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Article Not peer-reviewed version
Optimization of Roof Photovoltaic
Design for Industrial Plants Based
on MIV-BP Neural Network
Yunfeng Huang , Qi Huang * , Weidong Wu , Peng Ye , Hao Li , Qixiang Yan
Posted Date: 7 November 2023
doi: 10.20944/preprints202311.0424.v1
Keywords: Photovoltaic Power Generation; Industrial Building; MIV-BP Neural Network; Design Optimization
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Article
Optimization of Roof Photovoltaic Design for
Industrial Plants Based on MIV-BP Neural Network
Huang Yunfeng 1, Huang Qi 1,*, Wu Weidong 2, Ye Peng 1, Li Hao 1 and Yan Qixiang 1
1 School of Civil Engineering and Architecture,Anhui University of Science and Technology; Huainan
233000
2 School of Architecture, Anhui Science and Technology University; Bengbu 232000
* Correspondence: mmyolow@gmail.com; Tel.: +86 18155493545
Abstract: The study aims to analyze the characteristic parameters of rooftop photovoltaic (PV)
power generation on industrial plant buildings in the Ningxia region of China, in order to evaluate
the impact of passive design characteristic parameters on the benefits of PV power generation and
determine the degree of impact of different passive design characteristic parameters. The
methodology involves analyzing the characteristics of existing industrial plant buildings in Ningxia,
China, and conducting a series of regional studies on the parameters of plant PV power generation
influencing factors. The simulation results revealed that five features, including roof form, PV panel
laying pattern, PV panel laying area, azimuth angle, and PV module material, have a significant
impact on PV power generation benefits of industrial plant buildings.The study further uses
MATLAB 2022b to build a backpropagation neural network model with 5 neurons in the implicit
layer to predict the PV power generation benefits. The model calculates the whole-life cycle power
generation benefits and the whole-life cycle reduction of carbon emissions as output data. Finally,
the Mean Impact Value (MIV) method is employed to select the feature parameter values one by
one within their range, and the passive design feature parameters that have the greatest influence
on the prediction results are identified as the PV panel laying method, the PV panel tilt angle, and
the PV material parameters, respectively.
Keywords: photovoltaic power generation; industrial building; MIV-BP neural network; design
optimization
1. Introduction
The construction industry, as one of the major energy-consuming industries in China, plays a
crucial role in achieving the dual carbon goals through its low-carbon development. To address this
issue, building photovoltaics, with their efficient carbon reduction effect, have become an important
green building measure for achieving building low-carbonization. The Ministry of Housing and
Urban-Rural Development and the National Development and Reform Commission issued the
Carbon Peaking Plan for the Urban and Rural Construction Field, which clearly outlines the carbon
reduction targets and paths for China's urban and rural construction, aiming to achieve a coverage
rate of 50% for new public institutional buildings and new factory building roofs with rooftop
photovoltaics by 2025, and to retrofit existing public building roofs with solar photovoltaic systems.
Compared to general civil buildings, industrial plants have a more diverse and rich range of
structural forms in the treatment of building space, with larger roof areas, single roof forms, favorable
lighting conditions, and better conditions for the installation of solar photovoltaic panels. Industrial
buildings have high self-energy consumption and production energy consumption, and also cause a
large amount of pollution to the environment. The installation of photovoltaic power generation
systems can help reduce the self-energy consumption and carbon emissions of industrial plants.
Moreira M.O[1] proposed a new method based on artificial neural networks (ANN) to forecast
solar power generation in the next week using an ANN ensemble. The Design of experiments (DOE)
method was applied to photovoltaic time series factors and ANN factors. She then conducted cluster
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© 2023 by the author(s). Distributed under a Creative Commons CC BY license.
2
analysis to select the best network. The versatility of the proposed method allows for changes in
experimental arrangements, prediction models, and the number of factors used in the required
prediction range, thereby enhancing the determinacy of the prediction. Mellit A[2] studied and
compared the application of different types of deep learning neural networks (DLNNs) in short-term
power output prediction for solar photovoltaic power generation. The results showed that the
DLNNs studied had good accuracy. Gong Diyang[3] utilized a multi-scale regional solar power
prediction method based on sequence encoding reconstruction to maintain a good multi-scale
regional solar power prediction effect under conditions of limited data and low data collection costs.
Compared to the naive prediction method, the accuracy of the proposed model was improved.
