Estimating beam and diffuse solar irradiance components using multiple solar irradiance meters

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UPTEC E 19011

Examensarbete 30 hp Juni 2019

Estimating beam and diffuse

solar irradiance components using multiple solar irradiance meters

Tarik Delibasic

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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

Estimating beam and diffuse solar irradiance

components using multiple solar irradiance meters

Tarik Delibasic

In recent years, different renewable energy sources have been on the rise. Among these, solar power has shown great potential in both small and big scale. Since solar irradiance is the main input for

solar power systems, it is of great importance to examine how much of the solar irradiance actually reaches a certain location, and how much of the total solar irradiance consists of direct (beam), diffuse and reflected irradiance. This is usually done with expensive measurement meters, such as pyranometers and pyrheliometers.

In this thesis, incident solar irradiance data from a cheap sensor network is analyzed, a new proposed model for estimating beam and diffuse fraction is examined and the results are compared to another estimation model, namely Erbs model.

The comparison between the two models shows high correlation for beam irradiance, regardless of weather conditions, whereas the correlation for diffuse irradiance shows a highly varying result, much dependent on the weather conditions.

It is difficult to motivate how well the proposed model is performing on a broader scale, since the study is limited to a specific area during a short period of time.

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Sammanfattning

Under det senaste decenniet har användningen av solceller för att generera förnybar elenergi ökat markant, där både stora och småskaliga anläggningar kan skådas ute i allmänheten. För att kunna producera elektricitet måste solcellerna bestrålas av den infallande solinstrålningen. Denna solintrålning kan bestå av tre olika delar, nämligen direkt, diffus och reflekterad. Eftersom det är av stor betydelse att kvan- tifiera mängden av varje del, främst för planering och optimering av solcellssystem, har dyra mätutrustningar utvecklats under åren av just denna anledning.

Det här arbetet, som utförts på Uppsala Universitet i samarbete med forskargruppen Built Environment Energy Systems Group (BEESG), har som syfte att undersöka om det är möjligt att bygga upp ett billigt sensor nätverk för att estimera två av tre exsisterande solinstrålnings komponenter, nämligen den direkta och diffusa.

Arbetet inleddes med att erhålla solinstrålningsdata från BEESG, som baserar sig på mätningar runtomkring Ångströmslaboratoriet i Uppsala under vecka i Maj 2017.

Det här data utgör grunden för alla beräkningar i detta arbete. Därefter utfördes en förstudie där solvinklar och deras relation till jorden studerades, de olika solin- trålnings komponenterna samt utforskades de existerande mätinstrumenten, pyra- nometrar och pyrheliometrar.

Efter förstudien påbörjades en utveckling av metod. Metoden bygger på att ha två, vertikalt placerade, solinstrålnings mätare monterad mot varandra, där en är vänd mot söder och den andra mot norr. Idén grunder sig på att när solen står i söder, vilket sker mitt på dagen, så kan en approximation göras att den sensor som är vänd mot norr inte kommer att utsättas för någon direkt solinstrålning utan enbart diffus och sensorn som är vänd mot söder kommer bli ett föremål för diffus, direkt och reflekterande, där den sistnämnda inte tas i beaktande.

Utifrån dessa approximationer samt med vetskapen om att två sensorerna befinner sig i varsitt plan, så kan en välkänd estimeringsmetod vid namn Hay-Davies tilläm- pas på båda så att ett ekvationsystem erhålls där både den direkta och diffusa solinstrålningen kan estimeras. För att kunna bekräfta dessa resultat så placerades en sensor horisontellt i närhet av de vertikalt monterade sensorerna, där en annan estimeringsmetod tillämpades, nämligen Erbs metod.

Vid jämförelse av de två metoderna så visar resultaten att för den direkta solinstrål- ningen så är korrelationen väldigt hög, oavsett väderförhållandena. Däremot, för den diffusa solinstrålningen så är resultatet väldigt varierande, där molniga dagar visar på en negativ korrelation och soliga dagar på en positiv korrelation, vilket indikerar på att den föreslagna metoden är känslig för varierande väderförhållanden vad gäller estimering av den diffusa solinstrålingen.

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Preface

First of all I would like to express my deepest gratitude to my supervisor during this project, Dr. Joakim Munkhammar, who came up with the idea carried out in this project and for his humble, positive and helpful attitude during this semester.

I would also like to give a special thanks to my subject reader, Prof. Dr. Joakim Widén, for his valuable inputs during this project.

Lastly, I would like to thank my parents, Halim Delibasic and Mubera Delibasic, for their support throughout my life.

Uppsala, June 2019 Tarik Delibasic

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Nomenclature

BHI Beam horizontal irradiance CSP Concentrating solar power DHI Diffuse horizontal irradiance GHI Global horizontal irradiance PV Photovoltaic

SZA Solar zenith angle W/m² Watt per square meter

WMO World Meteorological Organization WRC World Radiation Center

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List of Figures

1 An illustration of the solar angles with respect to the horizontal and tilted

surface. . . 3

2 An illustration of the Earth angles. . . 4

3 Variation in the declination angle during a year. . . 5

4 Variation between solar time and standard time during each day. . . 6

5 Variation in the SZA during two different days in Uppsala, Sweden. . . . 6

6 A plot of the Sun path for one day per month for the first half of the year in Uppsala, Sweden. . . 8

7 Beam irradiance on a tilted surface. . . 9

8 Diffuse irradiance on a tilted surface. . . 10

9 Reflected irradiance on a tilted surface. . . 11

10 Global irradiance on a tilted surface. . . 12

11 The locations of the sensors. . . 17

12 Photos from the sensor network. In (a): Hobo meters mounted back-to- back (north-south) at yellow location seen in Figure 11. In (b): Hori- zontally mounted Hobo meter at green location seen in Figure 11 (Photo: Joakim Munkhammar, 2017). . . 17

13 Plots representing obtained data with 10 seconds resolution. In (a): Sen- sor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance. . . 22

14 Plots representing obtained data with 5 minutes resolution. In (a): Sen- sor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance. . . 23

15 Plots representing obtained data with 1 hour resolution. In (a): Sensor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance. . . 23

