Optimized management of lighting conditions in spaces with multiple users

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Optimized management of lighting conditions in spaces

with multiple users

João Pedro Pires Martins

Thesis to obtain the Master of Science Degree in

Engineering Physics

Supervisors:

Prof. Carlos Augusto Santos Silva

Prof. Luís Filipe Moreira Mendes

Examination Committee

Chairperson: Prof.

a

Maria Joana Patrício Gonçalves de Sá

Supervisor: Prof. Carlos Augusto Santos Silva

Member of the Committee: Prof. João Carlos Carvalho de Sá Seixas

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Acknowledgments

Em primeiro lugar gostaria de agradecer ao Professor Carlos Silva, pelas ideias, orientação e dis-cussões que tivemos. Serviços de Energia foi a cadeira que tive que me motivou para explorar esta área de conhecimento, pois foi das cadeiras que mais apreciei ao longo deste percurso académico. Sempre teve disponibilidade para me ajudar neste projecto.

Quero também agradecer aos meus amigos e colegas, em especial o Rúben, o Zé, o João Vargas, o Daniel, o Jorge, pelas parvoíces e conversas que tivemos. Pelos testes e exames partilhados, pelas frustrações comuns, por terem tornado este percurso académico mais fácil. Obrigado pelo apoio e motivação.

Quero agradecer à Ana, pela paciência que tem tido para comigo, pela força que me deu quando mais precisei, por ter estado sempre ao meu lado.

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Resumo

O consumo energético tem um peso cada vez maior na sociedade. Utilizar de forma responsável é uma preocupação devido ao consumo de energias fósseis. O maior consumo energético na sociedade provém de edifícios, e dentro destes, uma parte significativa provém da iluminação. Como tal, um passo para reduzir o consumo energético é aproveitar a luz solar. Além de providenciar iluminação, permite também reduzir o consumo de sistemas de ar condicionado, pois há menos calor gerado devido aos ganhos internos das lâmpadas durante o verão; no inverno, a luz solar permite o aquecimento das divisões, diminuindo igualmente o consumo de sistemas de ar condicionado e consequentemente o consumo eléctrico. Um espaço de trabalho bem iluminado pode aumentar a produtividade dos diversos utilizadores que estejam no espaço a trabalhar, contudo, é necessário ter em atenção a incidência directa de luz solar, causando desconforto e encadeamento. Assim surge o desafio de utilizar a luz solar de forma a criar condições favoráveis ao trabalho, sem causar encadeamento.

Este trabalho passa então por conseguir medir eficazmente a iluminação e conseguir gerir o controlo de persianas e iluminação eléctrica para fornecer um ambiente propício para bom rendimento dos utilizadores. Foi também feito um estudo sobre a iluminância ao longo do dia para compreender o seu comportamento e distribuição. Por fim, após a medição de iluminância determina-se se é necessário utilizar as persianas para diminuir ou subir a iluminância ao longo da sala, ou utilizar a iluminação eléctrica caso a iluminância seja demasiado baixa.

Palavras-chave:

Controlo automático, consumo energético, modelo de iluminância, opti-mização de iluminância.

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Abstract

Electrical consumption has an increasing weight in society. Using responsibly is a concern due to consumption of fossil fuels. The biggest energetic consumption derives from buildings, and from these, a significant consumption is from electrical lighting. As such, a step to reduce electrical consumption is to use sunlight. Besides providing illumination to the room in question, it also allows the reduction of use of cooling systems, as there is less heat generated through electrical lighting due to heat gains in summer; in winter, the sunlight heats the surrounding space, reducing likewise the use of cooling systems and therefore the electrical consumption. Having a space well lit can increase the productivity of several users that are working in the space, however, it is necessary to take into account direct sunlight hitting the users, causing discomfort and glare. Rises then a problem, in which is necessary to use sunlight, whenever possible, that provides favorable conditions to work, without glare.

This work has to measure efficiently the illumination and manage the control of the blinds and elec-trical lighting to provide a good working environment for the users. It was also made a study about the illuminance throughout the day to understand it’s behavior and distribution. Finally, after the measure of illuminance, it is determined if it is necessary the use of the blinds to lower or rise the illuminance through the room, or use the electrical lighting in case the illuminance is not high enough.

Keywords:

Automatic control, electrical consumption, illuminance model, illuminance optimiza-tion.

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List of Tables

2.1 Brightness coefficients for Perez anisotropic sky . . . 14

2.2 Best sun radiation models to different sky conditions . . . 15

2.3 Effects of different setting for various sensor types . . . 17

2.4 Reference illuminance values for a classroom . . . 21

3.1 Parameters obtained for the fit between sensors . . . 27

4.1 Relation between radiation and illuminance . . . 32

4.2 Prediction using different ratios . . . 33

4.3 Prediction of illuminance for blinds completely open during morning . . . 41

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List of Figures

1.1 Energy consumption in Portugal and EU-28 in 2014 . . . 2

1.2 Energy prediction in buildings in USA for 2015 . . . 3

1.3 Electromagnetic spectrum . . . 4

1.4 Representation of law of reflection . . . 4

1.5 Representation of light transmission . . . 5

1.6 Representation of Snell’s law of reflection . . . 6

1.7 Representation of one steradian . . . 8

1.8 Generic luminous intensity over one steradian . . . 9

1.9 Generic luminous flux . . . 9

1.10 Representation of illuminance and luminance . . . 9

2.1 Horizontal and vertical illuminance measured during summer . . . 11

2.2 Horizontal and vertical illuminance measured during winter . . . 12

2.3 Schematic of open and closed loop systems . . . 16

2.4 Illuminance measured with manual and automatic control . . . 19

2.5 Illuminance frequency with manual and automatic control . . . 19

3.1 Representation of algorithm proposed . . . 23

3.2 Characteristic of the light meter . . . 26

3.3 Relation between sensors . . . 26

3.4 Representation of interest points . . . 28

3.5 Illuminance measurements throughout the room . . . 28

3.6 Illuminance measurements throughout the room with log scale . . . 29

3.7 Representation of the algorithm for electrical lighting . . . 30

3.8 Representation of the position of the lamps . . . 30

4.1 Comparison of the different ratios . . . 34

4.2 Window’s transmittance expected in the classroom . . . 34

4.3 Transmittance setup in the classroom . . . 35

4.4 Transmittance measured in the classroom . . . 36

4.5 Distribution of illuminance provided by natural lighting . . . 37

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4.7 Representation of the lamps using configurations “L4” and “L4+L2” . . . 38

4.8 Representation of the lamps using configurations “L4t+L3t” and “L4t+L2+L3t” . . . 39

4.9 Impact of each lamps and configuration . . . 39

4.10 Representation of the algorithm used . . . 40

4.11 Prediction of illuminance for blinds completely open during morning . . . 41

4.12 Prediction of illuminance and it’s correction using blinds . . . 42

4.13 Prediction of illuminance and it’s correction using lamp L4 . . . 43

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Nomenclature

Greek symbols

αs Solar altitude angle [◦]

β Slope [◦]

