- Email: [email protected]
Algorithm for blinds control based on the optimization of blind tilt angle using a genetic algorithm and fuzzy logic
Available online at www.sciencedirect.com
Solar Energy 86 (2012) 2762–2770 www.elsevier.com/locate/solener
Algorithm for blinds control based on the optimization of blind tilt angle using a genetic algorithm and fuzzy logic ˇ ongradac ⇑, Marta Prica, Marija Paspalj, Dubravka Bojanic´, Darko C ˇ apko Velimir C Faculty of Technical Sciences, Trg D. Obradovic´a 6, 2100 Novi Sad, Serbia Received 29 March 2012; received in revised form 31 May 2012; accepted 14 June 2012 Available online 17 July 2012 Communicated by: Associate Editor J.-L. Scartezzini
Abstract This paper presents the calculation of the power of solar rays that pass through the window of an observed room and their impact on warming up and lighting of the room. The calculations were performed using a mathematical model that takes into account the geographical position of the object, time zone, orientation of windows, day of the year, and current time. This paper also includes the calculation of geometry of the solar radiation and its intensity, artificial light and cooling/heating demands. Based on data from above, the optimization of blind tilt angle was performed to achieve the best possible brightness of the room and energy savings when heating or cooling, depending on ambient temperature. Optimization was performed using a genetic algorithm and fuzzy logic. After an analysis of the results obtained from optimization of the blind tilt angle, an algorithm for blinds control was developed in order to achieve energy savings and comfort in the observed room. Based on the derived conclusions, an UML diagram was made that describes the algorithm for determining optimal blind tilt angle. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Blind tilt angle; Thermal gain; Lighting; Power consumption; Genetic algorithm; Fuzzy logic
1. Introduction Solar energy is a renewable and inexhaustible energy resource that can have an important role in the energy sector of every country, and provide a significant reduction in power consumption. During the year, the solar energy that reaches the Earth is 10,000 times greater than the energy necessary to fulfill the needs of the entire population of our planet. On average, each square meter of land is exposed to enough sunlight to receive 1700 kW h of energy every year, and more energy is generated if radiation is higher at the observed location. Heat gains derived from solar radiation during winter can be used for space heating, and thus reduce the needs of energy consumption. During
⇑ Corresponding author. Tel.: +381 631010120.
ˇ ongradac). E-mail address: [email protected] (V. C 0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.06.016
summer, heat gains are undesirable because they lead to room overheating, and therefore it is needed to spend more energy for cooling the room. This is why the usage of shading is required during the summer period. The shading is a very important factor in the whole story about passive design of the facilities. The angle of solar rays that hit the object is different in winter and summer, and this fact is used in shading. Between the tropics and the polar circles, the Sun is low in the winter and solar rays fall to the object under a small angle, while the situation is reversed in summer and solar rays fall under a larger angle. The change of angle is most important on the south side for buildings in the northern hemisphere. Depending on the area where the building is located, the maximum and minimum angle of solar rays can vary. The blinds are practical because they can adapt to the current needs and thus maximize protection from the Sun in summer, and heat gains in winter.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2763
Systems that control the amount of daylight that enters the building provide better usage of solar energy. These systems are designed taking into account the type, size and orientation of windows, and shading elements, such as shutters, blinds, roller shades, for example. Environmental effects, such as position of surrounding buildings and the nature of the environment in which the observed object is set, are also very important. All these elements comprise a major contribution in design of room lighting and temperature controls.
overcast overcast Ewindow overcast ¼ E diffuse þ E ground
2. Model development
Eovercast ¼ Ewindow overcast VT sovercast
½1x
ð3Þ
where Eovercast diffuse is the sky diffuse illuminance for an overcast day, Eovercast ground is the ground reflected illuminance for an overcast day. Total room illuminance for an overcast day is the maximum value of natural light in the room for an overcast day, considering visual transmittance of the window and optimal tilt angle of the blinds, or the maximum value of visual transmittance of blinds sovercast for that tilt angle. It is calculated by the following equation (Athienitis, 2002): ½lx
ð4Þ
Ewindow overcast
The mathematical model is based on calculations of global radiation, in order to get the values for external lighting and thermal gains. To calculate the external illumination it is necessary to know the latitude and longitude of the object, time zone, cloudiness, day of the year, and time for purposes of determining the exact position of the Sun (Long and Michael, 2012). This data, including the technical characteristics of window and room, is used to get values of the amount of light that enters the room and thermal gains that lead to warming up the space. Additional artificial lighting and requirements for additional space cooling or heating depend on these values. Solar heat gains depend on solar ray power, and environment characteristics such as transmission, reflection and absorption (Long and Michael, 2012). Final heat gains that pass through the window are given with mathematical equations and calculations related to the transmittance coefficient, view factors, reflection factors and other environment characteristics and materials that sunlight passes through (Athienitis, 2002).
is the total illuminance on the window surwhere face for an overcast day, VT is the visual transmittance of window, sovercast is the visual transmittance of blinds for an overcast day. During a clear day the solar radiation that falls on the window consists of all three radiation components: direct, diffuse and reflected radiation (Athienitis, 2002). Total illuminance on the window surface for a clear day can be calculated by simply summing the direct, diffuse and reflected light, using the expression (Athienitis, 2002):
2.1. Solar gain
Eclear hsky is the diffuse horizontal illuminance, FWS is a view factor between the window and sky, Eclear is horizontal illuh minance, FWG is a view factor between the window and ground, qG is albedo, E0 is average illuminance on a surface perpendicular to the solar rays just outside the earth’s atmosphere, f is the correction factor, c is the optical atmospheric extinction coefficient, m is the relative optical air
