Solar PV Potential Assessment of Urban Typical Blocks via Spatial Morphological Quantification and Numerical Simulation: A Case Study of Jinan, China

Abstract

With rapid urbanization, rooftop photovoltaic (PV) systems play an important role in mitigating the energy crisis and reducing emissions, yet achieving scientific and cost-effective deployment at the urban block scale remains challenging. This study proposes a transferable framework that integrates spatial morphology quantification, clustering, and numerical simulation to evaluate PV potential in residential blocks of Jinan, China. Six key morphological indicators were extracted through principal component analysis (PCA), and blocks were classified into five typical types, followed by simulations under different PV material scenarios. The main findings are: (1) Block type differences: Cluster 1 achieved the highest annual generation, 61.76% above average, but with a 75.08% cost increase and a 3.54-year payback. Clusters 4 and 5 showed moderate generation and the shortest payback of 2.91–2.97 years, reflecting better energy–economic balance. (2) PV materials: monocrystalline silicon (m-Si) yielded the highest generation, suitable for maximizing output; polycrystalline silicon (p-Si) produced slightly less but reduced costs by 32.43% and shortened payback by 19.58%, favoring cost-sensitive scenarios. (3) Seasonal variation: PV output peaked in February–March and September–December, requiring priority in grid operation and maintenance. The proposed framework can serve as a useful reference for planners in developing PV deployment strategies, with good transferability and potential for wider application, thereby contributing to urban energy transition and low-carbon sustainable development.

1. Introduction

1.1. Background of the Study

Rapid urbanization has intensified a range of challenges, including the urban heat island effect [1], air pollution [2], and traffic congestion [3]. Among these, urban energy consumption [4] presents one of the most critical threats, as it accelerates fossil fuel depletion and carbon emissions [5]. Previous studies suggest that modifying building forms and spatial layouts within urban blocks can reduce building energy use and carbon emissions [6]. While modifying building forms and spatial layouts has been shown to reduce operational energy use, such interventions often require demolition and reconstruction, leading to further carbon costs—thus limiting their feasibility as sustainable strategies.

With advancements in solar photovoltaic (PV) technology [7], installing PV panels on rooftops and façades has become a promising approach for harvesting solar energy. The electricity generated can supplement operational energy demands of buildings, thereby reducing urban reliance on fossil fuels and lowering overall urban energy consumption [8]. Ongoing innovations in PV technology have yielded diverse panel materials, such as monocrystalline silicon [9], polycrystalline silicon [10], and amorphous silicon. These materials exhibit varying conversion efficiencies and irradiance thresholds due to their distinct physical properties. Additionally, the initial investment costs of PV systems are influenced by panel specifications, installation methods, and spatial deployment configurations, all of which require careful consideration.

Urban blocks exhibit significant morphological variations due to multi-factorial influences [11]. Critically, buildings both within and surrounding a block affect light penetration into outdoor spaces through shading and reflection effects [12]. These phenomena directly impact the power generation efficiency of PV panels installed on building surfaces [13]. In this context, developing a scientific and scalable method to evaluate rooftop PV potential across diverse urban blocks is crucial for supporting informed design and planning decisions.

1.2. Related Work

In recent years, research on PV potential assessment at the building scale has gradually deepened. Many researchers have employed building simulation tools to model and evaluate the PV potential of individual buildings. For example, Tevis et al. [14] conducted a life cycle assessment using a sustainable office building planned for construction in Thailand as a case study, and analyzed four different energy supply scenarios. The results indicated that the use of PV systems could significantly reduce grid electricity consumption. Deltenre et al. [15] developed an algorithm based on empirical case studies of two high-rise buildings in Brussels to assess the technical, economic, and environmental performance of hybrid PV systems applied to tall buildings. Lim et al. [16] compared the performance of perovskite, sulfide, and organic solar cells with that of silicon cells, using a five-parameter logistic function to evaluate their energy, economic, and environmental performance in a typical residential building in Detroit. Bakmohammadi et al. [17] proposed a research framework that combines deep learning with multi-objective optimization algorithms to evaluate PV system design in two university buildings in Alberta, Canada. Their results showed that optimized system configurations could achieve electricity self-sufficiency rates of 5.16% and 6.78%, respectively. Tian et al. [18] adopted parametric modeling and machine learning algorithms to comprehensively assess solar potential at the building scale and analyzed the influence of surrounding environments on PV installation. These studies have achieved notable progress in parameter setting, simulation accuracy, and PV potential assessment at the building scale, laying a solid foundation for the theoretical framework and technical methodologies of PV potential evaluation. However, due to their focus on micro-scale analysis, certain limitations remain when addressing more complex spatial contexts or larger-scale application scenarios.