δ Declination of the sun [◦_]

γ Surface azimuth angle [◦_]

Ω Solid angle [sr] ω Hour angle [◦] φ Latitude [◦_] φL Luminous flux [lm] ρ Reflectance τ Transmittance

θ1 Incident angle of a beam [◦]

θ₁0 Reflected angle of a beam [◦] θ2 Refracted angle of a beam [◦]

θz Zenith angle [◦]

Roman symbols

F1 Circumsolar brightness coefficient

F2 Horizontal brightness coefficient

f[1,2],[1,2,3] Pèrez brightness coefficient

Fc-g View factor surface to ground

Fc-s View factor surface to sky

Ib Beam radiation

Id Diffuse radiation

IT Total radiation

Li Switch that controls lamp i

n Refractive index of the material nday Number of day

c Speed of light in vacuum [m/s] E Illuminance [lx]

I Luminous intensity [cd] L Luminance [cd/m2_]

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Chapter 1

Introduction

1.1 Background

Interior lighting in space offices accounts for approximately 25 − 35% of electricity used in buildings. Using daylight could reduce electrical consumption, and may help creating a better indoor environment. A higher indoor environment may increase visual comfort and rise the productivity of office users, and may reduce the need to use cooling systems, because there are less heat generated through electric lighting (usually called internal gains). All these factors help to reduce carbon footprint, which is a key point in today’s society [1, 2].

However, in an office space, it is also important to take into account glare and direct sunlight, which causes visual discomfort to the users. To avoid these issues, shading devices are a necessary solution. These devices can block or allow direct sunlight, depending on the season and hour, block or enable solar gains (during cooling season, it is necessary to block direct sunlight to reduce the load on cooling systems, while in heating season, it is necessary to allow direct sunlight and thus to have solar gains, which in turn reduce the load in heating systems), can diffuse direct sunlight from clear skies (not causing visual discomfort) or transmit direct sunlight in overcast days [3, 4, 5]. There are two ways to control these shading devices: with manual or automatic control. Automatic control is a more attractive option, as it can monitor and control several devices at the same time, whatever is the space of the office, while with manual control it is only possible to control one system at the time, and it may not be optimal.

When natural lighting is not enough to ensure visual comfort, it is necessary to use artificial lighting systems. These can also be manually or automatically controlled. Automatic controlled lighting systems can substantially reduce the energy consumption on an office space using different methods. These systems are divided in three types: timers, daylight linked controls, and occupancy based controls. As the name suggests, timers turn light on/off during a specific time. Daylight controls, besides controlling on and off, can also regulate the dimming of lights, taking as input the illuminance of indoor lighting. Occupancy based controls can control lights depending if occupancy sensors detect someone [2].

As such, knowing how to control shading devices and artificial lighting systems, and thus obtaining energetic savings becomes of utmost importance. This document will provide an overview of how to

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control lighting systems (shading, artificial, etc) and how it impacts the illuminance measured, and the control made to guarantee that the illuminance in a given room is always within the comfort range for its users.

1.2 Energy demand overview

When analyzing the energy consumption in 2014, for EU-28 [6], there are three categories that amounted to 83.9% of all energy: transport, which used 353 Mtoe or 33.2%; industry, responsible for 275 Mtoe, meaning 25.9% of all energy; and households, using 264 Mtoe or 24.8%, as it is possible to see from Fig. 1.1. MToe stands for million tonne of oil equivalent, which is a unit of energy and is equivalent to the amount of energy released when burning a tonne of crude oil. One tonne of oil equivalent is equal by convention to 11.3 ×109kWh or 4.19 ×1010MJ.

For Portugal, in regards to the same year [6], the distribution of electrical demand alone is slightly different. From the figure it is possible to see that most of energy used is for industry, consuming 17.304 ×109kWh, amounting a total of 34.47% of energy used, followed by the use in domestic (11.907 ×109 kWh – 25.79%) and non-domestic (12.136 ×109 kWh – 26.28%). Typically, the use of energy in buildings is mostly to electrical lighting, heating and cooling system (HVAC – heating, ventilation and air conditioning), and other electrical equipment (as computers, printers, etc.).

(a) EU-28 (b) Portugal

Figure 1.1: Energy consumption in EU-28 and in Portugal in 2014 [6].

Analyzing the energy consumption in buildings located in United States, represented in Fig. 1.2, over half of energy is used in heating/cooling systems, followed by equipment’s consumption and lastly lighting. Lighting and HVAC systems can be both controlled in an integrated manner and it’s use dimin-ished by using daylight. From [7], the energy for HVAC systems is 14.70 ×1015Btu (4.31 ×1012 kWh), for equipments is 9.21 ×1015 Btu (2.70 ×1012 kWh) and for lighting is 4.65 ×1015 Btu (1.363 ×1012 kWh). Therefore, the integrated control of lighting and climatization is important to reduce the worldwide energetic consumption.

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Figure 1.2: Energy prediction in 2015 for buildings located in USA [7].

1.3 Objectives

The objectives of this work are to develop, simulate and analyze lighting and climatization manage-ment algorithms in spaces with multiple users. To do so, the following tasks are proposed to be done:

• Development of simplified models that estimate luminosity;

• Develop algorithms capable of managing lighting without intervention of users; • Development of lighting management algorithms;

• Comparison of the different strategies based on energy consumption and user’s comfort.

1.4 Definitions

1.4.1 Visible light

Visible light is the electromagnetic radiation spectrum that lies between two wavelengths (from about 380 and 780 nanometers). This is the only type of electromagnetic radiation (from the whole spectrum) that it is absorbed by the human eye, allowing humans to see. Below 380 nanometers is the infrared radiation, which corresponds to radiation with longer wavelengths, and above 780 nanometers is the ultraviolet radiation, which has shorter wavelengths, as it is shown in Fig. 1.3. We can define light by its direction, its intensity, its polarity, and its wavelength (or frequency).

We can decompose visible light using an optical prism, and we can see it is a mixture of seven different colors: violet, blue, cyan, green, yellow, orange, and red. This split of colors occurs because each color has its own wavelength. When they are propagating in the optic prism, its refractive index changes with wavelengths. This effects causes light to refract differently, separating the colors. The overlap of these colors gives the white light.

When we observe a given object, the color which we see is due to the fact that it reflects the light that gives that specific color, and absorbs the other ones. For example, when we observe a red object, what happens in fact is the red color being reflected, while the others are being absorbed. This can be extended to other colors. If an object is perceived as black, then it is because all colors are absorbed; in the opposite direction, if the object is white, then all colors are reflected.

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Figure 1.3: Electromagnetic spectrum (Credit: NASA’s Imagine the Universe) [8].

1.4.2 Properties of light

When light hits an object or surface, it can be reflected from or refracted through the surface into the material beneath. Once it hits the material, it can be transmitted, absorbed or diffused.

Reflection. There are two types of reflection, which are specular and diffuse. In specular reflection the light is reflected at the same angle as the incoming light’s angle, and the properties of the beam remain the same (the beam maintains its form). This is characteristic of mirrors and polished surfaces. Diffuse reflection occurs when light hits a non polished surface, causing the reflected beams to disperse. After hitting the surface, light bounces through all directions, making it to be diffuse. Ideally, the luminance should be the same for all directions.

