Estimation of solar radiation for buildings with complex architectural layouts

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Estimation of solar radiation for buildings with
complexarchitectural layouts

• Arch. Stoyanka Ivanova
• University of Architecture, Civil Engineering and
  Geodesy
• Sofia, Bulgaria

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1 Introduction

• If we want the solar friendly architectural
  thinking to be accepted widely, then we have to
  think how it could be applied still in the
  beginning of the architectural creative process
  when the idea of the building is shaped and
  especially in the process of creating of the
  architectural layout.
• Its possible to use a computer program not only
  to draw a desired layout, but also to create it.
  Its hard to simulate the architectural creative
  process, but with the increase of the present
  computer might this is not already a mission
  impossible.

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1 Introduction

• The program ArchiPlan is created to assist the
  architect in the process of searching of initial
  architectural idea architectural layout.
• The program generates hundreds of 2D orthogonal
  architectural layouts for just few seconds.

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1 Introduction

• In the beginning the architect describes the
  elements (rooms) of the desired layout
• names of rooms
• square surface of each room
• functional relations between rooms
• requirements for each element for exposure
• desired grid, etc.

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1 Introduction
Example (15 rooms)
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1 Introduction
Matrix of functional relations between rooms
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1 Introduction
With these data the program ArchiPlan generates
602 architectural layouts for less than 4
seconds
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1 Introduction
Exemplary architectural layouts, generated by the
program ArchiPlan
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1 Introduction

• These layouts have to be evaluated, so the
  program can offer the architect only the best of
  them. The program uses the following criteria to
  rank all generated layouts
• compactness (as a planning quality)
• constructions requirements
• energy effectiveness (energy gains and losses)
• The weight of these three criteria could vary,
  regarding the architects final goal.

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1 Introduction
The program ArchiPlan sorts the generated
architectural layouts on compactness Lets see
worst 5 and top 10 layouts
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2 Methodology
The energy effectiveness of an architectural
layout has two sides energy losses and energy
gains. In this too early moment of the
architectural process the energy losses could be
evaluated with the compactness of the building -
the surface-area-to-volume ratio - a proportion
between the total exterior surface and internal
volume. As less is this number, as more
compact is the building and lower the energy
losses.
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2 Methodology

• Since June 30th a new calculation of supposed
  energy losses was added to the program. It uses a
  difference between inside and outside air
  temperature and supposed heat transmission
  coefficient.
• The energy effectiveness is calculated as follows

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2 Methodology
To evaluate energy gains, the program ArchiPlan
estimates the quantity of incoming solar energy
Wh to the building outside surface (exterior
walls and roof) for the whole heating season.
In this so early stage is convenient to use
2.5D model with only horizontal and vertical
surfaces.
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2 Methodology
Two methods of solar energy estimation are
created. The final goal of the first method is
to rank the hundreds of generated
architectural layouts considering their energy
effectiveness. In this case is important to
receive quick results, even with some little
inexactness. This is why we need to simplify
computation of the summary solar radiation,
received by all exterior surfaces.
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2 Methodology
The second method is created to estimate the
solar radiation, received by each particular
vertical wall of a layout. The goal is to allow
the architect to study how a specific
architectural layout can utilize the incoming
solar energy in best way. Such information could
help him to find the best positions for the wall
apertures - windows and glazed doors on the walls
of a complex architectural layout.
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3.1 Quick analysis of summary beam radiation
The exterior surface of our 2.5D model is
projected on a plane, normal to solar beam.
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3.1 Quick analysis of summary solar beam radiation
Area of roofs projection
Area of walls projection
df front of projection
Beam radiation
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3.2 Quick analysis of summary diffuse radiation
For the diffuse radiation RD W is valid the
formula

• Dic W.m-2 - the diffuse irradiance on each
  external surface (walls or roof) of the building
• Ai - area of this surface m2
• Hofierka and Šúri in their work The solar
  radiation model for Open source GIS described
  how to estimate the diffuse irradiance on
  horizontal and inclined surfaces, when they are
  sunlit, potentially sunlit or shadowed. But this
  model has to be extended for the cases, when one
  or more near objects with limited size hide parts
  of the sky, as it is for the buildings with
  complex architectural layouts.

