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Journal of Asian Architecture and Building Engineering

ISSN: 1346-7581 (Print) 1347-2852 (Online) Journal homepage: https://www.tandfonline.com/loi/tabe20

Versatile Design Protocol of Architectural

Integration of Photovoltaics

Takaaki Ikeda

To cite this article: Takaaki Ikeda (2002) Versatile Design Protocol of Architectural Integration of

Photovoltaics, Journal of Asian Architecture and Building Engineering, 1:1, 183-188, DOI: 10.3130/

jaabe.1.183

To link to this article: https://doi.org/10.3130/jaabe.1.183

Published online: 23 Oct 2018.

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Journal of Asian Architecture and Building Engineering/March 2002/188 183

Versatile Design Protocol of Architectural Integration of Photovoltaics

Takaaki Ikeda

Unico International Corp.,

Nakagawa Tsukiji Bldg. 5F.,5-4, Tsukiji 3-Chome,Chuo-ku,

Tokyo 104-0045 Japan(T.Ikeda@unico-intl.co.jp)

Abstract

By simply taking a fish-eye lens photograph once at the location, or performing the equivalent operation by

computer graphics using geographical data of the location, one can see how much photovoltaic energy will be

obtained in each season there. No restriction is required regarding the layout design of photovoltaic cells or

installation location. As an eventual discovery, a theory of design rules pertaining to PV integration, which is

characterized by “inner symmetry” was developed, as the integrated PV energy obtained remain unchanged

towards any arbitrary rotation around an axis.

Keywords: photovoltaic; solar; versatile; design; architecture

Introduction

Photovoltaic (PV) is a typical renewable energy di-

rectly convertible from solar irradiation and its integra-

tion in the built environment is a new world wide trend

in architecture.

Table 1 provides typical meteorological data of the

Tokyo region. It suggest that more than half of the

year, during the summer season, indirect irradiation en-

ergy from the sky surpasses direct irradiation energy

from the sun.

Therefore, it is very important to establish a method

of photovoltaic engineering which is able to provide re-

liable account of photovoltaic energy by indirect sky-

irradiation as well as that by direct sunshine.

It is recognized that architectural PV integration can

not be performed by separating design work from PV

engineering. However, conventional method of PV en-

gineering is unable to provide satisfactory answers for

versatile architectural PV designs and location condi-

tions, especially related to indirect irradiation from the

sky.

The Versatile Design Protocol here provides an inno-

vative method which makes possible such PV engi-

neering of versatile roof design based upon insitu loca-

tion conditions clearing architectural PV integration of

its conventional uncertainties and design constraints.

As an eventual discovery, design rules pertaining to

PV integration, which is characterized by “inner sym-

metry” were conducted on a theoretical basis, as the

integrated PV energy obtained remains unchanged to-

wards any arbitrary rotation around an axis.

One can install such a “PV system of inner symme-

try” without having to give consideration to the azi-

muthal direction to which the whole of the PV system

faces, which frees configuration design and installation

works from the conventional azimuthal constraints.

Method

1) Sky-irradiation condition

A new methodology was developed to obtain the lo-

Contact Author: Takaaki Ikeda, Unico International Corp.,

Nakagawa Tsukiji Bldg.,5F.,5-4, Tsukiji 3-Chome, Chuo-ku, To-

kyo 104-0045 Japan

Tel: +81-3-5148-0603 Fax: +81-3-5148-0478

e-mail: T.Ikeda@unico-intl.co.jp

(Received October 8, 2001; accepted December 20, 2001)

Table 1. METEOROLOGICAL DATA OF THE TOKYO RE-

GION

Fig. 1. Iso-projective mesh pattern

184 JAABE vol.1 no.1 March 2002 Takaaki Ikeda

calized value of sunshine irradiation both from direct

sunshine and indirect sky-irradiation at a specific loca-

tion point where the PV system will be installed from

regional data prepared by the authority.

In Fig.1, a photovoltaic panel is placed at the point of

origin “O” with its unit normal vector pointing to “n” in

three dimensional space. The mesh-pattern is drawn

on the surface of a concentric sphere so that sky-irra-

diation arrives at the surface of the photovoltaic cell

through each elemental mesh becomes equal so far as

the irradiation is spatially uniform over the sky.

Fig. 2a represents the virtual location of photovoltaic

installation point surrounded by trees and a building.

Fig. 2b is the supposed fish-eye view to be taken at

the installation point to the zenith direction which is

drawn by CG.