Figure 1.4: Law of reflection.

The law of reflection can be shown by specular reflection. When the light hits an object, it has a well defined angle (incidence angle), which is defined between the incident ray and a imaginary line that is perpendicular to the surface (or plane of incidence), defined as normal, as it is possible to see from Fig. 1.4. The angle between the reflected ray and the normal is called reflected angle.

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Absorption. When light shines on an object, that same object can absorb part of the light. This absorption is a ratio between the light that is absorbed and the light that hits the object. It can contribute to the rise of internal temperature, can change the shape, and can also change the state of the object that is absorbing. However, from the point of view of lighting, this factor isn’t relevant.

Transmission. This property represents the fraction of light that is capable of going through a medium (different from the medium of propagation, which is typically the air) that is adjacent to the incidence plane. Usually the adjacent medium has a different index of refraction, which is responsible for the difference in the angles (angle of incidence and angle of refraction). There are two types of transmission: direct and diffuse. Direct transmission is the case where the angle of exit of the beam is equal to the angle of incidence, and diffuse transmission is the case where the light is diffused as it exits the second medium. Both types of transmission are represented in Fig. 1.5.

Figure 1.5: Representation of light transmission [9].

Refraction. When light travels from one medium to a different one, it refracts (meaning it changes it’s trajectory and velocity). This refraction depends on two factors: the refractive index of the material (defined as the letter n), and the incidence angle of the beam. The index of the material is defined as the ratio of the speed of light in vacuum (defined as c) over the speed of light in the material (defined as v), as such:

n = speed of light in vacuum speed of light in the material =

c

v. (1.1)

The speed of light in air is almost the same as the speed of light in vacuum, so the index of refraction for air is considered 1. Because the speed of light in other materials is lower than the speed of light in the air, the index of refraction for these other materials is greater than the index of refraction for air, as it is possible to see from expression 1.1.

It is possible to show the relation between the incident angle and refractive angle using Snell’s law of refraction, given by:

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n1sin θ1= n2sin θ2, (1.2)

where:

n1- refractive index of medium 1;

n2- refractive index of medium 2;

θ1- incident angle;

θ2- refracted angle;

θ0₁- reflected angle.

In Fig. 1.6 is shown a representation of Snell’s law of refraction. The angles represented are all in respect to the normal, as is depicted in the figure.

Figure 1.6: Snell’s law of refraction [10].

Using Snell’s law (expression (1.2)), when the incidence angle is 0◦ (meaning the light hits the surface perpendicularly, as the normal representation), the light doesn’t change it’s trajectory in the new medium, that is, θ2as the same value as θ1, which is 0.

When, however, the light travels from different mediums, one of two cases can happen: if the first medium has a lower index value (such as n1 < n2) than the second medium, the light, as it makes the

transition between mediums, bends towards the normal; the opposite effect occurs if the first medium has a higher index value (as n1> n2), and the light bends away from the normal.

Another phenomenon that can occur with reflection is the total internal reflection, and it happens when light travels from one medium with higher index of refraction to another. If the light’s beam of incidence bends further away from the normal, it will reach a critical point – called critical angle θc –

at which the light will be refracted along the boundary (not being reflect nor refracted). If the angle of incidence increases, all the light will be reflected at the boundary and will stay in the medium. A common application for this phenomenon is fiber optics, allowing to transport light along their length with little or no losses.

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1.4.3 Solar Angles and Definitions

Due to the movement of the Earth around the Sun, and as well it’s rotation along it’s axis, there are some variables and angles which are important to define and are fundamental to this work [11]:

Latitude (φ). It is defined as the angle between the place in question and the equator, and is defined as −90◦ _{≤ φ ≤ 90}◦_{, where it is defined as positive the locations above the equator line (90}◦ _{being the}

North Pole).

Declination (δ). It is the angle the sun makes at solar noon, measured with the plane of the equator. It can be calculated using the formula

δ = 23.45 × sin 360 ×284 +nday 365 , (1.3)

where ndayrepresents the number of the day of the year.

Slope (β). This represents the angle between the plane of the surface and the horizontal, and has values between 0◦ ≤ β ≤ 180◦ _{(when β > 90}◦_{, then the slope is facing downward).}

Angle of incidence (θ). Is the angle the light makes between a surface and it’s normal.

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

(1.4)

Surface azimuth angle (γ). Making a projection of the surface on a horizontal plane, it is the angle between the projection and the normal of the surface. It has values between −180◦ _{< γ < 180}◦_{, where}

if the surface is facing south, the value is 0, if facing east is negative (γ = −180◦_{), and positive if facing}

west (γ = 180◦).

Solar time. This time is based on the rotation the earth does around the sun, giving the movement the sun is moving across the sky. The time in which the sun crosses the meridian of the zone of the observer is defined as the solar noon. It is possible to relate solar time with local time, with the use of the expression

Solar time − Standard time = E + 4 × (Lst− Lloc) − 60ST

E = 2.292(0.0075 + 0.1868 cos(B) − 3.2077 sin(B) − 1.4615 cos(2B) − 4.089 sin(2B)),

(1.5)

where Lstis the standard meridian for the local timezone, Llocis longitude of the local in which is the

calculus of the solar time, E is the equation of time, which is calculated in minutes, and ST is 1 if daylight saving is being used and 0 if it is not. The value from equation (1.5) is given in minutes.

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Hour angle (ω) . This value is due to the rotation the earth makes around the sun, giving a variation of 15◦ per hour to east or west of the local meridian. In the morning this value is negative, at noon is zero, and at the afternoon the value is positive. This value can be calculated using the following expression

ω = 15 × (ts− 12), (1.6)

where tsis the solar time.

Zenith angle (θz). This value measures the angle the line of the sun makes with the normal of a

horizontal surface (or the angle of incidence of the beam).

Solar altitude angle (αs). Is the angle between the surface and the line of the sun (it is complimentary

to the zenith angle).

1.4.4 Interior Lighting

To allow the quantification of light and to better understand it, it is necessary to define additional concepts, such as:

Solid angle (Ω). A solid angle is a three-dimension representation of a two-dimension angle, and it’s unit of measurement is steradian (sr). To define a solid angle, it is necessary a sphere with a radius r. A steradian is a cone shaped section that has an area equal to r2_{. A visual representation is shown in}

Fig. 1.7.

Figure 1.7: Sphere with a one sr removed and a solid angle measuring one sr [10].

A steradian can be defined with use of the expression

Ω = A

r2. [sr] (1.7)

Luminous intensity (I). This value corresponds to the light emitted by a light source in a specific direction of a solid angle. The unit of this measurement is the candela (cd).

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Figure 1.8: Generic luminous intensity over one steradian.

Luminous flux (φL). Having a light source, the amount of light emitted every second by a given solid

angle is defined as luminous flux, and is measured in lumens. A lumen is the flux generated in a solid angle measuring one steradian by a light source with a luminous intensity of one candela.

