An Estimation of the Available Spatial Intensity of Solar Energy in Urban Blocks in Wuhan, China

Abstract

Urban form is an important factor affecting urban energy. However, the design of urban form and energy mostly belong to two separate disciplines and fields, and urban energy planning research rarely considers their mutual relationship. The available space intensity (ASI) of solar energy is formed on the basis of energy planning and urban design; the objective of this research is to evaluate the impact of urban form on the ASI of solar energy and to propose strategies for planning of the space that is available for solar energy so as to improve the efficiency of urban energy utilization and achieve sustainable urban development. Methodologically, this study firstly proposes a model to quantify the ASI of solar energy using three indicators: solar radiation intensity (SRI), solar installation intensity (SII), and solar generation intensity (SEGI). Then, we quantitatively calculate the solar ASI of nine types of typical urban blocks in a sub-center of Wuhan City, Nanhu. Correlation analysis and multiple linear regression analysis are then used to analyze the correlation between the form indicators and solar ASI, as well as the degree of influence. The results show that the differences in SRI, SII, and SEGI amongst the nine types of city blocks were as high as 114.61%, 162.50%, and 61.01%. The solar ASI was mainly affected by three form indicators: the building coverage ratio, the average building height, and the volume-to-area ratio. Reducing the building coverage ratio and increasing vertical development at the same time can effectively improve the ASI of solar energy. The results of this study and the established method provide an important reference and rapid calculation tool for urban energy planning and design, reducing the data and time usually required for solar analysis at the block scale.

1. Introduction

1.1. Background

Currently, more than 50% of the world’s population lives in cities, which consume 76% of the world’s coal, 63% of its oil, and 82% of its natural gas [1]. How to adjust the urban built environment and reduce carbon emissions is an issue faced by governments around the world [2]. The development and utilization of renewable energy is the inevitable approach to achieve net zero emissions [3]. Under the promotion of the Chinese government, solar energy has shown a trend of rapid development, and the installed capacity of solar energy reached about 43 GW in 2022, taking the top position globally [4]. Of this capacity, building-based distributed photovoltaics account for more than 50% [5], which include building-attached photovoltaics (BAPV) and building-integrated photovoltaics (BIPV). Compared with other forms of power generation, these systems have a flexible layout, strong local consumption, and high land use efficiency, and it is expected they will meet 25–49% of the global electricity demand by 2050 [6]. From 2013 to 2022, the total annual reduction in carbon emissions due to BIPV and BAPV will increase from about 0.10 Mt/a to 12.18 Mt/a in China, and the total cumulative carbon emissions reduction will reach 46.18 Mt [7]. Building-based distributed photovoltaics will become a primary pathway to achieve carbon neutrality in cities in the future [8].

Available solar space refers to the construction space on a building’s surface that meets the conditions for solar energy facilities to obtain power generation, including the roof and façade [9]. Cities are multi-level and multi-functional cooperative systems [10]; factors such as the local climate [11], building function [12], and urban form [13] limit the application rate of solar energy utilization on building surfaces, also known as the available space intensity (ASI) of solar energy [14]. However, energy and urban design belong to two separate fields, and the management of both regarding the use of building photovoltaics is mostly developed independently, without considering their interdependent relationship [15]. Therefore, the development of solar energy in urban buildings suffers from fragmented development and inefficient utilization [16].

In addition, the Chinese government is actively promoting the “14th Five-Year Plan for Modernized Energy System”, which clearly points out the need to optimize the layout of solar energy development and the promote its large-scale development [17]. Therefore, in light of this policy, it is necessary to comprehensively consider the impact of urban form on the solar ASI and to propose a planning strategy for the available solar energy space to promote the effective combination of energy and urban design, thus achieving sustainable urban development.

1.2. Literature Review

1.2.1. Urban Block Form and ASI of Solar Energy

The use of solar energy in the urban environment mainly depends on the surrounding built environment and the overall urban form on a larger scale [18]. At present, the research on urban form and the solar ASI is mainly reflected on three scales: the city scale [19,20], the block scale [21,22], and the individual building scale [23,24]. An urban block is an urban unit space enclosed by an urban road, which is the “cell unit” of the overall spatial structure of the city [25]. The utilization of solar energy on the block scale constitutes not only the synthesis and improvement of the solar energy utilization of individual buildings, but also the concrete implementation of a solar energy urban planning strategy. Therefore, many scholars aim to improve the solar ASI of urban blocks by adjusting building layouts, building heights, and other indicators on the block scale.

K Jerome Henri Kampf et al. [26] created a PV optimization design for three forms of building layout in Switzerland: panel, strip, and courtyard. Through a comparison of the results, it was found that the layout of the courtyard could obtain more solar radiation while maintaining a similar building volume. Michele Morganti et al. [27] selected 14 blocks in the Mediterranean region and counted seven form indicators, including density, plot ratio, and average height of the samples. The indicators with the most significant influence were found to be the density, the ratio of land elevation, and the sky view factor. Although these studies analyze the influence of urban form on the ASI of solar energy from different perspectives, most of the research objects are based on typical building layout forms with little or no changes, or only consider a certain type of building [28,29], such as residential buildings [30] and office buildings [31], often without considering the functional diversity and spatial form regularity of urban blocks.

With the increasing level of urbanization, Chinese cities are characterized by large populations and high densities. In order to improve the land utilization rate, strict urban planning laws and regulations have led to the formation of urban blocks with clear functions in China; that is, urban blocks are divided according to their function and the type of land [32]. In addition, in order to meet the demand for sunshine and ensure fire safety in high-density building environments, indicators such as the floor area ratio and building coverage ratio of each block need to be within a specified range, and form indicators have a certain regularity, which is a rare phenomenon in the construction process of European and American cities.

