Determination of optimum tilt angle and accurate insolation of BIPV panel influenced by adverse effect of shadow

Accepted Manuscript Determination of optimum tilt angle and accurate insolation of BIPV panel influenced by adverse effect of shadow M. Tripathy, S. Yadav, P.K. Sadhu, S.K. Panda PII:

S0960-1481(16)31090-4

DOI:

10.1016/j.renene.2016.12.034

Reference:

RENE 8371

To appear in:

Renewable Energy

Received Date: 26 September 2016 Revised Date:

9 December 2016

Accepted Date: 16 December 2016

Please cite this article as: Tripathy M, Yadav S, Sadhu PK, Panda SK, Determination of optimum tilt angle and accurate insolation of BIPV panel influenced by adverse effect of shadow, Renewable Energy (2017), doi: 10.1016/j.renene.2016.12.034. 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

Determination of Optimum Tilt Angle and Accurate Insolation of BIPV

2

Panel Influenced by Adverse Effect of Shadow

3

M TRIPATHY*, S YADAV#, P K SADHU@, and S K PANDA$ Department of Electrical Engineering, Indian School of Mines,

#, $

5

Department of Civil Engineering, Indian School of Mines, Dhanbad-826004, India.

6 *

[email protected], #[email protected], @[email protected], $ [email protected],

Abstract

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7 8 9 10 11

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*, @

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Building Integrated Photovoltaic (BIPV) technology is an immerging area of recent

13

development which has a high potential to be implemented in urban areas. PV panels of

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BIPV system serve as structural elements and are required to be fixed at optimum tilt angle

15

for maximum insolation. For open fields with no obstructions, HDKR (Hay, Davies, Klucher,

16

Reindl) model is employed effectively for calculating the optimum tilt angle. For urban areas,

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it is required to consider the adverse effect i.e., shading and sky view blocking of building for

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accurate calculation of optimum tilt angle for determining maximum insolation. This is an

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attempt to calculate optimum tilt angle of a BIPV panel surrounded by buildings of different

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heights which are located at different radial distances from panel by employing modified

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HDKR model. The present mathematical model gives accurate insolation values as it

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accounts both shading and sky view blocking effects. This sky view blocking effect is

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expressed by a factor and is calculated by integrating the sky trapped curve plotted for any

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given tilt angle of the panel. Optimum tilt angle and insolation of BIPV panel are presented

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for different state capital of India by considering shadow effect because of surrounding

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buildings.

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Keywords: BIPV; HDKR Model; Optimum Tilt Angle; Sky View Factor; Shading Coefficient.

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Nomenclature

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Hex

Monthly average daily extraterrestrial radiation on a horizontal surface (kWh/m2/day)

Hg

Monthly average daily global radiation on a horizontal surface (kWh/m2/day)

Iex

Hourly extraterrestrial radiation on a horizontal surface (kWh/m2)

Ig

Hourly global radiation on a horizontal surface (kWh/m2)

1

ACCEPTED MANUSCRIPT Ibeam

Hourly beam/direct solar radiation on a horizontal surface (kWh/m2)

Idiffuse

Hourly diffuse solar radiation on a horizontal surface (kWh/m2)

IbeamT

Hourly beam solar radiation on a tilted surface (kWh/m2)

IdiffuseT

Hourly diffuse solar radiation on a tilted surface (kWh/m2)

IreflT

Hourly reflected solar radiation on a tilted surface (kWh/m2) Hourly total solar radiation on a tilted surface (kWh/m2)

IcsT

Circumsolar diffuse solar radiation

IisoT

Isotropic diffuse solar radiation

IhzT

Horizontal brightening component

Fsky

Sky view factor

AI

Anisotropy index

Isc

Solar constant

Rb

Ratio of the average daily beam radiation on a tilted surface to that on a horizontal surface

N

Number of days of the year starting from first of January

ns

Monthly average daily hours of bright sunshine

N

Monthly average day length

KT

Clearness index

Ksc

Shading coefficient

A

Regression constant

B

Regression constant Coefficients Tilt angle

α

Altitude angle

ϕ

Latitude of the site

ωs δ

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ω

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β

θ

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A,B

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IT

Zenith angle

Mean sunrise hour angle for a given month Mean sunset hour angle for the given month

Solar declination angle

ρ

Surface albedo

γ

Azimuth angle

1 2 3 2

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1. Introduction For better environmental perspective, generation of solar energy is one of the best

4

options among other renewable resources. It is approximated that one year of world’s energy

5

budget can be achieved by solar energy received in less than one hour [1]. Photovoltaic

6

technology is one of the elegant technologies available for the efficient use of solar power

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[2]. In BIPV technology, the conventional construction materials are replaced by photovoltaic

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modules which become true construction elements and serves as building exterior for façade,

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roof or skylight [3]. These exteriors also serves as weather protection, thermal insulation,

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noise protection etc. The BIPV technology reduces the total building cost and mounting cost

11

as BIPV panels serves as building component [4]. For a cost effective BIPV system, some

12

factors must be considered such as PV module temperature, partial shadowing, installation

13

angle and orientations etc. Tripathy et al. [5] reviewed on BIPV products and their suitable

14

applications as different components of the buildings i.e., flat roof, pitch roof, curved roof,

15

façades, skylight, etc. Foil products were found to be more flexible and large range of

16

applications, whereas glazing products have a great esthetical look. Posnansky et al. [6]

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investigated on new PV material for roof and façade which can be integrated in conventional

18

buildings having any shape because of its flexibility. Beneman et al. [7] discussed on

19

different BIPV modules and different BIPV projects. In their research, they anticipated that

20

BIPV market shall emerge with towering rate in near future. The designers and architects are

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using BIPV products with innovative methods whereas manufacturers continue to create new

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compatible products to meet their demands. Sanyo, Schott solar, Sharp and Sun-tech are

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some major companies which are active on production of new BIPV products for façade, sky

24

light and windows. Implementation of Feed-in Tariff (FiT) and other government support

25

schemes for solar energy have caused wide acceptance throughout the world [8]. From recent

26

studies, it is observed that there is a sustainable growth of market of BIPV product in both

27

Eastern and Western Europe. However, the U.S government has given greater attention for

28

growth of BIPV market. Emphasis should be laid on suitable architectural design in BIPV

29

systems which enhance both the aesthetic of building as well as efficiency of BIPV system.

30

Hagemann [9] studied the reason for lack of design quality of BIPV and discussed the

31

changes needed from an architectural point of view. It was observed that by integration of

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BIPV into building system, aesthetics and technical performance can be achieved

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simultaneously. Pagliaro et al. [10] studied the market trend of BIPV in construction industry.