To support urban-scale PV planning, recent studies have extended the evaluation unit to the urban block level. Due to the vast scale of urban environments, computational constraints make it difficult to assess all city blocks within a limited timeframe. An effective solution is to select morphologically representative blocks for simulation analysis and then extrapolate the results to estimate the city-wide PV potential. For example, Xu et al. [19] developed a multidimensional solar potential assessment method for industrial blocks, analyzing morphological parameters of 48 typical industrial blocks in Chinese cities. Their results revealed significant differences in solar potential across block types, with building density identified as the most influential factor. Xie et al. [20] used data from 55 dormitory blocks located at Wuhan University and employed a multiple regression model to investigate the impact of urban morphology on building energy consumption and solar potential. The study found that differences among block types could lead to a maximum variation of 12.25% in building energy use, offering planning insights for improving energy efficiency. Liu et al. [21], using a residential block case in Jianhu, China, proposed a multi-objective urban morphology design optimization framework based on the Grasshopper platform. The study demonstrated significant correlations between urban form, building energy demand, and solar potential, and suggested corresponding energy-saving design strategies. Yang et al. [22], through observations of Macau’s urban morphology and literature review, identified five typical block types and developed a parametric modeling and simulation workflow to analyze building energy performance and solar radiation characteristics. The study proposed block-specific strategies for the optimized deployment of solar technologies. Tang et al. [23] evaluated the energy and economic performance of rooftop and façade PV and radiative cooling (RC) technologies in typical old residential blocks in Shenzhen using the Rhino–Grasshopper platform. Their findings suggested that PV systems are more suitable for rooftops, while RC performs better on façades. Tang et al. [24] simulated the building PV potential in 15 cities based on 50 simplified local climate zone models and applied multiple linear regression and random forest models to analyze the impact of urban morphology and climate variables on Building-integrated photovoltaics generation. Li et al. [25] classified 56 office blocks into 14 morphological subtypes based on layout and height characteristics and developed a five-level PV potential assessment framework. This strategy effectively avoids the high computational cost of simulating every urban block individually and demonstrates strong practical feasibility and application value. However, in most studies, the selection of representative blocks still relies mainly on expert judgment, subjective interpretation, or relatively simplified classification criteria. The lack of standardized and quantitative selection metrics may undermine the objectivity and reproducibility of the results.

To address the above issues, scholars have proposed introducing quantitative spatial morphological indicators combined with clustering algorithms to classify urban blocks more scientifically, and then conducting quantitative analysis based on the classification results, thereby effectively reducing selection bias. In fact, spatial morphology analysis and clustering methods have been widely applied in various domains, such as urban texture recognition, the impact of block morphology on microclimate, the relationship between urban form and socioeconomic development, the influence of block morphology on traffic pollution dispersion, urban energy consumption, thermal environment, and urban vitality assessment (

Table 1. Applications of spatial morphology and clustering methods in previous studies.

Authors	Study Area	Research Direction	Performance Evaluation	Research Methods	Morphological Indicators
This work	Jinan, China	Solar PV potential	PV power generation, Solar income, PV panel cost, PV payback period	Principal component analysis (PCA), Gaussian mixture model (GMM), Density-based cluster algorithm (DBSCAN), Spectral clustering (SC), K-means	Building area ratio (BAR), Block site area (BSA), Minimum spacing between buildings (MBS), Floor area ratio (FAR), Standard deviation of average orientation angle of buildings to the south (OASsd), Average building-to-block-center distance (BTC)
[26]	Wuhan, China	Urban texture recognition	-	PCA,K-means	BSA, FAR, Average building area (BA), Standard deviation of BA (BAsd), Building coverage ratio (Rbc), Average building height (BH), Number of buildings (BN), Building compactness (BC), Fineness, Cohesion
[27]	Crete, Greece; Gubbio, Italy; New York, USA	Urban microclimate	Environmental indicators	K-means	FAR, BH, Sky-view-factor (SVF), Aspect ratio
[28]	Shenzhen, China	Urban microclimate	Heating degree days, Cooling degree days	PCA, GMM	BSA, BH, Characteristic length, Block site perimeter, Building volume, Building surface area
[29]	Nanjing, Shanghai, Hangzhou, Suzhou, China	Urban socioeconomic level	City ranking, Gross domestic product	T-distributed stochastic neighbor embedding	Vertical spatial density, Boundary complexity, Scale diversity, Building type uncertainty, Building mass dispersion
[30]	Wuhan, China	Urban traffic pollution	Pollutant concentration, Fluxes, Pollution removal	PCA,K-means	FAR, BH, Rbc, BAsd, BTC, MBS, Standard deviation of BH (BHsd), Block shape factor (Fblock), Average windward area ratio (WD)
[31]	Wuhan, China	Urban energy consumption	Energy use intensity (EUI), PV-adjusted energy use intensity (EUI-PV), PV substitution rate (PSR)	K-means	FAR, BH, Fblock, SVF, Building density (D), Block length, Block width, Block orientation, Height-to-width ratio
[32]	Beijing, China	Urban morphology analysis	Trends of morphological indicators	Ward’s hierarchical clustering	FAR, BSA, Fblock, Rbc, BAsd, Network density, Plot shape regularity
[33]	Changsha, China	Urban thermal environment	Mean air temperature	K-means	D, Fblock, FAR, BH, WD, SVF, Green space ratio (GCR), Impervious surface ratio, Building height otherness, Points of interest (POI)
[34]	Nanjing, China	Urban thermal environment	Land surface temperature	K-means	BH, D, GCR
[35]	Seoul, Republic of Korea	Urban vitality assessment	POI	DBSCAN	Density, Land use, Street connectivity, Public transportation
[36]	Istanbul, Turkey	Urban energy consumption	EUI	K-means	BC, BA, FAR, Total floor area, Building elongation ratio, Open space ratio, Average distance to neighboring buildings

