Optimization method for photovoltaic integration in residential houses

Abstract

Good design and sizing of photovoltaic (PV) systems is very important in order to effectively harvest energy and minimize the investment cost. The optimum tilt and azimuth angles at which a PV system should be installed are often debated. This paper evaluates the tradeoff between annual energy generation and payback period reduction through the analysis of a small house with pitched roof integrated PVs in both East and West sides. Validated irradiance
and PV models were used for the analysis. The optimum tilt and azimuth angles are found to be 35° and 10° respectively. Finally, a contour map plot illustrating all possible tilt and orientation angles, corresponding to a payback period less than 20 years, is provided. The results are valid for different building typologies and locations with similar climate conditions as Prague.

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Optimization method for photovoltaic integration in residential houses
To cite this article: Sofiane Kichou et al 2019 J. Phys.: Conf. Ser. 1343 012093
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CISBAT 2019
Journal of Physics: Conference Series 1343 (2019) 012093
IOP Publishing
doi:10.1088/1742-6596/1343/1/012093
1
Optimization method for photovoltaic integration in
residential houses
Sofiane Kichou, Nikolaos Skandalos and Petr Wolf
University Centre for Energy Efficient Buildings, Czech Technical University in
Prague Třinecká 1024, 273 43 Buštěhrad, Czech Republic.
Corresponding author’s e-mail: sofiane.kichou@cvut.cz
Abstract. Good design and sizing of photovoltaic (PV) systems is very important in order to
effectively harvest energy and minimize the investment cost. The optimum tilt and azimuth
angles at which a PV system should be installed are often debated. This paper evaluates the trade-
off between annual energy generation and payback period reduction through the analysis of a
small house with pitched roof integrated PVs in both East and West sides. Validated irradiance
and PV models were used for the analysis. The optimum tilt and azimuth angles are found to be
35° and 10° respectively. Finally, a contour map plot illustrating all possible tilt and orientation
angles, corresponding to a payback period less than 20 years, is provided. The results are valid
for different building typologies and locations with similar climate conditions as Prague.
1. Introduction
Photovoltaics (PV) is one of the most deployed technologies for generating clean energy and reducing
CO2 emissions. The total worldwide installed capacity has been exponentially increased during last
decade, while one Tera Watt peak (TWp) of total installed PV capacity is forecasted to be reached in the
next few years.
A good design and sizing of PV systems is very important in order to effectively exploit energy and
reduce the payback period of the investment. Tilt and azimuth angles of an installation are key
parameters that determine the amount of solar radiation received on the PV modules and thus the yield
of the PV system. The assessment of the optimum tilt angle for the maximization of solar energy
harvesting is still subject of interest, and researchers are still actively working on the topic [1-4].
This paper evaluates the trade-off between annual energy losses and possible electricity generation
cost reductions through adapting PV installation angles on residential buildings in Prague, Czech
Republic and other locations with similar conditions. A small house with pitched roof was used for the
analysis of the PV generation in relation to the tilt angle and orientation of the roof based on validated
irradiance and PV models. Finally, considering the actual costs of the selected thin-film PV system,
conclusions are drawn indicating the range of tilt and azimuth angles limits in such houses for making
a PV system investment beneficial and at least have a payback period equal to a PV module lifetime.
2. Experimental setup description
An experimental house located near Prague (Latitude: 50°09'24.2"N, Longitude: 14°10'10.5"E) with
pitched roof, depicted in Fig. 1a, was used for the analysis of the behaviour of two thin-film PV systems
(CdTe) integrated in different orientations (East-West). The PV systems outputs and weather data are