Figs. 3a, 3b, and 3c are superimposed images of fish-

eye transforms of the same mesh patterns of three dif-

ferent directions over the same fish-eye view of a sky-

scape taken at the point of origin “O” in the zenith di-

rection “Z” axis. The center of each web-like mesh

locate the direction of the normal vector “n” respec-

tively as inclined 15 from the zenith direction “Z”,

which are rotationally symmetrical with each other.

The shadowed parts in the field of the fish-eye view

represent images of surrounding objects such as build-

ing and trees which intercept the irradiation from the

shadowed parts of the sky window to arrive at original

point “O”.

One can measure the portion of the sky-irradiation

energy arriving at the surface of the inclined solar cell

as located by dividing the number of elemental meshes

open to the sky “Nopn” in the field of the superimposed

fish-eye view by the total number “N” of spatial ele-

ments in the meshed pattern as drawn over half of the

sphere.

The value of sky-irradiation energy Esky that arrives

at the surface of the solar cell is calculated like as:

Esky = (Nopn/N) EHSKY

where EHSKY is the value of the sky-irradiation energy

that arrives at the horizontal plane located in plain field

in the same region which is usually provided among the

meteorological data issued from the authority.

The reflex flux from the surroundings can be well

defined in the same manner as sky-irradiation based on

the following assumption:

1) The reflex may be supposed to be completely

diffusive.

2) The reflectance of the surrounding surface

(albedo value) is given and the input energy on

the surface is provided or well calculated.

2) Drawing the mesh-pattern

We introduce a new concept of spatial property

around the axis “n” over the concentric circular area on

half of the sphere called “coaxial solid angle” to be de-

fined as:

W = (1-cos 2 θ′ ) / 2

We then draw concentric circles around the axis “n” on

the sphere so that each difference in the value of W

between the next enclosure circles become equal.

Thereafter, iso-gonic longitudinal division should be

drawn around the same axis “n” on the sphere so that

we can obtain “iso-projective mesh pattern” around the

axis “n” over the sphere as shown in Fig.1.

The fish-eye transformed image of the mesh pattern

on the sphere over the fish-eye view taken at the point

of origin “O” can be drawn by computer graphics as

shown in Figs. 3a, 3b, and 3c.

3) Direct sunshine conditions

The location of direct sunshine which arrives at the

point of origin “O” could be seen by superimposing

fish-eye transforms of the solar orbits over the same

fish-eye view as shown in Fig. 3d.

The direct sunshine irradiation conditions are given by

insulation duration by solar time on each orbit which

can be read by the hourly solar time scale from the

meridian point as drawn in Fig. 3d. The location condi-

tions and eventual PV is summarized in Table 2.

4) Inner symmetry of irradiation

A certain solar roof consisting of several oblique

planes with their unit normal vectors n1, n2 , ..., n

(hereinafter referred to as “roof vectors”) is to be con-

sidered, where the following formula (1) should be re-

alized by choosing the appropriate positive values;

JAABE vol.1 no.1 March 2002 Takaaki Ikeda 185

Table 2. Location conditions and estimated PV energy at the location of Fig. 2a

Fig. 3. Sky irradiation conditions and direct sunshine conditions

186 JAABE vol.1 no.1 March 2002 Takaaki Ikeda

1, 2, . . . , , and *

1 n1 + 2 n2 + . . . + n = * ez ---(1)

ez is the unit vector of “Z” axis which, in other words

should be obtained from positive synthesis of the roof

vectors.

As indicated in Fig.4, s is a small elemental sky-

area with its normal vector having its norm

|| || = s, and 1, 2, . . . ,

are its orthogonal projections on the roof planes, and

w, upon the horizontal plane.

Then the following linear algebraic product:

V (n1,n2, .... ,n ) s = 11 + 22 +

. . . + -----(2)

will be introduced.

Whereas the value of (2) becomes * w as:

V(n1,n2, .... ,n ) s = * ez= * w

Also, it remains unchanged towards any continuous

rotation around “Z” axis standing for:

V([ ]n1,[ ]n2 , ... , [ ]n ) s

= V(n1,n2, .... ,n )s -----(3)

Namely, the sum of the value of the projected elemen-

tal area of sky on the roof planes remains unchanged

towards any continuous rotation [ ] around the “Z”

axis.

This result holds true even though negative values of

the inner products incidental to the rotation are allowed.

In geometry, the negative value of the inner product

means the elemental irradiation arrives on the reverse

side of the plane, however, in PV integration, negative

value of the inner product should partake a negative

value of PV energy when irradiated on the reverse side

of the PV cell.

In other words, while this principle should be ap-

plied to the PV system so that all values of the inner

products remain positive in rotation, the value of the

inner products all remain positive when every surface

of the roof planes can be seen from s irrespective of

any azimuthal rotation of the roof around the “Z” axis.

