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Application of heliostat in interior sunlight illumination for large buildings
Accepted Manuscript Application of heliostat in interior sunlight illumination for large buildings
Jifeng Song, Geng Luo, Lei Li, Kai Tong, Yongping Yang, Jin Zhao PII:
S0960-1481(18)30011-9
DOI:
10.1016/j.renene.2018.01.011
Reference:
RENE 9616
To appear in:
Renewable Energy
Received Date:
20 August 2017
Revised Date:
07 November 2017
Accepted Date:
04 January 2018
Please cite this article as: Jifeng Song, Geng Luo, Lei Li, Kai Tong, Yongping Yang, Jin Zhao, Application of heliostat in interior sunlight illumination for large buildings, Renewable Energy (2018), doi: 10.1016/j.renene.2018.01.011
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ACCEPTED MANUSCRIPT
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Application of heliostat in interior sunlight illumination for
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large buildings
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JIFENG SONG1,*, GENG LUO2, LEI LI1, KAI TONG1 AND YONGPING YANG2, JIN ZHAO3
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1School
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2Schools
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3Beijing
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*[email protected]
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Abstract
of Renewable Energy, North China Electric Power University, Beijing 102206, China of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China Biomass Energy Technology Center, State Grid Energy Conservation Service LTD, Beijing 100053, China
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Heliostat daylighting systems, used to transmit sunlight deep into rooms where natural light cannot reach, are
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increasingly applied in buildings. A roof-mounted heliostat with an area of 22.95 m2 was developed in this work to verify
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the feasibility of high flux and long distance daylighting in large building interior. The developed heliostat system
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consists of a heliostat, a secondary reflector, and glass windows forming the light path within the building. The problem
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of gravitational deformation of the steel beams base of the heliostat was solved by a rectification algorithm embedded
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into the computer program, to realize vertical daylighting. The spectrum and chromaticity of the heliostat daylighting
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system developed was measured, and the results verify the good visual quality of the interior illumination. The light
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transmission distance is more than 70 m, and the system can provide a level of 20-80 klux daylighting illuminance in the
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daytime. An economic analysis was carried out, and data indicates a good cost-effectiveness of the heliostat daylighting
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system developed. It is hoped that this research will be of some reference value to the design of heliostat daylighting
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systems in large buildings.
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Keywords
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Daylighting; heliostat; solar tracking; deformation
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1. Introduction
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Daylight is usually considered to be able to improve human’s visual comfortability and to make a great impact on
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people's daily life and work. Generally, the electric consumption for artificial lighting can take account of about 30% of
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the total energy consumed in office buildings[1, 2]. The use of daylighting can contribute to energy savings and the
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reduction of greenhouse gas emissions[3-5]. Furthermore, daylight is benefit for physiological rhythm and reduces the
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effects of illnesses [6, 7]. So the design of daylighting systems in buildings is very important.
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The traditional way for daylighting is fenestration on the wall or roof of a building, which cannot track sunlight, so
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called passive daylighting method here. However, windows are hard to solve the problem of interior daylighting for tall
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multi-story buildings constructed in urban areas[8, 9]. In order to introduce more sunlight and meet the need for deep
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indoor illumination, a variety of daylighting systems have been developed to realize remote transmission of sunlight.
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These can be roughly divided into three kinds, including light pipes, optical fiber daylighting system and heliostats
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daylighting system[10]. Generally, the transmission distance of those daylighting devices are of, respectively, about 0-4
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m, 20-50 m and 50-2000 m.
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Light pipe systems utilize an inner mirror surface of the pipe to transmit sunlight by multiple reflections. A typical
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light pipe system consists of an outside collector, a mirror pipe and a luminaire that releases light into the interior[11].
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Light pipe systems could be used to enhance interior illumination for buildings, such as schools or industrial
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buildings[12, 13]. Light pipes for daylighting are easy to install and cost effective. But due to multiple reflections, light
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loss is serious and the transmission distance is only a few meters[14, 15], what limits its application. In terms of 1 / 15
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structure, most of light pipe systems belongs to passive daylighting technique[16] .
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When compared with passive daylighting system, active systems[16] can track sunlight and greatly improve the
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transmission distance of daylight, such as optical fiber daylighting and heliostat daylighting systems. Fiber daylighting
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systems consist of a sun tracking system, lens and optical fibers. The advantages of fiber daylighting systems include
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flexibility in installation and longer transmission distance. A lot of research have been carried out to develop and verify
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optical fiber systems, which covers concentrator studies [17-23] and solar tracking studies [24, 25]. The disadvantage of
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fiber daylighting system is its transmission loss due to fiber attenuation. In general, fiber attenuation rate is closely
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related to wavelength. For example, silica fiber has low transmission loss in the infrared band, with its transmission loss
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being 0.2dB / km at 1550 nm [26]. However, in the visible range, the attenuation can reach up to 15 dB / km at 600 nm
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[27]. In addition, optical quartz fiber bundles are too expensive to be popularly applied to daylighting systems. Fiber
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daylighting systems commonly use plastic fibers - polymethyl methacrylate (PMMA)[23] - and the attenuation of
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PMMA fiber at 650 nm is about 200 dB/km. Therefore, the transmission distance of fiber daylighting system is usually
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not more than 50 m, most case to 20 m[28]. For large buildings high than 50 m, it is difficult for light pipe or optical fiber
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daylighting system to realize inner nature lighting.
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To solve the problem of sunlight transmission distance, heliostat daylighting systems got researchers’ attention. The
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function of a heliostat is to reflect sun's rays to a given direction to project irradiation onto a target. Compared to light
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pipe systems and optical fiber daylighting systems, sunlight in heliostat systems travels straight in air other than pipes or
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optical fibers and the transmission distance of sunlight can easy reach up to kilometers. Research on heliostats for
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daylighting have reported in literature[29]. Those researches show that heliostats have a competitiveness in transmission
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distance for building daylighting [30-33].
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Most of heliostat daylighting systems reported adopt small mirrors with an aperture of less than 7 m2. Rosemann, A.
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et al.[33] tested a heliostat system, including a heliostat combined with light pipes and artificial light. The area of the
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heliostat mirror was 6.25 m2, and the sunlight could penetrate 3 floors to afford nature light for 12 m high stairs. Pohl and
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Anselm[34] developed a heliostat system, which contained Fresnel lens and light pipes (diameter 0.3 m ). It realized an
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illuminance level of 100 ~ 1200 lux for a windowless basement room (7.8m long, 4.5m wide, 2.4m high). Gon Kim et
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al.[29] designed a heliostat with a diameter 0.75 m mounted on the roof of a 4-floors building. The secondary mirror
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faces the window of the first floor. The transmission distance is about 15 m. Tests verified that, compared to non-
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heliostat systems, there is a certain improvement in the indoor average illumination, and the effect is satisfying.