Figure 1.9: Generic luminous flux.

Illuminance (E). This value is a ratio between the luminous flux (φL) and a surface of area A in which

the light hits, and is measured using lux (lx). This unit represents the measurement of the light’s intensity, as perceived by the human eye. As such, illuminance can be computed using

E = φ

A. [lx] (1.8)

Luminance (L). This is the luminous flux reflected by a surface of reflectance ρ in a given direction. This represents the perception the human eye has if the surface is well lit or not, and it’s unit is candela by square meter [cd/m2]. In Fig. 1.10 is represented both illuminance and luminance.

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1.5 Organization

This document has been divided in 6 chapters:

1. The first chapter (current one) will consist in the objectives proposed for this work, and the funda-mental definitions regarding light;

2. The second chapter will describe some work and studies that were made in the area of interest, which are relevant to this work;

3. The third chapter is described the methodology used for this work; 4. The fourth chapter presents the obtained results;

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Chapter 2

State-of-art

2.1 Daylight impact on illuminance in a room

The sun emits electromagnetic radiation, which spawns from X-rays to radio waves. However, from that range, the most that reaches the surface of the Earth is visible light. Direct light is the light that shines directly on a surface, while diffuse light is light that is overall homogenous, due to the reflections of light in other materials. The first type of light is characteristic of sunny days, and the second type is characteristic of overcast days. Because the days are different between each other, the quantity and type of light that reaches a specific place may vary. With a clear sky (generally with no clouds), and with plenty of direct sunlight, the measured illuminance will be high; on the other hand, with an overcast day (clouds covering the sky) and with diffuse sunlight, the illuminance measured will be much lower.

[12] has been studied the daylight illuminance measured in horizontal and vertical surfaces in a region in Spain. The sensors were placed on a flat platform at a certain height, to avoid shading from the vegetation. The measures were made on clear days, during one year. Some of the obtained results are presented in Fig. 2.1 and Fig. 2.2.

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Figure 2.2: Horizontal and vertical illuminance measured during winter (adapted from [12]).

From Fig. 2.1 and Fig. 2.2 it is possible to see some interesting aspects. For one, the illuminances detected in North, East, South and West orientations are not equal throughout the day. For the sensors turned to East, the peak of illuminance is measured in the morning, while the sensor oriented to West has its peak in the afternoon, and this is verified all year long. For the rest of they day, the type of radiation the sensors measure is diffuse sunlight.

Besides the illuminances being different throughout the day, they are also different throughout the year. For the horizontal orientation, the illuminance measured increases steadily until the summer sol-stice, where it is measured it’s maximum peak, and then decreases until the winter solsol-stice, where it is possible to measure it’s minimum. The solar angle also describes a behavior similar to the illuminance, where it’s peak is measured in the summer solstice. The solar angle and illuminance are correlated, as the higher the solar angle is, the more vertical the sun hits the surface, and the more illuminance is measured [13].

It is possible to conclude that the orientation of a window plays an important role in how much the sun light can be measured or how much can enter the room, and must be taken in consideration in the type of algorithm one wishes to use daylight to control electrical consumption from indoor lighting and heating/cooling systems [5]. Knowing that the room is turned to a specific direction, it is possible to use it’s direct and diffuse sunlight to light the room, avoiding the use of electrical lighting (unless it doesn’t achieve a pre-set lighting level), and use an algorithm coupled with automatic control to control the blinds to adjust the brightness of the room.

2.2 Sun radiation impact on illuminance

When it is only known the radiation on a horizontal surface, it raises a problem when one wishes to compute the radiation in a sloped surface, like a window. First it is needed the direction of direct and diffuse components of the beam that reach the surface in question. The direction of the direct component

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is the incidence angle, but the direction of the diffuse component depends of the cloudiness of the sky and the ground reflectance.

If it is assumed that the combination of diffuse and ground-reflected radiation to be isotropic (the same for all directions), then the sum of both these factors is the same whatever the direction is. A model was developed that took into account the beam component, the isotropic diffuse and the solar radiation reflected from ground, also diffuse. A surface that is tilted with an angle β has a view factor to the sky defined as Fc-s= (1 + cos(β))/2, while it has a view factor to the ground defined as Fc-g= (1 − cos(β))/2.

As such, the total solar radiation, defined as IT, on the tilted surface is

IT = IbRb+ Id 1 + cos β 2 + Iρg 1 − cos β 2 , (2.1)

where Ib is the beam radiation, or direct radiation, Rb is the ratio between the beam radiation on a

tilted surface and on a horizontal surface, Id is the diffuse radiation on an horizontal surface, I is the

sum of direct and diffuse radiation that it’s the ground and is reflected with the factor ρg[11].

This model is conservative, as it tends to underestimate IT. Most recent models have been

devel-oped to take into account the circumsolar diffuse, which is the diffuse radiation coming from all the sky, and direct components on a tilted surface, as well with anisotropic sky. The Perez model for total irradi-ance on a sloped surface is based on a more profound analysis of the diffuse components, as it is given by: Id,T = Id (1 − F1) 1 + cos β 2 + F1 a b + F2sin β , (2.2)

where F1is the circumsolar brightness coefficient, F2is the horizontal brightness coefficient, and a

and b are related to the angles of incidence of the cone of circumsolar radiation (radiation coming from a point in the sun), which are given by

a = max(0, cos θ) (2.3a) b = max(cos 85, cos θz). (2.3b)

The brightness coefficients F1 and F2depend on three factors: the zenith angle θz; the clearness

index ε, which represents overcast skies for low values (1 ≤ ε ≤ 1.23) and clear skies for high values (ε > 4.5) [14]; and ∆, the sky brightness index. ε on it’s turn is a function of Id– hour’s diffuse radiation

– and Ib,n – normal incidence beam radiation –,

ε = Id+Ib,n Id + 5.535 × 10 −6_{· θ}3 z 1 + 5.535 × 10−6_{· θ}3 z . (2.4)

The brightness parameter is given by the following expression,

∆ = mId Ion

, (2.5)

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atmosphere. The coefficients F1and F2are defined as F1= max 0, f11+ f12∆ + πθz 180f13 (2.6a) F2= f21+ f22∆ + πθz 180f23 . (2.6b)

The values for brightness coefficient fij for the Perez model are shown in the table 2.1. Adding

the beam and ground-reflectance contributions to expression 2.2 and using the equations 2.3a- 2.6b, it is possible to have the total radiation on a tilted surface, which includes five terms: the previous two, isotropic diffuse, circumsolar diffuse, and diffuse from the horizon [11], making the final expression 2.7:

IT = Ibeam+ Iisotropic diffuse+ Icircumsolar diffuse+ Idiffuse from horizon+ Iground reflected

= IbRb+ Id(1 − F1) 1 + cos β 2 + IdF1 a b + IdF2sin β + Iρg 1 − cos β 2 (2.7) Range of ε f11 f12 f13 f21 f22 f23 1.000–1.065 -0.008 0.588 -0.062 -0.060 0.072 -0.022 1.065–1.230 0.130 0.683 -0.151 -0.019 0.066 -0.029 1.230–1.500 0.330 0.487 -0.221 0.055 -0.064 -0.026 1.500–1.950 0.568 0.187 -0.295 0.109 -0.152 0.014 1.950–2.800 0.873 -0.392 -0.362 0.226 -0.462 0.001 2.800–4.500 1.132 -1.237 -0.412 0.288 -0.823 0.056 4.500–6.200 1.060 -1.600 -0.359 0.264 -1.127 0.131 6.200–∞ 0.678 -0.327 -0.250 0.156 -1.377 0.251

Table 2.1: Brightness coefficients for Perez anisotropic sky [11].