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ACCEPTED MANUSCRIPT It was observed that during last 5 years there is a significant growth of BIPV market as the

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BIPV technology is improved during this period. Peng et al. [3] investigated the issues

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concerning BIPV in architectural design in China and discussed how to choose between

4

BIPV and BAPV (Building attached photo voltaic). In their investigation, authors concluded

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that function, cost, technology and aesthetics of BIPV should be considered rather than solely

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the high integration. It was also suggested that in accordance of development of technology

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and growth of markets, photovoltaic structures and design should be focused on the

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maintenance and replacement of photovoltaic cell modules, rather than extending their lives.

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In order to increase the BIPV technology worldwide, architects need to be informed on the

10

potentials and limitations of integrating PV on the building envelope, since PV modules can

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have a considerable impact on the visual composition of buildings. A number of studies have

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concentrated on the architectural integration of PV in buildings [11-15], aiming at finding the

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best possible compromise between annual or seasonal energy generation and architectural

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composition. The single most important aspect affecting the performance of PV generators is

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the maximisation of the incoming solar irradiation on an annual basis.

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Shading on BIPV panel adversely affects the generation of solar energy. The

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performance of BIPV systems is also highly influenced by the orientations of PV modules

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[16]. To utilise efficiently the solar energy incident on a solar collector used in BIPV depends

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on many factors which includes local radiation climatology, orientation, tilt angle and

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different ground reflection properties. Many researchers [17-26] have established the relation

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between optimum tilt angle and latitude which are adopted by solar module installers for

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many locations. However, computation of solar radiation by experimental setup gives the

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accurate optimum tilt angle for a particular location. The value of tilt angle for different

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latitudes is computed by following analytical and experimental methods by many authors.

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Pour et al. [27] computed the optimum tilt angle of panel with zero azimuth by following the

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isotropic Liu and Jordan model [28]. The result shows that the fixed optimum tilt angle is

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approximately latitude of the location. A three component model was proposed by Heinrich

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Häberlin [29] for calculating radiation on inclined plane by considering only isotropic part of

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diffused radiation. Some authors used non-isotropic models [30] by considering azimuth

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angle for further accurate evaluation of the solar energy. Experimental investigation was

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carried out at Kuala lampur, Malaysia by Elhasaan et al. [31] for finding the optimum tilt

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angle of BIPV panel to generate maximum insolation. They used a setup with four PV

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modules inclined in north, south, east and west direction for evaluating optimum tilt angle.

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ACCEPTED MANUSCRIPT The optimum tilt angle for this location was found to be nearly equal to latitude of the

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location. Sun et al. [32] evaluated the optimum tilt angle of BIPV cladding with different

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orientations at Hong Kong by considering the shadow effect. Results showed that if the

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annual electricity generation per unit PV area is concerned, the orientation of South and

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Southwest are better choices and the maximum energy is achieved by installing PV modules

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on south façades at tilt angle of 10o. Siraki and Pillay [33] considered effect of adjacent

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buildings and incorporated these effects in their proposed anisotropic sky model. They

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elaborated the dependency of tilt angle on latitude of location and weather condition. It was

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also observed that for smaller latitude, the optimum tilt angle is close to the latitude value and

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for higher latitude the optimum tilt angle is smaller than the latitude angle. Kristl et al. [34]

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proposes a tool for analysing the possibilities of various site layouts on a given location,

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especially in the early stages of design. It can be used for new developments as well as for

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new buildings which are going to be incorporated into the existing building issue. Yang et al.

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[16] presented a mathematical model for calculating optimum tilt angles and azimuth angles,

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and is developed for the construction of buildings with integrated PV modules. Mutlu [35]

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proposed a model for obtaining the optimum slope of roofs fitted with PV panels. Sun et al.

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[36] studied the impact of building orientations, inclinations and wall utilisation fractions on

18

the energy performance of shading-type elements. Strzalka et al. [37] analysed PV

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implementation in urban environment including installations on roof or facade surfaces with

20

orientations that are not ideal for maximum energy production. Jayanta et al. [38] estimated

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insolation, PV output, PV efficiency, system efficiency, inverter efficiency and performance

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ratio (PR) for various PV surface orientation and inclination.

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In open literature, number of researcher dealt with the problem of optimum tilt angle

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without considering the real scenario of urban areas (surrounding buildings). Moreover, there

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is no such research work on effect of height and radial distance of the surrounding building

26

for calculating accurate insolation corresponding to optimum tilt angle of BIPV panel.

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Present investigators proposed a modified HDKR anisotropic sky model including the

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shadow effects of the surrounding obstacles. This modified model is used for capital of India

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to find out the optimum tilt angle by considering shadow effect due surrounding building.

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Here, the influence of building having different storey height and radial distances on BIPV

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panel have been studied by considering shadow effect. This effect is influenced significantly

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by a factor defined as sky view factor. This sky view factor has been calculated accurately by

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integrating the sky trapped curve for any given tilt angle of panel. Optimum tilt angle and

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ACCEPTED MANUSCRIPT 1

corresponding insolation for all state capitals of India have been presented by using HDKR

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model and present modified model. The paper is arranged as follows: Step by step methodology is given in section 2. The

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mathematical expressions of HDKR model are presented in sub section 2.1. Sub section 2.2

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elaborates the modified model where shadow effect has been considered. The details

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numerical results are discussed in section 3 with sub section 3.1 to sub section 3.5. The

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variation of Fsky , monthly optimum tilt angle and fixed optimum tilt angle with different H/R

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ratio are given in sub section 3.1, sub section 3.2 and sub section 3.3, respectively. Sub

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section 3.4 discussed on effect of H/R ratio on monthly insolation values and variations of

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insolation with varying heights and radial distances are given in sub section 3.5. Finally,

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conclusions are made in section 4.

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2. Methodology

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For evaluating optimum tilt angle and insolation of PV panel for BIPV application in

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urban areas, a method is proposed based on open literature [17]. In this study, the building of

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height ‘H’is consider around the BIPV panel at a radial distance of ‘R’. Here, the sky view

16

factor (Fsky) and shading coefficient (Ksc) have been considered for determining actual

17

insolation and optimum tilt angle.

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Step 1: Calculation of Hg for average day of each month on horizontal surface.

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Step 2: Calculation of Iex (Extra-terrestrial radiation on horizontal surface).

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Step 3: Calculation ofIg (Hourly insolation values for each hour of the average day of month).