In China, research on the ASI of solar energy in urban blocks has been limited, mainly focusing on the buildings’ access to sunlight. Ming lu et al. [33] studied the lighting and sunshine utilization of high-density residential blocks in northeast China and found that the “point” layout of square buildings had the best effect, while the “linear” layout of rectangular buildings had the worst effect. Gong F Y et al. [34] found that street orientation had a significant effect on solar radiation in street canyons in a high-density urban area of Hong Kong. Compared with the north–south street canyons, the east–west street canyons receive higher solar radiation in summer and lower solar radiation in winter. Shen Xu et al. [35] studied the PV utilization potential of seven types of industrial blocks, and the results showed that single-storey industrial blocks had the highest solar energy utilization potential, while high-rise buildings had the lowest solar energy utilization potential. However, existing studies focus on typical urban layouts, and it is difficult to comprehensively describe the urban forms. Therefore, it is necessary to study the ASI of solar energy in different functional blocks in China.

1.2.2. Quantification Method of ASI of Solar Energy

In order to more accurately and quickly quantify the ASI of solar energy in urban buildings, the research methods and tools used tend to include remote sensing, three-dimensional city models, and geographic information systems (GISs). Karteris et al. [36] used a GIS and a Digital Surface Model to extract samples from the facade features of multi-storey buildings in Greece, evaluating the available area for solar energy of different types of facades. Amado M et al. [37] combined Rhinoceros Grasshopper ^TM and Ecotect workflow to quantify solar energy utilization intensity in urban environments based on a parametric method. With the progress of computer technology, machine learning algorithms have been widely used and developed. Assouline et al. [38] combined a support vector machine and a GIS to evaluate the photovoltaic power generation potential of Swiss building roofs. On this basis, the random forest algorithm was used to evaluate and draw maps with higher spatial resolutions [39]. However, due to the lack of high-precision LiDAR data and the high computational cost in most areas of China, the application of this method is limited.

When spatial data are lacking or a large-scale evaluation is carried out, many scholars classify buildings according to their characteristics and functions, and calculate the availability coefficient of different representative buildings through stratified sampling [40]. There are some defects in the accuracy of this method, and the construction forms, policies and background climate in different study areas are quite different, so the value of the availability coefficient is different in different regions [41]. However, because this method can quickly assess the spatial intensity of PV utilization in cities, it still has positive significance for a large range of applications. In order to reduce the calculation cost and ensure high calculation accuracy, some studies combine multi-source data to optimize the quantization process, such as using digital terrain models with different resolutions to evaluate buildings separately, screening available roofs before calculating solar radiation [42]. In addition, the application programming interfaces (APIs) publicly provided by OpenStreetMap (OSM) are used as tools to obtain urban spatial data, and building contours and other information are automatically extracted. One can also build a three-dimensional digital model to further reduce technology costs [43,44].

1.3. Research Objectives and Structure

According to the above literature review, the relationship between urban form and the ASI of solar energy has been extensively studied, but most of the urban block prototypes used are based on developed countries in Europe and the United States, or only consider certain types of buildings, which have a limited reference significance for the large-scale utilization of solar energy in urban blocks in China. The objective of this research is to evaluate the impact of urban form on the ASI of solar energy, and propose strategies for planning the available space for solar energy to promote solar photovoltaic utilization and realize urban energy transformation. This research further develops knowledge surrounding the following research questions:

(1)

Does the form of urban blocks have an impact on the ASI? Which urban form indicators have the most significant impact?

(2)

How do we orderly develop and plan the available space for solar energy to ensure the rational utilization of solar energy resources and urban space?

On the basis of the above questions, we hypothesized that urban form would affect the solar ASI. In order to prove this hypothesis, this study proposed a model to calculate the solar ASI. Firstly, the solar ASI of nine types of urban blocks in Nanhu, the sub-center of Wuhan City, was calculated. Secondly, the correlation analysis and multiple linear regression methods were used to analyze the correlation between each form indicator and the solar ASI, as well as the influence degree, and finally, a development strategy for solar energy available space was proposed.

This paper is organized as follows: The methods for formulating the vernacular block typologies and assessing their solar ASI with three indicators are shown in Section 2. A case study of the sub-center of Wuhan City, Nanhu, is used as an example to demonstrate the methods. Section 3 presents the results and some preliminary analyses. On this basis, Section 4 extends discussions on the interactions between the form indicators and the solar ASI, presenting strategies for planning the available space for solar energy as well as the limitations of the results. Finally, we summarize our contributions and conclude the research in Section 5.

2. Methods and Materials

2.1. Framework for Evaluating the ASI of Solar Energy in Urban Blocks

The key research methods and ideas are as follows (as shown in Figure 1): This study firstly summarizes the spatial characteristics of the sub-center of the city of Wuhan, Nanhu, dividing it into nine typical urban blocks. Then, the spatial analysis and operation function of ArcGIS 10.2 was used to quantify the six types of form indicators selected. Thirdly, a solar ASI calculation model was established, and the 3D modeling software Rhinoceros 7 and parametric plug-ins Ladybug and Honeybee were used to quantify the SRI, SII, and SEGI of the blocks. Moreover, the bivariate model and multiple linear regression of the statistical analysis software SPSS Statistics 7.0 were used to analyze the correlation between form indicators and the SAI of solar energy, and the key indicators affecting the solar ASI were obtained. Finally, this study proposed a strategy for planning the available space for solar energy based on the different spatial types and different spatial locations.

2.2. Study Site

Nanhu, a sub-center of the city of Wuhan, is located in central China, between 113°41′ and 115°05′ E longitude and 29°58′ and 31°22′ N latitude, with a land area of 28.61 km² and a per capita living area of 32.50 m². It has a north subtropical monsoon climate. The total annual sunshine hours range from 1810 h to 2100 h, and the total annual radiation ranges from 104 kcal/cm² to 113 kcal/cm², which is within China’s solar energy resource availability area [45]. In the process of urban development, Nanhu has formed a multi-loop spatial structure, and there is a certain degree of variability in the block form of different areas, which provides this study with samples of urban blocks with varied and distinctly different form characteristics. Therefore, Nanhu can be used as a typical city to study the influence of urban block form on the ASI of solar energy.

