input power

0 -

Declination -

⌘ Eﬃciency - -

⌘

_{0M od}

Module eﬃciency stated in

data sheet - %

K Glazing extinction coeﬃcient 4 m

¹

L Glazing thickness 0.002 m

I, I

_T

Global radiation on horizon- tal and tilted planes over a time interval

- Wm

²

I

_T,hour

Incident irradiation during

one hour - Wm 2

I

_T,month

Incident irradiation during

one month - Wm 2

I

₀

⇠ G

0

Extraterrestrial radiation on

horizontal plane - Wm

²

I

_b

, I

_bT

Beam radiation on horizontal and tilted planes over a time interval

- Wm

²

I

_d

, I

_dT

Diﬀuse radiation on horizon- tal and tilted planes over a time interval

- Wm

²

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Nomenclature

I

_b

, I

_bT

Ground-reflected radiation on tilted plane over a time interval

- Wm

²

K

B

Angle dependent absorption

factor (Beam radiation) -

K

_G

Angle dependent absorption factor (Ground reflected radi- ation)

-

K

_I

Angle dependent absorption

factor (Diﬀuse radiation) -

N Number of modules - -

n Refractive index 1.526 -

P

_ac,hourly

Hourly power production - W

P

_ac,monthly

Monthly power production - W

P

_ac0

Rated max AC power for a

inverter - W

P

_dc0

DC power at which the AC

rating is achieved for inverter - W

P

_dc

Input DC power to inverter - W

P

_s0

Threshold power for a in-

verter - W

P

_T

Temperature coeﬃcient of

the maximum output power - %/ C

R

_b

Geometric factor - -

⇢

_g

Albedo of the ground 0.2-0.4 -

S Global insolation on the op-

erating cell - Wm 2

T Temperature - C

✓ Angle of incidence -

✓

_z

Zenith angle of incidence -

Tilt angle -

T

noct

Nominal operating cell tem-

perature - C

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List of Figures

2.1

Radiation on a horizontal plane. EDirect and EDif f use is equivalent to IbIdrespectively.

. . 15

2.2

Radiation on a tilted plane.

. . . 16

2.3

Figure showing the physical model of IAM created in MATLAB (same as in [11]).

. . . 18

2.4

Graphical description of how AM is defined.

. . . 20

3.1

The figure showing our definition of subsystem. M stands for Module. Multiple modules connected to a single inverter (DC/AC in figure) makes up subsystem. Multiple subsystems constitutes a system which can also be seen in the figure.

. . . 27

3.2

Median global insolation year constructed from data gathered by STRÅNG from 1999 to 2014.

30 3.3

Median direct insolation year constructed from data gathered by STRÅNG from years 1999 to 2014.

. . . 30

3.4

Median temperature year constructed from data gathered by SMHI from 1999 to 2014.

. . . 31

4.1

Work Package 1 model flow chart.

. . . 34

4.2

Work Package 2 model flow chart.

. . . 38

4.3

High resolution LiDAR data over Uppsala city.

. . . 41

4.4

Satellite overview image of the evaluation-example at Gräslöken.

. . . 43

4.5

Rooftop evaluation for Gräslöken using 1000kWh/m²/year as minimum irradiation limit.

. . 43

4.6

Closer look at two of the southernmost houses shown in the previous figure.

. . . 44

4.7

Work Package 3 model flow chart (I and T are vectors containing irradiation data and temperature data respectively).

. . . 45

4.8

Top plot: Total aggregated power consumption (grey), solar power production (green). Bot- tom plot: Net production for all customers in Herrljunga (green).

. . . 48

4.9

Investigated scenarios in Herrljunga municipality. More information regarding the scenarios can be seen in Table 5.8

. . . 50

5.1

Energy production for Vaksala Eke vägg.

. . . 51

5.2

Energy production for half the system at Ultuna Restaurang.

. . . 52

5.3

Energy production for Salagatan 18.

. . . 52

5.4

Production correlation for Ultuna Resturangen.

. . . 53

5.5

Production correlation for Salagatan 18.

. . . 53

5.6

Production correlation for Vaksala Eke wall.

. . . 54 5.7

Annual aggregated production. The figure shows the aggregated power production for the

time periods where all the system stated in Table 5.3 had recorded production and insolation

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LIST OF FIGURES

5.8

One week aggregated production, showing the real production versus the modelled production

from model 1.

. . . 59

5.9

Correlation of aggregated production for the systems presented in table 5.3

. . . 60

5.10

Output from the model showing the production, performance ratio and specific yield for subsystem 1 at site Granegården.

. . . 61

5.11

Output from the model showing the production, performance ratio and specific yield for subsystem 2 at site Granegården.

. . . 61

5.12

Recorded irradiation from sensor compared with irradiation data extracted from STRÅNG, at site Granegården with hourly resolution.

. . . 62

5.13

Comparison between production output from model 1 and model 2, versus real production for Granegården (1 hour resolution insolation data).

. . . 63

5.14

Comparison between production output from model 1 and model 2, versus real production with 1 day resolution insolation data at site Salagtan 18.

. . . 63

5.15

Correlation of the production output from model 2 versus real production data at site Sala- gatan 18 (Daily resolution).

. . . 64

5.16

Correlation of the production output from model 2 versus real production data, at site Granegården (Hourly resolution).

. . . 64

5.17

Output from the model that shows the production, specific yield and performance ratio over one year with hourly resolution.

. . . 66

5.18

Output from the model that shows the production, specific yield and performance ratio over one year with monthly resolution.

. . . 66

5.19

Installed power and annual energy production for the scenarios shown in Table 5.5

. . . 67

5.20

Monthly total energy yield for scenrio 2 and 4

. . . 68

5.21

Specific yield for the average day throughout one year of scenario 2 and 4.