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Step 4: Computation of clearness index (KT).

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Step 5: Determination of the value of Ibeam and Idiffuse (Hourly beam and diffused radiation on

23

horizontal surface) based on KT by using Erbs’s correlation.

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Step 6: Computation of sky view factor (Fsky) and shading coefficient (Ksc) due to adverse

25

shadow effect of surrounding building.

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Step 7: Calculation ofIbeamT (Beam radiation on tilted surface), IdiffuseT (Diffused radiation on

27

tilted surface), IrefT (Ground reflectance) using HDKR model for tilt angle varying 0o to 90o.

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ACCEPTED MANUSCRIPT Step 8: Calculation of IT (Hourly total solar radiation on a tilted surface) from 6 AM to 6 PM

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for each month (average day of month).

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Step 9: Determine an average hourly value of IT for average day of month for each value of

4

tilt angle from 0o to 90o.

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Step 10: Computation of the sum of insolation values of each hour for all months value of tilt

6

angle varying from 0o to 90o and determination of the angle at which maximum value of

7

insolation occurs. This angle is the optimum tilt angle for whole year.

10

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The monthly average daily extraterrestrial radiation on a surface can be calculated

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9

2.1.Mathematical Model (Hay, Davies, Klucher, Reindl model)

from the following equation. H ex =

24

π

I sc (1 + 0.033 cos

360 n π )(cos φ cos δ sin ω s + ω s sin φ sin δ ) 365 180

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1

(1)

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where, ‘Isc’ is the solar constant having value of 1367 W/m2; ‘n’ is the number of days of the

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year starting from first of January; ‘Φ’ is the latitude of the site; ‘δ’ is the solar declination

14

angle and ‘ωs’ is the mean sunset hour angle for the given month. ωs and δ are expressed as

ωs = cos−1(− tan φ tan δ )

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δ = 23.45 sin[

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360(284 + n ) ] 365

(2) (3)

Various climatic parameters have been used in developing empirical relations for predicting

18

the monthly average global solar radiation (Hg) i.e.,

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Hg H ex

n  = a + b s  N

(4)

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where ‘ns’ is the monthly average daily sunshine hour, ‘N’ is the monthly average day length

21

and ‘a’, ‘b’ are climatologically determined regression constants obtained from relationship

22

given by [39].

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a = −0.11 + 0.235cos φ + 0.323(ns / N ) b = 1.449 − 0.553cos φ − 0.694(ns / N )

(5)

where, ‘N’ is the possible daily maximum number of hours of insolation given by Iqbal [40]. N=

2 ωs 15

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(6)

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Hourly insolation calculation:

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Hourly global insolation value (Ig) is defined by

Ig = 3

24

( A + B cos ω )

cos ω − cos ωs Hg sin ωs − ωs cos ωs

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π π   A = 0.409 + 0.5016 sin  ωs −  and B = 0.6609 − 0.4767 sin  ωs −  3 3  

where,

(7)

Extraterrestrial radiation on a horizontal surface (Iex) is expressed as, I ex =

5

12 × 3600

360n   I sc 1 + 0.033 × cos  365  

π

π (ω2 − ω1 )   ×  cos φ cos δ ( sin ω2 − sin ω1 ) + sin φ sin δ  180  

(8)

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π

where, ω1 and ω2 are hour values and ω2>ω1

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Clearness index can be calculated for every hour of the average day of a particular month as,

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KT =

8

10

11

Iex

(9)

Hourly diffuse radiation (Idiffuse) is calculated by using Erbs’s correlation [41] defined in Eq.10 according to the value of clearness index (KT)

I diffuse Ig

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Ig

1.0 − 0.09 KT for KT ≤ 0.22    = 0.9511 − 0.1604 KT + 4.388KT 2 − 16.638KT 3 + 12.336KT 4 for 0.22 < KT ≤ 0.8 (10) 0.165  for KT > 0.8  

After finding hourly diffuse radiation, beam radiation incident to a horizontal surface can be

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calculated as,

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Ibeam = I g − Idiffuse

(11)

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After the evaluation of hourly diffuse and beam radiations on a horizontal surface, the hourly

16

total insolation value on a tilted plane can be calculated using following relation as,

17 18

(12)

Beam radiation on a tilted surface is defined as, I beamT = Rb ( I g − I diffuse )

19 20

I T = I beamT + I diffuseT + I reflT

where,

Rb =

cos(φ − β )cos δ sin ωs + ωs sin(φ − β )sin δ cosφ cos δ sin ωs + ωs sin φ sin δ 8

(13) (14)

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Diffuse radiation on a tilted surface (IdiffuseT) contains three parts: Circumsolar diffuse

2

radiation (IcsT); isotropic diffuse radiation (IisoT) and horizontal brightening radiation

3

(IhzT).These three components can be calculated by using anisotropic index. The index is

4

defined as,

6

I beam I ex

(15)

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AI =

5

Three diffuse radiations (IcsT, IisoT&IhzT) are defined as,

I   I − I diffuse  I csT = AIRb I diffuse =  beam  Rb I diffuse =  g  Rb I diffuse I ex  I ex   

(16)

8

 I   I ex − I g + I diffuse  I isoT = (1 − AI ) Fsky I diffuse = 1 − beam  Fsky I diffuse =   Fsky I diffuse I ex  I ex   

(17)

12

13 14 15 16

 1+ cos β  Fsky =    2 

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(18)

The sky view factor defined in above equation is as,

(19)

The ground reflectance ratio is defined as,

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 I  I −I +I  β  = 1 − diffuse   ex g diffuse  Fsky sin3   I diffuse  I g   I ex 2  

 1− cos β  IreflT = ρg   Ig  2 

(20)

Here, ρg value changes between 0.2 to 0.7 based on surrounding situation suggested by [42]

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I beam β (1 − AI ) Fsky sin3   I diffuse Ig 2

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2.2. Present modified model for urban application The HDKR model is an accurate sky model for normal roof top solar application.