However, more models have been developed. In [14], the authors used nine models to calculate the total irradiance, considering eight types of sky, in order to try to understand which model is more consistent and the most reliable. The results are presented in table 2.1. Two models were developed by the authors of the study: in the first one (M1), it was used a constant value for the diffuse luminous efficacy, for each vertical surface (North, East, West, and South), while in the second one (M2) the value used was constant, but different for each set of values of ε. Three models were variations of the pre-viously described Perez’s model: the first model (P1), the coefficients fij were obtained and analyzed

considering cities in the United States; the second model (P2), the coefficients were calculated for the location of the study, considering all four orientations together; the third model (P3), the orientations were considered separately. A sixth model is defined by Muneer, Gul and Kubie (Mu), correlating diffuse luminous efficacy to clearness index kt, which is defined as the ratio of the global irradiance over the

extraterrestrial irradiance, both measured on the horizontal plane. The final three models were devel-oped by Robledo and Soler, where the first one (R1) correlates diffuse luminous efficacy and the ratio between diffuse irradiance over the extraterrestrial irradiance, over the horizontal plane; the second one (R2), the diffuse luminous efficacy is correlated to the sinus of the solar altitude; and the last one (R3)

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is described the relation between diffuse luminous efficacy to the sky brightness index ∆. The last four model were developed to horizontal surfaces and were applied to vertical ones.

The measurements were made for the different intervals of ε, each representing a type of sky. The data was acquired every five minutes, and used to obtain the mean hourly values for illuminance and irradiance. For each direction, the nine models were applied to every ε, in order to compute and then determine the errors associated with each model. Having an average for all four directions and for all types of sky (ε > 1), the model with the lowest error was the model developed by the authors, where it was considered the luminous efficacy changes with ε – model M2. From table 2.2 it is possible to see which model is best for each direction and for each interval of ε. If all directions are to be considered together, all models behave in a similar way, with the exception of P1 model, being the models M2 and Mu the ones who are the best.

Range of ε

North

East

South

West

1.000–1.065

M2

Mu

1.065–1.230

M2

P2

M2

1.230–1.500

M2

P2

M2

1.500–1.950

M2

R1

M2

1.950–2.800

Mu

P3

M1

2.800–4.500

P3

M2

P3

4.500–6.200

P3

M2

P2

6.200–∞

P3

M2

P3

Table 2.2: Best models for each interval ε [14].

It is important to note that the model with the highest errors was the model considered as P1, as the values were adjusted to the United States, which has a different climate and it is not in the same latitude. Adjusting the models to the local climate is necessary to have good results, as well as considering the four orientations separately, which is why the model M2 and P3 have low errors.

2.3 Automatic control systems

Energy consumption for lighting in office spaces depends greatly of the space in which the office is located and also existence of automatic control systems. With simple automatic control systems (as timers), there will be times of day where lights will be on, even though there is a possibility that there is no one using the space. This will cause an unnecessary consumption of energy, and the opposite can occur, where the lights turn off while there are users still in the space. On the other hand, with more robust control systems (like occupancy-based controls), it is possible to have as little energy consumption as possible, since when it detects a user, it turns on the lights; when the user leaves, the lights turn off. This, however, raises a problem: the system may (or may not) detect a user, causing to turn the lights on/off incorrectly. It is also possible to control the intensity of light bulbs using daylight control systems. Using the daylight outside the office, these systems can dim the lights inside to adjust luminosity and

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thus be in range for user’s visual comfort [2, 15].

A simple, on-off algorithm is described for occupancy-based and daylight-based sensors. For the former, the sensors verifies if it detected someone or not. If it didn’t, then it starts a timer. If the timer is over some defined threshold, then it sets the space as not occupied and turns off the lights. If, however, detects someone before the timer is over, then it resets the timer and sets the space as occupied. For the latter, its possible to have either a closed loop or an open loop algorithm, witch are represented in Fig. 2.3. In a closed loop, the sensor is always measuring the indoor light, which includes the indoor lighting (coming from electrical lamps) and from daylight. This causes a feedback, and the sensor is always adjusting the electrical lamps, as the daylight isn’t constant along the day. In an open loop system, the sensor uses a reference system like time of the day or the schedule of the room, and the value is transmitted to the controller, adjusting the electrical lamps, in order to provide indoor lighting [2].

(a) Open Loop

(b) Closed Loop

Figure 2.3: Schematic of open and closed loop systems [2].

Table 2.3 shows how different settings can influence the performance of different control systems, where X means the factor influence those systems. These different systems account for different energy savings, and its usefulness can change from space to space: for daylight controls systems, savings can go from 9% to 30%, while with occupancy-based controls savings can range from 3% to 38% [2]. The variation on the results obtained is due to the fact there are different settings, such as daylight availability, control approach, occupancy patterns, etc. From these results, it becomes apparent that it is possible to achieve relevant energy savings with automatic control systems. It is however important that the systems are well adjusted. Due to its robustness, daylight-based controls have been used more frequently.

A study was conducted in order to discover and determine daylight throughout the day (through equations that relate indoor and outdoor illuminance), and from that data to regulate the use of indoor lighting [4]. The data was collected during a period of five months, and the blind had an angle to cover its complete range of operation (from 0o _{to 180}o_{). The blind tilt angle, incidence angle and sky conditions}

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Affecting factors’ category Affecting factors Timers Occupancy-based Daylight-based Typology Control strategy X X X

Occupancy pattern X X -Sensor’s location - X X Lighting system’s

characteristics System efficacy X X X Relationship between sensor signal

and related light output - - X Indoor daylight

availability Outdoor daulight availability - - X External obstructions - - X Glazing and shading typology - - X

Table 2.3: Effects of different settings (adapted from [15]).

taken as clear sky and overcast sky. The transmittance was determined as the result of dividing the illuminance measured with the indoor sensors by the illuminance measured in the outside. It was shown, for overcast days, that the blind’s angle has a strong effect in the measured transmittance. This can be explained by the fact that for these types of days, most of radiation is diffuse (direct sunlight is blocked by the clouds in the sky), so the most important parameter in this case is the blind, as it can control how much radiation can enter the space and as such influence the indoor lighting, and due to this type of radiation, the incidence angle doesn’t have as much important weight as has the blind.