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Although heliostat daylighting systems have a much longer transmission distance, heliostat daylighting system of
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high flux and long distance are rare studied or reported. The main reasons perhaps include gravity load effect and light
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path design inner buildings. This work focuses on the feasibility of a heliostat daylighting system of large size for large
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building. The aim of this work is to analyze the gravity load influence on the base of the heliostat system and to solve this
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phenomenon by a compensation algorithm embedded in the computer program. In this paper, a large-size heliostat with
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an area of 22.95 m2 was developed and installed on a 70 m high building to reflect direct irradiation from the roof to the
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ground floor. The light path system was also detailed in the paper. The gravity deformation of the base of the heliostat
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has been analyzed and the compensation algorithm was developed and tested. The illuminance results and the
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chromaticity of the daylighting system are described in detail in this paper. An economic analysis was also carried out to
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estimate the potential of the heliostat daylighting system of large aperture.
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2. System Configuration
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Fig.1 Diagram of system, (a) daylighting on ground, (b) the 8th floor light path, (c) the roof-mounted heliostat and second reflector, (d) overall layout,
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(e) the beam net of the roof, (f) the beam geometry of the 8th floor, (g) the zone for daylighting on the ground.
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The center of the building is designed with a hollow structure to enable the sunlight to travel downwards. The
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daylighting system consists of a heliostat and a secondary reflector, shown in Fig.1. The heliostat tracks the sun, then
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reflect horizontally the sunlight onto the surface of the secondary reflector. The secondary mirror is a flat mirror, with an
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angle of 45 ° from the horizontal, and can reflect sunlight exactly vertical to the ground bottom of the building. The
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characteristics of the system are listed in Table 1. 3 / 15
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Table 1 Geometric parameters Modules
Mirror
Stepping motor#1 Heliostat
Elevation Servo cylinder
Azimuth
Stepping motor#2 Planet reducer -
Secondary
Mirror
reflector Glass
Parameters
Units
Value
Length
m
5.1
Width
m
4.5
Reflectance
-
92%
Torque
N·m
4
Step angle
Deg
0.6/1.2
Stroke length
mm
1150
Lead
mm
5
Torque
N·m
36
Step angle
Deg
0.6/1.2
Reduction ratio
-
40
Weight
t
1.5
Length
m
6.6
Width
m
4.67
Reflectance
-
92%
Angle
Deg
45
Transmittance
-
90%
88 89
2.1 The heliostat
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（1）Structure
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The heliostat adopts a rectangular plane mirror, made from ultra-clear silver mirrors, whose reflectance averages
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around 92%. The large mirror is made up of 20 small mirrors with a total area of 22.95 m2 as shown in Fig.2a. The
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heliostat has an ability to move at two degrees of freedom, the azimuth and the elevation direction, respectively. The
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heliostat is installed on the steel beam net below the glass cover of the roof as shown in Fig.2b. The steel beam net acts as
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a base for the heliostat. Among the steel beam net, each joint is a bolted connection. Because of the big spacing (24m×
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24m ), the stiffness of the steel beam net is not high, which means gravity deformation will occur once the heliostat was
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installed on the beam net. Further, the gravity deformation of the beam net will cause a deviation on the coordinate
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system of the heliostat, and the sequential result is that the heliostat cannot track sun exactly, which means the heliostat
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daylighting system cannot project precisely sunlight onto the zone needing illuminance. In this research, this problem is
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solved by a special compensation algorithm embedded in the control program, presented in Section 3.
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Fig.2 Layout of the heliostat daylighting system. (a) The heliostat and the secondary reflector, (b) the steel beam net base of the heliostat system
（2）Control module
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The control module consists of sensors, motors and reducers, as well as controllers and a power supply. One motor
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rotates the heliostat in the azimuth direction, and another motor provides rotational movement in the elevation direction,
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ensuring that the heliostat constantly tracks the sun. It is needed to point out that the normal orientation of the heliostat
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mirror dose not point to sun disk, but to the bisector of the angle between the light ray from the center of sun disk and the
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line from the heliostat to the second reflect mirror. The sensors include an inclinometer for altitude and an encoder for
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azimuth, a GPS, and a wind sensor, which respectively feed information relating to the normal direction of the heliostat,
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time, longitude, latitude, and wind speed. The controller firstly works out sun’s position based on GPS signal, and then
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works out the theory value of the normal direction of the heliostat mirror. Then, the controller drives the motors to rotate
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in a loop control model to reflect sunlight horizontally onto the second reflector. The control logic is shown in Fig.3.
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114 115 116 117
Fig.3 Control logic of the heliostat daylighting system
2.2 The secondary reflector The secondary reflector is mounted at the center of the roof. The average reflectance is equivalent to that of the 5 / 15
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heliostat at around 92%. Mirrors are separated from outside environment by glass room as shown in Fig. 2a. This
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measurement can effectively reduce the accumulation of dust on the mirror. Coupled with its own downwards angle
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(45o), the mirrors can remain clean for a long time, thus keeps high reflectance and reduces the amount of cleaning work
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required.
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2.3 Building structure
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In order to reduce wind load on the heliostat, there are wind-break walls on the roof. The layout of the wind-break
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walls, the heliostat, and the secondary reflector on the roof is shown in Fig. 1(e). The entire steel beam net of the roof is
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symmetrical in east-west and north-south directions. The secondary mirror is located in the center of the roof. The
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heliostat is located on the north side of the secondary mirror, 9.29 m from the center and 4.17 m from the north wall. The
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north wall is 4.5 m high, while other walls are 3.94 m high. The wind-break wall can efficiently alleviate the wind load
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on the heliostat and reduce the deformation of the base (the steel beam net)
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When sunlight penetrates the 8th floor hole, it will be partially blocked by the steel beams. This steel beam net is
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symmetrical. As shown in Fig. 1(f), the total length is 8 m, and the steel beam spacings are 2.12 m and 1.88 m. In
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addition, the width of each steel beam is 0.2 m.
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The daylighting zone on the first floor is shown in Fig. 1(g). The atrium is a square with a 24×24 m size. During
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the experiment, five sets of illuminometers are used simultaneously to measure the flux distribution. There are 100
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sampling points which can be finished within 100 s. Generally, in a sunny day, the intensity of direct normal irradiation
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of sun changes slowly. The result shows that the fluctuation of intensity of flux on the ground is less than 2% within 100
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s in a clear sunny day (8 a.m.-17 p.m.).
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2.4 Effect of sunlight blocking
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The building is located in Beijing (N40.105537o, E116.365412o). The location of the heliostat is arranged in the
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norther direction of the secondary reflector to alleviate the cosine efficiency[35], so as to achieve a higher annual average
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sunlight collecting efficiency. However, it is needed to point out that the sunlight collecting efficiency of the heliostat
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cannot remain at a high value all the time because of the blocking caused by surrounding wind-break walls or the second
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reflector itself. The sunlight collecting efficiency, not the cosine effect, of the heliostat can be figured out by calculation
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according to the geometrical structure and the sun position curve. A concept, so called here, sunshine area rate (SAR) of
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the heliostat mirror is defined as the ratio of the sunshine area on the mirror to the total area of the heliostat mirror. The
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SAR changes all the time. The fluctuation of SAR at three typical days, the winter/summer solstice and the spring
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equinox, were calculated and shown in Fig. 4.