The nature of this “inner symmetry” regarding the

elemental irradiant holds true when integrated over the

domain where every surface of the roof planes can be

seen placed in any azimuthal direction, and hereinafter,

we call such a domain on the sky-sphere the “common

visible domain”.

To materialize such a nature in PV properties on the

roof, PV cells with their capacity balance correspond-

ing to each coefficient value 1, 2, . . . , are

placed on each plane.

Obviously, the solar roof being of an “inner symme-

try” in nature does not necessarily have to be geometri-

cally symmetrical as shown in Fig. 5 around the “Z”

axis.

If the roof is geometrically symmetrical as any of Fig.

5, the value of coefficients becomes equal and PV cells

of equal capacity should then be placed on each planes

of the roof.

The context heretofore holds true in the case of direct

sunshine irradiation by replacing by “sun vector”

which locates the spatial direction of the sun.

5) An acquired nature of “inner symmetry”

The integrated PV energies both of direct and indirect

irradiation remain unchanged towards any continuous

Fig. 4. Projection of surface element

Fig. 5. Geometrically symmetrical solar roofs

Fig. 6. Common visible domain and irradiation conditions

inside it

where [ ] is a rotation matrix around “Z” axis by ro-

tation angle as expressed:

JAABE vol.1 no.1 March 2002 Takaaki Ikeda 187

Fig. 8. Conceptual plan of Fishery Harbour, its bird’s-eye view and several view angles

Fig. 7. Photovoltaic sign

188 JAABE vol.1 no.1 March 2002 Takaaki Ikeda

Table 3. Estimated PV Energy of Fishery Harbor Around “Seto nai kai Sea”

rotation around the “Z” axis although the geometric

symmetry of the roof is lesser, for example in Fig. 5,

two times for Fig. 5a and Fig. 5b, and three times for

Fig. 5c.

The integrated PV energy as inner property of the sys-

tem thereby obtains a nature of “continuous symme-

try” around the “Z” axis, as an acquired hidden nature.

6) Irradiation conditions replaced by horizontal

plane

The solar roof of our concern having a nature of

“inner symmetry” should consists of seveal geometric

oblique planes in the form of a polyhedron rather than

the obvious single horizontal plane.

However, physically, it is possible to treat such a poly-

hedral solar roof having a nature of “inner symmetry”

as a single horizontal plane so far as irradiation within

the “common visible domain” is concerned, which holds

true both for direct sunshine irradiation and indirect sky-

irradiation.

With regards to “direct sunshine”, one can calculate

the minimum PV energy obtained from the polyhedral

solar roof from that of a single horizontal plane based

upon the direct irradiation condition within the “com-

mon visible domain”.

With regards to “sky-irradiation condition” of the

polyhedral roof, one can provide its minimum value by

replacing that of the horizontal plane within the “com-

mon visible domain” such as replacing those of Fig. 3a,

3b, and 3c with that of Fig. 6a.

In either case, the substitutive value of the PV ca-

pacity Ch assigned to the horizontal plane to replace

those C1 , C2 , ...., C on the polyhedral roof is

assumed as follows:

Ch = C1 cos 1 + C2 cos 2 + ... + C cos

where cos 1 , cos 2 , ... , cos are the value

of the inner products between ez and each unit roof

vector.

Installation example

Fig.7 shows one of the installation example of such

PV sign systems having a nature of “inner symmetry”

Park by the Japanese Government.

Fig.8 shows a conceptual plan of “Fishery Harbor”,

the roofs of its built facilities are composed of unit PV

roofs each having a nature of “inner symmetry” and

the total capacity of solar cells mounted is estimated to

be about 277.8KW with its PV energies as calculated in

Table 3 using meteorological data around “Seto nai kai

Sea”.

Conclusion

Architectural integration of PV will be provided with

powerful engineering tool by this Protocol enabling ver-

satile design at any location and under all conditions,

which will bring about both freedom and beauty in ar-

chitectural configuration as well as performance reli-

ability.

Acknowledgment

The author is grateful for having been given the

opportuinity to perform design and engineering of the

PV systems for Japanese Government implementation

such as PV signs and lightning.

Also it is a great honor for the author to receive “NEW

ENERGY AWARD” of the year of 2001 from the “NEW

ENERGY FOUNDATION” for the development of the

“Versatile Design Protocol”.

References

1) Japanese Patent #2791926 “Measurement method of irra-

diation and its conditions, installation of photovoltaic and its

systems” by T.Ikeda

2) Japanese Patent Application “Photovoltaic system having a

nature of inner symmetry” June 30, 1995 by T.Ikeda