Othman M.M[4] proposed an artificial intelligence method using artificial neural networks (ANN) and
random forests (RF) for short-term photovoltaic (PV) output current prediction (STPCF) for the next
24 hours. The Levenberg-Marquardde optimization technique was used as the backpropagation
algorithm for the ANN, and bagging-based bootstrapping technique was used in the RF to improve
the prediction results.
2. Research and Analysis of Industrial Plants in Ningxia
The Ningxia Hui Autonomous Region, located in the middle and upper reaches of the Yellow
River in northwestern China, is situated between latitude 35°14′-39°23′and longitude 104°17′′-107°39′.
The region enjoys abundant solar radiation and solar energy resources. The average sunshine
duration can reach 2180 to 3080 hours, with a solar radiation rate of 60% to 70%. The rich solar
resources in Ningxia are due to its geographical location and climate conditions, which provide a
unique advantage for the development of solar energy industry in Ningxia.
2.1. Analysis of Total Annual Horizontal Surface Radiation in Yinchuan Area
In this paper, meteorological data from Yinchuan, the capital city of the Ningxia Hui Autonomous
Region, were selected and analyzed using PVsyst software to obtain the monthly horizontal irradiance
and annual horizontal total irradiance in the Yinchuan area, as shown in Table 1.
Table 1. Horizontal radiation in Yinchuan
Meteo for YinChuan-Synthetical generated data from monthly values
Interval
beginning
Jan
Fe
b
Mar
Apr
Ma
y
Jun
Jul
Au
g
Sep
Oct
No
v
De
c
Year
GlobHor
kWh/m2/
mth
82.
7
98.
4
136.
3
166.
8
199.
4
193.
4
191.
1
172.
3
140.
8
115.
7
84.
8
73.
3
1654.
8
The development of building-integrated photovoltaics (BIPV) in the Ningxia region is relatively
late, but in recent years, with the support of policies and the advancement of technology, BIPV has
achieved some achievements. Currently, some large-scale buildings in the Ningxia region have
adopted BIPV technology, such as the library of the new campus of Ningxia University and the
Ningxia Autonomous Region People's Hospital. In addition, the Ningxia region has also issued a
series of policies to encourage and support the development of BIPV, such as the "Ningxia Hui
Autonomous Region Solar Photovoltaic Power Generation Application Plan".
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Figure 1. Distribution of industries in Ningxia
By analyzing the industrial plant buildings in the Ningxia region in Figure 2, it can be seen that
the steel structure type accounts for 70% of the industrial plant structures in the Ningxia region,
making it the main structure form. In terms of roof form, 70% of the roof forms are double slope roofs
with a roof slope of about 15°. In terms of building width-to-height ratio, the buildings with a width-
to-height ratio of 3:1 account for 55.6%. Only 15% of the buildings have installed photovoltaic panels,
and 85% of the buildings have not installed solar photovoltaic power generation systems. Therefore,
based on the survey and analysis of industrial plant buildings in the Ningxia region, the basic
information of industrial plant buildings in four aspects is statistically summarized, and the
industrial plant buildings will be modeled from these four aspects in the next section. The dominant
forms are extended based on the data ratio in the survey results, and the photovoltaic power
generation amount and carbon emissions of different forms of industrial plant buildings are
compared. By using neural network optimization algorithms, new reference data and theoretical
basis are provided for the optimization design of industrial plant buildings.
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Figure 2. Characteristic analysis of industrial plant buildings in Ningxia
3. Analysis of Factors Affecting Photovoltaic Power Generation in Industrial Plants
3.1. Plant Aspect Ratio
The height-to-width ratio of a building is the ratio of its height to width, and serves as a
reinforcement index for building height. It is a macroscopic control of the structural stiffness, overall
stability, load-bearing capacity, and economic rationality of buildings. It reflects the selection
standards of buildings from a more stringent perspective[5]. Philip Mckeen[6]conducted research on
the energy consumption of different height-to-width ratios in diverse residential buildings in
Canadian cities and concluded that the height-to-width ratio is one of the most important factors
determining energy efficiency. Nelson Y.O.Tong[7]conducted research on the relationship between
building height-to-width ratio and pollutant gas emissions and found a correlation with building
heating.
In this study, the width-to-height ratio of the factory walls, B, is divided into four cases: B=3,
B=2, B=1, and B=0.5, as shown in Figure 3, with a flat roof.