The model for a cloudy day implies that the direct solar radiation is practically absent. Therefore, total illuminance on a window surface contains only diffuse and reflected radiation (De Rosa et al., 2008, 2010). Sky diffuse illuminance on a window surface is given by equation (Athienitis, 2002): overcast Eovercast F WS diffuse ¼ E h
½lx
clear clear clear Ewindow clear ¼ Ediffuse þ E ground þ E direct
½lx
ð5Þ
where Eclear diffuse is the diffuse illuminance clear Eclear diffuse ¼ EhSky F WS
½lx
ð6Þ
Eclear ground is the ground reflectance clear Eclear F WG qG ground ¼ E h
½lx
ð7Þ
Eclear direct is the direct illuminance cm cosh Eclear direct ¼ E0 f e
½lx
ð8Þ
ð1Þ
where Eovercast is the diffuse horizontal illuminance, FWS is a h view factor between window and sky (FWS 0.5). Using Eq. (2) we can calculate the intensity of light reflected from the ground and falling on the window surface (Athienitis, 2002): overcast Eovercast F WG qG ground ¼ E h
½lx
ð2Þ
where Eovercast is the diffuse horizontal illuminance, FWG is a h view factor between the window and ground (FWG 0.5), qG is the reflection coefficient (albedo). Total illuminance on a window surface for an overcast day can be calculated by simply summing the diffuse and reflected light, using the expression (Athienitis, 2002):
Fig. 1. Cross-section of the window along with the incidence angle of direct radiation on the window and blind tilt angle.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2764
mass, and h is the incidence angle of direct radiation on the window which is presented in Fig. 1, along with the blind tilt angle. Using the Eq. (9) we can calculate the incidence anlge of direct radiation on the window h (Athienitis, 2002): cosðaÞ cosðjcjÞ þ j cosðaÞ cosðjcjÞj h ¼ a cos ð9Þ ½ 2 where a is solar altitude a ¼ a sinðcosðLÞ cosðdÞ cosðHAÞ þ sinðLÞ sinðdÞÞ
ð10Þ
c is the sun-window azimuth angle difference c ¼ U W ½
ð11Þ
U is solar azimuth angle sinðaÞ sinðLÞ sinðdÞ HA U ¼ a cos ½ cosðaÞ cosðLÞ jHAj
ð12Þ
d is solar declination, L is latitude, HA is hour angle
HA ¼ 15 ðAST 12Þ ½
ð13Þ
AST is apparent solar time LNG STM AST ¼ LT þ ET ½hours 15
ð14Þ
LT is precise local time, ET is equation of time, LNG is longitude of the observed object, STM is a particular time zone, and w is the window’s azimuth angle and it is determined by which way it faces, as measured from south. 2.2. Thermal gain To obtain the total sun power provided for the room, it is necessary to multiply the value of solar ray power through the window and blinds by the cooling load factor (CLF) (Axel, 1999; Katiyar, 2010). It is calculated by the following equation, for a clear and overcast day, respectively (Alessandro and Lucia, 2011; Dimitrije, 2003; Athanassios et al., 2007; Athanassios and Andreas, 2007; Orgill and Hollands, 1977; Handbook of Fundamentals Chapter 30, 2002): P clear ¼ P clear P overcast ¼ P overcast CLF ½W sun CLF ½W sun
to depends only on accurate local time and window orientation. Values used in this work were taken from a table given by ASHRAE (Ravinder, 2005). 2.3. Model of the room The features of the room are very important in order to determine the brightness, because they have a major impact on brightness changing. The relevant factors for lighting calculations are orientation and dimensions of the room, reflection factors of room surfaces, solar gain coefficients, window position (its distance from the ceiling, floor and walls), and height of desktop (work surface). It is important to mention that the room is a regular square shape, dimensions 6 5 3 m, with one outside wall and glazed surface on it (Fig. 2). To simplify the model, the surrounding buildings are neglected and object’s environment is presented as a grassy field. Geographic coordinates are taken for Belgrade, Serbia. It was necessary to calculate the brightness in the middle of the room. Therefore, definitions of specific surfaces within the room are required, and they include: window surface, window containing wall surface, floor surface, ceiling surface, opposite wall surface, right side wall surface, left side wall surface. View factors between characteristic surfaces show how the observed room surfaces will impact on each other, or how the light beam will reflect from one surface to another. They are defined separately for each two surfaces, and depend only on their mutual position. Because of that, the parallel and perpendicular surfaces are distinguished (Athienitis, 2002). View factor between two parallel surfaces is given by next few expressions (Athienitis, 2002). y x m ¼ ;m ¼ z z
ð17Þ
ð15Þ
where P clear is solar ray power through the window and sun blinds for a clear day, P overcast is solar ray power through sun the window and blinds for an overcast day termal P clear sun ¼ SHGclear S P sclear ½w
P overcast sun
¼ SHGovercast S P stermal overcast ½w
ð16Þ
SHGclear is solar heat gain in clear day, SHGovercast is solar heat gain in an overcast day, SP is surface of the window, stermal clear is thermal transmittance of blind for a clear day, stermal overcast is thermal transmittance of blind for an overcast day, and CLF is the cooling load factor (Ravinder, 2005). Calculation of cooling load factor requires a complex mathematical model, but can be approximated in a way
Fig. 2. Model of the room.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1 þ u2 Þð1 þ v2 Þ 0:5 ln þ v 1 þ u2 2 2 puv 1þu þv pffiffiffiffiffiffiffiffiffiffiffiffiffi v u atg pffiffiffiffiffiffiffiffiffiffiffiffiffi þ þ u 1 þ v2 atg pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ u2 1 þ v2 v atgðvÞ u atgðuÞ ð18Þ
FP ¼
where x is length of the observed surface, y is width of the observed surface, and z is the distance between two surfaces. View factor between two perpendicular surfaces is calculated using Eqs. (19) and (20) (Athienitis, 2002): y z u ¼ ;m ¼ ð19Þ x x pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 1 1 u atg FN ¼ þ v atg u2 þ v2 atg pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pu u v u2 þ v 2 " ( u2 1 ð 1 þ u2 Þ ð 1 þ v 2 Þ u2 ð 1 þ u2 þ v 2 Þ 0:25ln þ þ pu 1 þ u2 þ v 2 ð1 þ u2 Þð1 þ v2 Þ 2 v2 )# v ð1 þ u2 þ v2 Þ ð20Þ ð1 þ u2 Þð1 þ v2 Þ where x is common dimension, y is unique dimension of the first surface, and z is unique dimension of the second surface (Fig. 3). 2.4. Artificial lighting It was also necessary to calculate the requirements for artificial lighting of the room. About 500 lux was selected for optimal illuminance value, because the observed surface is the desktop. To calculate the required luminous flux on the desktop it is required to determine the useful height (distance between the desktop and light source) and room index. In designing of the artificial lighting the so-called Lumen method is applied. This method is based on fundamental laws and was chosen because of its simplicity and comprehensiveness. Dimensioning of the artificial lighting requires that the lamp efficiency level, required luminous flux, number of required lamps, actual average illuminance and maximum total consumption are calculated. Based on these values, the disposition of lamps is determined. The lamps
Fig. 3. Display of two perpendicular surfaces.