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Fig. 4 Sunlight collecting efficiency of the heliostat presented
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The dashed line in Fig. 4 is the proportion of the area of the heliostat mirror tower above the eastern wind-break
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wall, to the area of the heliostat mirror, which is about 30%. The advantage of this design is that the heliostat can capture 6 / 15
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the sunlight and begin to work the moment sun rising. From Fig. 4, it can be seen that at the summer solstice, the value of
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SAR rises fast after sun rising and reaches 100%. In fact, the entire heliostat mirror can receive sunlight during most of
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daytime (about 6:30 to 18:00). That means the heliostat daylighting system could afford a full function. Comparing to
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summer’s, at winter solstice, the SAR cannot maintain at a high level because of sunlight blocking by the second
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reflector and surrounding wind-break walls at a low altitude angle of sun. The curve of SAR at the spring equinox is
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between the summer solstice and the winter solstice, which is satisfactory.
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Fortunately, the curve of direct normal irradiation (DNI) of one day roughly consists with the SAR of the heliostat.
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On May 26th, 2017, a continuous experiment of direct illuminance was carried out. The flux intensity was recorded
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every 10 minutes, shown in Fig. 5.
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Fig. 5 Direct solar illuminance (Beijing, May 26th, 2017)
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For a sunny day, the direct normal irradiation can reach 50% of its maximum in half an hour after sunrise.
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Combined with the solar altitude curve, when the angle is greater than about 20 degrees, the illuminance is relatively
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stable and high, about 100 klux. With the addition of the influence of the tilt from the heliostats, the illumination on the
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ground at noon is best, and the illumination at 7: 00, or 16:00, is also satisfactory. So for most of daytime, a satisfactory
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lighting effect can be obtained
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Combining Fig. 4 and Fig. 5, we see that when the degree of blocking is serious (sunrise and sunset moment), the
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DNI is low. On contrast, for most of daytime, the DNI is high meanwhile shading block is much less. In summary, the
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shading block caused by wind-break walls and the second reflector is acceptable and does not pose a threaten for
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daylighting.
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3. Heliostat control model
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3.1 The algorithm of the heliostat
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Conventionally, the solar position can be represented by the elevation angle and azimuth angle , and the attitude
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of the heliostat is a function of the elevation angle s and the azimuth angle s. In this paper, the heliostat normal vector
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H is used to characterize the direction of the heliostat mirror. The heliostat normal vector H can be represented by
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azimuth and elevation angles, corresponding to the two motors.
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Fig. 6. Coordinate system of the heliostat mirror
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It is recognized that, based on the horizontal coordinate system (west-south-height), the solar elevation angle s and
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the azimuth angle s is a function of the geographical latitude , solar declination angle , hour angle , and other
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factors[36].
cos s sin s S cos s cos s sin s
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183 184
Thus, the unit vector S of the incident light is defined. The target position, the second reflector, is fixed, then the target unit vector T is easily represented.
0 T 1 0
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186 187
(1)
(2)
The unit normal vector H of the heliostat has the following relation with S and T and the incident angle as shown in Fig.6.
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cos 2 =S T
(3)
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cos H sin H 1 H cos H cos H (S T ) 2 cos sin H
(4)
190 191
From above formulas, the unit normal vector of heliostat is obtained. 3.2 The correction of the heliostat tracking
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The coordinate system of the heliostat is not constant due to two factors. One is the gravitational deformation of the
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steel beam net. The center of the roof which steel beam structure is shown in Fig. 2b will sink due to the gravity load of
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the secondary reflector and steel beam itself. The heliostat is located north of the center, so the base is tilted to the south.
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The other is the shift of the center of the gravity of the heliostat when the heliostat tracks sun during daytime as shown in
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Fig. 7. This shift is corresponding to the elevation angle of the heliostat, and the shift of the center of gravity leads to the
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deformation of steel beams. The above two effects can cause the heliostat tracking error. In this research, a correction
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algorithm was developed to solve this problem.
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The base of the heliostat tilts to the south, what can be described using the below rotation matrix 8 / 15
ACCEPTED MANUSCRIPT 0 1 Rwest ( ) 0 cos 0 sin
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201
0 sin cos
(5)
And the correction vector H concerning the center of gravity
0 H = 0 z
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(6)
203 204
Fig. 7 Mathematical model of center of gravity
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The parts of heliostat excluding the mirror and the mirror steel frame less affects the deviation of center of gravity
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because of the symmetry. So assuming that only the mirror and the mirror steel frame have a not-neglected influence on
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the deviation. From Fig. 7, the length of the deviation
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fit the relationship between G and the elevation-angle offset z c0 c1G c2 G o( G ) . Simplify the
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polynomial and ignore the third-order infinitesimal term to obtain the correction vector
G =b0 b1 sin H
2
0 H = 0 a0 a1 sin H a2 sin 2 H
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New heliostat vector
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Polynomial coefficients above, a, b and c, are undetermined constants.
214 215 216
3
(7)
H Rwest ( ) H H
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can be obtained. The polynomial is used to
0 1 H 0 cos 0 sin
0 0 sin H 0 a0 a1 sin H a2 sin 2 H cos
(8)
A series of experiments were conducted to record a series of data include the corrected elevation angle ’H, the corrected azimuth angle ’H and the corresponding time. Get the measured heliostat vector
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ACCEPTED MANUSCRIPT cos H sin H H cos H cos H sin H
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(9)
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The corrected angles can be got when the heliostat is manually adjusted to the best position. And the least squares
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method is adopted to calculate the value of , a0, a1 and a2. The error function and objective function are defined as
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follow.
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Error function
fi ( , a0 , a1 , a2 ) H i
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H i , H i
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Where M is the total number of measurements.
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Objective function
i 1, 2,3, , M
(10)
M
S ( , a0 , a1 , a2 ) f i 2 ( , a0 , a1 , a2 )
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(11)
i 1
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4. Experiment and analysis
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The four parameters obtained by the correction model above, =-1.225o, a0=0.01509, a1=-0.03122, a2=0.03036. So
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the correction algorithm is thus determined as shown in equation 8. The tracking errors before and after correction were
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measured on April 23rd and 24th, 2017 by a simple shade method. A needle was vertically placed on the ground and the
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length of the needle shade can indicate the value of tracking error. Fig. 8 shows the comparison of tracking errors before
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and after correction. This correction algorithm was embedded into the computer program to realize high precise solar
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tracking.
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Fig. 8 Errors of the azimuth angle and the elevation angle before (April 23rd, 2017) and after (April 24th, 2017) correction in Beijing.
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It can be seen that tracking errors of the azimuth and elevation angle can be kept within ± 0.1 degree after the
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correction, so the satisfactory control precision is achieved.
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The spectrum of sunlight entering the building was measured to verify its comfort to humans, and it is generally
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believed that the nearer light approximates to the spectrum of nature light, the visual environment is more comfortable.
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The experiment was carried out at 12:00 on May 26th, 2017.
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Fig. 9 Results of the spectrum and chromaticity, (a) spectrum, (b) chromaticity.