2.3. Type of Investigation

In order to include all urban blocks in the study area, this study determined the functional types of blocks according to China’s “Urban Land Use Classification and Planning and Construction Land Standard (GB501372016)” [46]. This study focused on four types of functional blocks: residential blocks, public service blocks, commercial blocks and industrial blocks. It should be noted that since this study aims to explore the differences in solar ASIs among building groups, small changes in individual building functions were ignored, and the building functions within the block were consistent with the planned site.

Then, according to the change in the average building height (ABH), the residential blocks were divided into three types: ABH $\le$ 18 m signifies low-rise residential blocks (LRBs); 18 m $<$ ABH $\le$ 54 m signifies multi-storey residential blocks (MRBs); and ABH $\le$ 54 m is classified as high-rise residential blocks (HRBs). The commercial blocks, public service blocks, and industrial blocks were divided into two types: ABH ≤ 24 m signifies low-rise industrial blocks (LIBs), multi-storey commercial blocks (MCBs), and multi-storey public service blocks (MPSBs); ABH $>$ 24 m signifies multi-storey industrial blocks (MIBs), high-rise public service blocks (HPSBs), and high-rise commercial blocks (HCBs). The distribution of urban blocks is shown in Figure 2. The nomenclature of the categories is detailed in Appendix A.

Finally, a combination of systematic sampling and stratified sampling was used to select 54 typical city block samples from the total sample of city blocks, as well as to ensure that the urban form indicators used in this study have obvious differences between samples. The sample of 54 typical urban blocks is shown in

Table 1. Spatial model of 54 blocks.

Type	Block Model
LRBs
	A1	A2	A3	A4	A5	A6
MRBs
	B1	B2	B3	B4	B5	B6
HRBs
	C1	C2	C3	C4	C5	C6
MCBs
	D1	D2	D3	D4	D5	D6
HCBs
	E1	E2	E3	E4	E5	E6
MPSBs
	F1	F2	F3	F4	F5	F6
HPSBs
	G1	G2	G3	G4	G5	G6
LIBs
	H1	H2	H3	H4	H5	H6
MIBs
	I1	I2	I3	I4	I5	I6

.

2.4. Data Sources and Pre-Processing

The research data included meteorological data, socio-economic survey data, plane vector data and three-dimensional spatial model data of the typical city block sample.

Firstly, the meteorological data were obtained from the Chinese Standard Weather dataset of Tsinghua University and the China Meteorological Administration, and the socio-economic survey data came from relevant studies, national regulations, etc. Then, the planar vector data of typical city blocks were obtained from the OpenStreetMap (OSM) platform, which is advantageous due to its open sharing, fast data update rate and timeliness. Urban road network data, urban building profiles, and building height spatial distribution data were obtained from OSM using the application programming interface. Among these, the spatial distribution data of urban building contours and building heights include building attribute information such as the building layer number and building base area. The data were corrected through the topology and data processing capabilities of ArcGIS, and the plane vector data of typical city blocks were obtained. Finally, the planar vector data were imported into Rhinoceros 7.0, and further stretched from the vector data into a three-dimensional model.

2.5. Urban Form Indicators

In order to provide a more comprehensive and accurate description of the urban block form, this study comprehensively considered the current characteristics of the study area and based on existing studies [47], selected three categories of indicators to measure the urban blocks’ spatial forms, architectural form characteristics, urban density characteristics, and spatial characteristics. The architectural form characteristics included the shape coefficient (SC) and average building height (ABH) [48]; the density indicators included the building coverage ratio (BCR) and volume-to-area ratio (V/A) [49]; and the spatial indicators included the sky view factor (SVF) and building façade index (FI) [50]. According to the definitions and calculation formula of the form indicators in

Table 2. Calculation formulas for urban form indicators.

Urban Form Indicators	Definition	Formula	Diagram
$SC$	Ratio of total building surface area to volume	$SC=\frac{S_B}{V_B}$
$ABH$	Height of individual buildings weighted according to their respective footprints	$ABH=\frac{{\sum }_{i=1}^n{h}_i{A}_i}{\sum _{i=1}^n{A}_B}$
$BCR$	Ratio of total building façade area to site area	$BCR=\frac{A_D}{S_G}$
$V/A$	Ratio of total building coverage	$V/A=\frac{V_B}{S_G}$
$FI$	Ratio of total building façade area to site area	$FI=\frac{S_f}{S_G}$
$SVF$	Degree of confinement of urban space	$SVF=1-{\displaystyle \sum _{i=0}^n}{\sin }^2\beta \times \left(\frac{\alpha }{360}\right)$

, the form indicators of typical block samples were calculated using tools such as spatial analysis and computational geometry in ArcGIS 10.2.

2.6. Quantitative Modeling of ASI of Solar Energy

Zquierdo et al. [51] proposed five levels to evaluate the utilization of solar energy, including physical potential, geographical potential, technological potential, economic potential and social potential. On the basis of previous studies, a quantitative model of solar ASI based on the climate and urban form characteristics of Wuhan city is proposed and includes SRI, SII and SEGI.

As shown in Figure 3, the SRI refers to the annual cumulative radiation of the building surface in a unit land area. Compared with other energy sources, the input of solar energy completely depends on the solar radiation of the natural environment, so the SRI is the primary basic condition for calculating the solar ASI of a block [52]. The SRI is mainly affected by the local geographical location [53], climate conditions [54] and urban form, especially the different shapes of blocks lead to different shading between buildings, thus affecting the SRI.