Figure 3. Four different aspect ratios for flat roofs
Based on the variable of the width-to-height ratio of factory walls, B, divided into four cases:
B=3, B=2, B=1, and B=0.5, and a flat roof, window-to-wall ratio of 0.3, and other factors kept constant,
a modeling analysis was carried out. The simulated model building length was 50m, width L=15m,
and height was divided into three heights, H=5m, H=7.5m, and H=15m, according to different width-
15%
15%
70%
Steelwork
Reinforced Concrete Structure
Brick Hybrid Structure
Total Percentage:
100
Percentage of structural forms of industrial plants
15%
70%
15%
Flat Roof
Double-Pitched Roof
Single Pitch Roof
Total Percentage:
100
Percentage of industrial plant roof forms
55.6%
16.7%
22.2%
5.6%
0.5
1
2
3
Total Percentage:
90
Industrial plant building aspect ratio as a percentage
85%
15%
Laying of photovoltaic panels
No photovoltaic panels
Total Percentage:
100
Percentage of industrial plants with photovoltaic panels
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5
to-height ratios. From the analysis results, it can be seen that when the wall width-to-height ratio of
the building is B=3 (building width of 15 meters and height of 5 meters), the average indoor
temperature in the space environment is better than the other two width-to-height ratios, especially
when the external environment temperature is low, with better insulation effect. When the external
environment temperature is high, the indoor temperature control is lower, as shown in Figure 4.
Figure 4. Monthly analysis of ambient temperature of indoor space
3.2. Roof Forms
Industrial plant roof forms mainly include flat roofs, sloping roofs, domes, multi-span roofs, and
multi-gable roofs. Common industrial plant roof forms mainly include flat roofs, double slope roofs,
and domes, which are similar in terms of the installation of solar photovoltaic panels. The main
factors affecting their power generation efficiency are the roof slope (radius) and azimuth angle.
Therefore, based on the results of section 2.1 with a width-to-height ratio of B=3, studies were
conducted on flat roof and sloping roof industrial plants, and domed industrial plants were not
described in detail.
3.2.1. Sloping Roof
Double-pitched industrial plants with roof slopes of 10°, 20°, and 30°were selected as research
objects, as shown in Figure 5. The plant parameters are listed in Table 2.
Figure 5. Schematic diagram of industrial buildings with different slopes
Table 2. Parameters of sloped-roof industrial buildings
Elevation
Aspect
Ratios
Building
widths/m
Length of
building/m
Site Area
/m2
Roof Area
/m2
10°
3
15
50
750
761
20°
3
15
50
750
798
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
14
16
18
20
22
24
26
Zone Operative Temperature (℃)
Monthly Frequency
Width To Depth Ratio 1：0.5
Width To Depth Ratio 1：1
Width To Depth Ratio 1：2
Width To Depth Ratio 1：3
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30°
3
15
50
750
866
From Table 2, it can be seen that as the slope of the industrial plant roof increases, the usable
area of the roof increases, and so does the area for the installation of photovoltaic panels.
3.2.2. Flat Roof
Compared to sloped roofs, flat roofs have a single structural form. In this simulation analysis,
the industrial plant with a width-to-height ratio of B=3, as shown in Figure 6, was selected as the
research object according to the experimental results in section 2.1. The plant parameters are listed in
Table 3.
Figure 6. Schematic diagram of flat roof plant
Table 3. Parameters of sloped-roof industrial buildings
3.3. Photovoltaic Panel Laying Methods
The two key factors that determine the photovoltaic power generation efficiency are the area of
photovoltaic panel installation and the installation angle. The advantage of industrial plant roofs
compared to other types of buildings is that they have enough space to install photovoltaic panels.
For flat roof industrial plants, the installation forms of photovoltaic panels can be divided into flat
and inclined. For other roof types with slopes, considering the structural safety, flat installation is
usually adopted. Compared to the independent photovoltaic systems with tracking ability, the
installation angle of building photovoltaic panels is usually kept constant and cannot be maintained
in real time to achieve the maximum solar radiation[8]. he following analysis considers the different
options brought by the two installation modes, flat and inclined, for the same industrial plant roof.