2765
should be distributed evenly on the ceiling, to ensure the best possible illuminance, and minimize side effects (in the form of shadows) (Kwang-Wood and Athienitis, 2003). 2.5. Heating and cooling demands For calculation purposes, the value 90 W/m2 is taken as the average annual power consumption per square meter of the room, which satisfies the needs of heating/cooling. The dimensions of the room must also be considered (Handbook of Fundamentals Chapter 30, 2002; Hendrik, 2010). 3. Optimization of blind tilt angle using a genetic algorithm and fuzzy logic By using a genetic algorithm it is possible to determine the optimal blind tilt angle, in order to achieve the desired comfort in the room. As a population of chromosomes in this study were used current blind tilt angles (simulated with a sine wave), binary coded to a length of 10 bits. Operators which are applied on this population of chromosomes are roulette wheel selection, single-point crossover, and mutation (Melanie, 1999). The blinds can rotate in both directions. Starting from the downward position (0°, blinds fully closed), the blind tilt angle b is measured anticlockwise, as shown with the arrow in Fig. 1. When the blinds are at the horizontal position, b is equal to 90°. When the blinds block the sunlight, b is greater than 90° and finally when the blinds are fully closed at the upward position, b is equal to 180° (Athienitis, 2002). To determine the optimal blind tilt angle, the fitness function is extremely significant. Here it depends on the current outdoor lighting, thermal gains, and current blind tilt angle, and its values vary between 0 and 1 (0 is the worst fitness and 1 is the best fitness). For example, if the outdoor lighting is greater than 1000 lux, the blind tilt angle which represents the chromosome is 70° and we observe the heating season, fitness function will be closer to 1. This is because during winter the algorithm tends to use the thermal gains, regardless on their values. Individual with the best fitness is directly transferred to the next generation. The fitness function differs for heating and cooling season. In the heating season angles that allow more light and heat to get into the room are more convenient. In case of cooling, individuals with the best fitness are angles that prevent heat entrance, because in this way the room is kept from overheating. However, it is significant to mention that energy saving has the priority during summer. This is done because more energy is spent on cooling than on artificial lighting. Power consumption required for artificial lighting and heating or cooling is calculated for the initial angles and those given by genetic algorithm. In this way it is possible to show the power savings. One more option for blind tilt angle optimization is the usage of fuzzy logic (Timothy, 2010; Mateja et al., 2006; Alam et al., 2005; Guillemin and Morel, 2001; Roisin et al., 2008; Anca et al., 2004). This approach is based
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2766
Fig. 4. Simulink model for heating season.
Initial angle [degrees]
primarily on definition of inputs which, in this case, involve current blind tilt angle, outdoor lighting and thermal gains. According to created inputs the rule-base is formed, which determines the optimal blind tilt angle for given conditions. Rules differ for heating and cooling seasons, just like in the genetic algorithm. Optimality criteria used in the fuzzy controller are achieving the desired brightness with better use of natural light and saving energy for heating and cooling. For testing of fuzzy controller, Matlab’s tool, called Simulink is used. One of inputs of the controller is the sinus signal that
represents the change of the blind tilt angle between 0° and 180°, Fig. 4.
4. Results Simulations were performed for all four cardinal directions (east, west, north, and south), taking into account if it is clear or an overcast day, and what time of day it is. In this way it is possible to monitor changes in the blind tilt angle during the day, and power consumption, as well as
200 150 100 50 0 0
5
10
15
20
25
30
35
40
45
50
35
40
45
50
35
40
45
50
35
40
45
50
Power consumption for initial angle [W]
Chromosome of the initial population 1500 1000 500 0
0
5
10
15
20
25
30
Optimized angle [degrees]
Chromosome of the initial population 95 90 85 80
0
5
10
15
20
25
30
Power consumption for optimized angle [W]
Chromosome of the final population 350 300 250 200
0
5
10
15
20
25
30
Chromosome of the final population
Fig. 5. Results of genetic algorithm for January 15th, 12 h, on a clear day, window facing to the south.
Initial angle [degrees]
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770 200 150 100 50 0 0
5
10
15
20
25
30
2767
35
40
45
50
35
40
45
50
35
40
45
50
35
40
45
50
Power consumption for initial angle [W]
Chromosome of the initial population 1300 1250 1200 1150 0
5
10
15
20
25
30
Optimized angle [degrees]
Chromosome of the initial population 180 175 170 165 160
0
5
10
15
20
25
30
Power consumption for optimized angle [W]
Chromosome of the final population 1268 1267 1266 1265 1264
0
5
10
15
20
25
30
Chromosome of the final population
Fig. 6. The results of a genetic algorithm for July 20th are given, 12 h, on a clear day, window facing to the south.
180 160
Blind tilt angle [degrees]
140 120 100 80 60 40
Initial angle [degrees]
20
Optimized angle [degrees]
0
0
1
2
3
4
5
6
7
8
Number of the observed angles
Time offset: 0
(a) Comparison of the initial and optimized blind tilt angle 1750
Power consumption for initial angle [W] Power consumption for optimized angle [W]
Electrical power consumption [W]
1700 1650 1600 1550 1500 1450 1400 1350 1300 1250
0
1
Time offset: 0
2
3
4
5
6
7
8
Number of the observed angles
(b) Comparison of power consumptions for initial and optimized blind tilt angle Fig. 7. The results of the fuzzy controller for January 15th, 12 h, on an overcast day, window facing to the south.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2768 180
Blind tilt angle [degrees]
160 140 120 100 80 60 40
Initial angle [degrees]
20
Optimized angle [degrees]
0
0
1
2
Time offset: 0
3
4
5
6
7
8
Number of the observed angles
(a) Comparison of initial and optimized blind tilt angle
Electrical power consumption [W]
1275
1270
1265
1260
1255 Power consumption for initial angle [W] 1250
1245
Power consumption for optimized angle [W] 0
Time offset: 0
1
2
3
4
5
6
7
8
Number of the observed angles
(b) Comparison of power consumptions for the initial and optimized blind tilt angle Fig. 8. The results of the fuzzy controller for July 20th, 12 h, on an overcast day, window facing to the south.
the comparison of energy consumption depending on orientation of the room. Displayed results of a genetic algorithm provide the possibility of simultaneous comparison of the initial blind angle (sine-wave signal, graph 1) and calculated consumption for it (graph 2), with optimized angle (graph 4) and its energy consumption (graph 3). In Fig. 5 the results of a genetic algorithm for January 15th are given, 12 h, on a clear day, and window facing to the south. It is obvious that the lowest power consumption is achieved for angle of 80°, and it represents the optimal blind tilt angle. In Fig. 6 the results of a genetic algorithm for July 20th are given, 12 h, on a clear day, and window facing to the south. For this example the optimal blind tilt angle is 160°. Figs. 5 and 6 show that the algorithm tends to open the blinds as much as possible during the heating season, in order to maximize the use of heat gains and good natural lighting. On the contrary, in the cooling season, the algorithm tends to close the blinds or to set them to a small angle, because although there is a good natural lighting, heat gains are large and they contribute to increasing power consumption for room cooling. Similar results are achieved using the fuzzy logic. One graph shows the comparison of initial and optimized blind
tilt angle, and the other the comparison of their power consumptions. The initial blind tilt angle and its power consumption are represented with the blue1 color, and the optimized blind tilt angle and its power consumption are represented with the violet color. In Fig. 7 the results of the fuzzy controller for January 15th are given, 12 h, on an overcast day, and window facing to the south. It is obvious that the lowest power consumption is achieved for the angle of 141°, and it represents the optimal blind tilt angle. In Fig. 8 the results of the fuzzy controller for July 20th are given, 12 h, on an overcast day, and window facing to the south. For this example the optimal blind tilt angle is 65°. Figs. 7 and 8 show that controller tends to close the blinds during an overcast day in heating season, in order to prevent heat loss from the room because heat gains are small and natural light is poor. On the contrary, during an overcast day in the cooling season, the controller tends to make better use of natural light, because heat gains are reduced.