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3.2 Quick analysis of summary diffuse radiation
According Hofierka for inclined surfaces in
shadow

• Dhc is diffuse irradiance on a horizontal
  surface
• F(?N) is a function, which convert the diffuse
  irradiance on a horizontal surface into diffuse
  irradiance on an inclined surface under
  anisotropic clear sky

• ri(?N)(1cos ?N)/ 2 is a fraction of the sky
  dome, viewed by an inclined surface.
• For unobstructed surfaces in shadow of our 2.5D
  model, N0.25227 according Muneer and Hofierka
• when ?N0 (for horizontal surface) F(?N)1
• when ?Np/2 (for vertical surface) F(?N)0.356

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3.2 Quick analysis of summary diffuse radiation
Lets consider this wall configuration
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3.2 Quick analysis of summary diffuse radiation
For the wall A0 a part of the sky is hidden by
both other walls. I propose such equation to the
mentioned model

• DFi is a function, which transforms the value of
  the diffuse irradiance on a horizontal surface to
  a value of diffuse irradiance, incoming from
  partially shaded anisotropic sky, onto an
  inclined surface (in our example its vertical)

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3.2 Quick analysis of summary diffuse radiation

• a1 and a2 are azimuths of the furthest ends of
  the neighbor walls A1 and A2
• C1,2 is a correction coefficient for the visible
  part of the sky in horizontal direction, between
  azimuths a1 and a2
• VT1 and VT2 are the correction values due of the
  spherical triangles T1 and T2 above the walls A1
  and A2 on the stereographic projection.

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3.2 Quick analysis of summary diffuse radiation
For estimation of C1,2 this equation is proposed
where a1arctg(dx1/dy1) and a2arctg(dx2/dy2). If
dy10 then a1-p/2 and VT10. If dy20 then
a2p/2 and VT20. If both dy1 and dy2 are 0,
then C1,21, VT1 and VT2 are 0. In all other
cases the values of VT1 or VT2 are greater than
0.
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3.2 Quick analysis of summary diffuse radiation
In the figure are illustrated the variable x1a
and angle ß1, which are necessary to estimate the
value of VT1. AT1 is the area of segment T1 in
the same figure.
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3.2 Quick analysis of summary diffuse radiation
I propose the following approximate equation of
VT1 to take into consideration at least partially
the anisotropic nature of the diffuse radiation
The transforming function DFi (corrected F(?N))
has to be used to calculate diffuse radiation
also on sunlit or partially shaded surfaces.
Within this quick method I estimate Dic only once
for the center of each examined vertical wall.
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3.3 Quick analysis of solar radiation under real
sky

• Finally the computation of overcast radiation
  for inclined surfaces is analogous to the
  procedure described for clear-sky model (Hofierka
  and Šúri), using the modified values of beam and
  diffuse irradiance because of the concrete values
  of beam and diffuse components of the clear-sky
  index (Kbc, Kdc).
• The layouts with best energy effectiveness are
  compact with southerly exposure of the larger
  dimension of the building and flat south vertical
  wall. As higher is the percent of diffuse
  radiation under the real sky, as more important
  is the compactness.

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3.3 Quick analysis of solar radiation under real
sky
The program ArchiPlan sorts the generated
architectural layouts on energy
effectiveness Lets see worst 5 and top 10
layouts
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4.1 Detailed analysis of beam and diffuse
radiation
When the rank list of all generated architectural
layouts is ready, the architect could examine the
best of them, with the help of a detailed
analysis of received solar radiation by each
vertical wall to find best place for windows and
glazed doors on each floor.
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4.1.1 Detailed analysis of incoming beam radiation

• According detailed methodology in Solar
  radiation and shadow modeling with adaptive
  triangular meshes by Montero et al
• B0c is the beam irradiance normal to the solar
  beam
• dexp is the solar incidence angle between the
  sun and an inclined surface
• Lf is calculated lighting factor for the
  concrete wall, day and time (0 completely
  shaded wall 1 - sunlit wall between 0 and 1
  partially shadowed wall)

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4.1.2 Detailed analysis of incoming diffuse
radiation
The quantity of diffuse radiation for each
fragment of each wall is different. So for a
detailed analysis each wall is divided in
horizontal and vertical directions and the
program applies to these small fragments the
estimations, described in the previous section.
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4.1.2 Detailed analysis of incoming diffuse
radiation
For this wall configuration
DFi the value of the diffuse transforming
function for the wall with length b and height h,
is

• M is number of fragments in horizontal direction
  
• N is number of fragments in vertical direction
• dx is size of a fragment in horizontal direction
  
• dz is size of a fragment in vertical direction
• (xj, zk) center of a fragment of this vertical
  wall