3.3.1. Flat Roof Laying Methods
Based on the model in section 2.1, a flat roof industrial plant with a width-to-height ratio of B=3,
building width of 15m, height of 5m, and length of 50m was selected as the research object. Its roof
usable area is 750m2. When installed in a flat manner, the theoretical maximum area of photovoltaic
panels can reach 750m2. When installed with an inclined angle, the area of photovoltaic panels will
be affected by the spacing between photovoltaic arrays. The spacing between photovoltaic arrays D
is determined by the fixed photovoltaic array spacing calculation formula[9], as shown in equation (1).
(1)
In the calculation formula, the length L of the inclined surface of the photovoltaic panel is taken
as 1.956m; β is the inclined angle of the photovoltaic panel, which is the angle between the
Roof Slope
Aspect
Ratios
Building
widths/m
Length of
building/m
Site
Area
/m2
Roof
Area
/m2
0°
3
15
50
750
750
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photovoltaic panel and the horizontal plane. The best horizontal tilt angle in Yinchuan, Ningxia is
30°[10] ; W is the latitude, and the latitude of Yinchuan, Ningxia is 38°47′. According to the formula,
the spacing between photovoltaic arrays D is determined to be 4.4m, which can weaken the shading
effect between photovoltaic panels. In the inclined installation mode, the theoretical maximum area
of photovoltaic panels that can be installed on a 750m2 roof is 391.2m2.
Table 4 shows a comparison of the power generation benefits of flat roof industrial plant
photovoltaic panels in flat and inclined installation modes. It can be seen from the table that the
installation area of photovoltaic panels is increased by the flat installation mode compared to the
inclined installation, with the annual power generation total increasing from 123109 kW·h to 201186
kW·h, while the average annual power generation of photovoltaic panels only decreases by 46.45
kW·h/m2.
Table 4. Comparison of power generation benefits of flat-roofed and tilted photovoltaic panels for
flat-roofed plants.
Installation
Forms
Photovoltaic system
parameters
Total area of
photovoltaic
panels
/m2
Total annual
power
generation
/（kW·h）
Average annual
power
generation per
unit area
/（kW·h/m2）
Photovoltaic
conversion
efficiency
Integrated
system
efficiency
Tilting
Type
0.17
0.893
391.2
123109
314.70
Pavement
0.17
0.881
750
201186
268.25
3.3.2. Sloped Roof Laying Methods
Compared to flat roof industrial plants, sloped roofs are simpler in terms of photovoltaic panel
installation, and usually use a flat installation method. The power generation benefits of photovoltaic
panels on sloped roofs depend on the influence of roof slope and installation area. As the slope
increases, the roof area for installing photovoltaic panels also increases, as does the annual total
power generation, but as the slope increases, the amount of solar radiation received by the north
slope gradually decreases, and the average annual power generation per unit area shows a
downward trend, as shown in Table 5.
Table 5. Comparison of power generation benefits of flat photovoltaic panels for sloping roof plants.
3.4. Azimuth
To allow photovoltaic components to receive more solar radiation, it is necessary to set
appropriate tilt angle and azimuth angle. The influence of azimuth angle on power generation
characteristics is derived from the changes in the direction of direct radiation in a day[11]. Building
photovoltaics usually adopt fixed photovoltaic forms, so it is necessary to consider the best
orientation in a fixed state to maximize the total power generation of photovoltaics over the entire
Elevation
Installation
Forms
Site Area
/m2
Roof
Area
/m2
Total annual
power generation
/（kW·h）
Average annual
power generation per
unit area
/（kW·h/m2）
10°
Pavement
750
761
161923
212.78
20°
Pavement
750
798
164376
205.98
30°
Pavement
750
866
171429
197.95
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year cycle. Wei Zidong[12] simulated the rules of solar altitude and azimuth angles in the entire year
cycle in Yinchuan, Ningxia, and analyzed the annual power generation of photovoltaic panels with
different tilt angles and orientations in Yinchuan. The results showed that the most advantageous
orientation for photovoltaic power generation in Yinchuan is facing the south, that is, when the
azimuth angle is 0°, the annual power generation is the largest among all orientations. Considering
the changes in azimuth angle due to site restrictions or factory arrangements in practical projects, the
relationship between the orientation of photovoltaic panels and the roof area for installing
photovoltaic panels will be explored. The following will compare and analyze the relationship
between the orientation of photovoltaic panels, the roof area for installing photovoltaic panels, and
the annual power generation amount from azimuth angles of 0°, 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°,
135°, 150°, 165°, and 180°, and calculate the photovoltaic power generation amount using Pvsyst
software.