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However, for urban application this model does not give accurate results as it does not

18

include the adverse effect of surrounding building. Hence, it is essential to incorporate some

19

correction factor to account for shadow effect caused by buildings. One of the factor is due to

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shading effect which occurs during the hour, when sun is trapped. Here, the beam radiation

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(IbeamT) and circumsolar radiation (IcsT) are zero as there is no direct sight of sun is available

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from panel.Based on that, the Eq. (13) and Eq. (16) are modified as Eq. (21) and Eq. (22),

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respectively. The modified equations are defined as, 9

ACCEPTED MANUSCRIPT I beamT = (1 − K sc ) Rb ( I g − I diffuse )

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 I − I diffuse I csT = (1 − K sc )  g I ex 

2

(21)

  Rb I diffuse 

(22)

The shading coefficient (Ksc) expressed in Eq. (21) and Eq. (22) is defined as the portion of

4

the calculation time step in which panel is under full shade. For instance for a 1h calculation

5

time step, 40 min shading will lead to a shading coefficient equal to ‘2/3’ for that specific

6

hour. For calculating shading coefficient (Ksc) the projection of surrounding building is

7

superimposed over sun path diagram, which can be done by converting coordinate of building

8

H in cylindrical coordinate as follows. Altitude angle (α) of a point is defined as: α = tan −1   R

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. Where, ‘H’ is height of building and ‘R’ is the radial distance of building from panel.

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Fig. 1. BIPV panel surround by neighbourhood building.

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Altitude Angle (α)

ACCEPTED MANUSCRIPT

Azimuth Angle (γ) 1

Fig. 2. Sun path diagram for latitude angle (Φ=28.6139) in conjunction with surrounding

3

building (H=6m and R=20m).

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This coefficient can be estimated for different hours of an average day (for each month of the

5

year) from sun path diagram shown in Fig. 2. For accurate estimation of shading coefficient

6

(Ksc), smaller time steps (10 mimutes) are taken and this is shown between 7th hour and 8th

7

hour. Fig. 1 shows a panel surrounded by building of height ‘H’ at radial distance of ‘R’.

8

This typical configuration of buildings around the panel is used to analyse the effect of ‘H/R’

9

ratio on Fsky & Ksc for evaluating the actual insolation and hence the optimum tilt angle. Fsky

EP

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& Ksc are the key factors for evaluating the actual insolation and optimum tilt angle. Similarly, second significant adverse effect of surrounding building is sky blocking

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effect. Here, certain portion of sky is blocked due to presence of obstacles around the panel.

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Hence, both isotropic (IisoT) and horizontal brightening (IhzT) radiations from the blocked

14

portion of sky is zero. Therefore, it is necessary to modify the sky view factor defined by Eq.

15

(19) in order to consider the above effect. A new sky view factor defined as [32],

16

Fsky = 1 −

1

π2

n

∑A s =1

s

(23)

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For calculating As integration approach is employed. Different parameters shown in Fig.3 are defined as,

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As = Net area of sky trapped by panel and building 11

ACCEPTED MANUSCRIPT 1

Astp = Area of sky trapped by panel itself.

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Acom = Common area of sky trapped by both building and panel.

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Fig. 3.Sky trapped diagram for 30° panel and surrounded by building of H=6m and R=20m.

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Astb = Area of sky trapped by building

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P= Point of intersection

8

α = Altitude angle of building

9

γ = Azimuth angle

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10

β = Tilt angle of panel

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There are two cases possible according to the value of ‘α’ and ‘β’ for calculating ‘As’.

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Case 1: Tilt angle of panel is greater than altitude angle of building (β ≥ α)

13

In this case, area occupied by building and panel intersect at some point ‘P’. It is required to

14

calculate point of intersection accurately. Total area of sky trapped by panel itself (Astp) is

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calculated from sky trapped diagram as,

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ACCEPTED MANUSCRIPT π

Astp = 2 ∫ tan −1 ( − tan β cos γ ) d γ

1

(24)

π

2

2

4

5

Common area of sky trapped by both building and panel is expressed as,

Acom

π  = 2  ∫ α dγ π 2

p  p   −  ∫ α d γ − ∫ tan−1 ( − tan β cos γ ) dγ  π π  2 2 

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Area of sky trapped (only building) is calculated from the Fig.3 as,

0

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π

Astb = 2 ∫ α d γ

6

(26)

Net area of sky trapped (As) by both panel and building is expressed as,

As = ( Astp + Astb − Acom )

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(25)

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Case 2: Tilt angle is smaller than altitude angle of building (β < α ) .

10

In this case, common area of sky trapped by panel and building is zero.

11

Area of sky trapped by panel is defined as,

(27)

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π

Astp = 2 ∫ tan −1 ( − tan β cos γ ) d γ

12

(28)

π

2

π

Whereas, area trapped by building is Astb = 2 ∫ α d γ

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13

Net area is expressed as,

15

3. Result and discussion

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As = ( Astb − Astp )

(30)

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(29)

0

3.1.Fsky variation with H/R Variation of sky view factor (Fsky) with altitude angle (α) of building is investigated

18

and presented in Fig.4.For a neighbourhood building of height ‘H’ and horizontal distance

19

H ‘R’, the altitude of building is defined as α = tan−1   . In present study, the different height R

20

of building (H) considered are 3m, 6m, 9m, 12m, and 15mfor each radial distances (R) of

21

10m, 20m, 30m and 40m.When ‘α’ value decreases up to the tilt angle of the panel, area of

22

sky trapped by the panel is included within area of sky trapped by building. In this range of

23

altitude angle of building, the net area of sky blocked is directly proportional to increase of 13

ACCEPTED MANUSCRIPT ‘α’. Hence, in this range the Fsky value increases linearly with decrease of ‘α’. For further

2

decrease of ‘α’, initially the net area of sky blocked decreases with decrease of ‘α’ and then

3

the net area of sky blocked increases nonlinearly with decrease of ‘α’. From the graph, it is

4

observed that there is an initial drop of value of ‘Fsky’ after attaining the ‘α’ value equal to

5

respective tilt angle (β = 10°, 20°,30° &40°) of the panel. In all the cases, after initial drop,

6

there is a nonlinear variation of Fsky value for further decrease in ‘α’ value.

RI PT

1

1.0

β=0

o

β = 10 o β = 20 o β = 30 o β = 40 o

SC

0.8

M AN U

Sky View Factor (Fsky)

0.9

0.7 0.6

0.4 0

10

20

30

40

50

Altitude of building (α)

EP

7

TE D

0.5

Fig. 4. Variation of sky view factor with altitude of building

9

Table 1a, 1b, 1c and 1d present the value of shading coefficients (Ksc) for buildings having

10

different heights (3m, 6m, 9m, 12m, & 15m) located at a radial distance of 20m from panel.

11

The tables show the duration in which panel is under full shade (Ksc =1), partial shade (Ksc<1)

12

or no shade (Ksc =0) for every hour of a day. The no of hours in which panel is under shade

13

increases for every month of a year with increase in storey height. It is observed that, the

14

panel is under shade for more hour of day in winter months as compared to summer months

15

for all storey heights of building.