18 Plots representing obtained data with 1 hour resolution. In (a): Sensor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance. . . 25

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21 Plots representing obtained data with 1 hour resolution. In (a): Sensor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance. . . 27 22 Plots representing obtained results with 10 seconds resolution. In (a): DHI

estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model. In (d): BHI estimated with Erbs model. . . 28 23 Plots representing obtained results with 5 minutes resolution. In (a): DHI

estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model. In (d): BHI estimated with Erbs model. . . 29 24 Plots representing obtained results with 1 hour resolution. In (a): DHI

estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model. In (d): BHI estimated with Erbs model. . . 30 25 Plots representing obtained results with 10 seconds resolution. In (a): DHI

estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model. In (d): BHI estimated with Erbs model. . . 32 28 Plots representing obtained results with 10 seconds resolution. In (a): DHI

estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model. In (d): BHI estimated with Erbs model. . . 34 31 Correlation between the proposed model and Erbs model regarding BHI. In

upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 35

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32 Correlation between the proposed model and Erbs model regarding DHI. In upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 36 33 Correlation between the proposed model and Erbs model regarding BHI. In

upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 37 34 Correlation between the proposed model and Erbs model regarding DHI. In

upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 38 35 Correlation between the proposed model and Erbs model regarding BHI. In

upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 39 36 Correlation between the proposed model and Erbs model regarding DHI. In

upper left, the histogram of proposed model. In lower right, the histogram of Erbs model. . . 39 37 In (a): Scatter plot of estimated BHI and DHI dependence using the pro-

posed model. In (b): Scatter plot of estimated BHI and DHI dependence using Erbs model. In (c): Scatter plot of BHI and DHI dependence using real measurement data from SMHI. . . 40

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1 Introduction

In recent years, solar power has been considered a major future power source to help satisfy the energy demand, resulting from phasing out gas and oil. In Sweden, a country that aims for 100 % renewable electricy production by 2040 [1, p.108] and where during 2017 almost 80 % of the total electricity production was made up by hydro and nuclear power [2], the solar power industry has grown rapidly the last decade [1, p.108-109].

With the help of photovoltaic cells (PV), usually made by silicon [3, p.26], the electromagnetic radiation that is emitted from the Sun’s surface is converted into electricity after it irradiates the PV cell, which are often connected into series that results in a PV panel, which can be seen installed in large scale next to highway roads, but also on rooftops, intended for small scale generation. With this said, the solar irradiance is the input for all solar power systems (from now only referred to as PV systems), and therefore one of the main components that needs to investigated in detail when planning a solar power system at a certain locality, meaning that one should investigate how much of the solar irradiance actually reaches chosen locality and from this conclude if it’s profitable to install it.

The total amount of solar irradiance differs depending on surfaces being irradiated, meaning that for a horizontal surface the total solar irradiance is a sum of two different irradiances, namely beam and diffuse [4, p.10]. For a tilted surface an additional component is added, which is known as reflected irradiance. The reasons for splitting up the total irradiance into these components are several. One of the main reasons is that horizontal irradiance data is often used as base when calculating irradiance on tilted surfaces. By splitting up the horizontal data into beam and diffuse irradiances, they can be converted to a tilted surface with existing estimation models [4, p.75]. Also, the beam irradiance itself is extremely important for the PV power industry, more precisely for concentrating solar power (CSP) which can only be of benefit when there is a high percentage of beam irradiance available [5].

To be able to measure the solar irradiance, well-developed and expensive equipments are typically used. These existing meters are called pyranometesr and pyrheliometers, respectively. The pyranometer has the ability to measure the total irradiance, the sum of beam and diffuse but also the ability to measure the diffuse irradiance alone. As for the pyrheliometer, it will only measure the beam component in all weather conditions [4, p.44].

Since measuring the solar irradiance is of great importance, both for companies which operates in the field of solar power and government agencies that use the information for research purpose, there is a large demand for developing a cheaper, robust and more simple system for measuring.

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1.1 Purpose and goals

The main purpose of this thesis is to examine if it is possible to construct a cheap sensor network, to log data from the incident solar irradiance, with the goal to estimate the two main components of solar irradiance, beam and diffuse, from a modified Hay-Davies model. This method will then be evaluated and compared with conventional method for conversion such as Erbs model.

1.2 Research questions

In this project, following questions have been answered:

• What are the results of the proposed model when applied to solar irradiance data?

• How well does the proposed model correlates with Erbs model?

1.3 Delimitations

In this project some delimitations have been made. To begin with, the meters that were used to build the sensor network are called "Hobo pedant meters" and are the only type of sensors that will be taken into consideration. The construction of this sensor network was made by the Built Environment Energy Systems Group (BEESG) at Uppsala University in 2017 and the related irradiance data is provided from the same and is one of two irradiance data sets that will be dealt with in this project, the other one being the extraterrestrial irradiance data generated from an online service. Furthermore, as a sensitivity analysis (apart from testing different weather conditions) three different resolutions are tested: 10 seconds, 5 minutes and 1 hour. Lastly, no economical aspects of the project will be considered.

1.4 Outline

In chapter 2, the thesis begins with explaining relevant information related to the Sun, the solar angles as well as the Earth angles, which are the foundations of the calculations.

Also, the different parts of the solar irradiance are examined, both on horizontal and tilted surfaces. Finally, previous and existing measurements meters are examined. In chapter 3, the method, data set and the proposed model are explained. In chapter 4, the results are examined. In chapter 5, the results are discussed and evaluated. Lastly, in chapter 6, conclusions regarding the thesis are found.

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2 Background

2.1 Solar angles

For humans, the Sun plays an important role. Besides being the center of our solar system, which all planets orbit around, it has a crucial role in many of the events on the Earth, whether it be about weather conditions, the survival of the human race or other organisms. Due to an internal fusion process [4, p.3], the Sun is able to emit a certain amount of energy each second in form of electromagnetic radiation, out to space. The emitted solar radiation can be divided up into three different types of radiation, namely infrared, ultraviolet and visible. Earth will receive a significant amount of this radiation, but a considerable amount of radiation that the Earth receives will be reflected back to space, while a significant part will be absorbed by the atmosphere and the rest will reach landmasses where it can be utilized. In order to understand further characteristics and behaviours of the solar radiation on Earth’s surface, it is of utmost importance to comprehend the basics of the solar angles. With the help of various solar angles (and Earth angles), such as the azimuth angle and elevation angle, the position of the Sun in the sky can be predicted for every minute of the day.