3.4.1. Flat Roof Azimuth
For flat roof industrial plants, when using a flat installation method, the total solar radiation
received by photovoltaic panels will not change due to differences in azimuth angle, and the annual
total power generation of photovoltaic panels will not change either. However, for inclined
installation, the best orientation of solar photovoltaic panels will change with changes in azimuth
angle, and the power generation will also change. The inclined installation of solar photovoltaic
panels is shown in Figure 7.
Figure 7. Schematic diagram of PV panel tilting mounting
1. If the orientation angle of the factory building is changed, the orientation angle of the solar
photovoltaic panels in the factory building remains the same. In this case, the area of the
photovoltaic panels does not change, but the amount of solar radiation received by the
photovoltaic panels will change due to the change in the orientation angle, and so will the power
generation benefits. As shown in Figure 8.
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Figure 8. Schematic diagram of laying of PV panels for flat roof plant with change of azimuth angle
2. If the orientation angle of the factory building is changed, the orientation of the solar
photovoltaic panels is kept at the optimal orientation angle. In this case, the roof area for
installing photovoltaic panels will change accordingly, and so will the power generation benefits.
As shown in Figure 9.
Figure 9. Schematic layout of PV panels for flat roof plant with constant azimuth angle
After calculation, the inclined installation of solar photovoltaic panels on the flat roof industrial
plant has the largest installation area of photovoltaic panels, which is 391.2m2 when the azimuth angle
is 0°. When the orientation angle of the factory building changes and the orientation angle of the
photovoltaic panels is not changed, the installation area of the photovoltaic panels also changes, but
it is always less than the installation area when the azimuth angle is 0°. When the orientation angle
of the factory building and the photovoltaic panels changes together, the maximum installation area
of rooftop photovoltaic panels can be referred to the layout in Figure 8. The specific parameter
statistics are shown in Table 6.
Table 6. Schematic representation of the area of PV panels that can be installed at different azimuths
in industrial buildings with flat roofs
Azimuth
Mounting
Inclination
Installatio
n form
RoofAre
a
Maximum installation
area
Optimally
orientated
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3.4.2. Sloped Roof Azimuth
Sloped roofs generally adopt a flat installation method for solar photovoltaic panels due to their
roof construction, and the power generation of photovoltaic panels is affected by the roof slope and
azimuth angle. As shown in section 2.3.2, the power generation of photovoltaic panels increases with
the increase of slope, and the power generation is the largest when the slope reaches the optimal
slope angle in the region. The roof area for installing photovoltaic panels on sloped roofs is different
from that on flat roofs, and is generally installed using a flat installation method. The installation area
of photovoltaic panels usually does not change with different azimuth angles. Figure 10 shows the
layout diagrams of sloped roofs with different azimuth angles.
/㎡
/㎡
installation area/㎡
0°
30°
Tilting
Type
750
391.2
391.2
15°
30°
Tilting
Type
750
391.2
230
30°
30°
Tilting
Type
750
391.2
235
45°
30°
Tilting
Type
750
391.2
237
60°
30°
Tilting
Type
750
391.2
239
75°
30°
Tilting
Type
750
391.2
244
90°
30°
Tilting
Type
750
391.2
293
105°
30°
Tilting
Type
750
391.2
244
120°
30°
Tilting
Type
750
391.2
239
135°
30°
Tilting
Type
750
391.2
237
150°
30°
Tilting
Type
750
391.2
235
165°
30°
Tilting
Type
750
391.2
230
180°
30°
Tilting
Type
750
391.2
391.2
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Figure 10. Schematic diagram of different azimuths of a sloped-roof factory building
3.5. PV Module Material Parameters
The parameters of photovoltaic module materials are one of the factors affecting the efficiency
of photovoltaic power generation, and many scholars have conducted a large amount of research and
verification on the performance of different types of photovoltaic materials. Nazek EI-Atab[13]used
laser ripple technology to develop single-crystalline silicon solar cells with world-record
stretchability (95%) and efficiency (19%). Chen Wenhao[14]achieved three different activation
phosphorus concentrations of polycrystalline silicon by adjusting the PH3 flow rate, SiOx thickness,
and activation temperature, thus improving the efficiency of polycrystalline silicon solar cells. Zheng
Guang-Fu[15]explored a novel semiconductor photovoltaic (PV) active material Culn 1-x Ga x Se 2
(CIGS) and thin film electrodeposit (ED) technology, which obtained high-quality CIGS
polycrystalline thin films, reduced costs, and improved efficiency.