. . . 68

5.22

Cumulative energy production throughout the studied year, done for scenario 2a-2d

. . . 69

5.23

Cumulative energy production throughout the studied year. normalizedwith respect to installed power for scenario 2a-2d.

. . . 70

5.24

Sorted energy production over one year for scenario 2a-2d. Sorted from highest to lowest energy production.

. . . 70

5.25

Cumulative energy production throughout the studied year. Done for scenario 4a-4d.

. . . . 71

5.26

Cumulative energy production throughout the year. normalizedwith respect to installed power for scenario 4a-4d.

. . . 72

5.27

Sorted energy over one year for diﬀerent irradiant limits. Note that the dates on the x-axis does not correspond to the y-axis values for scenario 4a-4d.

. . . 72

5.28

LV-grid level for the diﬀerent scenarios created for Herrljunga.

. . . 74

5.29

Voltage level for each customer bus in Herrljunga in three cases. Top plot: No PV-generation, middle plot: Scattered PV-instalment, bottom plot: Concentrated PV-generation.

. . . 76

8.1

GUI flow chart figure

. . . 85

8.2

GUI from MATLAB model for Work Package 1

. . . 86

8.3

Import Data and Transform Vectors flow chart figure

. . . 86

8.4

Over production flow chart figure from Figure 4.1

. . . 87

8.5

Import System Data flow chart figure

. . . 87

8.6

Command window flow chart figure

. . . 90

8.7

Import data flow chart figure

. . . 90

8.8

Adjust vectors flow chart figure

. . . 90

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LIST OF FIGURES

8.9

GUI flow chart figure

. . . 91

8.10

GUI from MATLAB model for Work Package 2

. . . 91

8.11

Electrical grid system for Herrljunga.

. . . 98

8.12

The two time periods described in section 5.2.

. . . 99

8.13

Hourly average normalized absolute error for Model 2 compared to real production, with notably high peaks as described in section 5.2. The average diﬀerence values at the y-axis are in percent.

. . . 99

8.14 Average normalized absolute errorfor Model 2 compared to real production, with

notably high peaks as described in section 5.2. The average diﬀerence values at

the y-axis are in percent. . . 100

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List of Tables

3.1 Insolation and Production data and its resolution for the 24 systems . . . 28

3.2 Errors of the output from the STRÅNG model for diﬀerent time horizons, com- pared to true values from meteorological stations. . . 29

3.3 Irradiance specification for the year 1999-2013 . . . 31

4.1 Example of how data points are sorted with respect to their azimuth and tilt angle. . . 46

5.1 Production and performance table. . . 55

5.2 Correlation and error table . . . 57

5.3 Errors and production comparison for systems included in the aggregated pro- duction. . . 58

5.4 Error evaluation for diﬀerent resolution at diﬀerent time periods . . . 65

5.5 Scenario evaluation . . . 67

5.6 Evaluation of scenario 2 when as the irradiance limit changes . . . 69

5.7 Evaluation of scenario 4 when as the irradiance limit changes . . . 71

5.8 Scenario evaluation . . . 75

8.1 Subsystem specification table 1 . . . 93

8.2 Subsystem specification table 2 . . . 95

8.3 Solar module and inverter specification . . . 97

8.4 HOBO-sensor installation details for each site . . . 97

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Chapter 1

Introduction

Throughout the last 100 years, electricity has been a key component in the modern world, and the demand has steadily increased throughout the years. For a long time, coal, natural gas and oil has stood for the majority of the energy production. Besides having negative eﬀects on the environment, these resources are getting more expensive to retrieve due to their limited existence.

With an increasing knowledge and acknowledgement of global warming, politicians and everyday people has started to turn their interest towards other forms of energy sources. This has made it possible for renewable energy companies to establish themselves and grow. During the last 10 years the renewable energy market has experienced an extremely fast technological and production progress partly cause of the huge investments done by countries like Germany, China, Japan etc. [22]. As a result of this, renewable energy has introduced itself as a large- scale energy source and competitor on the energy market, especially solar photovoltaics [23].

Solar photovoltaic is in contrary to the fossil fuels a energy source that neither emits any harmful gas nor draws from any finite resource. Instead, it harvests the solar energy by con- verting the suns light to direct current through semiconductors.

The combination of a fast technological progress and a decrease in manufacturing and material costs, PV panels oﬀers opportunities to integrate solar power into the electrical grid, either as big-scale PV farms or as small-scale systems installed at buildings. However, there are some challenges that comes with the increase of renewable energy sources that needs to be resolved.

With large amounts of renewable electricity in today’s power grid, an increasing need

for balancing power at diﬀerent time scales are needed, and the network may need to be

strengthened. If there is a comprehensive expansion of building applied photovoltaic systems

(BAPV) in Sweden, cities may become big power producers in the future. Solar produced

electricity, power fluctuations and availability will depend on the PV system’s orientation,

geographical location and weather. Hence, a model which can estimate the energy production

with high resolution for future planned PV-installations may be of great interest. Achieving

such a model would directly open up the possibility of evaluating and simulating the PV-

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CHAPTER 1. INTRODUCTION

regarding voltage levels. Such simulations are of importance to maintain delivery of electricity with high quality along with the indication of actions that might have to be executed in order to preserve a stable grid.