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Figure 1: An illustration of the solar angles with respect to the horizontal and tilted surface.

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Figure 2: An illustration of the Earth angles.

This valuable information is of great importance for many applications, especially in the PV industry where it is of importance to know the position and path of the Sun in order to optimize the tilt angle for a PV system, to be able to maximize the power output.

2.1.1 Declination angle

To begin with, the Sun declination angle, denoted as δ in Figure 2, is the angle between an incoming sunray and the midpoint of the Earth. Since the axis of the Earth is tilted, which contributes to the yearly seasons, the Sun declination angle will not be constant, rather it will vary between -23.45^◦≤ δ ≤ 23.45^◦[3, p.54], which can be noticed in Figure 3.

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Figure 3: Variation in the declination angle during a year.

So, when reaching its lower limit in the winter, i.e -23.45^◦, this contributes to a phenomena called the winter solstice and in the summer it will reach the upper limit where the summer solstice arise (which occurs on the 22nd of December and 1st of June, respectively).

The angle of declination is given as [6, p.31]:

δ = 23.45 sin

360284 + d 365

(1) where d is the day of the month.

2.1.2 Hour angle

The hour angle, represented as ω in Figure 2, is the rearrangement of the Sun relative to the line of longitude, i.e the meridian. Due to the Earth’s rotation around its own axis, the Sun will rearrange 15^◦each hour, the hour angle can be calculated in following manner [7, p.30-33]:

ω = 360 24

t_s

60− 12

= 15t_s

60− 12

(2) where ts is the solar time of the day given in minutes, expressed as:

t_s = t_st− 4 L_st− L_loc + E(d) (3) where t_st it the standard clock time in minutes starting from midnight, L_st being the standard meridian, L_loc the longitude of a certain locality and E_d is the equation of time, which describes the variation between the solar time and standard time for a specific day of the year, which can be seen in Figure 4 (a phenomena that occurs due to the Earth’s orbit around the Sun), given in minutes

E_d= 229.18(0.000075 + 0.001868 cos(B) − 0.032077 sin(B)

− 0.014615 cos(2B) − 0.04089 sin(2B)) (4)

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where B is defined as:

B = (d − 1)360

365. (5)

Figure 4: Variation between solar time and standard time during each day.

2.1.3 Solar zenith angle

The solar zenith angle (SZA) is the angle between the zenith and the center of the Sun and is taken into consideration for a horizontal plane, denoted as cos θ_z in Figure 1.

Figure 5: Variation in the SZA during two different days in Uppsala, Sweden.

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The SZA depends on several factors, such as the declination of the Sun (δ), the hour angle (ω), and the latitude of the location (φ), and in Figure 5 the variation of the SZA can be seen. It is given as [6, p.33]:

cos θ_z = cos φ cos δ cos ω + sin φ sin δ. (6) 2.1.4 Angle of incidence

Lastly, another important angle that needs to be taken into consideration when estimating the irradiance on tilted surfaces is the angle of incidence, marked as θ in Figure 1b. The angle of incidence is defined as the angle between the incoming sunray and the normal to the tilted plane. The angle of incidence in itself is related to other angles, just like in the case of the SZA.

Apart from the declination angle, hour angle and the latitude of the location which were encountered earlier, the angle of incidence is also dependent on the angle known as azimuth angle, denoted as γ in Figure 1. The azimuth angle being the angle on a horizontal plane between the line due south and the projection of the sun rays on the same plane, expressed in the following way [3, p.58]:

sin γ = cos δ sin ω

cos α (7)

where α is the elevation angle of the sun, in some cases also referred to as the the altitude angle, being the angle between the sun’s ray and the horizontal plane, which is demonstrated in Figure 12b. It is expressed in following way [3, p.58]:

sin α = sin δ sin φ + cos δ cos ω cos φ. (8) As mentioned earlier, with the help of these two angles the path of the Sun can be predicted for every day during a year for an optional locality. Due to this, the Sun path can be plotted in what is known as a Sun path diagram, shown in Figure 6, in order to facilitate when examining the location of the Sun.

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Figure 6: A plot of the Sun path for one day per month for the first half of the year in Uppsala, Sweden.

Having explained these angle that are of great importance when estimating solar position and other phenomenon related to the Sun, the derivation of the angle of incidence is expressed as [6, p.33]:

cos θ = sin δ sin φ cos β

− sin δ cos φ sin β cos γ + cos δ cos φ cos β cos ω + cos δ sin φ sin β cos γ cos ω + cos δ sin β sin γ sin ω.

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As one can see, for the case when the tilt angle is 0, i.e when β = 0, the solar angle of incidence is equivalent to the SZA.

2.2 Solar irradiance

When the Sun emits energy, in the form of electromagnetic radiation and this radiation strikes a surface, a process known as irradiance occurs. This irradiance can be of different type, such as beam horizontal irradiance (BHI), diffuse horizontal irradiance (DHI) and reflected irradiance. The sum of these three components makes up the global irradiance.

It is also important to point out that the global irradiance, for a horizontal surface, only consists of the beam and diffuse components, i.e the reflected component occurs if the surface that is being exposed to radiation is tilted, just like solar panels can sometimes be.

In order to calculate the different fractions of the global irradiance, both of tilted and horizontal character, several different models have been developed during the years, such as the Klucher model, Reindl model and Hay-Davies model [4, p.92-93]. Also, another conventional method of estimating the irradiance is the Erbs model that converts the global irradiance to beam and diffuse [7, p.4].