The SII is based on the total annual radiation and it corresponds to the building surface area that is suitable for photovoltaics installation in a unit of land area. Considering the radiation threshold to screen radiation that is greater than the threshold of the building surface and, at the same time [55], excluding the building surfaces which are not suitable for the installation of photovoltaics, the surfaces and area of the building which can be installed with photovoltaics can be determined [56].

The SEGI refers to the annual cumulative power generation of the building surface in a unit land area, which is the power generation efficiency of the photovoltaic system in the block, and it directly affects the scalability of photovoltaics. The SEGI is mainly affected by photovoltaic conversion and area [57]. The photoelectric conversion rate refers to the efficiency of photovoltaics converting solar radiation into electrical energy, which is mainly related to the photovoltaic material [58], and the photovoltaic area is mainly related to the arrangement of the photovoltaics and the installation angle [59].

2.6.1. Solar Radiation Intensity Calculation Method

In this study, the three-dimensional information modeling software Rhinoceros 7.0, the parametric design software Grasshopper 2.0, and the simulation plugins-Ladybug and Honeybee were used to simulate the annual solar radiation of a typical block. The algorithm core of Ladybug and Honeybee is the Radiance program [60], which has the advantage that it integrates diffuse reflections and reflections between buildings in the calculation of the spatial distribution of radiation. Therefore, compared with other software [1], it can calculate the radiation received by the building surface more accurately. The accuracy of the software has been experimentally verified in existing related studies [61,62].

The workflow of this study consists of modeling, simulation and data acquisition. In terms of parameterization, in order to improve the calculation accuracy, the surface grid of the building is divided into 1 × 1 m², and the simulation period is set to 1 year. In particular, due to the different building surfaces leading to differences in reflectance, we referred to the research results of Qing et al. [63] and set the test value of reflectance of building surfaces as 0.2 to ensure that the test value of the reflectance is as close to the real value as possible. The specific parameters are shown in

Table 3. Parameter settings for SRI simulation.

Parameter	Setting
Computing grid	1 × 1 m2
Weather data	China standard weather data
Computation period	00:00 on 1 January to 4:00 on 31 December
Computing interval	1 h
Reflectance of building and ground	0.2
Location	Wuhan

. Referring to the study of Omid Veisi et al. [64] on the calculation method of solar radiation in blocks, the formula for calculating the $SRI$ is shown in Equation (1).

$$SRI=\frac{G_t}{S_G}$$

(1)

where $SRI$ is the annual cumulative radiation of the building surface in the unit land area ((kwh/(m²·a)); $G_t$ is the total annual solar radiation on the building surface kwh/(m²·a)); and $S_G$ is the land area of the block (m²).

2.6.2. Solar Installation Intensity Calculation Method

Whether photovoltaics can be installed on a building’s surface is mainly affected by the radiation threshold and the building’s structure [65]. The radiation threshold, which was first proposed by Compagnon R [66], refers to the amount of radiation that satisfies the balance between PV input and output. This study draws on the research results of Jingtao Li [67] and takes 530 kWh/m² as the radiation threshold, which comprehensively considers the influence on the threshold of factors such as the geographical climate, policy subsidies and the conversion efficiency of photovoltaics in Wuhan, and is relatively more scientific and accurate.

Building surfaces that meet the radiation threshold may not necessarily be fit for installing photovoltaics; it is important to also consider the space occupied by various rooftop facilities (such as elevator rooms, chimneys, water tanks, etc.), while on the facade, it is necessary to consider spaces such as doors and windows that are not suitable for PV installation. However, due to the diversity of building types, the roofs and facades of almost every building are different. This study aims to study groups of buildings, so the differences of individual buildings are ignored and the concept of the installation coefficient is introduced. The installation coefficient refers to the proportion of the building surface that can be installed with photovoltaics, and includes the roof installation coefficient ($C_r$) and facade installation coefficient ($C_f$) [68]. Referring to the study on the solar potential of residential blocks by Jia Tian et al. [69], the formulas for the roof ${SII}_r$, façade ${SII}_f$, and block ${SII}_b$ are shown in Equations (2)–(4).

$${SII}_r=\frac{A_{r>t}\times C_r}{S_G}$$

(2)

$${SII}_f=\frac{A_{f>t}\times C_f}{S_G}$$

(3)

$${SII}_b={SII}_r+{SII}_f$$

(4)

where ${SII}_r$, ${SII}_f$, and ${SII}_b$ are the solar installation intensities of roofs, façades, and blocks (m²); $C_r$ and $C_f$ are the proportion of roofs and façades that can be used to install photovoltaics; $A_{r>t}$ and $A_{f>t}$ are the areas of roofs and façades exceeding the radiation thresholds (m²); and $S_G$ is the land area of the block (m²).

The value of $C_r$ refers to the research results of Zhang Hua et al. [70], who comprehensively reviewed the rooftop photovoltaics installation coefficient of built-up land types in major Chinese cities by combining the three influencing factors of cities, blocks and building monomers. For the value of $C_f$, we take into account the geographical location of Wuhan City and refer to the provisions on window and wall areas in the “General Code for Energy Efficiency and Renewable Energy Application in Buildings (GB 50137-2011)” [71]. The specific values are listed in

Table 4. Values of installation coefficients.

Typology	Existing Research Values (Cr) [70]	Average Value (Value of This Study)	Existing Research Values (Cf) [71]	Average Value (Value of This Study)
LRB	0.30–0.50	0.40	0.6–0.8	0.7
MRB	0.44–0.69	0.57	0.6–0.8	0.7
HRB	0.25–0.41	0.41	0.6–0.8	0.7
MCB, MPSB	0.7–0.85	0.78	0.4–0.6	0.5
HCB, HPSB	0.22–0.56	0.39	0.4–0.6	0.5
LIB, MIB	0.8–0.9	0.85	0.9	0.9

.