1 For interpretation of color in Figs. 1, 5–8, the reader is referred to the web version of this article.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
From these examples it is easy to notice that inconvenient blind tilt angle leads to significant increasing of electrical power consumption. Taking advantage of natural light can save from 50% to 80% on lighting costs. Analysis of simulation results led to the conclusion that optimizing the blind tilt angle generates energy savings over 25% in the heating season, and over 35% in the cooling season, depending on the orientation of the window. The greatest savings are achieved for orientation towards the south and west, and little less for orientations towards north and east. 5. UML diagram Data necessary for developing an algorithm for blind control is derived after an analysis of the results given by the genetic algorithm and fuzzy controller. Simulations were performed for different orientations of windows, time of day and weather conditions in order to get a more general algorithm. Results of the genetic algorithm and fuzzy logic match almost entirely, and differences between energy savings or blind tilt angles are insignificant or there are no any. One of the important conclusions was the fact that the fuzzy controller is more convenient for its development. This convenience is due to structure of fuzzy controller’s rule base which is given as if–then notations, and is easier to convert into a form that corresponds to the blind controller. First condition that needs to be considered is the external temperature, used to determine whether it is necessary to heat or cool the space. Then, the measured values of the external light, calculated heat gains and the current position of blinds are taken into account, upon which the decision of new blind tilt angle is made. For the realization of this control the algorithm assumes the existence of a sensor that measures the external temperature, and sensor for measuring external lighting. Thermal gains are calculated by expressions given in mathematical model. After collecting the necessary data, the controller makes a decision about setting blinds in an optimal position. It has an option of selecting between manual or automatic mode for blinds control. In the automatic mode, the decision of blind slats position is made by controller, and in manual mode this decision is left to the user. In the automatic mode of data collecting the changing of blind position is made every 15 min, because it is considered that this is a period in which there is no drastic change of external conditions, or change in the position of the sun. Of course, this time period of changing the blinds position is also one kind of protection of the mechanism which moves or rotates the slats. 6. Conclusion The size of glass in buildings is an important factor that affects the energy consumption. Modern systems that provide protection from sun and weather conditions, combined with intelligent control systems can increase energy savings. The largest consumers of electricity in commercial buildings
2769
are air conditioning and artificial light. Use of daylight affects comfort, increases performance in the workplace and reduces energy costs. The algorithm presented in this paper has the goal to reduce cooling energy demands during summer, by setting blinds in the optimal position, and by doing so preserve the space from overheating due to sunlight, without increasing the cost of artificial lighting. During the winter it is necessary to make better use of thermal gains in order to reduce power consumption for space heating. Simulation results show that using artificial intelligence enables the finding of an optimal blind tilt angle which saves energy at a given moment, without affecting the user’s comfort in the aspect of lighting. The UML diagram which describes the algorithm for blind control presents a simplified version of the fuzzy controller. In this paper the fuzzy logic is proved to be the most suitable for determining the optimal blind tilt angle, and at the same time as the simplest method of control that can be transformed to a form suitable for the controller. Taking the range of values from membership functions for defining inputs and outputs, and on rule-base of the fuzzy controller, an algorithm for blinds control is developed. More study needs to be undertaken to determine the validity and applicability of the proposed algorithm. References Alam, S.M., Saha Kumar, Sushata., Chowdury, M.A.K., Saifuyyaman, Md., Rahman, M., 2005. Simulation of solar radiation system. In: American Journal of Applied Sciences, vol. 2. Science Publications, 2005. Alessandro, Quintino, Lucia, Fontana, 2011. Fenestration peak solar heat gain: a review of the cloudless day condition as conservative hypothesis. Thermal Science 15, 223–234. Anca, Galasiu D., Morad, Atif R., Robert, MacDonald A., 2004. Impact of window blinds on daylight-linked dimming and automatic on/off lighting controls. Solar Energy 76, 523–544. Athanassios, Tzempelikos, Andreas, Athienitis K., 2007. The impact of shading design and control on building cooling and lighting demand. Solar Energy 81, 369–382. Athanassios, Tzempelikos, Andreas, Athienitis K., Panagiota, Karava, 2007. Simulation of facade and envelope design options for a new institutional building. Solar Energy 81, 1088–1103. Athienitis, K.A., 2002. Tzempelikos athanassios: a methodology for simulation of daylight room illuminance distribution and light dimming for a room with a controlled shading device. Solar Energy 72, 271–281. Axel, Bring, Per, Sahlin, Mika, Vuolle, 1999. Models for building indoor climate and energy simulation. Journal of Research and Development. De Rosa, A., Ferraro, V., Kaliakatsos, D., Marinelli, V., 2008. Calculating diffuse illuminance on vertical surfaces in different sky conditions. Applied Energy 33, 1703–1710. De Rosa, A., Ferraro, V., Kaliakatsos, D., Marinelli, V., 2010. Calculating indoor natural illuminance in overcast sky conditions. Applied Energy 87, 806–813. Dimitrije, Lilic´, 2003. Influence of window and door position at the wall on the radiation heat exchange in relation to interior room surfaces. Energy and Buildings 35, 533–538. Guillemin, A., Morel, N., 2001. An innovative lighting controller integrated in a self-adaptive building control system. Energy and Buildings 33, 477–487.
2770
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
ASHRAE Handbook of Fundamentals, 2002. New York, USA [Chapter 30]. Hendrik, Voll, Teet-Andrus, Koiv, Teet, Tark, Monika, Sergejeva, 2010. Cooling demand in commercial buildings – the influence of daylight window design. WSEAS Transactions on Applied and Theoretical Mechanics 5. Katiyar, K.A., Kumar, Akhilesh, Pandey, K.C., 2010. Correlations for the estimation of monthly mean hourly diffuse solar radiation: a time dependent approach. International Journal of Energy and Environment 1, 833–840. Kwang-Wood, P., Athienitis, A.K., 2003. Work plane illuminance prediction method for day lighting control systems. Solar Energy 75, 277–284. Long, Shi, Michael, Chew Yit Lin, 2012. A review on sustainable design of renewable energy systems. Renewable and Sustainable Energy Reviews 16, 192–207.
Mateja, Trobec Lah, Borut, Zupancˇic´, Jozˇe, Peternelj, Alesˇ, Krainer, 2006. Daylight illuminance control with fuzzy logic. Solar Energy 80, 307–321. Melanie, Mitchell., 1999. An Introduction to Genetic Algorithms. In: A Bradford Book, vol. 5. The MIT Press. Orgill, J.F., Hollands, K.G.T., 1977. Correlation equation for hourly diffuse radiation on a horizontal surface. Solar Energy 19, 357–359. Kumar, Ravinder, Umanand, L., 2005. Estimation of global radiation using clearness index model for sizing photovoltaic system. Renewable Energy 30, 2221–2233. Roisin, B., Bodart, M., Deneyer, A., D’Herdt, P., 2008. Lighting energy savings in offices using different control systems and their real consumption. Energy and Buildings 40, 514–523. Timothy, Ross J., 2010. In: Fuzzy logic with engineering applications, vol. 3. Wiley.