AC C

8

14

ACCEPTED MANUSCRIPT

Table 1(a) Shading coefficient (Ksc) for H/R=3/20. Feb 1 0.5 0 0 0 0 0 0 0 0 0 0.83

Mar 1 0 0 0 0 0 0 0 0 0 0 0.25

Apr 0.58 0 0 0 0 0 0 0 0 0 0 0

Mar 1 0.67 0 0 0 0 0 0 0 0 0 1

Apr 1 0.17 0 0 0 0 0 0 0 0 0 0.5

May 0.42 0 0 0 0 0 0 0 0 0 0 0

Time 6:00-7:00 7:00-8:00 8:00-9:00 9:00-10:00 10:00-11:00 11:00-12:00 12:00-13:00 13:00:14:00 14:00-15:00 15:00-16:00 16:00-17:00 17:00-18:00

Jan 1 1 0.5 0 0 0 0 0 0 0 0.83 1

Feb 1 1 0.083 0 0 0 0 0 0 0 0.5 1

May 1 0 0 0 0 0 0 0 0 0 0 0.25

EP

Table 1(b) Shading coefficient (Ksc) for H/R=6/20.

AC C

4 5

TE D

3

Jun 0.25 0 0 0 0 0 0 0 0 0 0 0

Jul 0.33 0 0 0 0 0 0 0 0 0 0 0

Jun 0.83 0 0 0 0 0 0 0 0 0 0 0.083

6 15

Aug 0.5 0 0 0 0 0 0 0 0 0 0 0

Sept 0.92 0 0 0 0 0 0 0 0 0 0 0.0833

Oct 1 0.17 0 0 0 0 0 0 0 0 0 0.67

Nov 1 0.67 0 0 0 0 0 0 0 0 0 1

Dec 1 0.83 0 0 0 0 0 0 0 0 0.25 1

Aug 1 0.083 0 0 0 0 0 0 0 0 0 0.42

Sept 1 0.5 0 0 0 0 0 0 0 0 0 0.93

Oct 1 1 0 0 0 0 0 0 0 0 0.25 1

Nov 1 1 0 0 0 0 0 0 0 0 0.75 1

Dec 1 1 0.58 0 0 0 0 0 0 0 0.92 1

RI PT

Jan 1 0.75 0 0 0 0 0 0 0 0 0.0833 1

SC

Time 6:00-7:00 7:00-8:00 8:00-9:00 9:00-10:00 10:00-11:00 11:00-12:00 12:00-13:00 13:00:14:00 14:00-15:00 15:00-16:00 16:00-17:00 17:00-18:00

M AN U

1 2

Jul 0.92 0 0 0 0 0 0 0 0 0 0 0.17

ACCEPTED MANUSCRIPT

Table 1(c) Shading coefficient (Ksc) for H/R=9/20. Feb 1 1 0.83 0 0 0 0 0 0 0.083 1 1

Mar 1 1 0.42 0 0 0 0 0 0 0 0.5 1

Apr 1 0.92 0 0 0 0 0 0 0 0 0.083 1

Mar 1 1 0.83 0 0 0 0 0 0 0.17 1 1

Apr 1 1 0.42 0 0 0 0 0 0 0 0.58 1

Time 6:00-7:00 7:00-8:00 8:00-9:00 9:00-10:00 10:00-11:00 11:00-12:00 12:00-13:00 13:00:14:00 14:00-15:00 15:00-16:00 16:00-17:00 17:00-18:00

Jan 1 1 1 1 0 0 0 0 0.5 1 1 1

Feb 1 1 1 0.42 0 0 0 0 0 0.75 1 1

EP

Table 1(d) Shading coefficient (Ksc) for H/R=12/20.

AC C

4 5

Jun 1 0.42 0 0 0 0 0 0 0 0 0 0.75

TE D

3

May 1 0.67 0 0 0 0 0 0 0 0 0 0.83

Jul 1 0.5 0 0 0 0 0 0 0 0 0 0.7

Aug 1 0.83 0 0 0 0 0 0 0 0 0 1

Sept 1 1 0.17 0 0 0 0 0 0 0 0.42 1

Oct 1 1 0.67 0 0 0 0 0 0 0 1 1

Nov 1 1 1 0.083 0 0 0 0 0 0.5 1 1

Dec 1 1 1 0.42 0 0 0 0 0 0.83 1 1

Jul 1 1 0 0 0 0 0 0 0 0 0.25 1

Aug 1 1 0.25 0 0 0 0 0 0 0 0.5 1

Sept 1 1 0.75 0 0 0 0 0 0 0 1 1

Oct 1 1 1 0.17 0 0 0 0 0 0.58 1 1

Nov 1 1 1 0.93 0 0 0 0 0.17 1 1 1

Dec 1 1 1 1 0.17 0 0 0 0.67 1 1 1

RI PT

Jan 1 1 1 0.33 0 0 0 0 0 0.75 1 1

SC

Time 6:00-7:00 7:00-8:00 8:00-9:00 9:00-10:00 10:00-11:00 11:00-12:00 12:00-13:00 13:00:14:00 14:00-15:00 15:00-16:00 16:00-17:00 17:00-18:00

M AN U

1 2

May 1 1 0.083 0 0 0 0 0 0 0 0.33 1

6 16

Jun 1 0.92 0 0 0 0 0 0 0 0 0.17 1

ACCEPTED MANUSCRIPT

Table 1(e) Shading coefficient (Ksc) for H/R=15/20. Feb 1 1 1 1 0 0 0 0 0.5 1 1 1

Mar 1 1 1 0.42 0 0 0 0 0 0.58 1 1

Apr 1 1 0.92 0 0 0 0 0 0 0.083 1 1

6

EP

5

AC C

4

TE D

3

May 1 1 0.67 0 0 0 0 0 0 0 0.83 1

Jun 1 1 0.5 0 0 0 0 0 0 0 0.67 1

Jul 1 1 0.5 0 0 0 0 0 0 0 0.75 1

17

Aug 1 1 0.67 0 0 0 0 0 0 0 1 1

Sept 1 1 1 0.0833 0 0 0 0 0 0.5 1 1

RI PT

Jan 1 1 1 1 0.92 0 0 0.0833 1 1 1 1

SC

Time 6:00-7:00 7:00-8:00 8:00-9:00 9:00-10:00 10:00-11:00 11:00-12:00 12:00-13:00 13:00:14:00 14:00-15:00 15:00-16:00 16:00-17:00 17:00-18:00