2.6.3. Solar Electricity Generation Intensity Calculation Method

When the installable area of photovoltaics is determined, the photovoltaics placement form and angle have a direct relationship to the photovoltaics surface area [72]. There is occlusion between the installed photovoltaics modules, so only a portion of the available floor area is utilized. The ratio of the surface area of photovoltaics to the floor area it occupies is known as the ground coverage ratio ($GCR$). Except for the $GCR$, a certain amount of safe access ($SA$) should be maintained between PVs in order to meet the requirements for routine maintenance and fire prevention [73]. Referring to Shen Xu’s research on the calculation model of photovoltaic power generation [35], the formula for calculating the $SEGI$ is shown in Equations (5)–(7).

$$A_{pv}=GCR\times SA\times A_a$$

(5)

$$E_P=A_{PV}\times G_t\times \gamma \times \eta$$

(6)

$$SEGI=\frac{E_P}{A_b}$$

(7)

In Equations (5)–(7), $A_{pv}$ is the surface area of photovoltaics (m²); $A_a$ is the the area of PV installation on the building surface (m²); $GCR$ is the ground occupancy of PV; $SA$ is the proportion of safe passage area; $E_p$ is the annual photovoltaics power generation of the building (kwh/a); $G_t$ is the amount of radiation received on the PV (kwh/a); η is the conversion efficiency (%); and $\gamma$ is the operating efficiency (%).

In this study, TSM-250-P05A polycrystalline silicon cell photovoltaic panels, which are the most commonly used in China, were selected for the calculation. The values of $GCR$ and $SA$ are based on the research results of Byrne et al. [40]. The recommended best inclination angle for grid-connected photovoltaics in the Wuhan area is 20°; the value of the $GCR$ is 0.51; and the value of the $SA$ is 0.93. The specific parameters are shown in

Table 5. Selected PV basic parameters.

Product Model	Component Size	Rated Power	Peak Voltage	Peak Current	Conversion Efficiency	System Efficiency
TSM-250-PD05	1650 × 992 × 35 mm3	250 Wp	30.3 V	8.27 A	22%	90%

.

2.7. Statistical Analysis

In this study, the statistical analysis software SPSS Statistics 7.0 was used to analyze the correlation between various form indicators and the solar ASI.

Firstly, the mean value and standard deviation of the SRI, SII and SEGI were calculated and compared for nine types of blocks, and the distribution and change of the solar ASI were described with box charts and bar charts. Then, an F-test was performed on the results to determine whether there is a significant difference in the solar ASI for the nine types of blocks. Before the F-test, it is necessary to test if there is a normal distribution of independent variables, and only when the hypothesis of the normal distribution of variables is satisfied, can it be analyzed. Finally, in order to ensure the accuracy of the analysis, the results are verified by correlation analysis and backward regression in linear regression. We also perform a comparative analysis to determine the key urban form indicators that affect the solar ASI of solar energy in urban blocks.

3. Result and Analysis

3.1. Solar Radiation Intensity

Figure 4 shows the roof and facade SRI of 54 blocks, the average SRI of which was 836.92 kwh/(m²·y). As shown in Figure 5a,b, the block types with the highest and lowest roof SRIs were LIBs (487.17 kwh/(m²·a)) and HRBs (169.17 kwh/(m²·a)), with a difference of 318.00 kwh/(m²·a) and a percentage difference of 187.97%. The standard deviation of the roof SRI of the nine types of blocks was 103.48.

The changes in the facade SRI were even greater: the largest type of blocks were HRBs (783.83 kwh/(m²·a)), and the lowest type were LIBs (113.54 kwh/(m²·a)), with a difference of 670.29 kwh/(m²·a) and a percentage difference of 590.03%. The standard deviation of the facade SRIs of the nine types of blocks was 251.84. An F-Test was performed on the results, and if the result was less than 0.05, there was no significant difference between the two variances. The results of the F-test are shown in

Table 6. Results of F-test.

Building Surface	SRI		SII		SEGI
	F	p	F	p	F	p
Roof	69.06	0.01	14.01	0.02	13.21	0.02
Facade	32.86	0.00	18.11	0.02	18.67	0.01
Block	22.44	0.01	12.65	0.03	15.42	0.02

. A comparison of the standard deviation and F-Test shows that the block types have a greater impact on the SRI of the block facade than that of the roof. This is consistent with the results of previous studies, and the same phenomenon was observed by Juan Jose Sarralde et al. [74], who found that changes in the block type caused an increase in solar radiation on the roof of only about 9%, while the increase in the vertical surface could be up to 45%.

Figure 5c shows the trend in total SRI of the nine types of blocks. The average values of total SRI of the nine types of blocks were as follows: HCBs (1145.33 kwh/(m²·a)) > HPSBs (1115.50 kwh/(m²·a)) > HRBs (953.01 kwh/(m²·a)) > MPSBs (905.83 kwh/(m²·a)) > MRBs (874.67 kwh/(m²·a)) > LRBs (743.33 kwh/(m²·a)) > MIBs (654.51 kwh/(m²·a)) > LIBs (600.83 kwh/(m²·a)) > MCBs (533.67 kwh/(m²·a)). The maximum and minimum difference between the total SRIs of blocks was 611.66 kwh/(m²·a), with a percentage difference of 114.61%, and a standard deviation of 238.65. There are significant differences in the total SRI of different types of blocks. As shown in Figure 5d, in LIBs, MIBs and MCBs, the rooftop SRI accounted for more than 50% of the whole block, but in residential blocks, public service blocks and HCBs, the facade SRIs occupied the major portion. These results show that the trend in total SRI is the same as that of the facade of a block, that is, high-rise blocks have higher SRI than low-rise blocks.