Solar Energy 86 (2012) 2762–2770 www.elsevier.com/locate/solener
Algorithm for blinds control based on the optimization of blind tilt angle using a genetic algorithm and fuzzy logic ˇ ongradac ⇑, Marta Prica, Marija Paspalj, Dubravka Bojanic´, Darko C ˇ apko Velimir C Faculty of Technical Sciences, Trg D. Obradovic´a 6, 2100 Novi Sad, Serbia Received 29 March 2012; received in revised form 31 May 2012; accepted 14 June 2012 Available online 17 July 2012 Communicated by: Associate Editor J.-L. Scartezzini
Abstract This paper presents the calculation of the power of solar rays that pass through the window of an observed room and their impact on warming up and lighting of the room. The calculations were performed using a mathematical model that takes into account the geographical position of the object, time zone, orientation of windows, day of the year, and current time. This paper also includes the calculation of geometry of the solar radiation and its intensity, artificial light and cooling/heating demands. Based on data from above, the optimization of blind tilt angle was performed to achieve the best possible brightness of the room and energy savings when heating or cooling, depending on ambient temperature. Optimization was performed using a genetic algorithm and fuzzy logic. After an analysis of the results obtained from optimization of the blind tilt angle, an algorithm for blinds control was developed in order to achieve energy savings and comfort in the observed room. Based on the derived conclusions, an UML diagram was made that describes the algorithm for determining optimal blind tilt angle. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Blind tilt angle; Thermal gain; Lighting; Power consumption; Genetic algorithm; Fuzzy logic
1. Introduction Solar energy is a renewable and inexhaustible energy resource that can have an important role in the energy sector of every country, and provide a significant reduction in power consumption. During the year, the solar energy that reaches the Earth is 10,000 times greater than the energy necessary to fulfill the needs of the entire population of our planet. On average, each square meter of land is exposed to enough sunlight to receive 1700 kW h of energy every year, and more energy is generated if radiation is higher at the observed location. Heat gains derived from solar radiation during winter can be used for space heating, and thus reduce the needs of energy consumption. During
⇑ Corresponding author. Tel.: +381 631010120.
ˇ ongradac). E-mail address: [email protected] (V. C 0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.06.016
summer, heat gains are undesirable because they lead to room overheating, and therefore it is needed to spend more energy for cooling the room. This is why the usage of shading is required during the summer period. The shading is a very important factor in the whole story about passive design of the facilities. The angle of solar rays that hit the object is different in winter and summer, and this fact is used in shading. Between the tropics and the polar circles, the Sun is low in the winter and solar rays fall to the object under a small angle, while the situation is reversed in summer and solar rays fall under a larger angle. The change of angle is most important on the south side for buildings in the northern hemisphere. Depending on the area where the building is located, the maximum and minimum angle of solar rays can vary. The blinds are practical because they can adapt to the current needs and thus maximize protection from the Sun in summer, and heat gains in winter.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2763
Systems that control the amount of daylight that enters the building provide better usage of solar energy. These systems are designed taking into account the type, size and orientation of windows, and shading elements, such as shutters, blinds, roller shades, for example. Environmental effects, such as position of surrounding buildings and the nature of the environment in which the observed object is set, are also very important. All these elements comprise a major contribution in design of room lighting and temperature controls.
overcast overcast Ewindow overcast ¼ E diffuse þ E ground
2. Model development
Eovercast ¼ Ewindow overcast VT sovercast
½1x
ð3Þ
where Eovercast diffuse is the sky diffuse illuminance for an overcast day, Eovercast ground is the ground reflected illuminance for an overcast day. Total room illuminance for an overcast day is the maximum value of natural light in the room for an overcast day, considering visual transmittance of the window and optimal tilt angle of the blinds, or the maximum value of visual transmittance of blinds sovercast for that tilt angle. It is calculated by the following equation (Athienitis, 2002): ½lx
ð4Þ
Ewindow overcast
The mathematical model is based on calculations of global radiation, in order to get the values for external lighting and thermal gains. To calculate the external illumination it is necessary to know the latitude and longitude of the object, time zone, cloudiness, day of the year, and time for purposes of determining the exact position of the Sun (Long and Michael, 2012). This data, including the technical characteristics of window and room, is used to get values of the amount of light that enters the room and thermal gains that lead to warming up the space. Additional artificial lighting and requirements for additional space cooling or heating depend on these values. Solar heat gains depend on solar ray power, and environment characteristics such as transmission, reflection and absorption (Long and Michael, 2012). Final heat gains that pass through the window are given with mathematical equations and calculations related to the transmittance coefficient, view factors, reflection factors and other environment characteristics and materials that sunlight passes through (Athienitis, 2002).
is the total illuminance on the window surwhere face for an overcast day, VT is the visual transmittance of window, sovercast is the visual transmittance of blinds for an overcast day. During a clear day the solar radiation that falls on the window consists of all three radiation components: direct, diffuse and reflected radiation (Athienitis, 2002). Total illuminance on the window surface for a clear day can be calculated by simply summing the direct, diffuse and reflected light, using the expression (Athienitis, 2002):
2.1. Solar gain
Eclear hsky is the diffuse horizontal illuminance, FWS is a view factor between the window and sky, Eclear is horizontal illuh minance, FWG is a view factor between the window and ground, qG is albedo, E0 is average illuminance on a surface perpendicular to the solar rays just outside the earth’s atmosphere, f is the correction factor, c is the optical atmospheric extinction coefficient, m is the relative optical air