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2.2.1 Beam irradiance

The beam irradiance, also known as the direct irradiance, is one of the main components of the solar irradiance. As the name reveals, this radiation comes directly in line, i.e perpendicular, from the Sun and is not scattered before it irradiates a surface, illustrated in Figure 7. As a clear example, one could imagine a cloudy day where the sunlight falls at the atmosphere of the Earth, where it initially will be a absorption of the sunlight by different air molecules, and due to cloud coverage the sunlight will interact with the clouds and because of this a part of the light will be scattered, which is defined as the diffuse irradiance, remaining part being the beam irradiance. Also, it is worth mentioning that this only applies for a horizontal surface, meaning that for a tilted surface the reflected irradiance needs to be considered as well.

Figure 7: Beam irradiance on a tilted surface.

With the help of advanced measurements meters, called pyrheliometers, the BHI can be measured. The BHI can also be expressed (and then also estimated) with the help of several different methods that will be examined in more detail later in this report.

For now, a formula for estimating this part of the irradiance on a horizontal surface, is expressed as [3, p.97]:

I_b = I_bn× cos(θ_z) (10)

where θ_z is the SZA, which has been encountered in the discussion about the solar angles, and I_bn being the direct terrestrial intensity. Since the zenith angle can vary, this implies that the BHI is neither constant during the hour, day, month, nor year, and that the irradiance will reach its peak during a day when the Sun is in the zenith position, i.e when cos(θ_z) = 1.

Since equation (10) only applies to a horizontal surface and there can be different types of surfaces that are irradiated, such as a tilted surface which is a common way of installing a PV system in order to extract maximum solar energy as possible, which is demonstrated

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in Figure 7. In this case the beam irradiance will not be the same, one would first have to calculate an important factor, namely the ratio of total radiation on the tilted surface to the ratio horizontal surface [4, p.87]:

R = total radiation on tilted surface

total radiation on horizontal surface = cos(θ)

cos(θ_z). (11)

With the help of this factor, one can estimate the beam irradiance for a tilted surface in the following manner [3, p.97]:

I_{T ,b} = I_bR. (12)

2.2.2 Diffuse irradiance

The DHI, which was briefly discussed in previous section, is the irradiance that has been scattered in the clouds by e.g molecules before it hits a surface. Unlike beam, which originates directly from the Sun’s position in the sky, the DHI can come from anywhere in the sky, as illustrated in Figure 8, which makes it more unpredictable. Just as for the BHI, there is a meter to measure the DHI, called pyranometer. Pyranometers are usually used to measure the global horizontal irradiance (GHI), although if a shading ring that shade the direct incoming sunray is mounted on it, it can also measure the diffuse part of irradiance as well.

Figure 8: Diffuse irradiance on a tilted surface.

Also, it is possible to express and estimate the DHI (Id) in terms of GHI (Ig) and BHI (I_b):

I_d= I_g− I_b. (13)

When discussing diffuse irradiance, it is of importance to mention the different types of diffuse irradiance that exists. In short, there exists two additional types of diffuse irradiance besides the isotropic part, namely horizontal-brightening, i.e diffuse from the horizon, and circumsolar diffuse [4, p.97].

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2.2.3 Reflected irradiance

The third and last component of irradiance, that is only taken into consideration when dealing with tilted surfaces, is denoted as the reflected irradiance. In short, the sunlight that has passed through the atmosphere and has been reflected by a surface that are of non-atmospheric characteristics, such as the lawn in Figure 9.

Figure 9: Reflected irradiance on a tilted surface.

Depending on whether it is snow, the ground or the lawn the light is being reflected off is directly linked to a factor known as the albedo factor, denoted as ρ, which determines how much will be reflected. A high albedo results in high reflection, and a low albedo will result in a low reflection. A table for typical albedo factors of different chosen surfaces is shown in Table 1.

Surface Albedo, ρ Oceans 0.05 - 0.1 Asphalt 0.05 - 0.2 Trees 0.15 - 0.18 Grass 0.25 - 0.3

Ice 0.3 - 0.5 Old snow 0.65 - 0.81 Fresh snow 0.81 - 0.88

Table 1: Albedo values of different surfaces [8].

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Generally speaking, the reflected irradiance doesn’t contribute as much as beam and diffuse to the global irradiance, although as one can see in table the reflected component can increase drastically depending on the season of the year, for example during the winter when there is alot of fresh snow on the ground the reflected irradiance will be higher compared to a summer day when there is grass on the same surface.

2.2.4 Global irradiance

The global irradiance (Ig), as mentioned earlier and also demonstrated in Figure 10, is the sum of all three irradiance components for a tilted surface, and the beam (I_b) and diffuse (I_d) components for a horizontal surface:

I_g = I_b+ I_d (14)

and for a tilted surface, the reflected irradiance (Iref) is included:

I_T = I_b + I_d+ I_ref. (15)

Figure 10: Global irradiance on a tilted surface.

The global irradiance can change due to seasonable reasons, but it can also change hourly, daily and monthly, which can have a direct impact on e.g PV systems where the global irradiance plays a crucial role for the output power, making the PV system installations dependent on geographical locations, defined by the coordinates longitude and latitude.

2.3 Pyrheliometer

In order to retrieve valuable information about the BHI, an advanced and well-developed meters are used, called the pyrheliometers, which has been briefly encountered in earlier sections. The World Meteorological Organization (WMO) has set standards for the

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pyrheliometers, due to the importance of characterizing the accurate irradiance and its possible impact on the climate.

The pyrheliometers can be placed in two different categories; primary standard and secondary standard. Pyrheliometers that are placed in the first category needs to fulfill certain criteria which, among other things, includes high measurement accuracy, sensitivity and stability to name a few. In the second category, called secondary standard, pyrheliometers that have relatively high accuracy but doesn’t fulfill requirements to be classified as primary standard. These pyrheliometers also have their calibration determined based on the standards set by the primary pyrheliometers [9, p.228-231]. In conventional design, to be able to work properly and log quality data, the pyrheliometer needs to face the Sun directly and constantly follow its motion with the help of a tracker. Throughout history several different pyrheliometers have been developed and continuously improved, a summary of them will follow.