M AN U

1 2

Oct 1 1 1 0.67 0 0 0 0 0 1 1 1

Nov 1 1 1 1 0.5 0 0 0 1 1 1 1

Dec 1 1 1 1 1 0.17 0 0.5 1 1 1 1

ACCEPTED MANUSCRIPT 1

3.2.Optimum tilt angle variation with H/R ratio Figures 5a, 5b, 5c and 5d present the monthly variation of tilt angle for different

3

‘H/R’ ratios. It is observed that the value of monthly optimum tilt angle for maximum

4

insolation decrease from January to June and then increase from June to December. Fig. 5a

5

present the result for the surrounding buildings having radial distance ‘R’ of 10m and height

6

of buildings considered are from 3m (single storey) to 15m (five storey). It is observed that

7

for 3rd, 4th and 5th storied building, the optimum tilt angle varies from 90o to 0o from January

8

to June and from 0o to 90o from June to December. However, for single and double storied

9

buildings, the tilt angle range is from 55o to 0o from January to June and 0o to 55o from June

10

to December. The reason of different monthly optimum tilt angle for different height of the

11

building is because of shading effect of building and blocking of certain portion of sky. For

12

radial distance of 20m, 30m and 40m, the monthly optimum tilt angle varies from 55o to 0o

13

from January to June and 0oto55o from June to December for all buildings heights. Similarly,

14

the optimum tilt angle variation for different height of building are shown in Fig.5b, Fig.5c

15

and Fig.5d for horizontal distance of 20m ,30m and 40m, respectively.

M AN U

SC

RI PT

2

100

70

EP

60 50 40

AC C

Tilt Angle (degree)

80

H/R =3/10 H/R=6/10 H/R=9/10 H/R=12/10 H/R=15/10

TE D

90

30 20 10

16 17 18

Ju l A ug Se p O ct N ov D ec

Ja n Fe b M ar A pr M ay Ju n

0

Months

Fig. 5a. Monthly variation of tilt angle for different height of building (H) at a fix value of R=10m.

18

ACCEPTED MANUSCRIPT

60

H/R=3/20 H/R=6/20 H/R=9/20 H/R=12/20 H/R=15/20

40

RI PT

Tilt Angle (Degree)

50

30 20

SC

10

Months

1

Fig. 5b. Monthly variation of tilt angle for different height of building (H) at a fix value of R=20m.

60

EP

40 30

AC C

Tilt Angle (Degree)

50

H/R=3/30 H/R=6/30 H/R =9/30 H/R=12/30 H/R=15/30

TE D

2 3

Ju l A ug Se pt Oc t N ov D ec

M AN U

Ja n Fe b M ar Ap r M ay Ju n

0

20 10

4 5 6

Ju l A ug Se pt Oc t No v De c

Ja n Fe b M ar Ap r M ay Ju n

0

Months

Fig. 5c. Monthly variation of tilt angle for different height of building (H) at a fix value of R=30m.

19

ACCEPTED MANUSCRIPT

H/R=3/40 H/R=6/40 H/R=9/40 H/R=12/40 H/R=15/40

60

RI PT

40 30 20 10

Ju l A ug Se pt O ct N ov D ec

M AN U

Ja n Fe b M ar A pr M ay Ju n

0

SC

Tilt Angle (Degree)

50

Months

1

Fig. 5d. Monthly variation of tilt angle for different height of building (H) at a fix value of R=40m.

4 5

3.3.Variation of fixed optimum tilt angle at varying height and radial distances of building

TE D

2 3

Variation of optimum tilt angle for different storey height of building is presented in

7

Fig.6. It is depicted in the graph that for each radial distance of building (R= 10m, 20m, 30m

8

and 40m ), the value of optimum tilt angle decreases with increase of storey height from 3m

9

to 15m i.e., from single storey to fifth storey. Moreover, the range of variation of optimum tilt

10

angle with respect to height of building is more for lower value of radial distance. It is

11

observed that for ‘R’ value 10m, 20m, 30m and 40m, the range of optimum tilt angle is 31° to

12

19.5° , 32° to 28° , 32° to 30° and 32° to 31.5°, respectively. The large variation of optimum

13

tilt angle for building with close proximity is because of higher influence of shading and sky

14

view blocking effect. Similarly, the values of optimum tilt angle increases with increase in

15

radial distance from 10m to 40m. Moreover, the range of variation of optimum tilt angle with

16

respect to radial distance is more for higher storey height. It is also observed that for ‘H’

17

value 3m, 6m, 9m, 12m, and 15m, the range of variation of tilt angle is 31° to 32°, 29.5° to

18

32°, 24° to 31°, 19.5o to 31oand 19.5° to 31°, respectively. The variation of fixed optimum tilt

19

angle with different radial distances are shown in Fig.7. For each storey height of building

AC C

EP

6

20

ACCEPTED MANUSCRIPT (from single storey to fifth storey), the variation is maximum for higher storey building due to

2

more influence of Ksc and Fsky.

32

R=40m

30

R=30m

28

R=20m

RI PT

Optimum fixed tilt angle (degrees)

1

26

SC

24 22

R=10m

M AN U

20 18 3

6

9

12

15

Height of building (m)

3

Fig. 6. Variation of fixed optimum tilt angle with varying height of building.

TE D

4

EP

30 28 26

AC C

Optimum fixed tilt angle (degrees)

32

24

H=3 m H=6m H=9m H=12m H=15m

22 20

10

20

30

40

Radial distance of building (m)

5 6

Fig. 7. Variation of optimum fixed tilt angle with radial distance between panel and

7

building. 21

ACCEPTED MANUSCRIPT

RI PT

33°

33° 32°

31°

28°

M AN U

27°

27°

32°

28° 28° 26°

26°

TE D

24°

20°

20°

EP

19°

AC C

16°

15° 11°

1 2 3

Fig. 8. Map showing value of optimum tilt angle for different state capital of INDIA for BIPV application for a typical building of ‘H’ 6m&‘R’ 20m from panel.

4 5 22

30°

31°

27°

22°

31°

30°

29°

26°

SC

32°

30°

1

Table 2.