3.2. Solar Installation Intensity

Figure 6 shows the roof and facade SIIs of 54 blocks after taking into account the effects of radiation thresholds and installation coefficients, and the average SII is 0.32 m². As shown in Figure 7a,b, similar to the SRI results, the block types with the highest and lowest roof SIIs were LIBs and HRBs, and the block types with the highest and lowest facade SIIs were HRBs and LIBs. However, there is little difference in the proportion of roof and facade SIIs in HPSBs, with averages of 0.11 m² and 0.09 m². But the roof SII of MPSBs contributes more to the total block than the facade, primarily because the installation coefficient of MPSB roofs (0.78) is much larger than that of their facade (0.5).

As shown in Figure 7c, the total SIIs of nine types of blocks were as follows: MRBs (0.42 m²) > MIBs (0.41 m²) > LIBs (0.38 m²) > MCBs (0.37 m²) > HRBs (0.35 m²) > MPSBs (0.26 m²) > LRBs (0.24 m²) > HPSBs (0.21 m²) > HCBs (0.16 m²). The SII extreme variance for the nine types of blocks was 0.22 m², the percentage difference was 162.50%, and the standard deviation was 0.09. Compared with the total SRI values, the SIIs of the industrial blocks showed a significant increase, and the values of the HCBs decreased significantly. There are two main reasons: Firstly, because HCBs have a smaller roof area and more roof facilities, as well as more windows and doors on their facades, the C_r and C_f of HCBs are 0.39 and 0.5, which are much smaller than the same values of other types of blocks. Second, in order to ensure maximum economic efficiency, HCBs have a high-density spatial form, and their facades are greatly affected by the mutual shading between buildings, leading to a failure to meet the required radiation threshold and significantly reduced SII values. However, industrial blocks are the opposite.

3.3. Solar Energy Generation Intensity

The SEGI is based on the SRI and the SII, taking into account the photovoltaic surface area and photovoltaic efficiency. As shown in Figure 8, the average SEGI for the 54 city blocks was 28.01 kwh/(m²·a). The SRI, SII, and SEGI of MRBs and HRBs all reached the average value, which means that they have more available space for solar energy. As shown in Figure 9a,b, only for HRBs and HCBs were the facade SEGI values larger than those for the roof. The average facade SEGIs of the two types of blocks were 24.09 kwh/(m²·a) and 13.41 kwh/(m²·a), and their contribution rates to the total blocks were 70.37% and 52.39%. The average values for roof SEGI of the other seven types of blocks were in the range of 14.35 kwh/(m²·a)–21.23 kwh/(m²·a), accounting for 53.08–87.09% of the total. Compared with the SRI and SII, the roofs showed a relatively stable power generation capacity in the total block.

As shown in Figure 9c, the total SEGIs of the nine types of blocks were as follows: MRBs (34.15 kwh/(m²·a)) > HRBs (32.85 kwh/(m²·a)) > MCBs (29.67 kwh/(m²·a)) > LRBs (26.61 kwh/(m²·a)) > HPSBs (25.73 kwh/(m²·a)) > MIBs (25.13 kwh/(m²·a)) > HCBs (24.23 kwh/(m²·a)) > LIBs (23.74 kwh/(m²·a)) > MPSBs (21.21 kwh/(m²·a)). The difference in SEGI between MRBs and MPSBs was 12.94 kwh/(m²·a), the percentage difference was 61.01%, and the variance between the nine types was 3.22. There were significant differences in the overall SEGI of the different types of blocks. It is worth noting that the facade SRI, SII and SEGI of the HRBs were all larger than those of their roofs, but the roof SRI, SII and SEGI of industrial blocks were all larger than those of their facades.

4. Discussion

4.1. The Effect of Urban Form Indicators on the ASI of Solar Energy

4.1.1. Correlation of Form Indicators with the ASI of Solar Energy

In this section, scatter plots between six independent variables (SC, ABH, BCR, V/A, VF, and FI) and three dependent variables (SRI, SII, and SEGI) are drawn and a Pearson correlation analysis is conducted to interpret the results and analysis of the case study. Herein, we address the first research question listed in Section 1.3: urban form greatly affects the solar ASI, which accepts the null hypothesis. BCR, ABH and V/A are the key indicators.

To be specific, as shown in Figure 10 and Figure 11, the SRI correlations are similar to those of SEGI, with both of them having the highest correlation with ABH and V/A. SRI has an R² of 0.72 with ABH and 0.68 with V/A, while SEGI has an R² of 0.63 with ABH and 0.67 with V/A; all are positively correlated. Furthermore, SRI and SEGI are negatively correlated with BCR, the R² values of which are 0.59 and 0.49, indicating a general correlation. Finally, SVF is positively correlated with the SRI, whereas SC and FI are not significantly correlated with the SRI.

There are two factors that cause ABH and V/A to be significantly and positively correlated with SRI and SEGI. Firstly, the increase in building height increases the shade between buildings, but also means that the area of solar radiation on the facade will also increase. Secondly, since SRI and SEGI in this study are defined based on the unit land area, increases in ABH and V/A lead to an increase in the total proportions of buildings on the land.

As shown in Figure 12, in contrast with SRI and SEGI, SII is affected by the installation coefficient and radiation threshold, but has no significant correlation with ABH or V/A. SII is positively correlated with BCR with an R² of 0.51, while being negatively correlated with SCB and SVF, with R² values of 0.49 and 0.53, respectively. This is consistent with previous studies: Ming et al. [33] found that BCR, ABH and V/A are key indicators that affect the solar energy potential in northeast China and also have consistent effects on the solar energy potential in different regions of China.