2.3.1 Abbot silver-disc pyrheliometer

The silver-disc pyrheliometer that was constructed by Abbot in the beginning of last century [4, p.45], consists of a silver disc that acts as the sensor of the system with the side that is exposed to radiation being blackened, to absorb better. Furthermore, this silver disc is designed with a hole where a thermometer is placed, and is placed in a copper cylinder, which in turn is encapsulated in a wooden box to protect it. On top of this pyrheliometer, a shutter is installed and alternates between two modes; admitting radiation and shading the silver disc. The thermometer measures the temperature of the silver disc when being exposed to radiation and when shaded, and uses the changes in the temperature to calculate the radiation [4, p.45].

2.3.2 Ångström compensation pyrheliometer

Another type of meter used to measure the irradiance is the "Ångström compensation pyrheliometer" that was constructed by Knut Ångström in the end of the 19th century [10, p.343]. This pyrheliometer is build up with the help of two identical rectangular manganin strips, attached to a thermocouple which measures the temperature of each strip. Manganin being an alloy of three different elements, namely copper, nickel and manganese. These strips are based on the end of a tube and are blackened just as the silver disc in previous set up.

In order to be able to retrieve the information about the irradiance, these strips are ranged in a way that a shutter on top of the tube can expose one of the strips to sunlight and shades the other one simultaneously. The strip that is shaded gets heated by an electrical current in order to reach the same temperature as the strip that is exposed to sunlight, and when the temperature is the same for the strips, the solar radiation that is absorbed by the non shaded strips must equal the power used the to heat up the shaded strip [10, p.343-344].

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2.3.3 CHP1 pyrheliometer

A new technology that has emerged in recent years is the CPH1 pyrheliometer, developed and designed by the company Kipp&Zonen, and seen as a high quality pyrheliometer [11, p.5]. It is designed as a tube, with a window at the front through which the sunbeam will be transmitted before being absorbed by a thermopile which acts as a sensor.

The thermopile is structured with the help of several thermocouples connected in series, which can convert the thermal energy that occurs due to temperature differences between the thermocouples when the radiation falls on them to a electrical output signal, i.e a voltage measurement. In order to actually obtain the irradiance, the output signal is divided by the pyrheliometers sensitivity factor [11, p.8].

2.4 Pyranometer

The pyranometer is used to measure the global irradiance, but can also be designed to measure the diffuse component alone, if direct sunlight is blocked out, which can be done by using a static shading ring, which will be discussed in more detail in Section 2.4.2.

Unlike for the pyrheliometers, there are no "primary standard" pyranometers that can be used to calibrate the other pyranometers rather all of these instruments are calibrated by reference to another measurement instrument, such as the standard for pyrheliometers.

Although, manufactured pyranometers can be of different qualities when it comes to accuracy, response time and stability which has also led to the fact that they have also been categorized by the WMO in following manner; high quality, good quality and moderate quality [9, p.233-237].

In order to measure the global irradiance, both for horizontal and tilted surfaces, the pyranometer needs to be positioned in that manner as well. Since PV systems often can be seen installed in tilted positions in order to maximize their output power, the pyranometer is installed at the same inclined angle as the PV cells. Furthermore, to be able to measure the diffuse component alone same pyranometer can be used, but with some extra additions to shade off the beam irradiance. Lastly, since the reflected irradiance often is considered as a form of diffuse irradiance and is of utmost importance when estimating the global irradiance on a tilted plane, special pyranometer setups, called albedometers, have been constructed so that albedo factor can be measured.

2.4.1 Eppley 180^◦ pyranometer

One of the older and most common pyranometer that has been in use (is no longer produced) is the Eppley 180^◦pyranometer, designed and produced by the Eppley Laboratory [4, p.48]. In order to measure the irradiance, a sensor which consisted of two silver ring that are concentric, where the outer ring is coated with magnesium-oxide which is white in nature, while the inner ring is of opposite character being coated in Parson’s black.

Since the two silver rings absorbed the irradiance differently (the inner ring had a higher absorption and the outer a lower, due to their characterestics) [4, p.48-49] the temper-

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ature between the two would also differ and this difference was detected by a thermopile which consisted of two different alloys, namely platinum-rhodium and gold-palladium, connected in series. This measure was then treated as obtained irradiance [12, p.32].

This type of pyranometer was made in two different models, where the difference was in how many junctions a thermopile had, either 50-junctions or 10-junctions, a difference that had an impact on the sensitivity, resistance and time response [13, p.103].

2.4.2 CMP 6 pyranometer

The CMP 6 pyranometer is a recent technology and one of six models in the so called

"CMP series", developed by Kipp&Zonen [14, p.10]. All six models are designed to measure the global irradiance on a horizontal surface and they all rely on the same working principle, although they can differ in the design of the sensor that detects the radiation.

In particular, the CMP 6, apart from its body structure, is designed with an outer and an inner glass dome that can detect incoming sunlight from all different angles, since the diffuse component of the irradiance is scattered. Through this dome, irradiance will be transmitted and absorbed by a sensor that has the same working principle as the CHP1 pyrheliometer.

In order to only measure the diffuse component of the total irradiance, a static shading ring can be mounted to block the beam irradiance from the glass dome. Since the Sun is following a predictable path and the ring that is mounted above the pyranometer is static, this way to screen of the direct sunlight will require a frequent manual movement of the ring in relation to the Sun’s path.

To avoid doing this readjustment, an alternative way of shading the glass dome from the direct sunlight is available. This shading technique uses a dual-axis solar tracker that can follow the Sun’s movement based on a calculations with the of time and locality. In order to shade off the pyranometer from the Sun, a ball that is spherical in shape is mounted on a stand to cover the glass dome completely [14, p.18].

2.4.3 CMA pyranometer

In this series, called the CMA series developed and constructed by Kipp&Zonen which contains two meters, CMA 6 and CMA 11 [14, p.10]. With these types of meters, widely known as albedometers, it is possible to measure both the global irradiance and also the albedo factor of a surface. What makes this possible, is that this setup contains two CMA albedometers mounted back-to-back, both of them with an individual detector. The upper measures incoming global solar radiation and the lower measures solar radiation reflected from the surface below. When the two signal outputs have been converted to irradiance (W/m²), the albedofactor can be estimated as the ratio of the two irradiances [14, p.17].