For the type of windows used and the location this study took place, the maximum transmittance value was measured for a blind tilt angle of 60o_{, which corresponds to a transmittance measured of}

38.2%. For clear days, as most of radiation that hits the window will be direct, both the incidence angle and the blind tilt angle will play a strong effect in controlling how much sunlight will enter the room. As the incidence angle rises, the transmittance of the window will be lower; however, with the blind’s tilt angle, the transmittance will increase until a certain point, and after that will start to decrease. The blind also plays an important role in controlling the glare that can affect users. In fact, adjusting the tilt angle allows to completely avoid glare, as the sunlight that enters the room will enter through reflections the light suffers from the blind. The maximum transmittance in this conditions was measured as 55%, with an incidence angle of 15oand a blind tilt angle of 78o.

Besides controlling the blinds and computing the transmittance, it was also controlled the dimming of the light, to assure that the illuminance on the work plane reached a predetermined set-point (500 lx). The dimming was calculated for all working hours of the day, both for clear and overcast days. In overcast days, the dimming greatly improves the illuminance of the space, as it gives a better distribution of light and ensures the illuminance reaches the set-point. For clear days, when there isn’t enough light, the lights activate and adjust to reach the set-point. When compared with an office space without dimming and on/off switch (meaning the lights are always on), the energy savings can be as high as 76% for overcast days and 92% for clear days. This shows how important using daylight can be to achieve energy savings.

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taking into account the users’ interaction [16]. In the first phase, it was monitored the lighting system, which users would control manually. This was done so to determine and evaluate the electric consump-tion related to the lighting systems. The user’s behavior and their response was recorded in order to analyze the lighting conditions in the offices due to the use of electric lighting. After this, the next phase took place and was considerably longer than the first one, as it consisted in installing and calibrating a new automatic lighting system, using the user’s requirements. In this second monitoring, the lighting control system was operated using automatic and manual control, and it’s objective was to check if the lighting control system was working as intended and to see it’s efficiency in providing energy savings and sufficient lighting conditions.

The data was recorded over a year, which included the horizontal illuminance of a desk, the illumi-nance estimated by the sensor, the percentage of dimming for each luminaire, and the electric energy consumption. The illuminance measured on the work planes was compared with target values which were defined before: when the lighting system was controlled manually, the target value was defined as 500 lx, while when the system was controlled automatically, the target value was defined for each of the offices, taking into account the requirements of the occupants. It is important to note that the values were measured in different time periods, and as such, comparisons and conclusions must take into account the different type of weather and external conditions.

From Fig. 2.4, it is possible to see that using manual control, it was verified the illuminance measured in a desk (750 lx) was often and substantially higher than the recommended value (500 lx). This can be explained as it is impossible to control the lighting system as a function of daylight; either it is on or off, and the system is controlled by the users. However, using automatic control which could be overruled with manual control – automatic with manual control –, the illuminance measured drastically decreased (to about 400 lx) and became much closer to recommended value, as the lamps could be dimmed automatically.

The frequency distribution of illuminance, which is in Fig. 2.5, also sustains this claim, as with manual control the lighting on the surface of the work plane was as high as almost 70% of times above the recommended value, but with automatic control, these values decreased to below 50%. These results, however, could be a consequence of the period of the year in which took place the data acquisition.

After the monitoring, questionnaires were distributed in order to evaluate the degree of satisfaction of the users. In regards to the first phase, the users were satisfied with the lighting conditions and were not interested in regulating the luminous flux. For the second phase, which used automatic and manual control, the users reported that for the different seasons, there were not many situations with too much or too little light in their work plane, they reported that they were indifferent concerning the others users’ interaction with the system, and the main reason to interact with the system was because it did not work properly [16]. However, for this last point, this can be explained as the automatic systems seem to be more accepted when exists a manual override and when they are easy to use [2, 16].

Combining shading with automatic control generally gives the highest energy saving results, as it was studied in [17]. For example, having a system controlling the blinds position coupled with an occupancy-based detector allows the control of the blinds, opening them when a user isn’t detected in a room, thus

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Figure 2.4: Illuminance measured with manual and automatic control (adapted from [16]).

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heating the room (due to high solar gains) and reducing the load of heating systems. When, on the other hand, the user is detected, the blinds close, for glare considerations and to cool the room, reducing the need to use cooling systems. If necessary, it can be used artificial lighting in case there is a risk to cause glare to the user if the blinds were open.

This system takes as inputs season, direct outside horizontal illuminance, inside and outside tem-perature, among others, and optimizes the system to compute the most comfortable setting. The opti-mization is done each night, with the objective to look for the most efficient set of parameters. This is done using a genetic algorithm, and applying small variations to the parameters used during the day to the current controller. This setup shows the differences between two automatic controllers, one well-adjusted to the space able to control the blinds, and a conventional controller (an on/off switch). The well-adjusted controller managed to control the heating power and the lighting system whether there was a user using the room or not, and also managed to avoid overheating the room. Using this setup, it has been possible to achieve 25% energy savings in comparison with the conventional controller. How-ever, one problem raised by this controller is the fact that it does not take into account the user’s wishes. For instance, if the user changes the position of the blind, the system holds that position for a time set period, and then changes back to the optimal one.

It is important, however, to have in consideration the space in which it is intended to optimize lighting. There are external factors (such as shading and orientation) that can influence indoor lighting, but there are as well indoor factors, such as the lifetime of lamps. One initial approach, when dimming lamps, is to consider the variation of intensity as directly proportional to its energy consumption. This, however, can produce different result if one intends to have a higher precision.

[18] studied the impact for two types of lamps sets (4 x 14 W fluorescent and LED lamps) the relation between energy consumption and dimming and found it was not linear, but rather a polynomial function. Comparing both sets, for higher levels of dimming, the power consumption of the fluorescent lamps (20.6W) will be considerably higher than the LED lamps (2.8W). Comparing the values measured for no dimming and for a given percentage of dimming, it is seen that LED lamps have higher luminous efficacy than fluorescent lamps, as with 0% of dimming the former can output 47.6 lm/W, while the latter can only output 36.3 lm/W, and with 97% dimming it can output 23.6 lm/W and 3.0 lm/W respectively.

2.4 Visual comfort

Several studies have analyzed the effects of excessive or lack of illuminance in working environments. Having the illuminance values in a defined threshold can guarantee the comfort of the users. However, having a well defined threshold is a difficult task. For one, it does not take into account the glare, and secondly, it is a temporary measurement (can be calculated using expression 1.8, meaning it is necessary to continuously take measurements. Besides this, the comfortable values are relative to users: some users may prefer better lit environments than ones less lit. As such, it can be defined a loose threshold, where there is not a set value which can not be crossed, but rather a suggestion of values to be used.

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The space in question, the type of work done and where the work is done weights in the values used. For a typical classroom, the work surface is the most common surface where this value is measured, and the value 500 lux is the value considered as the reference value. From certification for sustainable constructions [19], it is recommended to have illuminance values between 300 and 3000 lux.

The values recommended for office spaces are shown in table 2.4, which were adapted from [20]. As seen, a consensus set range of acceptable values can not be reached, due to the preferences of each user in the room. Instead, it is preferable to try to set a range of values for the room in question.