1.1 Background

In this thesis, which is part of the larger research project UppScaleSolar, financed by the Swedish Energy Agency and carried out by the BEESG (Built Environment Energy Systems Group) at Uppsala University, power production from large-scale expansion of BAPV char- acterised in future scenarios for urban and rural settlements in the municipalities Uppsala and Herrljunga are determined. Solar power at city level will be modelled and validated by using measurement networks consisting of existing photovoltaic plants supplemented by solar radiation measurement. During the project a large number of plants are evaluated and the plant owners will have a chance to get involved in the project through workshops.

The properties of the electricity distribution grid will be evaluated with respect to existing criterion regarding voltage levels. This will be done in order to see the aﬀect of having large- scale implementation of PV generation in the electrical system along with its influence on power flows. This evaluation will be done for diﬀerent scenarios regarding the geographic placement of PV installations, rural and urban areas included.

1.2 Goals

The project’s aim is to determine power production from dispersed building applied PV- systems (BAPV) in Uppsala and its impact on the distribution grid. Due to non-existing data regarding electricity consumption in Uppsala, the analysis regarding the grid impact of power production from dispersed BAPV is to be made for Herrljunga were such data were available.

The BEESG have previously made some evaluation regarding this in Herrljunga but did not investigate the diﬀerence between the grid impact from dispersed and concentrated BAPV [21].

In order to fulfil the aim of the project, the following goals were set:

(a) Characterisation of daily and seasonal variation (MWh/h and MWh/month) for dis- persed PV-production in urban and rural areas.

(b) The impact of having dispersed and concentrated PV-installations in urban and rural distribution grids.

The project includes Uppsala municipality own goal; to create scenarios where 30MW installed PV-power could be realised until 2020 and 100MW until 2030.

1.3 Milestones and work packages

The purpose of the thesis was partly to evaluate a number of existing PV-systems around

Uppsala, and partly to develop a model that could estimate production at locations where

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CHAPTER 1. INTRODUCTION

future planned solar system would be installed. The model is validated through comparison of gathered real production data. In order to achieve this, the following milestones were set:

• Gather data from PV systems at a number of places around and in Uppsala. The data will include information about the true insolation and energy production at the locations, and will be used to evaluate the diﬀerent systems.

• Calculate aggregated power production from the model and examine if it is possible to achieve a deviation from the real aggregated production of the PV-systems with no more than 5% in average.

¹

• To create scenarios for future installations of PV-systems in the urban area of Uppsala.

• To investigate how the implementation of PV-systems would aﬀect load profiles and overload of components in the distribution grid at Herrljunga that is representative for Uppsala.

These milestones were contained within four smaller work packages.

Work package 1

Data collection from the PV system. Collection of solar irradiation data and solar electricity production data from roughly 15 systems. The data will be available for a full year and is used to evaluate systems (solar radiation in the module level, power output per installed kW, performance ratio, etc.) and for validation of the other work packages. A model that aggregates the production of the networks of PV-systems is to be created and used in the analysis.

Work package 2

Development and validation of models for BAPV. Here, a model is developed and imple- mented for converting irradiation on a horizontal plane to irradiation on arbitrary oriented planes. Further development of existing computational models within BEESG is to be done.

The modelling is done in detail for the evaluated systems and is validated with the collected irradiation data and power generation data used in model 1.

Work package 3

Construction of scenarios for the development of BAPV in Uppsala. Lantmäteriets property map (SW:Fastighetskarta), in combination with LiDAR data will be used to identify available roof surfaces in the municipalities studied. Constructing scenarios for large-scale deployment that can be used to achieve the goals of installing 30MW until 2020 and 100MW until 2030.

The interleaved solar power in the scenarios are calculated with help of the developed models and data from work package 1 and 2.

1Since the insolation data from STRÅNG used in this model had some major flaws, the aggregated power evaluation was after discussion with the project leader moved to Work Package 1 where real insolation data,

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CHAPTER 1. INTRODUCTION

Work package 4

The impact on the power grid. Power flow simulations of the electrical grid in Herrljunga is carried out to quantify how various deployment scenarios for solar energy aﬀects the voltage profiles and overload of components of the network.

1.4 Delimitations

The focus of the work will be to get the models to work and achieve valid results trough them.

The model that calculates production for arbitrary oriented PV:s will not take shadowing from objects in consideration. Errors that occur in the model due to the irradiation data from STRÅNG, will not be considered for.

The thesis is mainly focused on reaching the goals from a technical perspective. This means that the scenarios created for deployment of BAPV in Uppsala will not be evaluated with electricity prices, PV-panel prices, installation costs etc in mind. No economical aspects will be taken in consideration.

1.5 Outline of the report

The thesis starts with giving relevant information regarding the theory behind the calculations

necessary to obtain the energy output from PV-panels and the impact of having PV-panels

implemented in an electrical grid. This is presented in chapter 2, which also includes theory

for the validation of the models. Chapter 3 describes what kind of data that was gathered

and used in order to fulfil the goals and milestones set for the project. In chapter 4, a detailed

explanation regarding the methods used to create the models for work package 1 and 2 are

presented. In the same chapter, methods how these models were used in order to perform

the rooftop evaluations in work package 3 and the power flow simulations in work package 4

are explained. The results of the scenarios created, along with validation of the models, is

found in chapter 5. Finally, discussion and conclusions of the evaluation and models is found

in chapters 6 and 7 respectively.

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Chapter 2

Theory

2.1 Irradiation

Solar energy is the most abundant energy source in the world. When the sun rises in the morning, earth receives power in form of electromagnetic waves, also known as solar irradiance.

The total solar radiation received on a horizontal plane is called the global radiance, and is defined as the sum of diﬀused and beam radiation [1]. Diﬀuse radiation is radiation that has been scattered by the atmosphere or clouds while beam radiation is the part of the global radiance that hasn’t been scattered.