The experimental results are shown in Fig. 9. The spectrum of the daylighting in this work is shown in Fig. 9 (a)II,
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which is very close to the spectrum of nature light(I). Meanwhile the color rendering index can reach 98.3, providing
244
residents an approximate natural lighting environment, especially beneficial to those who draw or need physical therapy.
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Compared with the spectrum in (a)I, the relative intensity of short wavelengths (about 380nm) are filtered out a lot, and
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the part of long wavelength is relatively reduced by a little. What affects the interior spectrum is exactly the mirrors and
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glued double-glass, but the impact is small. In addition, the spectrum of the fluorescent lamp(III) and the spectrum of the
248
incandescent lamp(IV) are also measured as shown in Fig. 9 (a). They are obviously different from nature light spectrum.
249
The points in the CIE1931 chromaticity diagram are also drawn as shown in Fig. 9 (b). Point I and point II closely
250
overlap and the chromaticity of interior sunlight is very close to the nature light. However, the fluorescent lamp and the
251
incandescent lamp are less healthy, so the advantage of the system is able to bring healthy sunlight.
252 253
At 5:30, 7:00, 12:00, 16:00, 19:00, on May 26th, 2017, the illuminance distribution on the surface area was measured, and the post-processing data results are shown as Fig. 10.
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Fig. 10 Illuminance distribution, (a) 7:00, (b) 12:00, (c) 16:00, (Fig. a b and c share a legend) (d) roof at 19:00, (e) 5:30, (f) 19:00, (g) ground at 14:00.
256
(Beijing, May 26th, 2017)
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It can be seen that the presence of steel beams affects the distribution of illuminance, so that the illuminance in the
258
area corresponding to steel beams is significantly lower. However, owing to the fact that sunlight is not parallel, after
259
long distance transmission, the corresponding part of the ground can receive a strong illuminance, at around 20 klux.
260
From the distribution of the illuminance, it can be seen that only when the distribution in Fig. 10 (b) is at 12:00 is
261
there a complete rectangle, while the others are not complete. Distributions in Fig. 10 (a) and (c) are caused by the tilt of
262
the heliostats. Obviously, in the morning and afternoon, the heliostat does not face the secondary mirrors, and the
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projection area of the heliostat mirror on the vertical plane is less than the projection when it does so. The projection
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shape is non-rectangular, and so the sunlight does not fall on the entire secondary mirror. At 7:00, the heliostat mirror
265
faces the southeast, with the corresponding southwest corner of the distribution missed. At 16:00, the heliostat mirror
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faces the southwest, and thus, similarly, the southeast corner of the distribution is missed. The missing areas in Fig. 10
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(e) and (f), in addition to the effects of the tilt, are mainly affected by wall occlusion. As shown in the photographs in
268
taken at 19.00 in Fig. 10 (d), the projection on the secondary mirror is only a strip area near the north side, so in terms of
269
illuminance distribution, only a small part of the area near the north side is covered in sunlight. And the photograph on
270
the ground as shown in Fig. 10 (g). Furthermore, this validates previous analysis.
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5. Cost analysis
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The flux density projected by the heliostat (~30 klux) is far higher than that of traditional artificial lamps (~300 lux),
273
such as LED. Therefore, a considerable electric saving is realized. An analysis of cost recovery was carried out. Among
274
the cost, the heliostat and the secondary reflector account for a large share because they are customized, including the
275
heliostat (about 6.8k dollar), the secondary reflector (about 1.7k dollar) and the labor (about 4.2k dollar). The
276
maintenance of the heliostat mainly includes mirror cleaning, oil bearing maintenance and control system electricity, a
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total of 75.6 dollars per year. The economic benefit of the equipment is converted according to the average light effect of
278
fluorescent lamp of 60 lm/W [37] and the price of 0.09 dollars/kWh. And the system can provide the average daily
279
illumination about 30klux, experimental lighting area about 50.9 m2 and working hours 8 h. We take 2016 as a typical
280
year, and there are 153 sunny days and 88 cloudy days in Beijing. Suppose a cloudy day is converted to 0.4~0.8 sunny
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days. So 3.5~4.1k dollar can be earned in 2016 from the following equation.
282
Annual income = illuminance × area / light efficiency × (sunny days + 0.4~0.8 × cloudy days) × working hours ×
283
electricity price 12 / 15
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Suppose the discount rate is 10%. The dynamic payback period[38] can be estimated, and it takes 3.9~4.9 years to
285
recover the cost of the equipment economically. The high density of direct normal irradiation and the high transmission
286
efficiency of sunlight jointly offer the heliostat system a satisfactory capacity to supply large flux daylighting for
287
buildings.
288
6. Conclusion
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This research focuses on the deep inner daylighting of large building. This work aims to transmit high flux to a long
290
distance, to realize daylighting for building by using a heliostat mirror of large size. The experiments show that large-size
291
heliostats can meet the demand for high flux (30 klux), long-distance (70 m) interior daylighting in large buildings. The
292
factors that affect the efficiency of light transmission are the reflectance of mirrors, the transmittance of glass, the
293
coverage of steel beams in the system, and the SAR. In the air, the transmission attenuation is slight and can be
294
neglected. In terms of visual quality, the spectral results verify that the interior daylight can get the high-fidelity nature
295
light spectrum to provide a healthy lighting environment. The gravitational deformation of the steel beam roof caused a
296
tilt of the heliostat base which could further led to tracking errors. In addition, the shift of the center of gravity of the
297
heliostat during tracking also aggravate this tilt. To solve this problem, an elaborated geometrical algorithm was
298
developed and embedded into the computer program. The results demonstrated that this compensational algorithm can
299
successfully ensure the daylighting beam perpendicular to ground with a precision of 0.1 degree.
300
Due to the large size of the heliostat and high windy roof, the system has some installation limitations, and it is
301
necessary for the building to reserve a large space for the sunlight path. These limitations make the layout of the heliostat
302
system inflexible. So building lighting integrated design is recommended to adopt. The wind-break walls will block the
303
sunlight in the early morning and evening, and the secondary reflector will block the heliostat at noon. To achieve a good
304
SAR, the layout of roofs and heliostats needs to be considered carefully.
305
This paper demonstrated the feasibility of the application of large-scale heliostats for deep inner daylighting in large
306
buildings. Cost analysis shows that the daylighting system has a good capacity on electric saving for lighting. For the
307
heliostat system presented, the payback period is about 3.9-4.9 years. It is hoped that the results of this research will be a
308
useful reference for designs of heliostat daylighting systems in large buildings.
309 310
Acknowledgements
311
Financial support from National Natural Science Foundation of China (No.61372183) and National Basic Research
312
Program of China (973 Program) (2015CB251505). Partly supported by State Grid Science and Technology Program
313
(No. GTLN201706-KJXM001).