The model for a cloudy day implies that the direct solar radiation is practically absent. Therefore, total illuminance on a window surface contains only diffuse and reflected radiation (De Rosa et al., 2008, 2010). Sky diffuse illuminance on a window surface is given by equation (Athienitis, 2002): overcast Eovercast F WS diffuse ¼ E h
½lx
clear clear clear Ewindow clear ¼ Ediffuse þ E ground þ E direct
½lx
ð5Þ
where Eclear diffuse is the diffuse illuminance clear Eclear diffuse ¼ EhSky F WS
½lx
ð6Þ
Eclear ground is the ground reflectance clear Eclear F WG qG ground ¼ E h
½lx
ð7Þ
Eclear direct is the direct illuminance cm cosh Eclear direct ¼ E0 f e
½lx
ð8Þ
ð1Þ
where Eovercast is the diffuse horizontal illuminance, FWS is a h view factor between window and sky (FWS 0.5). Using Eq. (2) we can calculate the intensity of light reflected from the ground and falling on the window surface (Athienitis, 2002): overcast Eovercast F WG qG ground ¼ E h
½lx
ð2Þ
where Eovercast is the diffuse horizontal illuminance, FWG is a h view factor between the window and ground (FWG 0.5), qG is the reflection coefficient (albedo). Total illuminance on a window surface for an overcast day can be calculated by simply summing the diffuse and reflected light, using the expression (Athienitis, 2002):
Fig. 1. Cross-section of the window along with the incidence angle of direct radiation on the window and blind tilt angle.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2764
mass, and h is the incidence angle of direct radiation on the window which is presented in Fig. 1, along with the blind tilt angle. Using the Eq. (9) we can calculate the incidence anlge of direct radiation on the window h (Athienitis, 2002): cosðaÞ cosðjcjÞ þ j cosðaÞ cosðjcjÞj h ¼ a cos ð9Þ ½ 2 where a is solar altitude a ¼ a sinðcosðLÞ cosðdÞ cosðHAÞ þ sinðLÞ sinðdÞÞ
ð10Þ
c is the sun-window azimuth angle difference c ¼ U W ½
ð11Þ
U is solar azimuth angle sinðaÞ sinðLÞ sinðdÞ HA U ¼ a cos ½ cosðaÞ cosðLÞ jHAj
ð12Þ
d is solar declination, L is latitude, HA is hour angle
HA ¼ 15 ðAST 12Þ ½
ð13Þ
AST is apparent solar time LNG STM AST ¼ LT þ ET ½hours 15
ð14Þ
LT is precise local time, ET is equation of time, LNG is longitude of the observed object, STM is a particular time zone, and w is the window’s azimuth angle and it is determined by which way it faces, as measured from south. 2.2. Thermal gain To obtain the total sun power provided for the room, it is necessary to multiply the value of solar ray power through the window and blinds by the cooling load factor (CLF) (Axel, 1999; Katiyar, 2010). It is calculated by the following equation, for a clear and overcast day, respectively (Alessandro and Lucia, 2011; Dimitrije, 2003; Athanassios et al., 2007; Athanassios and Andreas, 2007; Orgill and Hollands, 1977; Handbook of Fundamentals Chapter 30, 2002): P clear ¼ P clear P overcast ¼ P overcast CLF ½W sun CLF ½W sun
to depends only on accurate local time and window orientation. Values used in this work were taken from a table given by ASHRAE (Ravinder, 2005). 2.3. Model of the room The features of the room are very important in order to determine the brightness, because they have a major impact on brightness changing. The relevant factors for lighting calculations are orientation and dimensions of the room, reflection factors of room surfaces, solar gain coefficients, window position (its distance from the ceiling, floor and walls), and height of desktop (work surface). It is important to mention that the room is a regular square shape, dimensions 6 5 3 m, with one outside wall and glazed surface on it (Fig. 2). To simplify the model, the surrounding buildings are neglected and object’s environment is presented as a grassy field. Geographic coordinates are taken for Belgrade, Serbia. It was necessary to calculate the brightness in the middle of the room. Therefore, definitions of specific surfaces within the room are required, and they include: window surface, window containing wall surface, floor surface, ceiling surface, opposite wall surface, right side wall surface, left side wall surface. View factors between characteristic surfaces show how the observed room surfaces will impact on each other, or how the light beam will reflect from one surface to another. They are defined separately for each two surfaces, and depend only on their mutual position. Because of that, the parallel and perpendicular surfaces are distinguished (Athienitis, 2002). View factor between two parallel surfaces is given by next few expressions (Athienitis, 2002). y x m ¼ ;m ¼ z z
ð17Þ
ð15Þ
where P clear is solar ray power through the window and sun blinds for a clear day, P overcast is solar ray power through sun the window and blinds for an overcast day termal P clear sun ¼ SHGclear S P sclear ½w
P overcast sun
¼ SHGovercast S P stermal overcast ½w
ð16Þ
SHGclear is solar heat gain in clear day, SHGovercast is solar heat gain in an overcast day, SP is surface of the window, stermal clear is thermal transmittance of blind for a clear day, stermal overcast is thermal transmittance of blind for an overcast day, and CLF is the cooling load factor (Ravinder, 2005). Calculation of cooling load factor requires a complex mathematical model, but can be approximated in a way
Fig. 2. Model of the room.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
pffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1 þ u2 Þð1 þ v2 Þ 0:5 ln þ v 1 þ u2 2 2 puv 1þu þv pffiffiffiffiffiffiffiffiffiffiffiffiffi v u atg pffiffiffiffiffiffiffiffiffiffiffiffiffi þ þ u 1 þ v2 atg pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ u2 1 þ v2 v atgðvÞ u atgðuÞ ð18Þ
FP ¼
where x is length of the observed surface, y is width of the observed surface, and z is the distance between two surfaces. View factor between two perpendicular surfaces is calculated using Eqs. (19) and (20) (Athienitis, 2002): y z u ¼ ;m ¼ ð19Þ x x pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1 1 1 u atg FN ¼ þ v atg u2 þ v2 atg pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pu u v u2 þ v 2 " ( u2 1 ð 1 þ u2 Þ ð 1 þ v 2 Þ u2 ð 1 þ u2 þ v 2 Þ 0:25ln þ þ pu 1 þ u2 þ v 2 ð1 þ u2 Þð1 þ v2 Þ 2 v2 )# v ð1 þ u2 þ v2 Þ ð20Þ ð1 þ u2 Þð1 þ v2 Þ where x is common dimension, y is unique dimension of the first surface, and z is unique dimension of the second surface (Fig. 3). 2.4. Artificial lighting It was also necessary to calculate the requirements for artificial lighting of the room. About 500 lux was selected for optimal illuminance value, because the observed surface is the desktop. To calculate the required luminous flux on the desktop it is required to determine the useful height (distance between the desktop and light source) and room index. In designing of the artificial lighting the so-called Lumen method is applied. This method is based on fundamental laws and was chosen because of its simplicity and comprehensiveness. Dimensioning of the artificial lighting requires that the lamp efficiency level, required luminous flux, number of required lamps, actual average illuminance and maximum total consumption are calculated. Based on these values, the disposition of lamps is determined. The lamps
Fig. 3. Display of two perpendicular surfaces.