CISBAT 2019
Journal of Physics: Conference Series 1343 (2019) 012093
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doi:10.1088/1742-6596/1343/1/012093
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being continuously monitored in five-minute timesteps since September 2018. There are two Si-
RS485TC-2T-MB irradiance sensors (for both East and West) with external temperature sensors glued
to the back side of PV modules. Additionally, there is a Kipp & Zonen SMP11 pyranometer installed
on the West side of the roof. All the sensors are measuring the irradiance at the roofs’ tilt angle of 30°.
The PV system size in each part of the roof is 1.92 kWp, and it is composed of 24 CdTe PV panels
connected to two micro-inverters. Each micro-inverter has four channels, and every channel (connecting
one string composed of three PV modules) is monitored separately. Additionally, as the house is at an
azimuth angle of -22° (turned to East), measured data from various irradiance sensors (Fig. 1b) in
different azimuth and tilt angles –Horizontal, South (90°, 60° and 30°), East (60° and 30°), West (60°
and 30°)– installed 30 meters from the house were used for the calibration of the irradiance model.
Figure 1. a) The studied house, and b) Solar irradiance sensors.
2.1. Measured solar irradiance
One-year monitored data in one-minute timesteps obtained from the irradiance sensors shown in Fig. 1b,
were used for the analysis of the solar potential in different orientations and tilt-angles. Fig. 2 shows the
hourly average data of the measured irradiance profiles for summer and winter days. It can be seen that
the highest irradiance values in winter are obtained for the tilt-angle 60° South. However, in summer,
the tilt-angle with higher solar intensities is 30° South. Tilt-angles of 30° and 60° for East and West
orientations provide better performance in summer time with maximum values that are 40% higher
compared to the winter period. Regarding the horizontal (0°S) and vertical irradiance (90°S), profiles
obtained for summer and winter days, show that, the vertical surfaces receive high irradiance in winter
compared to summer, while the opposite is observed for the horizontal surfaces.
Figure 2. Measured solar irradiance at different tilt and azimuth angles in Summer and Winter days.
2.2. Measured PV power
The monitored PV outputs from the East and West roofs indicate that the West PV system is performing
better than the East one. Table 3 shows that the East-facing PV system generates up to 45% less energy
per month compared to the West-facing system. The difference between the East and West energy
generation is mainly due to the orientation of the house (22° to the East).

CISBAT 2019
Journal of Physics: Conference Series 1343 (2019) 012093
IOP Publishing
doi:10.1088/1742-6596/1343/1/012093
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The low East PV system energy generation affects the payback period of the system. Thus, the
present work is conducted to assess and find the maximum azimuth and tilt angles limits in order to get
a payback period lower than the lifetime of the project.
Table 1. Monitored PV outputs and on-plane solar irradiance (G).
East roof
West roof
Months
PV (kWh)
G (kWh/m2)
PV (kWh)
G (kWh/m2)
Sep-18
99.2
62
155.2
86.7
Oct-18
47.3
29.7
84.6
50
Nov-18
27.3
18.2
52
30.9
Dec-18
17.8
13.2
30.1
19
Jan-19
24.1
17.5
42.7
26.1
Feb-19
55.9
32.8
107.9
59.9
Mar-19
112.6
66.6
153.8
86.7
Apr-19
175.2
103.2
271.7
151.7
3. Methodology
The optimum angles at which a PV system should be mounted are often debated. In this context, an
irradiance model was utilized for the analysis of solar radiation on tilted surfaces using a typical
meteorological year (TMY) of a Global Horizontal Irradiance (GHI) for the city of Prague. One-year
data of solar irradiance obtained from the setup (see Fig. 1b) were also used for the analysis and for the
validation of the model. The effects of tilt and azimuth angles are presented on contour plots, which are
convenient for cost analysis and the determination of the annual insolation on building surfaces.
3.1. Irradiance model
The estimation of the total radiation incident on each surface requires knowledge of total and diffuse (or
beam) radiation on a horizontal surface as well as the sun's position. In general, the total tilted surface
radiation is calculated by estimating and adding beam, diffuse and reflected radiation components on
the tilted surface. The contribution of beam radiation on a tilted surface can be calculated by using a
geometric factor dependent on the horizontal tilt, surface azimuth, declination angle and latitude (Eq.1).
The contribution of reflected radiation on a tilted surface is calculated by assuming the ground acts as
an isotropic reflector (Eq.2). Finally, the diffuse radiation on a tilted surface is determined by using
Perez model [5]. This model accounts for circumsolar, horizon brightening, and isotropic diffuse
radiation by empirically derived “reduced brightness coefficients (F1 and F2)” given in Eq.3.
!"#$ % &'(#)
*+,-.&/01234/5 6 34/2/01534/ 78 9 8,7
(1)
!:#$ % !;
<
=>?@*A
B
C
D E:
(2)
!F#G+HG % !F
<
=I?@*A
B
C&
J 9 K=
.
6 K=?@*L
?@*LM6 KBNOPQ5
(3)
where, Ih,B is the horizontal beam radiation (Wh/m2), β is the inclination angle, IG is horizontal global
radiation (Wh/m2), α is the solar altitude (rad),
E
g is the ground reflectance, γ is solar azimuth, γn is the
azimuth angle of the normal of the surface (rad),
R
SNT1UN
R
NTVWNXYWNSW10XYNT1Z[WNT1UNT1Z[WN4\N0130UW13W.
3.2. PV model
The Sandia Array Performance Model (SAPM) was used for the estimation of the output power
generated by the PV array at the maximum power points (MPP) [6]. This model is empirical and is
described by the following equations:
]^%;
;_
(4)
!`% ab:
c
!`@
&
de]^6 d=]^
B
.<
JN 6N2'`b
&
f?9 f?
_
.Cg (5)