I = I

_d

+ I

_b

, (2.1.1)

where I is the global irradiation on a horizontal plane, I

d

the direct radiation and I

b

the beam radiation.

. . .

Reflection

Scattering Direct radiation

E

_Diffuse

E

_Direct

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CHAPTER 2. THEORY

During this thesis, we will work with irradiance on the tilted plane and it is therefore necessary to account for the ground reflected radiation (I

gT

), see Figure 2.2.

2.1.1 Irradiation on tilted plane I

T

Pitched PV-panel Direct

radiation Diffuse radiation

Reflected radiation

Ground

Figure 2.2:

Radiation on a tilted plane.

The formula for the total irradiance on a tilted plane (I

T

) is:

I

_T

= I

_dT

+ I

_bT

+ I

_gT

, (2.1.2)

where I

dT

and I

bT

is the component of I

d

and I

b

that hits the tilted plane [1].

2.1.1.1 Beam radiation on tilted plane I

bt

Beam radiation on a tilted plane is determined by using the angle which relates the orientation of the plane to the position of the sun along with the usage of a geometric scaling factor which converts beam radiation between planes.

I

_bt

= R

_b

I

_b

cos(✓

_z

), (2.1.3)

where ✓

z

is the zenith angle of incident and R

b

is the geometric scaling factor. R

b

is defined as the fraction of the beam radiation on the tilted plane and beam radiation on the horizontal plane:

R

_b

= I

_bt

I

_b

= cos(✓) cos(✓

_z

) , where ✓ is the angle of incidence.

One have to be observant of the values that R

b

can take. During sun rise and sun set ✓

z

becomes very small, leading to unrealistically high values.

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CHAPTER 2. THEORY

2.1.1.2 Diﬀuse radiation on tilted plane

In order to determine diﬀused radiation on a tilted plane, parameters which describes how much of the sky that is visible to the plane and how much of the extraterrestrial radiation that is preserved as beam radiation after it has passed through the atmosphere has to be considered.

I

_dt

= I

_d

"

(1 A

_i

) 1 + cos( ) 2

!

+ A

_i

R

_b

#

, (2.1.4)

where is the tilt angle and A

i

is the ratio between the beam radiation and the extraterrestrial radiation:

A

_i

= I

_b

I

₀

.

This describes how much of the extraterrestrial radiation that is preserved as beam radiation after it has passed through the atmosphere.

2.1.1.3 Radiation reflected from the ground on tilted plane I

gt

The last component included in the expression of total radiation on a tilted plane is considering the radiation that is reflected from the ground. It is depending on factors that describes how much of the ground that is visible from the planes perspective and how good reflectance the ground has.

I

gt

= I⇢

g

1 cos( ) 2

!

, (2.1.5)

where I is the total irradiance on a horizontal plane and ⇢

g

the albedo of the ground.

The three previously described radiations (beam, diﬀused and ground reflected) represents the total radiation on a tilted plane (I

T

) [1]:

I

_T

= I

_bt

+ I

_dt

+ I

_gt

$ I

T

= I

_b

R

_b

+ I

_d

"

(1 A

_i

) 1 + cos( ) 2

!

+ A

_i

R

_b

# +

+(I

_b

+ I

_d

)⇢

_g

1 cos( ) 2

! (2.1.6)

2.1.2 Sandia Incident Angle Modifier (IAM) Model

The incident angle is the angle between the radiation beam and the normal of the solar panels

surface. As the incident angle increases the amount of reflected radiation increases and thereby

decreasing the amount of radiation that is transmitted through the protective glassing. In order

to get closer to reality, it is thereby of interest to use an angle modifier which describes this

behaviour. The angle (✓

r

) with which the non reflected radiation will penetrate the protective

glassing is described below:

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CHAPTER 2. THEORY

where n is the refractive index of the panel glass and ✓ the angle of incident.

Equation 2.1.8 describes how well a protective glassing transmits radiation at a given angle of incident, whereas equation 2.1.9 describes this when the angle of incident equals 0 degrees.

Equation 2.1.10 describes the ratio of the two previous equations [10].

⌧ (✓) = e

^cos(✓r)^KL

"

1 1

2 sin

²

(✓

_r

✓)

sin

²

(✓

r

+ ✓) + tan

²

(✓

_r

✓) tan

²

(✓

r

+ ✓)

!#

, (2.1.8)

where K is the glazing extinction coeﬃcient and L the glazing thickness.

⌧ (0) = lim

✓!0

⌧ (✓) = e

^KL

"

1 1 n

1 + n

!

2

#

(2.1.9)

IAM = ⌧ (✓)

⌧ (0) (2.1.10)

If IAM is less than 1, power production will decrease due to a decreasing short circuit current.

To determine how big the eﬀect is on the short circuit current, an empirically determined polynomial relating the short circuit current to the angle of incident (equation 2.1.11) is used [9].

f (✓) = b

₀

+ b

₁

✓ + b

₂

✓

²

+ b

₃

✓

³

+ b

₄

✓

⁴

+ b

₅

✓

⁵

(2.1.11)

0 10 20 30 40 50 60 70 80 90

Angle of incidence [deg]

0 0.2 0.4 0.6 0.8 1

IAM

Figure 2.3:

Figure showing the physical model of IAM created in MATLAB (same as in [11]).

Figure 2.3 describes in percentage (0 being 0% and 1 being 100%) how much the irradiation

has to be modified at a range of incident angles [10]. The same figure is applicable for incident

angles that ranges from 0 to -90 .

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CHAPTER 2. THEORY

2.1.3 Reflection losses

The angle of incident for each type of radiation has to be calculated in order to determine the reflection losses. This is done to achieve a model which is more closely related to reality.