Currently, the most commonly used photovoltaics are single-crystalline silicon, polycrystalline
silicon, and thin film photovoltaics. Scholars generally believe that single-crystalline silicon
photovoltaics have high conversion efficiency and stability, but are relatively expensive;
polycrystalline silicon photovoltaics have slightly lower conversion efficiency than single-crystalline
silicon photovoltaics, but are superior in terms of low cost and short payback period for
transformation costs; thin film photovoltaics have lower photoelectric conversion rates than
crystalline silicon photovoltaics under sufficient light conditions, and are more expensive than
crystalline silicon photovoltaics, but have good weak-light effects and better decorative effects. The
following are several common photovoltaic module parameter tables, as shown in Table 7.
Table 7. Parameters of 6 types of PV modules
PV Module
Module
Area/m2
Rated Power/W
Efficiency/%
A-Si
1.12
64
6.3
CdTe
0.72
50
6.9
CIS
1.73
60
8.2
P-Si
0.64
75
11.6
M-Si
1.26
170
13.5
HIT
1.18
180
17.3
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4. Analysis of Photovoltaic Power Generation Based on PVsyst Software
4.1. Flat Roof Power Generation Analysis
This paper takes M-Si (polycrystalline silicon) as the research object and discusses the annual
power generation of industrial plants on flat roofs under different azimuth angles and different
photovoltaic panel installation areas based on the statistical data in Table 5, as shown in Figure 11.
Figure 11. Comparison of annual electricity generation of flat roof plants with different azimuths and
PV panel laying areas
From Figure 11, it can be concluded that for the flat roof industrial plant, the annual power
generation amount of the photovoltaic panels installed in an inclined manner with a constant
installation area and a changing orientation angle, decreases first and then increases with the increase
of the orientation angle. When the orientation angle is 90°, the power generation amount reaches the
minimum value, and the maximum value is reached when the orientation angle is 0° or 180°. When
the orientation angle of the photovoltaic panels is kept unchanged and always at 0°, and the
orientation angle of the building is changed, the roof area for installing photovoltaic panels also
changes. When the orientation angle is 0° to 15°, the power generation amount decreases; when the
orientation angle is 15° to 90°, the power generation amount increases; when the orientation angle is
90° to 165°, the power generation amount decreases; and when the orientation angle is 165° to 180°,
the power generation amount increases. The reason for the large change in power generation amount
when the orientation angle is between 0° and 15° and 165° and 180° is that the roof area for installing
photovoltaic panels decreases when the orientation angle is 15° and 165°, and the roof space
utilization is at its lowest value.
4.2. Analysis of Power Generation on Sloping Roofs
This paper takes M-Si (polycrystalline silicon) as the research object and discusses the annual
power generation of industrial plants on sloped roofs under different azimuth angles and different
photovoltaic panel installation areas based on the statistical data in Table 4, as shown in Figure 12.
0° 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180°
70000
80000
90000
100000
110000
120000
130000
Annual total power generation (KWh/year)
Azimuth
Maximum installation of roof photovoltaic panel area
Optimal orientation installation of photovoltaic panels
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Figure 12. Comparison of annual electricity generation of sloped-roof plants with different roof slopes
and different azimuths
From Figure 10, it can be concluded that for sloped roof industrial plants, the annual power
generation amount increases with the increase of azimuth angle within the range of 0°~90°, and the
growth ratio is positively correlated with the slope of the roof. The larger the slope of the roof, the
larger the azimuth angle, and the more power generation amount of the photovoltaic panels. When
the azimuth angle reaches 90°, the power generation amount tends to reach the maximum value.
When the azimuth angle is within the range of 90°~180°, the annual power generation amount
decreases with the increase of azimuth angle, and the reduction ratio is positively correlated with the
slope of the roof. The magnitude of the increase in power generation amount is also related to the
slope of the roof. When the slope approaches the optimal solar photovoltaic tilt angle in the local area,
the power generation amount is more.