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4.1.2 Detailed analysis of incoming diffuse
radiation
Instead with this double sum, the exact value of
diffuse transforming function for the same
vertical wall can be estimated with this double
definite integral
The value of the integral is
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4.1.2 Detailed analysis of incoming diffuse
radiation
For different wall configurations the double
integral and its result looks also different.
There are 4 basic double integrals and many
combinations between them for different wall
configurations . I still work on some
combinations.
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4.2 Balance principles of incoming and received
diffuse radiation
Balance principle 1 The quantity of diffuse
radiation, crossed an opening (with area Aopening
), is equal to sum of the quantities of diffuse
radiation, received by the surfaces (with areas
Ai ), which are behind this opening. From this
is easy to come to

• DFopening is value of the diffuse transforming
  function for the planar surface of the opening
• DFi is the value for each receiving surface
  behind the opening

• DFj and Aj are value of the transforming
  function and area of a small fragment j of the
  surface i

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4.2.1 Balance principle 1 - example
Opening EFGH
Wall ABFE
Wall BCGF
Wall CDHG
Wall ADHE
Base ABCD
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4.2.1 Balance principle 1 - example
For isotropic sky and AB2, BC1, AE3
2 2
All values of DF are calculated with different
combinations of mentioned double integral.
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4.2.2 Balance principle 2 of incoming and
received diffuse radiation
Balance principle 2 The quantity of diffuse
radiation, crossed two or more openings (with
area Ak ), is equal to sum of the quantities of
diffuse radiation, received by the surfaces (with
areas Ai ), which are behind each of the
openings. From this is easy to come to

• DFk is value of the diffuse transforming
  function for opening k
• DFik is the value for the surface i, generated
  by the incoming diffuse radiation through opening
  k.
• DF has to be defined twice for the planes of
  vertical openings - for inside and outside face
  of examined volume.
• The value of the transforming function of the
  surface i with fragments j, for the incoming
  diffuse radiation from all openings, is

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4.2.2 Balance principle 2 - example
Opening EFGH
Opening ABFE
Surface ABFE
Wall BCGF
Wall CDHG
Wall ADHE
Base ABCD
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4.2.2 Balance principle 2 - example
For isotropic sky and AB2, BC1, AE3
5 5
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4.2.2 Balance principle 2 - example
Here is another viewpoint to the same example
Wall BCGF
Wall CDHG
Wall ADHE
Opening EFGH
Opening ABFE
Here we have 2 interesting equalities 3
3 5 5
The summary product of DF and Area for these 3
vertical walls is 3.646776
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4.2.2 Balance principle 2 - example
This is the main practical advantage from both
balance principles. It helps to calculate very
easy the summary diffuse radiation on a complex
wall configuration. The main part of it (pink
values) comes across an endless high vertical
opening, so for these values we can simplify the
outline of the layout in this way
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5 Discussion

• Both equations from the balance principles can
  be proved for isotropic sky analytically with
  already mentioned double integrals. Its really
  beautiful mathematics, just music of the
  projected spheres.
• I wasnt able to prove both balance rules for
  anisotropic sky numerically. The proof is not
  obvious and will be more difficult. It could be
  possible with better knowledge of skys
  anisotropy.
• In spite of this the consequences of the second
  balance rule can be implemented into calculations
  for obstructed anisotropic sky and to receive
  values with good approximation. Under real sky
  this inexactness will be even more unimportant.
• Both balance principles and corresponding
  equations could
• also be applied to beam and total radiation, to
  sunlit or
• partially shadowed surfaces, and for different
  sky types.

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6 Conclusion and future work

• Its proposed a numerical model for estimation of
  the solar radiation on the external vertical
  walls of a building with complex architectural
  layout. This could help the architect to think
  more about the solar gains and to choose the best
  solar friendly architectural layout.
• Further research is needed to precise the
  calculation of the diffuse radiation from
  anisotropic sky for spherical triangles above the
  vertical walls.
• The balance principles and corresponding
  equations are a good start base for further
  improvement of this model for both isotropic and
  anisotropic sky.
• Calculations of reflected radiation and analysis
  of solar radiation in summer will be added in the
  future.

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7 References

• Muneer, T., Solar radiation model for Europe.
  Building services engineering research and
  technology, 1990, vol. (11)
• Hofierka, J., Šúri M., The solar radiation model
  for Open source GIS implementation and
  applications, Open source GIS - GRASS users
  conference, Trento, Italy, 2002
• Montero, G. et al, Solar radiation and shadow
  modeling with adaptive triangular meshes, Sol.
  Energy, 2009, doi10.1016/j.solenar.2009.01.004
• Thank you!