Comparing the results for SRI, SII and SEGI shows that different form indicators have different effects on these indicators, and it is impossible to improve the ASI by adjusting only one index, so their combined effects must be considered. For example, reducing BCR has a direct effect on improving SRI and SII, but this will inevitably lead to a reduction in SII. Moreover, urban blocks provide relevant economic benefits, and it is difficult to simply reduce BCR. Therefore, in order to improve the solar ASI of urban blocks, it is necessary to reduce BCR and increase vertical development while optimizing the needs for sunlight and fire prevention.

4.1.2. Multiple Linear Regression Model Predicts ASI of Solar Energy

In order to ensure the accuracy of the analysis results, we assume that SRI, SII, and SEGI can be predicted as linear functions of the corresponding form indicators. In order to eliminate the collinearity effect of the variables, backward regression was selected as the linear regression method to conduct a comparative verification of the correlation analysis.

Table 7. Results of multiple regression analysis.

Dependent Variable	Predictive Variable	Nonstandard Coefficient		Standard Coefficient	Sig.	VIF	R2	Durbin–Watson
		B	Standard Error	Beta
SRI	Constant	399.76	63.42	-	0.01	-	0.71	1.51
	V/A	37.64	12.54	0.85	0.01	3.47
	FI	−62.47	36.42	−0.26	0.01	3.00
	SVF	478.35	52.36	0.48	0.01	1.38
SII	Constant	0.19	0.09	-	0.01	-	0.53	1.45
	BCR	0.46	0.25	0.41	0.00	1.07
	FI	0.03	0.02	0.34	0.01	1.41
	SC	−0.21	0.12	−0.21	0.01	1.48
SEGI	Constant	29.61	2.16	-	0.00	-	0.68	1.56
	V/A	0.52	0.17	0.55	0.00	2.08
	SC	−8.72	3.23	−0.25	0.00	2.23
	SVF	1.85	2.33	0.14	0.01	3.21

shows the adjusted final regression models for SRI, SII, and SEGI. The R² values were 0.71, 0.53, and 0.68, indicating a good degree of fitting, and the variance expansion factors (VIF) were all less than 10, indicating that there was no significant collinearity for any variable. The results were statistically significant.

The multiple linear regression results showed that three form indicators had significant effects on the $SRI$ (in order of standardized beta values): the $V/A$ (0.85) had the largest effect, followed by the $SVF$ (0.48) and the $FI$ (−0.26). For a one unit increase in the $V/A$, the $SRI$ increases by 37.64 kwh/(m²·a); and for a 0.1 unit increase in the $SVF$, the $SRI$ increases by 47.84 kwh/(m²·a). On the other hand, for a one unit increase in the $FI$, the $SRI$ decreases by 62.47 kwh/(m²·a). The $SRI$ can be calculated using Equation (8).

$$SRI=399.78+37.64V/A-62.41FI+478.35SVF$$

(8)

The results of the multiple linear regression showed that three form indexes had a significant influence on the $SII$: the $BCR$ (0.41) had the greatest influence, followed by the $FI$ (0.34) and the $SC$ (0.21). For a one unit increase in the $BCR$, the $SII$ decreases by 0.46 m², and for a one unit increase in the $SC$, the $SII$ decreases by 0.02 m². However, for a one unit increase in the $FI$, the $SII$ increases by 0.03 m². The $SII$ can be calculated using Equation (9).

$$SII=0.19+0.46BCR+0.03FI-0.21SC$$

(9)

The multiple linear regression results showed that three form indexes had a significant effect on the $SEGI$: the $V/A$ (0.55) had the greatest influence, followed by the $SC$ (−0.25) and the $SVF$ (0.14). For each one unit increase in the $V/A$, the $SEGI$ increases by 0.52 kwh/(m²·a), and for a 0.1 unit increase in the $SVF$, the $SEGI$ increases by 0.19 kwh/(m²·a). However, for a 0.1 unit increase in the $SC$, the $SEGI$ decreases by 0.87 kwh/(m²·a). The $SEGI$ can be calculated using Equation (10).

$$SEGI=29.61-8.72SC+0.52V/A+1.85SVF$$

(10)

4.2. Planning Strategies for Solar Available Space in Urban Blocks

Considering the relationship between land function, building layout and solar ASI, this study proposes planning and implementation strategies to ensure available solar energy space on two levels (different spatial types and locations) in the Nanhu sub-center city of Wuhan.

4.2.1. The Strategies of Differential Development Based on Different Spatial Types

According to the research results, due to the differences in spatial types, the solar ASI of the roofs and facades of blocks are different. Therefore, for urban blocks with different spatial types, differentiated development strategies should be implemented to realize the focus of development and improve energy utilization efficiency, as shown in Figure 13a.

In residential blocks, the facade SRI, SII, and SEGI values in high-rise residential blocks were larger than those of their roofs, accounting for more than 70% of the whole block. For low-rise and multi-storey residential blocks, the contribution rates of the facade SRI to the whole block SRI were 68.86% and 72.67%, respectively, while the contributions of the facade SII to the whole block SII were 56.51% and 64.15%, respectively. However, the contribution rates of the facade SEGI to whole block SEGI were slightly reduced at 46.92% and 45.36%, respectively. Therefore, when developing available space for solar energy in residential blocks, it is necessary to focus on the façades of high-rise residential blocks and the entirety of low-rise and multi-storey residential blocks.

The roof SRI, SII and SEGI of two types of industrial blocks were much larger than those of facades, accounting for more than 65%. For public service blocks, the façade SRI of multi-storey and high-rise public service blocks accounted for 65.88% and 65.42%, but the percentage of façade SII and SEGI was significantly lower in two types of blocks. The facade SII and SEGI in the multi-storey service blocks accounted for 27.38% and 30.73%, and the facade SII and SEGI in the high-rise service block accounted for 50.41% and 36.44%. Therefore, the rooftops of public service blocks and industrial blocks should be focused on as a stable source of power generation.