Equation 2.1.12 and 2.1.13 describes the eﬀective angle of incident for ground reflected irradi- ation and diﬀuse radiation respectively, derived by Brandemuehl and Beckman (1980).

✓

_Groundref.

= 90 0.5788 + 0.002693

²

(2.1.12)

✓

Dif f useref.

= 59.7 0.1388 + 0.001497

²

(2.1.13) Inserting ✓, ✓

Dif f useref

and ✓

Groundref

in equation 2.1.11, the angle dependent absorption for each case can be determined [16]; K

B

, K

I

and K

G

for beam, diﬀused and ground reflected radiation respectively.

Applying these constants to I

bt

, I

dt

and I

gt

, the amount of absorbed radiation can be deter- mined:

I

BT

= K

B

I

_b

(2.1.14)

I

_DT

= I

_d

⇥

K

_I

(1 A

_i

) 1 + cos( ) 2

!

+ K

_B

A

_i

R

_b

⇤

(2.1.15)

I

GT

= K

G

I⇢

g

1 cos( ) 2

!

(2.1.16)

The total absorbed irradiation on the tilted plane:

I

_A

= I

_BT

+ I

_DT

+ I

_GT

(2.1.17)

2.2 PV-systems

PV-panels (Semiconductors) behaves diﬀerently under various operation conditions. A PV

module is typically rated at so-called "Standard test conditions" (STC), that is at 25 C under

an insolation of 1000 W/m

²

and with an air mass of 1.5 (AM1.5). In general, air mass (AM)

refers to how long the radiation has to travel in the earths atmosphere before it hits the panel,

see Figure 2.4

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CHAPTER 2. THEORY

Ground Atmosphere

θ

_Z

AM=1 AM=2.0

AM=1.5

Figure 2.4:

Graphical description of how AM is defined.

During operation out in the field the PV-panels are usually operating at a larger range of temperatures and at slightly lower insolation levels. Since the power output of the solar module is dependent on the operation temperature, it is crucial to find the expected operation point. A parameter called the "Nominal Operation Cell Temperature" NOCT or T

N OCT

, is therefore introduced and is defined as the temperature that is reached by operating the module with open-circuited cells during the following conditions:

• Insolation at cell surface=800W/m

²

• Air temperature=20 C

• Wind speed=1 m/s

• Mounting=Open back side

An approximate equation, calculating the cell temperature is given by the equation be- low [4].

T

_cell

= T

_Ambient

+ G

₀

T

_{N OCT}

20 800

!

(1 ⌘

_{0M od}

), (2.2.1)

where G

0

is the extraterrestrial irradiation on the horizontal plane and ⌘

0M od

is the eﬃciency stated in the modules data sheet.

Eﬃciency of a solar module is defined as how much of the suns irradiation that hits the

surface of a PV panel can be converted to electrical energy. The eﬃciency of a PV panel

is varying, depending on the material of the panel; for commercial usage, either thin film

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CHAPTER 2. THEORY

(CdTe, CiGS) or polycrystalline (Silicon) is used. The record of best efficiency for these two technologies rises above 20% [7]. However, in the commercial use the range is lower, typically 9-17%, depending on the technology used [8]. Other factors that affects the efficiency is the cell temperature (T

cell

) and a coefficient that states how much the maximum power output decreases with increasing temperature. This coefficient is individual for different types of panels, and is found in the data sheet of the panel. In this thesis we refer to it as P

_T

. Equation 2.2.2 describes the module eﬃciency when taken these factors into consideration.

⌘

_mod

= ⌘

_{0M od}

⇥

1 + P

_T

(T

_cell

25) ⇤

. (2.2.2)

The theoretical possible DC power produced by a solar module can be calculated by mul- tiplying the solar irradiance with the number of modules, module eﬃciency and the active area. But some additional losses has to be accounted for, such as mismatches in output power between modules due to small variations between the properties of each individual cell in a module. This variance of cell-properties results in small tolerances in the output power, typ- ically 3% for PV-panels at the market today (but can reach up towards 5%) [3]. Soiling on solar panels will also cause additional losses, losses ranging from 2-50% depending on your geographic location [17]. Taking just these two factors into account, 10% additional losses are taking into consideration when determining the theoretical possible DC power.

P

DC

= ⌘

_mod

G

0

⇥

N A(1 addLoss) ⇤

, (2.2.3)

where N is the number of modules, A the module area and addLoss the additional losses.

2.2.1 Sandia Inverter Eﬃciency and Power Output Model

In order to get the DC-power produced by an array of PV-modules to match the AC-power on the grid, one needs to use an inverter which converts the DC-power to AC-power. In this thesis a model from Sandia were used, which is applicable to all commercial inverters used in photovoltaic power systems. A number of coeﬃcients and parameters are needed to get a good accuracy on the inverters ac-to-dc conversion [9].

P

_ac

= P

_ac0

P

_dc0

P

s0

C

₀

(P

_dc0

P

_s0

)

!

(P

_dc

P

_s0

) + C

₀

(P

_dc

P

_s0

)

²

, (2.2.4) where P

ac0

is the rated maximum AC power for the inverter, P

dc0

the DC power at which the AC rating is achived, P

s0

the threshold power, C

0

the curvature defining parameter between the AC output power and DC input power, and P

dc

the input DC power.

2.2.2 Specific Yield

In order to investigate and/or compare the PV-systems a ratio called "Specific Yield" is used.

This measures the production per installed power, kWh/kW

p

, and is a very good way of mea-

suring the performance of PV-systems since the production is proportional to the potential

earnings of the system while the installed power reflects the cost of the system. A low value

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CHAPTER 2. THEORY

in Uppsala, Sweden, is about 800 kWh/kW

p

[25]. This value works as a reference regarding validation of the models used in this thesis.