2

Optimum tilt angle with insolation of Indian state capitals. State Capitals with latitude

HDKR model

angle Insolation

Amravathi(16.83)

0.44275

Arunachal Pradesh

Itanagar(27.0844)

0.38025

Assam

Dispur(26.1433)

Bihar

Insolation

Optimum tilt

(kWh/m2/hr)

angle (β)

21

0.421972

20

33

0.350639

31

0.454333

33

0.421167

32

Patna(25.5941)

0.536972

30

0.504417

27

Chhattisgarh

Raipur(21.1797)

0.464083

27

0.438472

26

Goa

Panaji(15.4909)

0.5075

21

0.476417

19

Gujarat

Gandhinagar(23.2156)

0.478

28

0.446833

26

Haryana

Chandigarh(30.7333)

0.530972

34

0.49

32

Himachal Pradesh

Simla(31.1048)

0.520222

35

0.481056

33

Jammu & Kashmir

Srinagar(34.0837)

0.491028

37

0.430722

33

Jharkhand

Ranchi(23.3441)

0.444417

29

0.412639

27

Karnataka

Bangalore(12.9716)

0.473778

18

0.451278

16

0.471472

12

0.448972

11

EP

AC C

Kerala

TE D

Andhra Pradesh

angle (β)

Present model

M AN U

(kWh/m2/hr)

Optimum tilt

SC

Indian States

RI PT

ACCEPTED MANUSCRIPT

Triruvananthapuram(8.5241)

Madhya Pradesh

Bhopal(23.2599)

0.471722

29

0.439139

27

Maharashtra

Mumbai(19.0760)

0.482639

25

0.435222

22

23

ACCEPTED MANUSCRIPT

3 4 5

32

0.408

30

Meghalaya

Shillong(25.5788)

0.427667

33

0.396833

31

Mizoram

Aizawl(23.7271)

0.441361

30

0.410389

28

Nagaland

Kohima(25.6586)

0.436556

33

0.401528

30

Odisha

Bhubaneswar (20.2961)

0.436639

26

0.414333

24

Punjab

Chandigarh(30.7333)

0.530972

34

0.49

32

Rajasthan

Jaipur(26.9124)

0.549167

30

0.514194

28

Sikkim

Gangtok(27.3389)

0.458139

32

0.424944

30

Tamil Nadu

Chennai(13.0827)

0.498167

16

0.476056

15

Telangana

Hyderabad(17.3850)

0.503583

22

0.477056

20

Tripura

Agartala(23.8315)

0.441778

30

0.410833

28

Uttar pradesh

Lucknow(26.8467)

0.469694

31

0.440306

29

Uttarakhand

Deheradun(30.3165)

0.522111

35

0.479917

32

West Bengal

Kolkata(22.5726)

0.492028

28

0.463778

26

TE D

M AN U

SC

RI PT

0.440083

EP

2

Imphal(24.8170)

AC C

1

Manipur

6

24

ACCEPTED MANUSCRIPT The contour map of fixed optimum tilt angle for different state capital of India for

2

BIPV application is shown in Fig.8. The influence of Ksc and Fsky are incorporated by

3

considering a typical building of height ‘H’ of 6m and radial distance of ‘R’ 20m from panel

4

location. It is observed that the fixed optimum tilt angle gradually increases from southern

5

part of India to north of India for BIPV application. Table 2 presents the insolation value with

6

respect to optimum fixed tilt angle for HDKR model and present modified HDKR model. It is

7

noted that there is a significant difference of above results between HDKR model and present

8

modified HDKR model as present model accounts for shadow effect.

9

RI PT

1

3.4.Effect of H/R ratio on insolation

Figure 9 shows the insolation values of a panel placed at a radial distance 20m from

11

the two storied building all around the panel. The height of each storey is considered to be

12

3m. The insolation value is presented for both HDKR model and the present modified HDKR

13

model. It is observed that the insolation value of HDKR model is more than that of modified

14

model as HDKR anisotropic sky model does not include the effect of surrounding obstacles

15

which causes shade on panel and block certain portion of sky. In present modified HDKR

16

model, these effects are considered by introducing shading coefficient (Ksc) and sky view

17

factor (Fsky).

0.75

EP

HDKR Model Present Modified HDKR Model

0.65 0.60

AC C

2

Insolation (kWh/m /hr)

0.70

TE D

M AN U

SC

10

0.55 0.50

Months

18 19 20

Ju l Au g Se pt Oc t No v De c

Ja n Fe b M ar Ap r M ay Ju n

0.45

Fig. 9. Insolation for HDKR model and present modified HDKR model for latitude (Φ) = 28.6139, R=20m & H=6m. 25

ACCEPTED MANUSCRIPT 1

The difference of insolation is significant during the months January to April and October to

2

December because of higher influence of shading effect during these months. During this

3

period, the value of Ksc is higher and is calculated from sun path diagram. Sky view factor

4

also influences the insolation value and is directly proportional to insolation. Figure 10 presents the variation of average hourly insolation in a year for different

6

altitude angle (α) of the building. For each of radial distance of building i.e.,10m, 20m, 30m

7

and 40m, the height of the building considered are 3m, 6m, 9m, 12m and 15m. There are 15

8

combinations of radial distance and vertical distance, and for each combination the insolation

9

value has been plotted. It is observed from the figure that with increase of ‘α’, the insolation

10

value decreases because of shadow effect. The shadow effect is much significant when the

11

‘α’ value is more than 30o. This is because for higher value of ‘α’, the panel is under shade

12

for more duration and also the portion of sky which is blocked by building is more.

M AN U

SC

RI PT

5

0.4 0.3 0.2

EP

0.1

TE D

2

Insolation(kWh/m /hr)

0.5

13 14

AC C

0.0

10

20

30

40

50

60

Altitude of building (Degree)

Fig. 10. Variation of average hourly insolation in a year with altitude of building.

15

26

ACCEPTED MANUSCRIPT

60 50 40

RI PT

Percentage loss of insolation

70

30 20

SC

10 0 10

2

60

M AN U

1

20 30 40 50 Altitude of building (Degree)

Fig. 11. Percentage loss of insolation due to shading and sky view blocking effect. Percentage loss of insolation due to shading and sky view effect for all fifteen

4

different altitude angle is plotted in Fig.11. The loss is computed by the difference of

5

insolation between HDKR model and present modified HDKR model. For higher altitude

6

angle, the solar panel is under shade for more duration and also the portion of sky which is

7

blocked is more. Hence, the insolation loss percentage is higher for higher altitude angle, e.g.,

8

for building having altitude angle of 4.28o (H/R=3:40), the loss of insolation is 9.14%

9

whereas, for altitude angle of 56.3o (H/R=15:10) the loss is 72.17%. It is observed that the variation in loss of insolation variation with altitude angle is approximately like parabolic.