For commercial blocks, the multi-storey roof SRI, SII and SEGI were larger than those of multi-storey facades, and the contribution rates of the roof SRI, SII, and SEGI to the whole block were 58.80%, 71.99%, and 67.69%, respectively. The façade SRI and SII of high-rise commercial blocks contributed 65.74% and 64.94% to the entire block, but these blocks’ façade SEGI contributed 52.39% to the entire block. Therefore, the roofs of multi-storey commercial blocks and the entirety of high-rise commercial blocks should be developed.

4.2.2. The Strategy of Gradual Development Based on Different Spatial Locations

Based on the differential development of spatial types, this study combined the spatial locations of nine types of blocks to form a hierarchical group within Nanhu, comprising four main groups. According to their different functional orientations, the development pattern and sequence of each group are also different, necessitating the implementation of a gradual development strategy with sequential planning. The development sequence is shown in Figure 13b and is divided into two phases.

Group A functions as “industrial blocks + commercial blocks”. It can be seen from the research results that industrial block roofs have a stable ASI. However, commercial blocks are greatly affected by windows and roof facilities, decreasing their ASI. In addition, for commercial blocks, in practice, there is greater concern for the value of commercial development with their building surfaces being utilized as advertising space, which limits the development of photovoltaics in these areas. Therefore, the first phase of the development of this group revolves around industrial blocks, where a demonstration block with a certain scale of power generation is built on the roof. The second development phase involves driving the surrounding commercial blocks to install photovoltaics.

The functional composition of Group B is mainly residential blocks, which account for the highest proportion of the total area among the nine categories of blocks and have the largest SII and SEGI. However, the installation of solar power generation facilities in old residential blocks impacts the building structures and the safety of the building cannot be guaranteed. Therefore, in this group, priority should be given to the development of newly built residential blocks and optimizing the layout of old residential areas by reducing building density and increasing vertical development, as well as conducting system assessments on whether solar energy can be installed.

The function of Groups C and D is “public service blocks + residential blocks”. This group is dominated by public service blocks and will gradually have a positive impact on the surrounding residential blocks. First, public service blocks mainly consist of schools, and the construction area and building stock in these areas are high. Secondly, the introduction of solar power into schools has a huge social awareness effect, prompting urban residents to change their ideas about solar energy utilization. England, Germany and Australia are actively promoting the introduction of solar energy into schools [75,76].

4.3. Limitations

This study focuses on the influence of the spatial layout and function of buildings in a block on their solar energy utilization. We simplified the forms of urban blocks and the external surface of the buildings in the research process by regarding the buildings as cubes, focusing only on their length, width, and height in order to facilitate the simulation. Furthermore, some shielding factors affecting the photovoltaics efficiency were simplified. Some factors like wind-driven dust, snow, and trees could cause a shielding effect on photovoltaics and decrease solar transmission through the photovoltaics surface glass, which affects the power output.

5. Conclusions

In order to explore the influence of urban form on the intensity of the available space for solar energy, as well as to propose strategies for planning of the space that is available for solar energy, this study firstly proposed a model to quantify the ASI of solar energy with three indicators: SRI, SII, and SEGI. Then, we calculated the solar ASI of nine types of typical urban blocks in a sub-center of Wuhan City, Nanhu, Finally, correlation analysis and linear regression were used to analyze the correlation between SC, ABH, BCR, V/A, SVF, FI, and ASI. The specific conclusions are as follows:

• Urban form leads to significant differences in SRI, SII and SEGI, reaching differences of 114.61%, 162.50% and 61.01%, respectively. Multi-storey and high-rise residential blocks all had average values, corresponding to intermediate levels of available space for solar energy.
• According to the results of the correlation analysis, ASI is mainly affected by three form indicators: the building coverage ratio, the average building height, and the volume-to-area ratio. The established multiple linear regression model can effectively predict the SRI, SII and SEGI, the fit degrees of which are 0.71, 0.53 and 0.68.
• It is suggested to focus on the utilization of solar energy on the roofs of industrial blocks, public service blocks, and multi-storey commercial blocks; the facades of high-rise residential blocks; and the entirety of low-rise residential blocks, multi-storey residential blocks, and high-rise commercial blocks. The development of available space for solar energy in urban blocks should be realized in a gradual and orderly development from point to surface.

Based on these original urban block typologies that have not be systematically examined before, as well as the results thus derived from our new quantitative model, this study provides convincing evidence from a theoretical point of view that urban form matters to a great extent in terms of the utilization of solar energy. Depending on the urban block typology selected, significant improvements in solar energy harvesting and energy use efficiency of buildings can be achieved through the deployment of photovoltaic systems on external building surfaces.

The results also highlight the necessity and importance of exploring innovative urban planning and architectural design strategies aiming towards the efficient application of renewable energy technologies. The significant planning and form indicators related to solar ASI in this study have crucial implications for urban planning and architectural design practices.

This study implemented a novel methodology for investigating the interactions between solar energy use and urban design using vernacular block typologies. Such block typologies use simplified building geometries for high transferability and computational efficiency. They could be applied in other climatic regions and cities for solar potential assessment and the application of photovoltaic technologies to identify the most effective design solutions suitable for the local context. The findings can also be generalized on a city-wide scale.

The city is a complex system, characterized by its interconnected multi-sectoral cooperation, which forms the backbone of modern society. Solar energy utilization as a new energy still needs to comprehensively consider transportation, buildings, industry and other perspectives to improve energy utilization efficiency. This study only considers the relationship between urban form and energy, and future studies should take into account climatic, economic and societal factors when investigating the interaction of solar energy design and urban planning and design. At the same time, it is necessary to analyze the solar output of various spaces and predict the energy demand, as well as to consider the impact of residents’ behavior on the internal thermodynamics of the building [77], so as to refine the environmental performance and management procedures of available solar spaces.