CISBAT 2019
Journal of Physics: Conference Series 1343 (2019) 012093
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doi:10.1088/1742-6596/1343/1/012093
4
h
`% a*:
i
h
`@ 6 dBa*j
&
f?
.
klm
&
]^
.
6 dna*
&
j&f?.klm&]^.
.
B6 5o`b]^
&
f?9 f?
_
.p (6)
j
&
f?
.
%Qq
&
f?6rstuJv
.
wx
(7)
where, Imo (A) and Vmo (V) are the PV module current and voltage of the MPP at standard test condition
(STC). C0 and C1 are empirically determined coefficients (dimensionless) which relate Imp to the
effective irradiance. αImp (°C-1) is the normalized temperature coefficient for Imp, C2 (dimensionless) and
C3 (V-1) are empirical coefficients which relate Vmp to the effective irradiance, δ(Tc) is the thermal voltage
per cell at temperature Tc, q is the elementary charge, 1.60218 10-19 (coulomb), k is the Boltzmann’s
constant, 1.38066 10-23 (J/K) and βVmp (V/°C) is the module temperature coefficient Vmp at STC.
The SAPM reposes on some coefficients (C0, C1, C2, C3, n, αImp and βVmp) in order to reproduce the
real behaviour of the PV module/array. The extraction of these coefficients is done from real measured
profiles of the PV module/array following the same procedure published previously in [7].
3.3. Integration of PV and economic analysis
Apart from energy yield, it is very important to investigate the economic profitability and provide
guidelines for the optimal integration of the PV system considering the tilt angle and orientations of the
pitched roof. In this context, the Net Present Value (NPV) – defined as the sum of present incoming
(benefits) and outgoing cash flows over the lifetime of the project – was calculated according to Eq.8.
ayh % 9d 6
z
{
&
G
.
&
=I+
.
|
}
G~=
(8)
where, C is the initial investment cost (€), F(t) is the annual generated income (€/year), N is the lifetime
of the PVs and i is the real rate of interest for the Czech Republic. The initial investment includes the
cost of the PV modules, electrical components and claddings. Considering the actual size of the
installation in each part of the roof (1.92 kWp), a typical value of 1200 €/kWp was assumed representing
the current PV costs in the Czech Republic [8]; 1%/initial cost was also considered for O&M.
The annual cash inflows are calculated considering the annual PV generation (100% of PV self-
consumption) and PV degradation rate (%/year) [9], as well as the energy price and the discount rate
valid for the particular moment in the Czech Republic [10]. Then, cash flow over the life-time of the PV
system (25 years-expected) is calculated and results are given for the NPV and payback time.
4. Results and discussion
4.1. Models validation
The Matlab® environment was used for the implementation of the irradiance and PV models previously
described. The validation of the models showing simulated data versus measured ones is given in Fig. 3.
The irradiance model was validated by a measured data obtained for a tilt angle of 30° facing the South.
Selected ten days’ data represent different weather conditions, and it can be observed that the model
performs very well in reproducing the real data. Regarding the validation of the PV model, monitored
data of one channel –one string composed of three PV modules– and same data length considering
different weather conditions were used. A good match between simulated and measured data can be
seen. Calculated Root Mean Square Error (RMSE) values, for both models are less than 5%.
The validated irradiance model was used for the estimation of the solar radiation on surfaces with
different tilt angles variating from 0° to 90°, considering 360° azimuth angle variations. In that way,
yearly irradiation values can be obtained for each set of tilt and azimuth angles. The obtained results for
the location of the studied house are given in Fig. 4 (Left) as a contour plot. The South, East, West are
represented by 0°, -90° and 90° respectively. The highest solar radiation of 1200 kWh/m2 is obtained
for the azimuth angles variating from -10° to 30° and for tilt angles between 25° and 45°.
The annual PV energy generation was also calculated based on the irradiance obtained for each set
of tilt and azimuth angles. The PV energy generation is calculated for the CdTe PV modules technology
in kWh per unit area. The obtained annual PV energy values shown in Fig. 4 (Right) represent the real
PV outputs including all power losses. The results show that the PV energy values are affected similarly