5. Design Optimization Based on MIV-BP Neural Network
5.1. Description of the BP Neural Network Model
BP neural network, as a kind of artificial neural network, is a multi-layer neural network with
three or more layers. It has self-learning, arbitrary function approximation and fast seeking of optimal
solutions. In selecting feature parameters of neural networks, the Mean Impact Value (MIV) method
can reflect the impact of input feature parameters on the prediction results, which can be used to
enhance the stability of the output results and improve the accuracy of the model in BP neural
networks. In this study, a BP neural network model with one input layer, one hidden layer and one
output layer was developed. The initial weights were randomly set, and then modified according to
the difference between the calculation values during the training process and the actual simulation
results. The BP neural network model developed in this study selects the building roof form,
photovoltaic panel layout, photovoltaic panel tilt angle, azimuth angle and photovoltaic module
material parameters as input parameters, and the life cycle photovoltaic power generation benefits
and carbon emission reduction values as output parameters. In addition, the activation function of
the hidden layer is the Tansig function, as shown in equation 2.
(2)
Select the linear activation function, Purelin function, as the activation function for the output
layer to transmit from the hidden layer to the output layer:
(3)
0° 15° 30° 45° 60° 75° 90° 105° 120° 135° 150° 165° 180°
162000
164000
166000
168000
170000
172000
174000
176000
178000
Annual total power generation (KWh/year)
Azimuth
Photovoltaic panel inclination angle 10°
Photovoltaic panel inclination angle 20°
Photovoltaic panel inclination angle 30°
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The BP neural network model with 5 neurons in the input layer and 2 neurons in the output
layer is shown in Figure 13.
Figure 13. BP neural network model framework
5.2. Data Preparation and Number of Hidden Neurons
In this study, the 360 samples generated in the previous simulation were randomly divided into
two groups, used for training (80%) and testing (20%) of the BP neural network model. To improve
the training and prediction efficiency, all data should be normalized to the range of 0 and 1. The
calculation formula is as shown in equation 4.
(4)
Where yi is the normalized data [-], xi is the original data [kwh], xmin is the minimum value of the
original data [kwh], and xmax is the maximum value of the original data [kwh]. After preprocessing
all the data used, one of the most important steps is to determine the number of neurons in the hidden
layer, which can be calculated using equation 5.
(4)
Where M is the number of neurons in the hidden layer, n is the number of neurons in the input
layer, f is the number of neurons in the output layer, and e is a constant in the range of 1 to 10.
According to equation (5), the number of neurons in the hidden layer is between 3 and 13. To
determine the optimal number of neurons in the hidden layer, a BP neural network model was
established using MATLAB 2022b, and the training was carried out by changing the number of
neurons in the hidden layer. The change trend of the mean squared error (MSE) with different hidden
layer neurons is shown in Figure 14. The change trend of the correlation with different hidden layer
neurons is shown in Figure 15.
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Figure 14. Trends in forecast errors
Figure 15. Trends in correlation
The lower the error (MSE) value, the more accurate the data results; the higher the change value
of the correlation, the closer the number of neurons in the hidden layer is to the real data. As can be
seen from Figures 14 and 15, when the number of neurons in the hidden layer is 5, the error (MSE)
value is the lowest and the correlation is the highest. Therefore, it can be determined that the model
with 5 neurons in the hidden layer has an ideal validation effect.
The R value is usually used to measure the correlation between the output and the target. An R
value close to 1 indicates a close relationship between the predicted results and the output data,
indicating a high degree of accuracy in the predictions. Figure 16 shows the regression effect of the
true values and predicted values of the testing dataset with 5 hidden layer neurons (BP) and the
regression effect of the true values and predicted values of the testing dataset with feature selection
(MIV-BP). The R values obtained were 0.9936 and 0.99455 when the number of hidden neurons was
5. Compared with the original algorithm, the error precision was improved by 0.095%, further
indicating that the MIV-BP neural network in this study has a good predictive effect. Therefore, the
number of neurons in the hidden layer is defined as 5.
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Figure 16. Regression analysis of the model.
As can be seen from Figure 17, the error distribution of the true values and predicted values of
the testing dataset with 5 hidden layer neurons (BP) is mostly concentrated in the interval of -3.1e+04
to 1.2e+05; the sample error of the true values and predicted values of the testing dataset with feature
selection (MIV-BP) is mostly concentrated in the interval of -3.4e+04 to 6.9e+04.