314 315 316
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ACCEPTED MANUSCRIPT Highlights Large-size heliostat for long distance inner daylighting of building Correction algorithm for shift of coordinate system Cost effectiveness analysis
Jifeng Song, Geng Luo, Lei Li, Kai Tong, Yongping Yang, Jin Zhao PII:
S0960-1481(18)30011-9
DOI:
10.1016/j.renene.2018.01.011
Reference:
RENE 9616
To appear in:
Renewable Energy
Received Date:
20 August 2017
Revised Date:
07 November 2017
Accepted Date:
04 January 2018
Please cite this article as: Jifeng Song, Geng Luo, Lei Li, Kai Tong, Yongping Yang, Jin Zhao, Application of heliostat in interior sunlight illumination for large buildings, Renewable Energy (2018), doi: 10.1016/j.renene.2018.01.011
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
1
Application of heliostat in interior sunlight illumination for
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large buildings
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JIFENG SONG1,*, GENG LUO2, LEI LI1, KAI TONG1 AND YONGPING YANG2, JIN ZHAO3
4
1School
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2Schools
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3Beijing
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*[email protected]
8
Abstract
of Renewable Energy, North China Electric Power University, Beijing 102206, China of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China Biomass Energy Technology Center, State Grid Energy Conservation Service LTD, Beijing 100053, China
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Heliostat daylighting systems, used to transmit sunlight deep into rooms where natural light cannot reach, are
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increasingly applied in buildings. A roof-mounted heliostat with an area of 22.95 m2 was developed in this work to verify
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the feasibility of high flux and long distance daylighting in large building interior. The developed heliostat system
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consists of a heliostat, a secondary reflector, and glass windows forming the light path within the building. The problem
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of gravitational deformation of the steel beams base of the heliostat was solved by a rectification algorithm embedded
14
into the computer program, to realize vertical daylighting. The spectrum and chromaticity of the heliostat daylighting
15
system developed was measured, and the results verify the good visual quality of the interior illumination. The light
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transmission distance is more than 70 m, and the system can provide a level of 20-80 klux daylighting illuminance in the
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daytime. An economic analysis was carried out, and data indicates a good cost-effectiveness of the heliostat daylighting
18
system developed. It is hoped that this research will be of some reference value to the design of heliostat daylighting
19
systems in large buildings.
20
Keywords
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Daylighting; heliostat; solar tracking; deformation
22
1. Introduction
23
Daylight is usually considered to be able to improve human’s visual comfortability and to make a great impact on
24
people's daily life and work. Generally, the electric consumption for artificial lighting can take account of about 30% of
25
the total energy consumed in office buildings[1, 2]. The use of daylighting can contribute to energy savings and the
26
reduction of greenhouse gas emissions[3-5]. Furthermore, daylight is benefit for physiological rhythm and reduces the
27
effects of illnesses [6, 7]. So the design of daylighting systems in buildings is very important.
28
The traditional way for daylighting is fenestration on the wall or roof of a building, which cannot track sunlight, so
29
called passive daylighting method here. However, windows are hard to solve the problem of interior daylighting for tall
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multi-story buildings constructed in urban areas[8, 9]. In order to introduce more sunlight and meet the need for deep
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indoor illumination, a variety of daylighting systems have been developed to realize remote transmission of sunlight.
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These can be roughly divided into three kinds, including light pipes, optical fiber daylighting system and heliostats
33
daylighting system[10]. Generally, the transmission distance of those daylighting devices are of, respectively, about 0-4
34
m, 20-50 m and 50-2000 m.
35
Light pipe systems utilize an inner mirror surface of the pipe to transmit sunlight by multiple reflections. A typical
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light pipe system consists of an outside collector, a mirror pipe and a luminaire that releases light into the interior[11].
37
Light pipe systems could be used to enhance interior illumination for buildings, such as schools or industrial
38
buildings[12, 13]. Light pipes for daylighting are easy to install and cost effective. But due to multiple reflections, light
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loss is serious and the transmission distance is only a few meters[14, 15], what limits its application. In terms of 1 / 15
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structure, most of light pipe systems belongs to passive daylighting technique[16] .
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When compared with passive daylighting system, active systems[16] can track sunlight and greatly improve the
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transmission distance of daylight, such as optical fiber daylighting and heliostat daylighting systems. Fiber daylighting
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systems consist of a sun tracking system, lens and optical fibers. The advantages of fiber daylighting systems include
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flexibility in installation and longer transmission distance. A lot of research have been carried out to develop and verify
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optical fiber systems, which covers concentrator studies [17-23] and solar tracking studies [24, 25]. The disadvantage of
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fiber daylighting system is its transmission loss due to fiber attenuation. In general, fiber attenuation rate is closely
47
related to wavelength. For example, silica fiber has low transmission loss in the infrared band, with its transmission loss
48
being 0.2dB / km at 1550 nm [26]. However, in the visible range, the attenuation can reach up to 15 dB / km at 600 nm
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[27]. In addition, optical quartz fiber bundles are too expensive to be popularly applied to daylighting systems. Fiber
50
daylighting systems commonly use plastic fibers - polymethyl methacrylate (PMMA)[23] - and the attenuation of
51
PMMA fiber at 650 nm is about 200 dB/km. Therefore, the transmission distance of fiber daylighting system is usually
52
not more than 50 m, most case to 20 m[28]. For large buildings high than 50 m, it is difficult for light pipe or optical fiber
53
daylighting system to realize inner nature lighting.
54
To solve the problem of sunlight transmission distance, heliostat daylighting systems got researchers’ attention. The
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function of a heliostat is to reflect sun's rays to a given direction to project irradiation onto a target. Compared to light
56
pipe systems and optical fiber daylighting systems, sunlight in heliostat systems travels straight in air other than pipes or
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optical fibers and the transmission distance of sunlight can easy reach up to kilometers. Research on heliostats for
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daylighting have reported in literature[29]. Those researches show that heliostats have a competitiveness in transmission
59
distance for building daylighting [30-33].
60
Most of heliostat daylighting systems reported adopt small mirrors with an aperture of less than 7 m2. Rosemann, A.
61
et al.[33] tested a heliostat system, including a heliostat combined with light pipes and artificial light. The area of the
62
heliostat mirror was 6.25 m2, and the sunlight could penetrate 3 floors to afford nature light for 12 m high stairs. Pohl and
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Anselm[34] developed a heliostat system, which contained Fresnel lens and light pipes (diameter 0.3 m ). It realized an
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illuminance level of 100 ~ 1200 lux for a windowless basement room (7.8m long, 4.5m wide, 2.4m high). Gon Kim et
65
al.[29] designed a heliostat with a diameter 0.75 m mounted on the roof of a 4-floors building. The secondary mirror
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faces the window of the first floor. The transmission distance is about 15 m. Tests verified that, compared to non-
67
heliostat systems, there is a certain improvement in the indoor average illumination, and the effect is satisfying.
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Although heliostat daylighting systems have a much longer transmission distance, heliostat daylighting system of
69
high flux and long distance are rare studied or reported. The main reasons perhaps include gravity load effect and light
70
path design inner buildings. This work focuses on the feasibility of a heliostat daylighting system of large size for large
71
building. The aim of this work is to analyze the gravity load influence on the base of the heliostat system and to solve this
72
phenomenon by a compensation algorithm embedded in the computer program. In this paper, a large-size heliostat with
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an area of 22.95 m2 was developed and installed on a 70 m high building to reflect direct irradiation from the roof to the
74
ground floor. The light path system was also detailed in the paper. The gravity deformation of the base of the heliostat
75
has been analyzed and the compensation algorithm was developed and tested. The illuminance results and the
76
chromaticity of the daylighting system are described in detail in this paper. An economic analysis was also carried out to
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estimate the potential of the heliostat daylighting system of large aperture.