CISBAT 2019
Journal of Physics: Conference Series 1343 (2019) 012093
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doi:10.1088/1742-6596/1343/1/012093
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as the irradiance by tilt and azimuth angles. Moreover, the effect of temperature is also present, and
leads to a broader range of tilt and azimuth angles associated with the maximum PV generation (in the
range of 90 kWh/m2 per year).
Figure 3. Validation of the irradiance model, and PV model.
Figure 4. Contour plots of annual solar yield (Left side) and annual PV energy generation (Right side)
4.2. Optimal integration of PV
Results from the assessment were also plotted as contour maps indicating the limits of azimuth and tilt
angle for positive value of the NPV (Fig. 5). In accordance with the PV generation, maximum NPV was
obtained for 35° tilt and 10° azimuth angle, leading to 13.5 year payback time. Fig. 5 (Left) shows an
optimal position slightly shifted to the West. However it can be seen that NPV is relatively insensitive
to minor deviations (between -30° to +30°) of azimuth from the sub-optimal orientation. Regarding the
tilt angle, integration is suggested up to 10° regardless the orientation. When orientation is concerned,
maximum benefits can be achieved for tilt angles between 20° and 45°, limiting the payback time under
the 15 years.
Finally, the right side of Fig. 5 depicts all the possible values of tilt and azimuth angles which give a
payback period lower than 20 years. These values were obtained from the analysis of one side of the
roof (1.92 kWp). Thus, in order to get a payback period less than 20 years for a building with a symmetric
pitched roof, its orientation should be 10°, and the roofs inclination angle equal or lower than 30°.
5. Conclusions
The present work showed the effect of azimuth angle on the performance of PV systems integrated to
the pitched roof of an experimental house located near the capital of Czech Republic, Prague. The
analysis carried out for the determination of the optimum tilt and azimuth angles is based on a validated
irradiance and PV models. The accuracy of the calibrated model throughout real measured data showed
a RMSE values lower than 5%. The obtained results from the analysis of the variation of tilt and azimuth
angles revealed that, the optimum angles for maximizing the solar yields correspond to tilt = 35° and
azimuth = 10°. For the maximization of the yearly energy PV generation, it was found that there is a
specific range of tilt and azimuth angles which can give the same maximum values. Finally, based on

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the actual costs of the studied thin-film PV system, the maximum NPV value that can be obtained after
25 years of operation under optimum tilt and azimuth angles is of 1156 Euros.
Figure 5. NPV sensitivity to tilt and azimuth angles and relative limits for increased profitability.
Acknowledgements
This work has been supported by the Ministry of Education, Youth and Sports within National
Sustainability Program I (NPU I), project No. LO1605 -University Centre for Energy Efficient
Buildings- Sustainability Phase and by the Operational Program Research, Development and Education
of the European Structural and Investment Funds, project CZ.02.1.01/0.0/0.0/15_003/ 0000464 Centre
for Advanced Photovoltaics.
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