2765
should be distributed evenly on the ceiling, to ensure the best possible illuminance, and minimize side effects (in the form of shadows) (Kwang-Wood and Athienitis, 2003). 2.5. Heating and cooling demands For calculation purposes, the value 90 W/m2 is taken as the average annual power consumption per square meter of the room, which satisfies the needs of heating/cooling. The dimensions of the room must also be considered (Handbook of Fundamentals Chapter 30, 2002; Hendrik, 2010). 3. Optimization of blind tilt angle using a genetic algorithm and fuzzy logic By using a genetic algorithm it is possible to determine the optimal blind tilt angle, in order to achieve the desired comfort in the room. As a population of chromosomes in this study were used current blind tilt angles (simulated with a sine wave), binary coded to a length of 10 bits. Operators which are applied on this population of chromosomes are roulette wheel selection, single-point crossover, and mutation (Melanie, 1999). The blinds can rotate in both directions. Starting from the downward position (0°, blinds fully closed), the blind tilt angle b is measured anticlockwise, as shown with the arrow in Fig. 1. When the blinds are at the horizontal position, b is equal to 90°. When the blinds block the sunlight, b is greater than 90° and finally when the blinds are fully closed at the upward position, b is equal to 180° (Athienitis, 2002). To determine the optimal blind tilt angle, the fitness function is extremely significant. Here it depends on the current outdoor lighting, thermal gains, and current blind tilt angle, and its values vary between 0 and 1 (0 is the worst fitness and 1 is the best fitness). For example, if the outdoor lighting is greater than 1000 lux, the blind tilt angle which represents the chromosome is 70° and we observe the heating season, fitness function will be closer to 1. This is because during winter the algorithm tends to use the thermal gains, regardless on their values. Individual with the best fitness is directly transferred to the next generation. The fitness function differs for heating and cooling season. In the heating season angles that allow more light and heat to get into the room are more convenient. In case of cooling, individuals with the best fitness are angles that prevent heat entrance, because in this way the room is kept from overheating. However, it is significant to mention that energy saving has the priority during summer. This is done because more energy is spent on cooling than on artificial lighting. Power consumption required for artificial lighting and heating or cooling is calculated for the initial angles and those given by genetic algorithm. In this way it is possible to show the power savings. One more option for blind tilt angle optimization is the usage of fuzzy logic (Timothy, 2010; Mateja et al., 2006; Alam et al., 2005; Guillemin and Morel, 2001; Roisin et al., 2008; Anca et al., 2004). This approach is based
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2766
Fig. 4. Simulink model for heating season.
Initial angle [degrees]
primarily on definition of inputs which, in this case, involve current blind tilt angle, outdoor lighting and thermal gains. According to created inputs the rule-base is formed, which determines the optimal blind tilt angle for given conditions. Rules differ for heating and cooling seasons, just like in the genetic algorithm. Optimality criteria used in the fuzzy controller are achieving the desired brightness with better use of natural light and saving energy for heating and cooling. For testing of fuzzy controller, Matlab’s tool, called Simulink is used. One of inputs of the controller is the sinus signal that
represents the change of the blind tilt angle between 0° and 180°, Fig. 4.
4. Results Simulations were performed for all four cardinal directions (east, west, north, and south), taking into account if it is clear or an overcast day, and what time of day it is. In this way it is possible to monitor changes in the blind tilt angle during the day, and power consumption, as well as
200 150 100 50 0 0
5
10
15
20
25
30
35
40
45
50
35
40
45
50
35
40
45
50
35
40
45
50
Power consumption for initial angle [W]
Chromosome of the initial population 1500 1000 500 0
0
5
10
15
20
25
30
Optimized angle [degrees]
Chromosome of the initial population 95 90 85 80
0
5
10
15
20
25
30
Power consumption for optimized angle [W]
Chromosome of the final population 350 300 250 200
0
5
10
15
20
25
30
Chromosome of the final population
Fig. 5. Results of genetic algorithm for January 15th, 12 h, on a clear day, window facing to the south.
Initial angle [degrees]
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770 200 150 100 50 0 0
5
10
15
20
25
30
2767
35
40
45
50
35
40
45
50
35
40
45
50
35
40
45
50
Power consumption for initial angle [W]
Chromosome of the initial population 1300 1250 1200 1150 0
5
10
15
20
25
30
Optimized angle [degrees]
Chromosome of the initial population 180 175 170 165 160
0
5
10
15
20
25
30
Power consumption for optimized angle [W]
Chromosome of the final population 1268 1267 1266 1265 1264
0
5
10
15
20
25
30
Chromosome of the final population
Fig. 6. The results of a genetic algorithm for July 20th are given, 12 h, on a clear day, window facing to the south.
180 160
Blind tilt angle [degrees]
140 120 100 80 60 40
Initial angle [degrees]
20
Optimized angle [degrees]
0
0
1
2
3
4
5
6
7
8
Number of the observed angles
Time offset: 0
(a) Comparison of the initial and optimized blind tilt angle 1750
Power consumption for initial angle [W] Power consumption for optimized angle [W]
Electrical power consumption [W]
1700 1650 1600 1550 1500 1450 1400 1350 1300 1250
0
1
Time offset: 0
2
3
4
5
6
7
8
Number of the observed angles
(b) Comparison of power consumptions for initial and optimized blind tilt angle Fig. 7. The results of the fuzzy controller for January 15th, 12 h, on an overcast day, window facing to the south.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
2768 180
Blind tilt angle [degrees]
160 140 120 100 80 60 40
Initial angle [degrees]
20
Optimized angle [degrees]
0
0
1
2
Time offset: 0
3
4
5
6
7
8
Number of the observed angles
(a) Comparison of initial and optimized blind tilt angle
Electrical power consumption [W]
1275
1270
1265
1260
1255 Power consumption for initial angle [W] 1250
1245
Power consumption for optimized angle [W] 0
Time offset: 0
1
2
3
4
5
6
7
8
Number of the observed angles
(b) Comparison of power consumptions for the initial and optimized blind tilt angle Fig. 8. The results of the fuzzy controller for July 20th, 12 h, on an overcast day, window facing to the south.
the comparison of energy consumption depending on orientation of the room. Displayed results of a genetic algorithm provide the possibility of simultaneous comparison of the initial blind angle (sine-wave signal, graph 1) and calculated consumption for it (graph 2), with optimized angle (graph 4) and its energy consumption (graph 3). In Fig. 5 the results of a genetic algorithm for January 15th are given, 12 h, on a clear day, and window facing to the south. It is obvious that the lowest power consumption is achieved for angle of 80°, and it represents the optimal blind tilt angle. In Fig. 6 the results of a genetic algorithm for July 20th are given, 12 h, on a clear day, and window facing to the south. For this example the optimal blind tilt angle is 160°. Figs. 5 and 6 show that the algorithm tends to open the blinds as much as possible during the heating season, in order to maximize the use of heat gains and good natural lighting. On the contrary, in the cooling season, the algorithm tends to close the blinds or to set them to a small angle, because although there is a good natural lighting, heat gains are large and they contribute to increasing power consumption for room cooling. Similar results are achieved using the fuzzy logic. One graph shows the comparison of initial and optimized blind
tilt angle, and the other the comparison of their power consumptions. The initial blind tilt angle and its power consumption are represented with the blue1 color, and the optimized blind tilt angle and its power consumption are represented with the violet color. In Fig. 7 the results of the fuzzy controller for January 15th are given, 12 h, on an overcast day, and window facing to the south. It is obvious that the lowest power consumption is achieved for the angle of 141°, and it represents the optimal blind tilt angle. In Fig. 8 the results of the fuzzy controller for July 20th are given, 12 h, on an overcast day, and window facing to the south. For this example the optimal blind tilt angle is 65°. Figs. 7 and 8 show that controller tends to close the blinds during an overcast day in heating season, in order to prevent heat loss from the room because heat gains are small and natural light is poor. On the contrary, during an overcast day in the cooling season, the controller tends to make better use of natural light, because heat gains are reduced.