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3 Methodology and data

In order to evaluate if it is possible to estimate the beam and diffuse components of irradiance from low-cost sensors, several aspects needs to be taken into account. As mentioned earlier in Section 2.2, there exists several models that can be used to estimate the irradiances. In this project, two different types of models are used, namely a decomposition model and a modified transposition.

In short, a decomposition model relies on available GHI data and usually use the clearness index and diffuse fraction in order to estimate the two remaining components of solar irradiance, while the transposition models needs two data sets, usually GHI and DHI, in order to calculate the remaining component [15]. In this project, Erbs model (decomposition model) and a modified Hay-Davies model (transposition model) are chosen as estimation models, both of them will be examined in more detail later in this section.

Furthermore, a data set that is based on several days of logging the incident solar irradiance received from the sensors and an additional data set that is generated online. This, together with already discussed solar angles in Section 2.1, constitutes the foundations of the calculations carried out in the software called MATLAB. The results of this are examined and evaluated to see if the modified transposition model correlates well with the decomposition model or not.

3.1 HOBO Pendant Temperature/Light Data Logger

^R

The HOBO Pendant Temperature/Light Data Logger (from now on only refered to asR

HOBO meter) is a device that is able to record light levels and temperature (indoor, out- door and underwater), designed and constructed by Onset Computer Corporation [16].

There exist two different models for these types of measurements, namely 8K model and 64K model. Both of these are based on the same working principle, the main difference is that the 8K model can store 6500 measurements of 10-bit readings while the latter can store 8 times more, i.e 52000 measurements. It is also important to highlight the fact that the HOBO meters, due to their design and sensitivity, have higher resolution for lower intensity data than for higher [17, p.3], which also results in more accurate estimations for those parts of the day.

In order to log the light intensity, the HOBO meter needs to be configured. This is done in an associated software called Hoboware. In Hoboware, the logging interval, among other things, are determined before the meter is ready for use. When put into use, the Hobo meter provides measurements on light intensity, in the unit of Lux [17, p.1]. Lux (or lumens/m²) that are the units used to measure the amount of light in a certain area, in the range of 0 to 320 000 Lux. When the event of logging is over the HOBO meter is again plugged into a computer and the measurements can be visualized in Hoboware.

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3.2 The sensor network setup

With the aim of estimating both the beam and diffuse irradiances from low-cost sensors, a network of the same was built up in 2017 during one week in May (22-29) on and around Ångströmslaboratoriet (59^◦N, 17^◦E). A figure of the locations of the meters can be seen in Figure 11.

Figure 11: The locations of the sensors.

(a) (b)

Figure 12: Photos from the sensor network. In (a): Hobo meters mounted back-to-back (north-south) at yellow location seen in Figure 11. In (b): Horizontally mounted Hobo meter at green location seen in Figure 11 (Photo: Joakim Munkhammar, 2017).

At each of these locations, except for the green one, two HOBO meters were mounted back-to-back, one oriented to north and the other one to south. At the green spot in

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Figure 11, a HOBO meter was mounted horizontally, the part of network that is examined in this project is seen in Figure 12. The reason for this kind of setup is to be able to use the estimation models for beam and diffuse calculations.

3.3 Erbs model

As mentioned previously, different types of models can be used for estimation for irradiance components. One of the more conventional methods of doing this is using Erbs model, which is shown to be among the better models for estimation [18, p.1-7]. Since being a decomposition model, it uses the clearness index (k_t) which is the ratio between GHI and extraterrestrial irradiance and diffuse fraction (k_d) for estimating the irradiance components [7, p.1-8]. The relation between the two is divided into three different in- tervals:

k_d= 1 − 0.09k_t for k_t ≤ 0.22

k_d= 0.9511 − 0.1604k_t+ 4.388k²_t − 16.638k_t³+ 12.336k_t⁴ for 0.22 < k_t≤ 0.80 k_d= 0.165 for k_t> 0.80.

Next, the beam and diffuse irradiance components are expressed as:

I_b = 1 − k_dI_g (16)

I_d= k_dI_g. (17)

The Erbs model was derived and based on data from four different stations in North America and one in Australia, which means that this model is not fitted for all locations on Earth [4, p.73-75], but still widely used as it is.

3.4 Hay-Davies model

Another often used estimation model is the Hay-Davies model which is considered a transposition model. What stands out particularly for this model is the way it treats the diffuse part of irradiance. As previously mentioned in Section 2.2.2, the diffuse irradiance can be of different character. In the Hay-Davies model, the horizontal-brightening is completely ignored as a part of the to total diffuse irradiance, and instead argues that the same is the sum of the two remaining components [4, p.92], isotropic and circumsolar, expressed in following manner:

Id,isotropic = Id

h

(1 − Ai)

1 + cosβ 2

i

(18) and the circumsolar part defined as:

Id,circumsolar = I_d(A_iR). (19)

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In equations (18) and (19) a new variable is introduced, namely Ai, which is the anisotropy index that describes how much of the diffuse irradiance is circumsolar, and it is directly linked to the beam irradiance (I_b) in following manner:

A_i = I_b

I₀ (20)

where I₀ is the extraterrestrial irradiance. Looking at equation (20), one can notice that during a cloudy day, when there is no beam irradiance, the diffuse irradiance will be completely isotropic.

Furthermore, Hay-Davies takes the reflected irradiance into consideration as well. By knowing the value of the albedo factor (ρ) that was discussed in Section 2.2.3, the diffuse (I_d) as well as the beam irradiance (I_b), the reflected fraction of the total irradiance can be expressed as follows:

I_ref = (I_d+ I_b)ρ1 − cosβ 2

. (21)

The β constant in equations (18) and (21) is the horizontal tilt angle, the angle between the horizontal surface and the tilted surface.