Figure 17. Histogram of error for 20 intervals
To determine the impact of the features used in this study on the life cycle photovoltaic power
generation benefits and carbon emission reduction values, the MIV method was used to screen the 5
features. Two completely new datasets were obtained by increasing and decreasing each feature by
10%, respectively, and then inputted into the model for prediction. This process was repeated to
obtain the impact of the 5 features on the life cycle photovoltaic power generation benefits and carbon
emission reduction values, as shown in Figure 18.
Figure 18. Graph analyzing the degree of influence of features on the results
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In the figure, the darker the color, the higher the impact degree. As shown in the figure, the main
factors affecting photovoltaic power generation benefits and carbon emission reduction are the solar
panel tilt angle, solar panel material parameters, and installation method. Among them, the
installation method has the highest proportion, reaching 30.84% and 30.97%; in this study, the impact
of azimuth angle on photovoltaic power generation benefits and carbon emission reduction is the
smallest.
5.3. Forecasting Results and Optimization Analysis
This study established a MIV-BP neural network model with a hidden layer containing 5
neurons. Normalized data was input into the model for training, with 80% of the data used as
learning samples and 20% of the data used to validate the trained model. Then, the validated model
was used to predict the remaining samples' photovoltaic power generation benefits and carbon
emission reduction values. The predicted results were denormalized using equation 5.
(5)
Seventy-two data sets were imported into the BP neural network model for validation and the
life cycle photovoltaic power generation benefits data were obtained. They were fitted with real data,
as shown in Figure 19.
Figure 19. Comparison of Life Cycle Generation Benefit Projections
As shown in Figure 19, the results simulated by the trained model have a high degree of fit with
the real values, with an average error of 4.12% for the 72 pieces of data. This proves that the model
has a good predictive effect.
After optimizing the data through MIV by removing feature parameters, the optimized data was
imported into the model for verification, and the results are shown in Figure 20.
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Figure 20. Comparison of MIV-BP whole life cycle power generation benefit prediction results
As shown in Figure 20, the results simulated by the optimized data imported into the model
after MIV feature elimination have a higher degree of fit with the real values, with an average error
of 3.45%. This proves that the optimization effect of MIV is significant, improving the accuracy of the
model.
6. Conclusions
The purpose of this study was to assess the impact of passive design feature parameters on the
photovoltaic power generation benefits of industrial buildings, and then optimize the values of
passive design feature parameters using the MIV-BP neural network model. The study simulated the
power generation and carbon emission reduction values of different passive feature parameters over
the entire life cycle of research buildings. The results showed that passive design feature parameters,
including roof form, photovoltaic panel layout, photovoltaic panel tilt angle, azimuth angle, and
photovoltaic module material parameters, had a significant impact on power generation benefits and
carbon emission reduction.
In this study, a MIV-BP neural network model with one input layer, one hidden layer, and one
output layer was developed. The five design parameters were used as input parameters, and the
photovoltaic power generation benefits and carbon emission reduction values calculated from the
photovoltaic panels' annual generation were used as output parameters. The number of hidden layer
neurons was determined to be 5. The predictive effect of the BP neural network was measured using
the MSE of 18829813560.8108 and the R value of 0.9936 for all data. The predicted results for power
generation benefits and carbon emission reduction were then compared with the calculated values,
with small differences further indicating the accuracy of the BP neural network model. In addition,
by selecting passive feature parameter values within their range using MIV, the impact of passive
parameters on the results was obtained. The comparative analysis of the prediction results indicated
that the best passive feature parameters were the photovoltaic panel layout, photovoltaic panel tilt
angle, and photovoltaic material parameters.
Author Contributions: “Conceptualization, Wu.Weidong. and Huang.Yunfeng.; methodology, Wu.Weidong.;
software, Huang.Qi.; validation, Huang.Qi., Ye.Peng. and Yan.Qixiang.; formal analysis, Li.Hao.; investigation,
Huang.Qi.; resources, Huang.Qi.; data curation, Ye.Peng.; writing—original draft preparation, Huang.Qi.;
writing—review and editing, Wu.Weidong.; visualization, Wu.Weidong.; supervision, Huang.Yunfeng.; project
administration, Huang.Yunfeng.; funding acquisition, Huang.Qi. All authors have read and agreed to the
published version of the manuscript.”.
Funding: “This research was funded by Research Fund of Anhui Provincial Department of Education, grant
number 2022AH040233” .
Conflicts of Interest: “The funders had no role in the design of the study; in the collection, analyses, or
interpretation of data; in the writing of the manuscript; or in the decision to publish the results”.
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