1 For interpretation of color in Figs. 1, 5–8, the reader is referred to the web version of this article.
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
From these examples it is easy to notice that inconvenient blind tilt angle leads to significant increasing of electrical power consumption. Taking advantage of natural light can save from 50% to 80% on lighting costs. Analysis of simulation results led to the conclusion that optimizing the blind tilt angle generates energy savings over 25% in the heating season, and over 35% in the cooling season, depending on the orientation of the window. The greatest savings are achieved for orientation towards the south and west, and little less for orientations towards north and east. 5. UML diagram Data necessary for developing an algorithm for blind control is derived after an analysis of the results given by the genetic algorithm and fuzzy controller. Simulations were performed for different orientations of windows, time of day and weather conditions in order to get a more general algorithm. Results of the genetic algorithm and fuzzy logic match almost entirely, and differences between energy savings or blind tilt angles are insignificant or there are no any. One of the important conclusions was the fact that the fuzzy controller is more convenient for its development. This convenience is due to structure of fuzzy controller’s rule base which is given as if–then notations, and is easier to convert into a form that corresponds to the blind controller. First condition that needs to be considered is the external temperature, used to determine whether it is necessary to heat or cool the space. Then, the measured values of the external light, calculated heat gains and the current position of blinds are taken into account, upon which the decision of new blind tilt angle is made. For the realization of this control the algorithm assumes the existence of a sensor that measures the external temperature, and sensor for measuring external lighting. Thermal gains are calculated by expressions given in mathematical model. After collecting the necessary data, the controller makes a decision about setting blinds in an optimal position. It has an option of selecting between manual or automatic mode for blinds control. In the automatic mode, the decision of blind slats position is made by controller, and in manual mode this decision is left to the user. In the automatic mode of data collecting the changing of blind position is made every 15 min, because it is considered that this is a period in which there is no drastic change of external conditions, or change in the position of the sun. Of course, this time period of changing the blinds position is also one kind of protection of the mechanism which moves or rotates the slats. 6. Conclusion The size of glass in buildings is an important factor that affects the energy consumption. Modern systems that provide protection from sun and weather conditions, combined with intelligent control systems can increase energy savings. The largest consumers of electricity in commercial buildings
2769
are air conditioning and artificial light. Use of daylight affects comfort, increases performance in the workplace and reduces energy costs. The algorithm presented in this paper has the goal to reduce cooling energy demands during summer, by setting blinds in the optimal position, and by doing so preserve the space from overheating due to sunlight, without increasing the cost of artificial lighting. During the winter it is necessary to make better use of thermal gains in order to reduce power consumption for space heating. Simulation results show that using artificial intelligence enables the finding of an optimal blind tilt angle which saves energy at a given moment, without affecting the user’s comfort in the aspect of lighting. The UML diagram which describes the algorithm for blind control presents a simplified version of the fuzzy controller. In this paper the fuzzy logic is proved to be the most suitable for determining the optimal blind tilt angle, and at the same time as the simplest method of control that can be transformed to a form suitable for the controller. Taking the range of values from membership functions for defining inputs and outputs, and on rule-base of the fuzzy controller, an algorithm for blinds control is developed. More study needs to be undertaken to determine the validity and applicability of the proposed algorithm. References Alam, S.M., Saha Kumar, Sushata., Chowdury, M.A.K., Saifuyyaman, Md., Rahman, M., 2005. Simulation of solar radiation system. In: American Journal of Applied Sciences, vol. 2. Science Publications, 2005. Alessandro, Quintino, Lucia, Fontana, 2011. Fenestration peak solar heat gain: a review of the cloudless day condition as conservative hypothesis. Thermal Science 15, 223–234. Anca, Galasiu D., Morad, Atif R., Robert, MacDonald A., 2004. Impact of window blinds on daylight-linked dimming and automatic on/off lighting controls. Solar Energy 76, 523–544. Athanassios, Tzempelikos, Andreas, Athienitis K., 2007. The impact of shading design and control on building cooling and lighting demand. Solar Energy 81, 369–382. Athanassios, Tzempelikos, Andreas, Athienitis K., Panagiota, Karava, 2007. Simulation of facade and envelope design options for a new institutional building. Solar Energy 81, 1088–1103. Athienitis, K.A., 2002. Tzempelikos athanassios: a methodology for simulation of daylight room illuminance distribution and light dimming for a room with a controlled shading device. Solar Energy 72, 271–281. Axel, Bring, Per, Sahlin, Mika, Vuolle, 1999. Models for building indoor climate and energy simulation. Journal of Research and Development. De Rosa, A., Ferraro, V., Kaliakatsos, D., Marinelli, V., 2008. Calculating diffuse illuminance on vertical surfaces in different sky conditions. Applied Energy 33, 1703–1710. De Rosa, A., Ferraro, V., Kaliakatsos, D., Marinelli, V., 2010. Calculating indoor natural illuminance in overcast sky conditions. Applied Energy 87, 806–813. Dimitrije, Lilic´, 2003. Influence of window and door position at the wall on the radiation heat exchange in relation to interior room surfaces. Energy and Buildings 35, 533–538. Guillemin, A., Morel, N., 2001. An innovative lighting controller integrated in a self-adaptive building control system. Energy and Buildings 33, 477–487.
2770
V. Cˇongradac et al. / Solar Energy 86 (2012) 2762–2770
ASHRAE Handbook of Fundamentals, 2002. New York, USA [Chapter 30]. Hendrik, Voll, Teet-Andrus, Koiv, Teet, Tark, Monika, Sergejeva, 2010. Cooling demand in commercial buildings – the influence of daylight window design. WSEAS Transactions on Applied and Theoretical Mechanics 5. Katiyar, K.A., Kumar, Akhilesh, Pandey, K.C., 2010. Correlations for the estimation of monthly mean hourly diffuse solar radiation: a time dependent approach. International Journal of Energy and Environment 1, 833–840. Kwang-Wood, P., Athienitis, A.K., 2003. Work plane illuminance prediction method for day lighting control systems. Solar Energy 75, 277–284. Long, Shi, Michael, Chew Yit Lin, 2012. A review on sustainable design of renewable energy systems. Renewable and Sustainable Energy Reviews 16, 192–207.
Mateja, Trobec Lah, Borut, Zupancˇic´, Jozˇe, Peternelj, Alesˇ, Krainer, 2006. Daylight illuminance control with fuzzy logic. Solar Energy 80, 307–321. Melanie, Mitchell., 1999. An Introduction to Genetic Algorithms. In: A Bradford Book, vol. 5. The MIT Press. Orgill, J.F., Hollands, K.G.T., 1977. Correlation equation for hourly diffuse radiation on a horizontal surface. Solar Energy 19, 357–359. Kumar, Ravinder, Umanand, L., 2005. Estimation of global radiation using clearness index model for sizing photovoltaic system. Renewable Energy 30, 2221–2233. Roisin, B., Bodart, M., Deneyer, A., D’Herdt, P., 2008. Lighting energy savings in offices using different control systems and their real consumption. Energy and Buildings 40, 514–523. Timothy, Ross J., 2010. In: Fuzzy logic with engineering applications, vol. 3. Wiley.