Thus, the global irradiance on a tilted surface according to Hay-Davies is given as:

IT = IbR + Id

h

(1 − Ai)

1 + cosβ 2

+ AiR i

+ (Id+ Ib)ρ

1 − cosβ 2

. (22)

3.5 Combined sensor estimation of beam and diffuse using the Hay-Davies model

To be able to estimate beam and diffuse components of the solar irradiance with the Hay- Davies model, two irradiances needs to be known. In order to obtain that data expensive measurement meters are required, which has been discussed earlier. Using two vertically mounted sensors (north-south), discussed in Section 3.2, that are in different planes, the Hay-Davies equation can be applied to both of them, although with some assumptions and modifications. Given the fact that the sensor 1, that is oriented south, has a tilt angle that corresponds to β₁ = 90^◦, and likewise for β₂ regarding the second sensor oriented north, also assuming that reflected irradiance is minimal and can therefore be omitted, provides an initial simplification of the Hay-Davies model in following manner:







I_{T 1}= I_bR₁+ I_dh

(1 − A_i) ¹₂i I_{T 2}= I_bR₂+ I_dh

(1 − A_i) ¹₂i (23)

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Furthermore, since the location of observation is in the Northern Hemisphere during the summer period of the year, it means that the Sun rises in the northeast and sets in the northwest. Having this in mind, and assuming that the Sun is located within +/ − 90^◦ from south in the above mentioned orientation, will result in that the sensor oriented north will not be exposed to any beam irradiance, contributing to I_b = 0. However, this is not true throughout the day, rather when the Sun is located south which occurs during midday. This means that during morning and evening hours the sensor oriented north will be exposed to beam irradiance, these hours are then also excluded in the analysis. In order not to be exposed to beam irradiance during the day, the sensor should be parallel to the path of the Sun. Also, the diffuse irradiance is assumed to be completely isotropic, meaning that A_i = 0. This gives a second simplification of Hay-Davies as follows:

(IT 1= IbR1+^I₂^d IT 2= ^I₂^d.

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(I_b = ^I^{T 1}_R^−I^{T 2}

1

I_d= 2I_{T 2.}

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The main task is then to calculate the beam and diffuse irradiance at each and every time- step. The calculations are done for different resolutions, namely 10 seconds, 5 minutes and 1 hour, with the help of solar angles that were discussed in Section 2.1.

3.6 The data set

The data sets that are used in this project are of different character, and can be divided into three different categories. The first category is the data that is received from the three different HOBO meters, namely the one that is oriented to north, to south and lastly the horizontally mounted one, all three located at the same place. The HOBO meters that are used were preinstalled in the HOBO software program to log data every 10 seconds. Since the HOBO meters provides measurements in the unit of Lux, it would reasonable to approximate the obtained data as irradiance scaled with a factor. This factor was determined to be 193.69 by comparing data output under laboratory conditions with irradiance of 1000 W/m², conducted at the Ångström laboratory in 2017. Thus, to obtain irradiance, the data sets were divided by a factor of 193.69.

The second category is the data from the extraterrestrial irradiance, which was needed in the case of the Erbs model. This data was generated from a irradiation service online [19]. The lowest time-step for the measurements that were available was 1 minute, which was chosen. Since MATLAB requires the same number of elements in the vectors when performing mathematical methods the extraterrestrial irradiance data set was repeated for 6 times with the help of the function repelem.

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Furthermore, the third category is the data based on radiometer measurements of GHI for one year obtained from the Swedish Meteorological and Hydrological Institute (SMHI) for Norrköping, Sweden (58^◦N, 16^◦E) during 2008 [20]. This data set will be used in order to compare the two used models, the modified Hay-Davies and Erbs, in order to see which of the models are most similar to real measurement data.

Furthermore, since one of the main objectives is to see how well the proposed model in this thesis correlates with Erbs model, a correlation analysis is conducted using the function corrcoef in Matlab, which by default calculates the Pearson correlation coefficient in Matlab [21]. In short, the Pearson corrleation indicates how strong the linear relationship is between two data sets, in this case the proposed model and Erbs. Also, both of these models will be compared to the real measurement data from Norrköping in order to observe which of the two models is most similar to it.

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4 Results

4.1 Representation of the data

In this section, the obtained measurements from the three mounted sensors at the yellow and green locations in Figure 12b will be presented and then processed as described in Section 3.6. Since the main idea is to test the method described in Section 3.5 during different weather conditions and for various resolutions as a sensitivity analysis, the following days were chosen for comparison and discussion: May 23, 24 and 28. May 23 corresponds well with a highly cloudy day, May 24 as a clear day and May 28 as a partly cloudy day. Also, the extraterrestrial data is presented in this section. The data sets are presented for the three different resolutions: 10 seconds, 5 minutes and 1 hour.

4.1.1 Data obtained during May 23

The representation of obtained data sets demonstrates what kind of weather prevailed during the day of observation. It is quite clear that the second day of observation, which is demonstrated in Figures 13, 14 and 15 during the midday, had a varied weather with a lot of peaks due to sunshine but also dips due to shadings can be frequently noticed.

Figure 13: Plots representing obtained data with 10 seconds resolution. In (a): Sensor oriented north.

In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance.

Looking at subplot (c) in Figure 13 an interesting phenomena can be noticed. It can be seen that the obtained irradiance peaks above the extraterrestrial irradiance for a while, which is likely due to so-called cloud enhancement, which means that the irradiance at a surface on Earth can peak during cloudy conditions for a short amount of time since the

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clouds have the ability to "boost" the incoming sunray.

Figure 14: Plots representing obtained data with 5 minutes resolution. In (a): Sensor oriented north.

Figure 15: Plots representing obtained data with 1 hour resolution. In (a): Sensor oriented north. In (b): Sensor oriented south. In (c): Horizontally mounted sensor. In (d): Generated extraterrestrial irradiance.

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Lastly, it can be noticed in subplot (a) in Figures 13 and 14 that the irradiance peaks high in the early morning hours. This occurs due to the path of the Sun, since it rises in the north-east, the sensor facing north will be exposed to sunlight. Also, there is possibility that this way of mounting gives an uncertainty of a few degrees.

During this day of observation, the weather conditions were mostly clear throughout the day except for some shadings of the Sun that seemed to occur in the late afternoon, observed in subplot (b) in Figures 16 and 17. Furthermore, in the same subplot the HOBO meter’s lower resolution for higher intensity values is displayed during the midday, which also was briefly discussed in Section 3.1.