Reference Illuminance recommended

Aries (2005) 500 lux is desired for the working plane but 800 lux is preferred U.S. Green Building Council (2013) Illuminance values between 300 and 3000 lux

Newsham (1994) 150 and 500 lux in working plane as reference values for electrical lighting Manav (2007) Users prefer 2000 lux instead of 500 lux

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Chapter 3

Methodology

This chapter presents and explain the method used for this work. The model is divided in three parts: the first one, involves using the Pèrez model, for the computation of solar radiation in a given point; the second one, is using the transmittance of classroom’s window, calculated using values measured with two sensors, and with that determine how much solar radiation enters the room; the third one, is using an algorithm to determine the distribution of illuminance in the room, using a conversion between radiation and illumination. A representation of the algorithm proposed is shown in Fig. 3.1.

Figure 3.1: Representation of the algorithm proposed.

The room in which will be studied the illuminance is the classroom V1.10, located in Pavilhão de Civil, in Instituto Superior Técnico. The classroom is located in the first floor, and is turned to East, meaning

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the peak of illuminance will be measured during the morning, while in the afternoon will be mostly from diffuse light.

In the next sub-chapters, not only it will be depicted how the calibration of the sensors was made, but the relation obtained for the values measured in the window and how it relate to the values near the walls (across the room) as well.

3.1 Sun radiation

3.1.1 Horizontal data

Instituto Superior Técnico has a meteorological station, located at the top of North Tower, which measures air temperature, humidity, solar radiation, among others, every minute. The solar radiation is measured in an horizontal plane. The group managing the weather station also provides hourly weather forecasts, including solar radiation, which can be used for control.

This allows to have experimental data of solar radiation over the course of a given day, which could be useful for the analysis of the illuminance in the room.

3.1.2 Pèrez Model

The Pèrez model, as described in the previous chapter, is a model that allows to determine the radiation which hits a certain surface, given its location, orientation, and inclination. The radiation was computed for an horizontal surface, with the same geographical coordinates and at a given height which was equal to the IST’s meteorological station, and then both were compared. This was done so to see if the values predicted by the model were consistent with the values measured.

The values used for the different parameters of Pèrez’s model were adjusted taking into account the local climate, using the parameters determined in Italy [14], specifically Arcavacata di Rende. It is located at a latitude extremely close to the latitude of the room in question, as the room has a latitude of 38.736◦, where Arcavacata di Rende is at 39.35◦, with similar types of climate.

3.2 Windows transmittance

As it was seen in chapter 1, the angle of incidence of a light beam influences the resulting transmitted light beam. Using Fresnel equation, it is possible to have for an S and P-wave (these types of waves represent the waves’ polarization) the following reflectance, assuming it is for non-magnetic media

Rs=     n1cos(θi) − n2 r 1 −n1 n2sin(θi) 2 n1cos(θi) + n2 r 1 −n1 n2sin(θi) 2     2 (3.1a)

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Rp=     n1 r 1 −n1 n2sin(θi) 2 − n2cos(θi) n1 r 1 −n1 n2sin(θi) 2 + n2cos(θi)     2 . (3.1b)

For a generic wave, in which it is not known the ratio between S and P-wave, it is assumed that the wave is unpolarised and as such the reflectance is given by:

RT =

1

2(Rs+ Rp). (3.2)

It was also seen in equation 1.4 that the incidence angle from the sun varies throughout the day. Using equation 1.4 in equation 3.2 it is possible to calculate the transmittance taking into account the position of the sun in the sky and thus the variation of the incidence angle since the sun raises until the sun sets.

Assuming the window does not absorb part of the radiation, then the only phenomena are reflection and transmission. Having this in consideration, then the transmittance is given by:

τ = 1 − RT. (3.3)

3.3 Calibration of sensors

To measure the illuminance of the room, two sensors from Adafruit R _{were used. The two TSL2591}

Adafruit R _{sensors, which could measure the illuminance instantaneously and could also take}

measure-ments within a set period the user could define previously. The sensors had different types of gain, as well as different times of integration. The gain of the sensors had a range of 1, ideal for situations with plenty of sunlight, until the maximum of 9,876, which was indicated for situations with extremely low light. Apart from that, the sensor performed an integration of the values measured, and it ranged from 100 ms, again for situations with bright light, up until 600 ms, typical for environments with low light, as the higher the integration time, the more light the sensor is able to integrate, being more sensible to low light [21]. The sensors were used with a gain of 1, as it would be hit by direct sunlight, and any gain would saturate the sensor, and an integration time of 100 ms, being the lowest, again for the same reason.

The sensors have a resolution of 1 lux, and the maximum value it can read is 88,000 lux, after which the sensor saturates. The code used for the sensors was the code provided by Adafruit open-source. The sensors would be connected, each one to a single Arduino, and those would be connected to a computer, in order to record the data. It was considered that a period of 15 minutes provides enough information to make the necessary adjustments throughout the day.

For the calibration of the sensors, it was used a light meter ISO-TECH 1332A. The light meter was placed alongside the Adafruit’s sensors, and the values measured were then compared. The light meter has a resolution of 0.1 lux, and has an accuracy of ±3% for values measured below 10,000 lux. The light meter was calibrated to a standard incandescent lamp at color temperature of 2,856 K. The spectral sensitivity characteristic is very close to the C.I.E. (International Commission of Illumination) photopic

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curve, which is displayed in Fig. 3.2.

Figure 3.2: Characteristic of light meter ISO-TECH 1332A.

Using the values from both types of sensors (Adafruit’s and the light meter) measured near the window, it is possible to determine a relation. As such, the result obtained between the two is in Fig. 3.3, using a linear function. The resulting fit allows a conversion from a measurement using an Adafruit sensor to illuminance in the region. It is important to note the slight dip near the region of 2,000 lux measured by the light meter. This is due to the working range of the light meter, as one of its range is 2,000. When one switches to another working range (the next one being 20,000 lux), the values near 2,000 are measured lower than with the previous range.

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The values obtain for a linear function used to fit the data is in table 3.1.

a b χ2

red R

2

2.510 ± 0.001 1.017 ± 7.145 9.356 × 102 _0.997

Table 3.1: Parameters obtained for the fit between sensors and light meter.

3.4 Daylight control

To control the amount of sunlight (and thus illuminance) that enters the room, it is necessary to have blinds and/or electrical lighting. Having blinds allows to control the amount of direct sunlight, and prevent glare that users may experience. However, if the illuminance measured in the space is not sufficient to ensure work in comfortable conditions, then electrical lighting might be needed to raise the lighting conditions. Both can be used (for example, where the sunlight is too strong but isn’t high enough when the blinds are open) to ensure the most comfortable conditions to the users. However, it is important to note that this solution increases the electrical consumption of the building.

The blinds can be controlled using a manual switch located near the window, which anyone can use, to adjust to the preferred light level. The blinds, when closing, close from the top and descend to the base of the window. When totally closed, and if one wishes to open them, the top third of the blinds rotate, being horizontal, and then the rest of the blinds follow, being completely horizontal. After this, they begin to rise, until the top.