Hourly specific yield:

SY

_hourly

= P

_ac,hourly

⌘

_{0M od}

N A , (2.2.5)

where P

ac,hourly

is the hourly power production.

Monthly specific yield:

SY

_monthly

= P

_ac,monthly

⌘

_{0M od}

N A , (2.2.6)

where P

ac,monthly

is the monthly power production.

2.2.3 Performance ratio

Another measurement parameter describing the performance of PV-systems is the perfor- mance ratio. This ratio evaluates a PV-system by taking the ratio of the actual production and the theoretical possible production, resulting in a dimensionless factor that is proportional to the actual energy available after thermal and conduction losses. It is independent of the orientation of the PV-system and the irradiation of the PV-plant makes it very desirable as a comparison of PV-systems placed at diﬀerent locations.

As the performance ratio approaches a high value (i.e 100%) the system is operating more eﬃciently. However, a value of 100% is impossible to achieve due to inevitable losses that is present in the PV-system. Typically, PV-modules used commercially are having a PR-ratio of 0.8 or less [14].

Hourly performance ratio:

P R

_hourly

= Actual prod.

T heoretical prod. = SY

_hourly

IT,hour

I_{ST C}

= 1000SY

_hourly

I

_T,hour

, (2.2.7)

where I

T,hour

is the incident irradiation during one hour.

Monthly performance ratio:

P R

_monthly

= 1000SY

_monthly

I

_T,months

, (2.2.8)

where I

T,months

is the incident irradiation during one month.

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CHAPTER 2. THEORY

2.2.4 Absolute, relative and average error

Two diﬀerent errors that are of importance when evaluating the errors of an experimental/sim- ulated measurement is often used, called absolute error and normalized absolute error. The absolute error is a measure on how far from the true value the experimental value is, or an indication of the uncertainty in the measurement. The normalized absolute error describes how large the error is normalized with the size of the object/data that is measured.

Absolute error:

Absolute error = |Actual value M easured value | normalized absolute error:

N ormalised absolute error = Absolute error Installed power

Another error used for the analysis of the results in Work Package 1 was the average rela- tive error. This is defined as the diﬀerence between the real and the calculated production in percentage. It is calculated for every data point within the time period of production for the aggregated power. The average value of this was determined as described in the equation below.

Average relative error:

1 n

X

n k=1

| M odel P roduction(k) Real P roduction(k)

Real P roduction(k) |,

where n is number of data points within the time period of production.

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CHAPTER 2. THEORY

2.3 Power flow analysis

When installing extensive photovoltaic on-site generation in today’s grid system, some of the old generating power station has to either turn down their production or entirely shut down.

Old power station usually produces its power with generators which, when connected to the grid, contributes to a mutual inertia. By shutting these oﬀ, the grid loses some of its inertia, making it more sensitive to sudden power flow changes. With a grid containing larger amount of renewable energy sources an increasing amount of power flow fluctuations are therefore un- avoidable. These power flow fluctuations leads to rapid frequency variations. Depending on the magnitude of the power change, the change of frequency may lead to a blackout.

Since solar power is a weather dependent source, the power production varies deterministi- cally and stochastically; high production during mid-day (when the sun is at its highest point) and low production during the morning and evening (when the sun is at its lowest point).

This production behaviour is the inverted behaviour for an every-day household electricity demand which makes the high production output during mid-day somewhat unfortunate as it may lead to critical voltage rise if there isn’t an eﬃcient way to store or sell the abundant energy. Another factor which is tied to solar power being a weather dependent source is rapid production changes. Clouds can block the suns irradiation and create temporary production dips, creating power changes and subjecting cables/lines for additional strain. A way to man- age/prevent some of these problems early on in the developing state is to analyse the load flow/power flow simulations. These simulations provides useful and important information such as; what type of cables/lines can be used, bus voltages, line currents, will reactive or active power compensations have to be used, and in the long run how the PV-systems should be distributed to minimize the strain on the grid and the risk of local blackouts etc.

2.3.1 Power flow calculations

In order to perform a power flow analysis, a matrix containing the inverse of all impedances in the chosen system has to be defined. This matrix is called the admittance matrix. Every row in the admittance matrix represents a bus which comprises the admittance values connected to/from the bus. Which bus the admittance is connected to is determined by its location in the row. Eg. Y

1,2

is the admittance between bus 1 and 2.

Admittance matrix Y:

Y = 2 6 6 4

Y

_1,1

... Y

_1,n

. ... . . ... . Y

_k,1

... Y

_k,n

3 7 7 5 ,

where Y

k,k

= total impedance connected to bus k and Y

k,n

= -total impedance connected be- tween bus k and n [19].

For every bus k, four variables are interlinked; real power flow P

k

, reactive power flow Q

k

, voltage magnitude V

k

and phase angle

k

.

The active and reactive power flow between two buses (k and n) can be determined as de-

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CHAPTER 2. THEORY

scribed in equation 2.3.1 and 2.3.2 respectively.

P

_k

= V

_k

X

N n=1

Y

_k,n

V

_n

cos(

_k _n _k,n

) k = 1, 2, 3, ..., N, (2.3.1)

Q

_k

= V

_k

X

N n=1

Y

_k,n

V

_n

sin(

_k _n _k,n

) k = 1, 2, 3, ..., N, (2.3.2) where

k,n

is the voltage angle between the reference bus k and the associated bus n and

n

is the phase angle of bus n.

The power flow analysis in this thesis will be done using the Newton-Raphson method.