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2. System Configuration
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79 80
Fig.1 Diagram of system, (a) daylighting on ground, (b) the 8th floor light path, (c) the roof-mounted heliostat and second reflector, (d) overall layout,
81
(e) the beam net of the roof, (f) the beam geometry of the 8th floor, (g) the zone for daylighting on the ground.
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The center of the building is designed with a hollow structure to enable the sunlight to travel downwards. The
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daylighting system consists of a heliostat and a secondary reflector, shown in Fig.1. The heliostat tracks the sun, then
84
reflect horizontally the sunlight onto the surface of the secondary reflector. The secondary mirror is a flat mirror, with an
85
angle of 45 ° from the horizontal, and can reflect sunlight exactly vertical to the ground bottom of the building. The
86
characteristics of the system are listed in Table 1. 3 / 15
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Table 1 Geometric parameters Modules
Mirror
Stepping motor#1 Heliostat
Elevation Servo cylinder
Azimuth
Stepping motor#2 Planet reducer -
Secondary
Mirror
reflector Glass
Parameters
Units
Value
Length
m
5.1
Width
m
4.5
Reflectance
-
92%
Torque
N·m
4
Step angle
Deg
0.6/1.2
Stroke length
mm
1150
Lead
mm
5
Torque
N·m
36
Step angle
Deg
0.6/1.2
Reduction ratio
-
40
Weight
t
1.5
Length
m
6.6
Width
m
4.67
Reflectance
-
92%
Angle
Deg
45
Transmittance
-
90%
88 89
2.1 The heliostat
90
（1）Structure
91
The heliostat adopts a rectangular plane mirror, made from ultra-clear silver mirrors, whose reflectance averages
92
around 92%. The large mirror is made up of 20 small mirrors with a total area of 22.95 m2 as shown in Fig.2a. The
93
heliostat has an ability to move at two degrees of freedom, the azimuth and the elevation direction, respectively. The
94
heliostat is installed on the steel beam net below the glass cover of the roof as shown in Fig.2b. The steel beam net acts as
95
a base for the heliostat. Among the steel beam net, each joint is a bolted connection. Because of the big spacing (24m×
96
24m ), the stiffness of the steel beam net is not high, which means gravity deformation will occur once the heliostat was
97
installed on the beam net. Further, the gravity deformation of the beam net will cause a deviation on the coordinate
98
system of the heliostat, and the sequential result is that the heliostat cannot track sun exactly, which means the heliostat
99
daylighting system cannot project precisely sunlight onto the zone needing illuminance. In this research, this problem is
100
solved by a special compensation algorithm embedded in the control program, presented in Section 3.
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101 102 103
Fig.2 Layout of the heliostat daylighting system. (a) The heliostat and the secondary reflector, (b) the steel beam net base of the heliostat system
（2）Control module
104
The control module consists of sensors, motors and reducers, as well as controllers and a power supply. One motor
105
rotates the heliostat in the azimuth direction, and another motor provides rotational movement in the elevation direction,
106
ensuring that the heliostat constantly tracks the sun. It is needed to point out that the normal orientation of the heliostat
107
mirror dose not point to sun disk, but to the bisector of the angle between the light ray from the center of sun disk and the
108
line from the heliostat to the second reflect mirror. The sensors include an inclinometer for altitude and an encoder for
109
azimuth, a GPS, and a wind sensor, which respectively feed information relating to the normal direction of the heliostat,
110
time, longitude, latitude, and wind speed. The controller firstly works out sun’s position based on GPS signal, and then
111
works out the theory value of the normal direction of the heliostat mirror. Then, the controller drives the motors to rotate
112
in a loop control model to reflect sunlight horizontally onto the second reflector. The control logic is shown in Fig.3.
113
114 115 116 117
Fig.3 Control logic of the heliostat daylighting system
2.2 The secondary reflector The secondary reflector is mounted at the center of the roof. The average reflectance is equivalent to that of the 5 / 15
ACCEPTED MANUSCRIPT 118
heliostat at around 92%. Mirrors are separated from outside environment by glass room as shown in Fig. 2a. This
119
measurement can effectively reduce the accumulation of dust on the mirror. Coupled with its own downwards angle
120
(45o), the mirrors can remain clean for a long time, thus keeps high reflectance and reduces the amount of cleaning work
121
required.
122
2.3 Building structure
123
In order to reduce wind load on the heliostat, there are wind-break walls on the roof. The layout of the wind-break
124
walls, the heliostat, and the secondary reflector on the roof is shown in Fig. 1(e). The entire steel beam net of the roof is
125
symmetrical in east-west and north-south directions. The secondary mirror is located in the center of the roof. The
126
heliostat is located on the north side of the secondary mirror, 9.29 m from the center and 4.17 m from the north wall. The
127
north wall is 4.5 m high, while other walls are 3.94 m high. The wind-break wall can efficiently alleviate the wind load
128
on the heliostat and reduce the deformation of the base (the steel beam net)
129
When sunlight penetrates the 8th floor hole, it will be partially blocked by the steel beams. This steel beam net is
130
symmetrical. As shown in Fig. 1(f), the total length is 8 m, and the steel beam spacings are 2.12 m and 1.88 m. In
131
addition, the width of each steel beam is 0.2 m.
132
The daylighting zone on the first floor is shown in Fig. 1(g). The atrium is a square with a 24×24 m size. During
133
the experiment, five sets of illuminometers are used simultaneously to measure the flux distribution. There are 100
134
sampling points which can be finished within 100 s. Generally, in a sunny day, the intensity of direct normal irradiation
135
of sun changes slowly. The result shows that the fluctuation of intensity of flux on the ground is less than 2% within 100
136
s in a clear sunny day (8 a.m.-17 p.m.).
137
2.4 Effect of sunlight blocking
138
The building is located in Beijing (N40.105537o, E116.365412o). The location of the heliostat is arranged in the
139
norther direction of the secondary reflector to alleviate the cosine efficiency[35], so as to achieve a higher annual average
140
sunlight collecting efficiency. However, it is needed to point out that the sunlight collecting efficiency of the heliostat
141
cannot remain at a high value all the time because of the blocking caused by surrounding wind-break walls or the second
142
reflector itself. The sunlight collecting efficiency, not the cosine effect, of the heliostat can be figured out by calculation
143
according to the geometrical structure and the sun position curve. A concept, so called here, sunshine area rate (SAR) of
144
the heliostat mirror is defined as the ratio of the sunshine area on the mirror to the total area of the heliostat mirror. The
145
SAR changes all the time. The fluctuation of SAR at three typical days, the winter/summer solstice and the spring
146
equinox, were calculated and shown in Fig. 4.