EP

10

TE D

3

Figures 12a, 12b, 12c and 12d present the variation of monthly average hourly

12

insolation for different months for varying ‘H’ values with different ‘R’ = 10m, 20m, 30m

13

and 40m, respectively. It is observed that with increase in height of building (H) for a

14

particular radial distance (R), the insolation value is reduced for all months of a year. The

15

above reduction is significant for January to March and October to December. At higher

16

radial distances (R=30 &40m), the difference in insolation for different height of building (H)

17

is small for all months of a year. For small radial distance i.e., R = 10m with height of

18

building H= 9m, 12m, and 15m, the insolation value is same for January and December.

19

However, for H= 12m and 15m, the insolation value is same for February and November.

20

This is because for above ‘H/R’ ratio, the value of shading coefficient becomes one (Ksc = 1).

AC C

11

27

ACCEPTED MANUSCRIPT 1.0 H/R=3/10 H/R=6/10 H/R=9/10 H/R=12/10 H/R=15/10

0.9

0.7 0.6

RI PT

0.5 0.4 0.3 0.2 0.1

Ju n Ju l A ug Se pt O ct N ov D ec

Ja n Fe b M ar A pr M ay

0.0

Months

M AN U

1

SC

2

Insolation (kWh/m /hr)

0.8

2

Fig. 12a. Variation of monthly average hourly insolation for different months for varying ‘H’

3

with ‘R’= 10m.

H/R=3/20 H/R=6/20 H/R=9/20 H/R=12/20 H/R=15/20

EP

0.6

0.4

AC C

2

Insolation (kWh/m /hr)

0.8

TE D

1.0

0.2

Ju n Ju l Au g Se pt Oc t No v D ec

Ja n Fe b M ar A pr M ay

0.0

Months

4 5

Fig. 12b. Variation of monthly average hourly insolation for different months for varying ‘H’

6

with ‘R’ = 20m.

28

ACCEPTED MANUSCRIPT 1.0

H/R=3/30 H/R=6/30 H/R=9/30 H/R=12/30 H/R=15/30

0.9

0.7 0.6

RI PT

0.5 0.4 0.3 0.2 0.1

Ju n Ju l Au g Se pt Oc t No v D ec

Ja n Fe b M ar A pr M ay

0.0

SC

2

Insolation(kWh/m /hr)

0.8

Months

M AN U

1 2

Fig. 12c. Variation of monthly average hourly insolation for different months for varying ‘H’

3

with ‘R’ = 30m. 1.0 0.9

0.6 0.5 0.4

TE D

0.7

EP

2

Insolation(kWh/m /hr)

0.8

H/R=3/40 H/R=6/40 H/R=9/40 H/R=12/40 H/R=15/40

0.3 0.2

AC C

0.1

4

Ju n Ju l A ug Se pt O ct No v D ec

Ja n Fe b M ar A pr M ay

0.0

Months

5

Fig. 12d. Variation of monthly average hourly insolation for different months for varying ‘H’

6

with ‘R’ = 40m.

7 8

29

ACCEPTED MANUSCRIPT 1

3.5.Variation of insolation at varying height and radial distance Variation of average hourly insolation in a year for different storey height of building

3

is presented in Fig.13a. It is depicted in the graph that for each radial distance of building

4

(R= 10m, 20m, 30m& 40m), the value of average hourly insolation in a year decreases with

5

increase of storey height from 3m to 15m i.e., from single storey to fifth storey. For these

6

storey heights and ‘R’ values of 10m, 20m, 30m and 40m,the range of average hourly

7

insolation in a year is 0.4916 to 0.148, 0.5122 to 0.3517, 0.5225 to 0 .4442and 0.5245 to

8

0.4780, respectively. It is observed that the difference of average hourly insolation in a year

9

for two different heights of building is more for lower value of radial distance. The large

10

variation of optimum tilt angle for building with close proximity is because of higher

11

influence of shading and sky view blocking effect.

M AN U

0.6

2

Insolation (kWh/m /hr)

0.5

0.3

EP AC C

3

13

R=10m R=20m R=30m R=40m

TE D

0.4

0.2

12

SC

RI PT

2

6

9

12

15

Height of building (H)

Fig.13a. Variation of average hourly insolation for different heights of building.

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H=3m H=6m H=9m H=12m H=15m

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Fig.13b. Variation of average hourly insolation for different radial distance between panel and building.

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Similarly in Fig.13b, the value of average hourly insolation in a year increases with

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increase in radial distance from 10m to 40m for each storey height. Moreover, the range of

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variation of average hourly insolation in a year with respect to above radial distances is more

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for higher storey height. It is observed that for ‘H’ values 3m, 6m, 9m, 12m, and 15m, the

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range of variation of tilt angle is 0.4916 to 0.5245, 0.413 to 0.5122, 0.2842 to 0.5073, 0.1968

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to 0.4916 and 0.1480 to 0.4780, respectively. The variation is maximum for higher storey

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building due to more influence of Ksc and Fsky.

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4. Conclusions

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For urban application of BIPV, the adverse effect of shadow because of surrounding

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building on energy production is an important aspect to be considered. The present

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mathematical model for calculating both optimum tilt angle and corresponding insolation is

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an updated HDKR model which calculates the insolation accurately by introducing shading

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coefficient (Ksc) and sky view factor (Fsky). Optimum tilt angle and corresponding insolation

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of BIPV panel have been evaluated by considering the adverse effect of surrounding building

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with certain heights and radial distances. A contour map of optimum fixed tilt angle of

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different state capital of India is presented by considering the shadow effect. Following are

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the key observations of the detailed studies. 31

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With decrease of the altitude angle of the surrounding building, the (Fsky) value

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increases linearly till the tilt angle of BIPV panel. Just after the tilt angle of the panel,

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there is a drop in (Fsky) value and then the (Fsky) value increases nonlinearly with

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decrease in altitude angle.

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from June to December.

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Optimum tilt angle of PV panel decreases from January to June and then increases

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For a giver storey height of a building around the BIPV panel, the optimum fixed tilt angle increases with increase in radial distance. Moreover, for a given radial distance

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of the building, optimum fixed tilt angle decreases with increase in height. Similar behaviour is also observed for insolation.

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With increase of altitude angle of building, percentage loss of insolation due to shading and sky view blocking effect increases.

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ACCEPTED MANUSCRIPT Highlights Variation of sky view factor with the influence of shadow by surrounding building

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Effect of height & distance of surrounding building on optimum tilt angle of panel

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Optimum tilt angle and insolation of BIPV Panel for all states capital of India.

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