The Newton-Raphson method applies the non-linear equations 2.3.1 and 2.3.2 to solve these

calculation for multiple bus systems. How this method works is described in: [20].

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Chapter 3

Data

3.1 Data collection

Data was supplied to us from the involved PV system owners. A few, far from all, could provide power production-and insolation data. Data regarding the PV system, such as; tilt, azimuth, type of module, number of modules etc. was easier to get and could be provided from all 24 parties involved. The entire list of the 24 parties and their corresponding PV system data can be seen in section 8.2.

3.1.1 PV System Data

The PV system data was gathered from the module data sheets and directly from the owners and operation managers. System data for every system can be seen in section 8.2 Table 8.1 and Table 8.2

3.1.2 Insolation Data

The insolation data collection started in the middle of March 2016. Exact date and mounting details for each system can be seen in Table 8.4. The equipment used to gather the insola- tion at each system was a HOBO Pendant® Temperature/Light 64K Data Logger (Part # UA-002-64). The logger has a broad range of light sensitivity, with a spectrum of wavelengths that ranges from ⇠150nm to 1200nm (see plot D in [13]). But the resolution steps are not identical for diﬀerent types of intensity. Low level intensity resolution steps are much smaller than for high level intensity. This means that the simulated production will be more accurate for the parts of the days when the light intensity that hits the panels are low [13], see Figure 5.4.

The HOBO logger collects the insolation data in Lux, and had to be converted to watt in order to use the data to perform the calculations. The conversion factor was empirically determined by BEESG to be 0.005163.

3.1.3 Production and Irradiance Collection

The production data had to be downloaded manually from diﬀerent websites such as sunny-

portal.com, solaredge.com, ihus.energiinfo.se. How many of the initial 24 parties that could

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CHAPTER 3. DATA

provide either production data or insolation data, or both, from these kinds of websites can be seen in Table 3.1.

Systems that could not provide suﬃcient data to evaluate the entire system, i.e could not provide production or irradiation data for all subsystems, were excluded in the evaluation process. For systems that had available insolation data, but not any production data, the evaluation was simplified to only be built upon the calculated production. Since Vaksala Eke Tracker is a tracker, it does not have a fixed azimuth or tilt angle which makes it impossible to evaluate with this model. This site was therefore also excluded.

In order to achive a correct evaluation, the resolution of production data and irradiation data had to be the same. Since the sensor which measured the irradiation gathered its data with 5 minute resolution, whilst the resolution of the production data could vary, a conversion from the 5 minute resolution had to made. This conversion was done by taking the average value of the 5 minute irradiation data that corresponded to the production data resolution time step. For example, if the production had a resolution of 15 minute, an average of the three irradiation data values corresponding to the specific 15 minute time-step were calculated.

Figure 3.1:

The figure showing our definition of subsystem. M stands for Module. Multiple modules connected to a single inverter (DC/AC in figure) makes up subsystem. Multiple subsystems constitutes a system which can also be seen in the figure.

We have chosen to define a subsystem as a number of modules connected to one rectifier.

In Figure 3.1, M1-M5 are smaller module groups that together constitutes one system, but the

system consists of multiple subsystems. Multiple smaller system with the same tilt and az-

imuth angle will have the same irradiation and be connected to the same rectifier and thereby

be classified as a subsystem, see Subsystem 1 in Figure 3.1.

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CHAPTER 3. DATA

T ab le 3. 1: In so la ti on an d P ro du ct io n da ta an d it s res ol ut io n fo r th e 24 sy st em s Sy st em N um ber of su bs ys tem s P ro vi ded pr od uct io n da ta N um ber of su bs ys tem s dat a w as pr ov id ed fo r

P ro du ct io n res ol ut io n P ro vi ded insolat ion dat a N um ber of su bs ys tem s dat a w as pr ov id ed fo r

In sol ati on res ol ut io n U lt un a R es ta ur an g 2 Y es 1 H ou r Y es 2 5 m in ut e Geo -cen tr um 3 Y es 3 M on th Y es 2 5 m in ut e Gr an eg år den 3 Y es 3 H ou r Y es 1 5 m in ut e Fy ri sh ov Ä ld re 5N o 0 - N o 0 - Fy ri sh ov N y 1 N o 0 - Y es 1 5 m in ut e Va ks al a E ke w al l 1 Y es 1 15 m in ut e Y es 1 5 m in ut e V ak sa la E ke T ra ck er 1 Y es 1 15 m in ut e Y es 1 5 m in ut e Salagat an 18 3 Y es 2 D ay Y es 1 5 m in ut e Bo la nd sg at an 3 Y es 3 D ay Y es 1 5 m in ut e Högåssk olan 6 Y es 6 5 m in ut e N o 0 - Gr än by Is ha ll 1 N o 0 - Y es 1 5 m in ut e Fr od e pa rk en 12 Y es 6 D ay Y es 12 5 m in ut e St or a T or get 3 Y es 3 H ou r N o 0 - Sci en ce P ar k 4 Y es 4 D ay Y es 3 5 m in ut e Sv alan 2 Y es 2 H ou r N o 0 - Sala 6 Y es 6 H ou r Y es 3 5 m in ut e K un gs än gen 2N o 0 - N o 0 - Bi om ed it 1 3 Y es 3 H ou r N o 0 - Bi om ed it 2 3 Y es 3 H ou r N o 0 - Go tt su nd a Cen tr um 1N o 0 - N o 0 - UAS 1 N o 0 - Y es 1 5 m in ut e Fy ri ss ko la n 10 No 0 - No 0 - Danmarkssk olan 2N o 0 - N o 0 - Å ng el st as ko la n 1 N o 0 - Y es 1 5 m in ut e

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CHAPTER 3. DATA

3.2 SMHI and STRÅNG

To get a model that works for arbitrary chosen locations one needs to find irradiation data that fits with the location, and preferably data with at least hourly resolution. In this work package, data was extracted from a model called "STRÅNG" which is financed by The Swedish meteo- rological and Hydrological Institute (SMHI) and the Swedish Radiation Safety Authority. This model is producing its data by using the mesoscale analysis system at SMHI, called "MESAN".