3.4.1 Blinds

In order to understand the distribution of illuminance from sunlight through the room, a set of points were picked and made measurements in those points. The measurements were made for different stages of blinds: from completely open to completely closed. There is another stage of the blinds, which is when the top third is open (parallel to ground) and the bottom two thirds is closed (named special). The time of measurement was in the early morning, in order to have the room hit entirely by direct sunlight. The points chosen were at the top of the tables, the same as working plane, and went from the window to the wall, being P1the point closest to the window, and P5the point closest to the wall. The points of

interest are represented in Fig. 3.4.

The measurements are represented in Fig. 3.5 and in Fig. 3.6. From it it can be seen the impact the blinds have for the illuminance. When totally open, the illuminance measured is extremely high, throughout the room. As the blinds begin to close, it can be seen that the values measure stay below 10,000 lux, a drastic decrease when compared with blinds totally open. Although it is higher value than recommended, it is no longer uncomfortable to work in the environment. As the blinds continue to close, the illuminance continues to decrease, as there is less direct sunlight hitting the room, until it is totally closed, at which point the illuminance measured will be the lowest for all points. It is important to note that when the blinds are in position special, the points P3to P5 have higher illuminance than points P1

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Figure 3.4: Representation of interest points.

and P2, as the sun hits that zone of the room (due to the top part of the blinds being open) but not the

zone near the window.

Figure 3.5: Illuminance measurements throughout the room.

3.4.2 Electrical lighting

Electrical lighting is another strategy used to allow the illuminance to stay at comfortable values, only in this case it is used to lift the illuminance measured. A method which can be used to compute the distribution of the provided light is considering the lamps as a single point and an uniform distribution, and using inverse square law [10], which is described by the following formula

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Figure 3.6: Illuminance measurements throughout the room with log scale.

I = E · d2, (3.4)

where

I- luminous intensity; E- illuminance;

d- distance between the light source and the point of interest.

Switching d for its relation with the height of the lamps and its angle to the point of interest, the expression can be written as

I =E · h

2

cos2_θ. (3.5)

An algorithm is portrayed in Fig. 3.7. First, it checks if it is necessary to use electrical lighting. If it is not needed, then the lamps are turned/remain off; if it is needed, taking into account the position of the lamps, its power and the position of points of interest, it computes the artificial lighting provided and sets the configuration of the lamps.

The position of the lamps is in Fig. 3.8. In the figure all lamps are turned on (displayed with the color yellow), and it was chosen this column as it is the same column as the points of interest.

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Figure 3.7: Representation of the algorithm for electrical lighting.

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Chapter 4

Results

In this chapter the results obtained will be presented. Firstly will be presented the results for the prediction of the lighting in the room using a ratio between radiation and illuminance, the transmittance determined for the window in the room using the sensors, and the distribution of illuminance in the room. A threshold was defined for comfortable levels of illuminance to the users, and depending of the value predicted, a control method is applied to bring the illuminance to that range.

4.1 Radiation to lux conversion

With the values from Pèrez’s model and the values measured from IST’s meteorological station, it is possible to estimate the radiation that hits a horizontal plane. Likewise, with the values measured from Arduino R_{’s sensors, it is possible to know the illuminance in two points in the room. From this, it can be}

done a simple relation between incident radiation and illuminance outside the room. This allows to give an estimate and it is not necessary to permanently use a sensor to measure the illuminance.

This conversion is made over the values measured experimentally. As such, the results obtained could only be used for this location, as for different locations (different latitude and longitude), the radia-tion that hits produces different values of illuminance, as the angle of incidence of the sun is different.

Using the values measured from the meteorological station located in Instituto Superior Técnico, and the values measured from the Adafruit’s sensors, for the same time, it was then compared, as it can be seen from table 4.1. From those values, a relation from radiation and luxs was then determined, using different approaches.

Firstly, it was attempted an average between all the values, from morning until early afternoon (de-fined as all day). However, the difference between calculated values and experimental data was high. Afterwords, the data was split into two categories: the first one, included all the values measured during the morning, which was when sunlight was hitting the sensors directly; the second one, included the values which was measured with diffuse light (called split average in table 4.2). The point in which the division was made is after 12h17m28s, local time. It was also used values determined in Italy for the brightness coefficient for Pèrez anisotropic sky, represented in table 2.1, to see if it could predict the

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Local time Adafruit sensors [lx] MeteoISTW · m−2 RatiohW · m−2· lx−1i 09:37:59 21,398.415 766 0.0358 09:47:29 20,601.830 789 0.0383 09:57:29 34,672.614 796 0.0230 10:07:29 23,781.726 831 0.0349 10:17:29 32,419.631 849 0.0262 10:27:29 52,377.068 861 0.0164 10:37:29 59,279.954 914 0.0154 10:47:29 62,453.492 929 0.0149 10:57:29 63,095.573 757 0.0120 11:07:29 58,450.552 1,058 0.0181 11:17:29 57,308.533 1,033 0.0180 11:27:29 54,016.046 992 0.0184 11:37:29 49,954.701 1,082 0.0217 11:47:29 42,948.936 1,034 0.0241 11:57:29 37,055.649 1,017 0.0274 12:07:29 16,925.888 993 0.0587 12:17:28 5,558.041 991 0.1783 12:27:28 6,413.490 1,001 0.1561 12:37:29 5,345.791 1,029 0.1925 12:47:30 4,776.763 995 0.2083 12:57:30 3,794.610 996 0.2625 13:02:45 3,262.040 995 0.3050

Table 4.1: Relation between radiation and illuminance for day

illuminance in the room without a high error [14].

After calculating the ratios, it was then computed the prediction of illuminance in the room. For this computation, it was used the radiation measured from meteoIST, and divided by the ratio previously calculated. This value, defined as lux prediction in table 4.2, was then compared to the value measured with the sensors, to see the difference between the two. This would give an indication if the value was close to the value perceived in the room or not.

The values are displayed in table 4.2. As it is possible to see from the table, making an average taking into account all the values recorded during a day will have the values with the highest difference between values predicted and values measured. This can be easily explained as the type of radiation that hits the sensors is different, that is, in the morning the prevailing type of radiation is direct (in this specific case), while in the afternoon there will only be diffuse radiation. As such, the value obtained when the average is being made includes both types, thus having higher difference; the error determined to this ratio can be as high as 550%. Using the value obtained for a location in Italy, it can be seen that the absolute values predicted are higher, even higher than the values recorded, meaning it over-estimates the values measured. The errors measured for this ratio do not fluctuate much; even though they are high, they range from 30% to about 85% for direct sunlight, and are at around 95% for diffuse sunlight. Finally, for the split average, there is a single point which has a high difference (the point at 10h57m29s) but overall it predicts the illuminance with an error lower than 40%. This ratio is the ration which could potentially have the best results, as the ratio would depend whether direct sunlight hit the room or not. As such, of the three methods, it is the one which has the lowest errors for the direct sunlight. For the diffuse

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