147 148
Fig. 4 Sunlight collecting efficiency of the heliostat presented
149
The dashed line in Fig. 4 is the proportion of the area of the heliostat mirror tower above the eastern wind-break
150
wall, to the area of the heliostat mirror, which is about 30%. The advantage of this design is that the heliostat can capture 6 / 15
ACCEPTED MANUSCRIPT 151
the sunlight and begin to work the moment sun rising. From Fig. 4, it can be seen that at the summer solstice, the value of
152
SAR rises fast after sun rising and reaches 100%. In fact, the entire heliostat mirror can receive sunlight during most of
153
daytime (about 6:30 to 18:00). That means the heliostat daylighting system could afford a full function. Comparing to
154
summer’s, at winter solstice, the SAR cannot maintain at a high level because of sunlight blocking by the second
155
reflector and surrounding wind-break walls at a low altitude angle of sun. The curve of SAR at the spring equinox is
156
between the summer solstice and the winter solstice, which is satisfactory.
157
Fortunately, the curve of direct normal irradiation (DNI) of one day roughly consists with the SAR of the heliostat.
158
On May 26th, 2017, a continuous experiment of direct illuminance was carried out. The flux intensity was recorded
159
every 10 minutes, shown in Fig. 5.
160 161
Fig. 5 Direct solar illuminance (Beijing, May 26th, 2017)
162
For a sunny day, the direct normal irradiation can reach 50% of its maximum in half an hour after sunrise.
163
Combined with the solar altitude curve, when the angle is greater than about 20 degrees, the illuminance is relatively
164
stable and high, about 100 klux. With the addition of the influence of the tilt from the heliostats, the illumination on the
165
ground at noon is best, and the illumination at 7: 00, or 16:00, is also satisfactory. So for most of daytime, a satisfactory
166
lighting effect can be obtained
167
Combining Fig. 4 and Fig. 5, we see that when the degree of blocking is serious (sunrise and sunset moment), the
168
DNI is low. On contrast, for most of daytime, the DNI is high meanwhile shading block is much less. In summary, the
169
shading block caused by wind-break walls and the second reflector is acceptable and does not pose a threaten for
170
daylighting.
171
3. Heliostat control model
172
3.1 The algorithm of the heliostat
173
Conventionally, the solar position can be represented by the elevation angle and azimuth angle , and the attitude
174
of the heliostat is a function of the elevation angle s and the azimuth angle s. In this paper, the heliostat normal vector
175
H is used to characterize the direction of the heliostat mirror. The heliostat normal vector H can be represented by
176
azimuth and elevation angles, corresponding to the two motors.
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177 178
Fig. 6. Coordinate system of the heliostat mirror
179
It is recognized that, based on the horizontal coordinate system (west-south-height), the solar elevation angle s and
180
the azimuth angle s is a function of the geographical latitude , solar declination angle , hour angle , and other
181
factors[36].
cos s sin s S cos s cos s sin s
182
183 184
Thus, the unit vector S of the incident light is defined. The target position, the second reflector, is fixed, then the target unit vector T is easily represented.
0 T 1 0
185
186 187
(1)
(2)
The unit normal vector H of the heliostat has the following relation with S and T and the incident angle as shown in Fig.6.
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cos 2 =S T
(3)
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cos H sin H 1 H cos H cos H (S T ) 2 cos sin H
(4)
190 191
From above formulas, the unit normal vector of heliostat is obtained. 3.2 The correction of the heliostat tracking
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The coordinate system of the heliostat is not constant due to two factors. One is the gravitational deformation of the
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steel beam net. The center of the roof which steel beam structure is shown in Fig. 2b will sink due to the gravity load of
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the secondary reflector and steel beam itself. The heliostat is located north of the center, so the base is tilted to the south.
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The other is the shift of the center of the gravity of the heliostat when the heliostat tracks sun during daytime as shown in
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Fig. 7. This shift is corresponding to the elevation angle of the heliostat, and the shift of the center of gravity leads to the
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deformation of steel beams. The above two effects can cause the heliostat tracking error. In this research, a correction
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algorithm was developed to solve this problem.
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The base of the heliostat tilts to the south, what can be described using the below rotation matrix 8 / 15
ACCEPTED MANUSCRIPT 0 1 Rwest ( ) 0 cos 0 sin
200
201
0 sin cos
(5)
And the correction vector H concerning the center of gravity
0 H = 0 z
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(6)
203 204
Fig. 7 Mathematical model of center of gravity
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The parts of heliostat excluding the mirror and the mirror steel frame less affects the deviation of center of gravity
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because of the symmetry. So assuming that only the mirror and the mirror steel frame have a not-neglected influence on
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the deviation. From Fig. 7, the length of the deviation
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fit the relationship between G and the elevation-angle offset z c0 c1G c2 G o( G ) . Simplify the
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polynomial and ignore the third-order infinitesimal term to obtain the correction vector
G =b0 b1 sin H
2
0 H = 0 a0 a1 sin H a2 sin 2 H
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New heliostat vector
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Polynomial coefficients above, a, b and c, are undetermined constants.
214 215 216
3
(7)
H Rwest ( ) H H
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can be obtained. The polynomial is used to
0 1 H 0 cos 0 sin
0 0 sin H 0 a0 a1 sin H a2 sin 2 H cos
(8)
A series of experiments were conducted to record a series of data include the corrected elevation angle ’H, the corrected azimuth angle ’H and the corresponding time. Get the measured heliostat vector
9 / 15
ACCEPTED MANUSCRIPT cos H sin H H cos H cos H sin H
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(9)
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The corrected angles can be got when the heliostat is manually adjusted to the best position. And the least squares
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method is adopted to calculate the value of , a0, a1 and a2. The error function and objective function are defined as
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follow.
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Error function
fi ( , a0 , a1 , a2 ) H i
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H i , H i
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Where M is the total number of measurements.
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Objective function
i 1, 2,3, , M
(10)
M
S ( , a0 , a1 , a2 ) f i 2 ( , a0 , a1 , a2 )
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(11)
i 1
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4. Experiment and analysis
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The four parameters obtained by the correction model above, =-1.225o, a0=0.01509, a1=-0.03122, a2=0.03036. So
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the correction algorithm is thus determined as shown in equation 8. The tracking errors before and after correction were
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measured on April 23rd and 24th, 2017 by a simple shade method. A needle was vertically placed on the ground and the
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length of the needle shade can indicate the value of tracking error. Fig. 8 shows the comparison of tracking errors before
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and after correction. This correction algorithm was embedded into the computer program to realize high precise solar
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tracking.
233 234
Fig. 8 Errors of the azimuth angle and the elevation angle before (April 23rd, 2017) and after (April 24th, 2017) correction in Beijing.
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It can be seen that tracking errors of the azimuth and elevation angle can be kept within ± 0.1 degree after the
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correction, so the satisfactory control precision is achieved.
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The spectrum of sunlight entering the building was measured to verify its comfort to humans, and it is generally
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believed that the nearer light approximates to the spectrum of nature light, the visual environment is more comfortable.
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The experiment was carried out at 12:00 on May 26th, 2017.
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ACCEPTED MANUSCRIPT
240 241 242
Fig. 9 Results of the spectrum and chromaticity, (a) spectrum, (b) chromaticity.