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Lastly, a common scenario occurs during this day regarding the sensor facing north, where the irradiance peaks high during the early morning hours, seen in subplot (a) in Figure 18.

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One of the last days of observation, May 28, offered a partly sunny day where around midday some clouds appeared that contributes to shadings during the afternoon, which is seen in subplots (b) and (c) in Figures 19 and 20.

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It can also be noticed during this day in Figure 21 that the irradiance peaks really high on the sensor facing north, which confirms the assumption that sensors have limitations for small solar angles and that the mounting gives an uncertainty of few degrees.

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4.2 Estimated solar irradiance fractions

In this section, the results for beam and diffuse from the two different estimation models are presented. As in the previous section, the data for the whole week will not be shown nor compared, rather the results from May 23, 24 and 28 during the observation week that are chosen for comparison and discussion. This part also presents the results for the three different resolutions; 10 seconds, 5 minutes and 1 hour.

4.2.1 Estimations during May 23

During this partly cloudy day some interesting observations can be made. Starting of with BHI that is estimated with the proposed model, it can be noticed in subplot (b) in Figures 22 and 23 that during early morning hours a dip occurs resulting in a negative irradiance. Interesting enough, this occurs at the same time as for the peak in the data for the sensor oriented north, although it is not likely that it is related to the limitation of the sensors for small solar angles, rather it depends on the model and the assumption that the Sun is located south.

Figure 22: Plots representing obtained results with 10 seconds resolution. In (a): DHI estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model.

In (d): BHI estimated with Erbs model.

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Figure 23: Plots representing obtained results with 5 minutes resolution. In (a): DHI estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model.

The comparison between the results of the two models and how they vary throughout the day are seen in Figures 23 and 24. It can be noticed in subplot (a) in Figure 23 that the result for DHI using the proposed model is slightly higher than for Erbs model during midday, which then leads to a higher BHI using the Erbs model, seen in subplot (d). In Figure 24, when comparing BHI result, it can be seen that a dip occurs at the same time, most probably due to shading.

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Figure 24: Plots representing obtained results with 1 hour resolution. In (a): DHI estimated with proposed model. In (b): BHI estimated with proposed model. In (c): DHI estimated with Erbs model.

During this sunny day, similar observations can be done as for the previous day. In the case of the estimated BHI using the proposed model, it can be noticed in Figures 25 and 26 that BHI for Erbs is slightly higher than for the proposed model, and it can also be seen that during midday DHI is higher for the proposed model than for the proposed model, although it is of importance to mention that the circumsolar diffuse that follows the beam irradiance is omitted in this model, meaning that DHI most probably would be slightly higher, since it is a mostly sunny day.

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It can also be noticed in subplot (b) in Figure 27 that a dip occurs at the same time as in the previous day, which strengthen the theory about the disadvantages with the proposed model.

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Also, it can be noticed that different resolutions can imply somewhat different results during the same day. A clear example of this can be seen in subplot (d) in Figure 27 when compared to subplot (d) in Figures 26 and 25. In the last two mentioned, one can observe that during early evening hours a dip occurs, most probably due to shadings of the Sun. However, this is not observed in Figure 27. This implies that the resolution plays an important role when estimating solar irradiance, especially in northern climates where the weather can have a high variations during short periods.

This day corresponds to a partly cloudy day, and the results are similar to the previous observation days. The estimated DHI using the proposed model is higher than for the case of Erbs model, and BHI using Erbs model is higher than for the proposed model, this best demonstrated in Figures 28 and 29, although it can be noticed in subplot (d) in Figure 30 that during the evening BHI peaks slightly, a phenomenon that is not noticeable when using the proposed model for estimating BHI.

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Lastly, a good indication of how close the results for beam and diffuse of the two compared models are, the mean difference of the two can be studied during different days and different resolutions, since one of the assumptions for the model is that the Sun is located south this evaluation will only be made during 10:00 - 15:00. The mean difference for beam is presented in Table 2 and the results regarding diffuse is found in Table 3.

Resolutions May 23 May 24 May 28 10 seconds 31.85 169.25 132.26

5 minutes 27.17 169.37 142.10 1 hour 173.14 193.03 84.82

Table 2: Mean difference between Erbs model and the proposed model regarding beam.

Resolutions May 23 May 24 May 28 10 seconds -37.98 -104.39 -103.84

5 minutes -30.7672 -104.06 -106.90 1 hour -120.02 -103.6204 -51.88

Table 3: Mean difference between Erbs model and the proposed model regarding diffuse.

When examining the results for beam in Table 2 it can be noticed that mean difference for the resolutions of 10 seconds and 5 minutes are quite close to each other, however during the cloudy days the mean difference for 1 hour resolution is quite different from 10 seconds and 5 minutes resolution, but looking at May 24 they are quite similar. In Table

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3 similar observations can be seen, the mean difference for 10 seconds and 5 minutes resolution doesn’t differ a lot when compared, although the results for 1 hour resolution deviates from them during a lot more during cloudy days than for the sunny day.

4.3 Correlations between the proposed model and Erbs model

In this part the correlations between the two compared models are presented. In general, the correlation value can vary between -1 and 1, where a negative correlation describes how two variables move in opposite directions, and a positive correlation means that two variables move in the same direction, at -1 an ideal negative correlation occurs, at 0 no correlation at all, and at 1 an ideal positive correlation occur. Since the results for both of the models are the same during the night, which doesn’t give a fair analysis of the correlations, the hours during the night are therefor cut-off from the data set and instead the correlations are studied between 10.00 - 15.00 during observation the days, this is also due to the assumption that the Sun is located south, which occurs during the midday.

4.3.1 Correlations during May 23

In Figure 31 the correlations between the two models regarding BHI can be seen. The histograms reveals the shapes of distributions for the estimated BHI during the day, both being skewed to the right, indicating a high positive correlation, which is also confirmed by looking at the scatter plots.

Figure 31: Correlation between the proposed model and Erbs model regarding BHI. In upper left, the histogram of proposed model. In lower right, the histogram of Erbs model.

In Figure 32, the correlations between the two models regarding DHI can be noticed.

Compared to the histograms seen in Figure 31 that had a similar distribution, it can