The "MESAN" analysis system describes the weather situation by using meteorological models which are taking account for the relevant physics/theory. These meteorological mod- els combined with interpolation of existing observations is then producing grids with a size of 11x11 km that calculates a number of meteorological parameters, such as temperature and solar irradiation [5]. Other sources that the STRÅNG model uses to produce its output parameters is ozone-fields from the European Centre for Medium-Range Weather Forecasts (ECMRWF), ice information from the oceanographic model (HIROMB) along with high res- olution limited area NWP (HIRLAM) [6].

A quality check of the results retrieved from the STRÅNG model is presented at their homepage [12]. This validation has been done by comparing the output parameters global radiation and direct radiation with real observations from 12 meteorological stations around Sweden. The validation results is presented in Table 3.2 below which presents the average error statistics for the period 1999-2009. Validation of the model is described by using the two common measurement methods "Mean Absolut Error" (MAE) and "Root mean squared error" (RMSE). Both of the methods expresses average error in the model, but have diﬀerent weight to larger or smaller errors. As seen from the validation table below, the error of the model is increasing with increased resolution.

Table 3.2: Errors of the output from the STRÅNG model for diﬀerent time horizons, compared to true values from meteorological stations.

Global radiation Direct normal radiation

Hourly MBE -0.2% -0.4 %

Hourly MAE 2.1 % 3.5 %

Hourly RMSE 30 % 57 %

Daily MBE -0.2 % 0.5%

Daily MAE 2.1 % 3.2 %

Daily RMSE 16 % 31 %

Monthly MBE 1.3 % 1.3 %

Monthly MAE 2.3 % 3.3 %

Monthly RMSE 8.9 % 14 %

Yearly <10 % <15 %

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CHAPTER 3. DATA

3.2.1 Median year estimation

Since the electricity production was supposed to be estimated for future installations of PV- modules, a median year was estimated using insolation & temperature data from SMHI and STRÅNG for years 1999 to 2014. The median year for global and direct insolation can be seen in Figure 3.2 and Figure 3.3 respectively, the median year for the temperature can be seen in Figure 3.4. The year were defined by taking the median for each hour throughout years 1999-2013.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan

Date/Time ²⁰¹⁵

0 100 200 300 400 500 600 700 800 900

Global insolation [W/m2]

Figure 3.2:

Median global insolation year constructed from data gathered by STRÅNG from 1999 to 2014.

Date/Time 2015

0 200 400 600 800 1000 1200

Direct insolation [W/m2]

Figure 3.3:

Median direct insolation year constructed from data gathered by STRÅNG from years 1999 to 2014.

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CHAPTER 3. DATA

Date/Time 2015

-10 -5 0 5 10 15 20 25

Temperature [oC]

Figure 3.4:

Median temperature year constructed from data gathered by SMHI from 1999 to 2014.

In Table 3.3 the annual total global and direct irradiance can be seen for the years 1999- 2013, the irradiances are compared to its respective median irradiance and the diﬀerence for the years 1999-2013 are determined, the RMSE for the two diﬀerent types of insolations are also calculated.

Table 3.3: Irradiance specification for the year 1999-2013

Year Annual Global Irradiance

[kW/m

²

]

Annual Direct Irradiance

[kW/m

²

]

Global Irradiance Diﬀerence

[%]

Direct Irradiance Diﬀerence

[%]

Global RMSE [%]

Direct RMSE [%]

1999 934.63 974.52 1.03 4.85 1.03 4.85

2000 971.78 991.05 2.90 3.24 2.90 3.24

2001 950.41 991.12 0.67 3.23 0.64 2.23

2002 953.72 1067.29 0.99 4.21 0.99 4.21

2003 948.71 1033.34 0.46 0.89 0.46 0.89

2004 940.87 992.33 0.37 3.11 0.37 3.11

2005 927.68 995.96 1.77 2.76 1.77 2.76

2006 946.77 1040.13 0.25 1.56 0.25 1.56

2007 931.96 1018.14 1.32 0.59 1.32 0.59

2008 943.04 1054.20 0.14 2.93 0.14 2.93

2009 941.18 1042.22 0.34 1.76 0.34 1.76

2010 933.32 994.54 1.18 2.90 1.17 2.90

2011 941.72 1026.90 0.28 0.26 0.28 0.26

2012 949.26 1052.22 0.51 2.74 0.51 2.74

2013 937.84 1014.36 0.69 0.96 0.69 0.96

The irradiance diﬀerences and RMSE were calculated with respect to the median year.

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CHAPTER 3. DATA

that the impact of the yearly irradiance variation are less than the impact of the given errors of the yearly STRÅNG data on the modelled PV-power output.

Since STRÅNG does not specify what the yearly resolution errors refers to nor specifies more exactly what the values of these might be, as they did for the other resolutions in Table 3.2, it is hard to exactly know what the impact will be on the PV-production. The error of the yearly resolution for the global and direct insolation was not taken in consideration during the design process since we wanted to build an as general model as possible; a model that did not assume any preconditioned or predefined insolation errors. The values given in Table 5.5 for the total energy production and installed power for the diﬀerent scenarios might therefore be slightly lower than what it could have been if better insolation data was used (See Figure 5.14).