The experimental results are shown in Fig. 9. The spectrum of the daylighting in this work is shown in Fig. 9 (a)II,
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which is very close to the spectrum of nature light(I). Meanwhile the color rendering index can reach 98.3, providing
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residents an approximate natural lighting environment, especially beneficial to those who draw or need physical therapy.
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Compared with the spectrum in (a)I, the relative intensity of short wavelengths (about 380nm) are filtered out a lot, and
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the part of long wavelength is relatively reduced by a little. What affects the interior spectrum is exactly the mirrors and
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glued double-glass, but the impact is small. In addition, the spectrum of the fluorescent lamp(III) and the spectrum of the
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incandescent lamp(IV) are also measured as shown in Fig. 9 (a). They are obviously different from nature light spectrum.
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The points in the CIE1931 chromaticity diagram are also drawn as shown in Fig. 9 (b). Point I and point II closely
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overlap and the chromaticity of interior sunlight is very close to the nature light. However, the fluorescent lamp and the
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incandescent lamp are less healthy, so the advantage of the system is able to bring healthy sunlight.
252 253
At 5:30, 7:00, 12:00, 16:00, 19:00, on May 26th, 2017, the illuminance distribution on the surface area was measured, and the post-processing data results are shown as Fig. 10.
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ACCEPTED MANUSCRIPT
254 255
Fig. 10 Illuminance distribution, (a) 7:00, (b) 12:00, (c) 16:00, (Fig. a b and c share a legend) (d) roof at 19:00, (e) 5:30, (f) 19:00, (g) ground at 14:00.
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(Beijing, May 26th, 2017)
257
It can be seen that the presence of steel beams affects the distribution of illuminance, so that the illuminance in the
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area corresponding to steel beams is significantly lower. However, owing to the fact that sunlight is not parallel, after
259
long distance transmission, the corresponding part of the ground can receive a strong illuminance, at around 20 klux.
260
From the distribution of the illuminance, it can be seen that only when the distribution in Fig. 10 (b) is at 12:00 is
261
there a complete rectangle, while the others are not complete. Distributions in Fig. 10 (a) and (c) are caused by the tilt of
262
the heliostats. Obviously, in the morning and afternoon, the heliostat does not face the secondary mirrors, and the
263
projection area of the heliostat mirror on the vertical plane is less than the projection when it does so. The projection
264
shape is non-rectangular, and so the sunlight does not fall on the entire secondary mirror. At 7:00, the heliostat mirror
265
faces the southeast, with the corresponding southwest corner of the distribution missed. At 16:00, the heliostat mirror
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faces the southwest, and thus, similarly, the southeast corner of the distribution is missed. The missing areas in Fig. 10
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(e) and (f), in addition to the effects of the tilt, are mainly affected by wall occlusion. As shown in the photographs in
268
taken at 19.00 in Fig. 10 (d), the projection on the secondary mirror is only a strip area near the north side, so in terms of
269
illuminance distribution, only a small part of the area near the north side is covered in sunlight. And the photograph on
270
the ground as shown in Fig. 10 (g). Furthermore, this validates previous analysis.
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5. Cost analysis
272
The flux density projected by the heliostat (~30 klux) is far higher than that of traditional artificial lamps (~300 lux),
273
such as LED. Therefore, a considerable electric saving is realized. An analysis of cost recovery was carried out. Among
274
the cost, the heliostat and the secondary reflector account for a large share because they are customized, including the
275
heliostat (about 6.8k dollar), the secondary reflector (about 1.7k dollar) and the labor (about 4.2k dollar). The
276
maintenance of the heliostat mainly includes mirror cleaning, oil bearing maintenance and control system electricity, a
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total of 75.6 dollars per year. The economic benefit of the equipment is converted according to the average light effect of
278
fluorescent lamp of 60 lm/W [37] and the price of 0.09 dollars/kWh. And the system can provide the average daily
279
illumination about 30klux, experimental lighting area about 50.9 m2 and working hours 8 h. We take 2016 as a typical
280
year, and there are 153 sunny days and 88 cloudy days in Beijing. Suppose a cloudy day is converted to 0.4~0.8 sunny
281
days. So 3.5~4.1k dollar can be earned in 2016 from the following equation.
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Annual income = illuminance × area / light efficiency × (sunny days + 0.4~0.8 × cloudy days) × working hours ×
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electricity price 12 / 15
ACCEPTED MANUSCRIPT 284
Suppose the discount rate is 10%. The dynamic payback period[38] can be estimated, and it takes 3.9~4.9 years to
285
recover the cost of the equipment economically. The high density of direct normal irradiation and the high transmission
286
efficiency of sunlight jointly offer the heliostat system a satisfactory capacity to supply large flux daylighting for
287
buildings.
288
6. Conclusion
289
This research focuses on the deep inner daylighting of large building. This work aims to transmit high flux to a long
290
distance, to realize daylighting for building by using a heliostat mirror of large size. The experiments show that large-size
291
heliostats can meet the demand for high flux (30 klux), long-distance (70 m) interior daylighting in large buildings. The
292
factors that affect the efficiency of light transmission are the reflectance of mirrors, the transmittance of glass, the
293
coverage of steel beams in the system, and the SAR. In the air, the transmission attenuation is slight and can be
294
neglected. In terms of visual quality, the spectral results verify that the interior daylight can get the high-fidelity nature
295
light spectrum to provide a healthy lighting environment. The gravitational deformation of the steel beam roof caused a
296
tilt of the heliostat base which could further led to tracking errors. In addition, the shift of the center of gravity of the
297
heliostat during tracking also aggravate this tilt. To solve this problem, an elaborated geometrical algorithm was
298
developed and embedded into the computer program. The results demonstrated that this compensational algorithm can
299
successfully ensure the daylighting beam perpendicular to ground with a precision of 0.1 degree.
300
Due to the large size of the heliostat and high windy roof, the system has some installation limitations, and it is
301
necessary for the building to reserve a large space for the sunlight path. These limitations make the layout of the heliostat
302
system inflexible. So building lighting integrated design is recommended to adopt. The wind-break walls will block the
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sunlight in the early morning and evening, and the secondary reflector will block the heliostat at noon. To achieve a good
304
SAR, the layout of roofs and heliostats needs to be considered carefully.
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This paper demonstrated the feasibility of the application of large-scale heliostats for deep inner daylighting in large
306
buildings. Cost analysis shows that the daylighting system has a good capacity on electric saving for lighting. For the
307
heliostat system presented, the payback period is about 3.9-4.9 years. It is hoped that the results of this research will be a
308
useful reference for designs of heliostat daylighting systems in large buildings.
309 310
Acknowledgements
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Financial support from National Natural Science Foundation of China (No.61372183) and National Basic Research
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Program of China (973 Program) (2015CB251505). Partly supported by State Grid Science and Technology Program
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(No. GTLN201706-KJXM001).
314 315 316
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ACCEPTED MANUSCRIPT Highlights Large-size heliostat for long distance inner daylighting of building Correction algorithm for shift of coordinate system Cost effectiveness analysis