). For example, Li et al. [26] employed Principal component analysis (PCA) and the K-means clustering algorithm, together with machine learning techniques, to investigate the morphological features and spatial distribution of urban blocks in support of smart city development and urban planning optimization. Pigliautile et al. [27] applied clustering analysis to environmental data collected along pedestrian transects to explore microclimate diversity in three different cities, demonstrating that this method can effectively identify similar morphological structures. Shen et al. [28] used PCA and the Gaussian mixture model (GMM) to cluster urban morphological data and assess the impact of climate change on urban microclimates. Qu et al. [29] employed the T-distributed stochastic neighbor embedding algorithm to cluster urban blocks in Nanjing, Shanghai, Hangzhou, and Suzhou, finding that morphological parameters combined with clustering analysis can effectively distinguish block types, and that the number of clusters is negatively correlated with the socioeconomic development level of comparable regions. Wu et al. [30] analyzed morphological parameters of 236 residential blocks in Wuhan, classifying them into five types using K-means clustering and further applying Computational fluid dynamics to simulate traffic pollutant dispersion across different block categories. Xu et al. [31] clustered residential blocks using K-means and incorporated the offset effect of PV generation into energy consumption analysis, introducing indicators such as Energy use intensity, PV-adjusted energy use intensity, and PV substitution rate to explore the relationship between block morphology and energy performance. Liu et al. [32] investigated morphological transformations of 194 urban blocks in Beijing, applying visualization and Ward’s clustering method to analyze spatial characteristics and the interaction between boundary and internal layers. Su et al. [33] divided the central area of Changsha into 121 plots, selected 11 morphological indicators, and applied K-means clustering combined with ENVI-met simulations to examine the relationship between block morphology and thermal environment. Zhu et al. [34] applied machine learning and K-means clustering to assess the influence of morphological characteristics within buffer zones on land surface temperature in Nanjing. Ha et al. [35] employed Density-based spatial clustering of applications with noise (DBSCAN) and Points of interest (POI) data to quantitatively evaluate the impact of the COVID-19 pandemic on the use of public spaces in Seoul’s commercial districts. Karli et al. [36] classified residential blocks in Istanbul into seven morphological types using K-means clustering, and further applied machine learning to evaluate the energy consumption of different block typologies.

Existing studies have therefore provided a mature and effective technical pathway for block morphology classification and analysis, confirming the influence of spatial morphology on building energy efficiency, environmental quality, and other multidimensional factors, and advancing research in related fields. Nevertheless, two critical limitations remain: first, although spatial morphology and clustering methods have been validated in domains such as urban microclimate and energy consumption, their application in PV potential assessment is still limited, and systematic studies that simultaneously incorporate both energy output and economic performance are lacking; second, most existing studies rely on a single clustering algorithm for block morphology classification, without comparative validation across different clustering methods, thereby undermining the robustness of classification results. Therefore, it is necessary to establish a systematic, urban-block-scale framework for the quantitative classification and evaluation of urban morphology, in order to support adaptive analysis of PV potential and the formulation of deployment strategies under different block typologies.

1.3. Aims and Originality

This study proposes a novel framework integrating multi-indicator spatial morphology analysis with solar PV potential simulation to assess urban solar energy capacity. 749 urban blocks within Jinan’s main urban district were evaluated using a suite of morphology indicators. Dominant indicators were then applied to classify blocks into distinct morphological clusters. Representative urban block prototypes were systematically extracted from each classified cluster to capture essential morphological characteristics. Solar energy yield was simulated for all building roofs within prototypes using a parametric modeling approach that accounts for panel orientation [37], tilt angles [38], and local shading effects [39]. Results derived from prototype simulations were scaled to estimate citywide PV potential, generating actionable insights for optimal panel selection, site-specific installation configurations, and energy yield prediction across Jinan. The main objectives of this study are as follows:

• To introduce a multi-indicator spatial morphology quantification approach by applying PCA and clustering algorithms to 749 urban blocks, thereby extracting key morphological indicators and establishing a systematic and replicable method for identifying representative block types.
• To conduct rooftop PV potential simulations on representative blocks using parametric modeling and high-efficiency simulation tools, and to propose a rapid assessment framework applicable at the urban block scale.
• To evaluate the applicability of various PV materials across different block types and propose material selection and deployment strategies based on specific design needs.
• To develop regression models between morphological parameters and PV potential, enabling fast estimation and scalable application of solar potential in urban contexts.

The remainder of the paper is structured as follows: Section 2 provides a detailed description of the research methodology, including data preparation and block selection, the definition and quantification of spatial morphological indicators, the identification of typical block types based on PCA and clustering algorithms, as well as the development of the rooftop PV potential simulation workflow using the Grasshopper platform and the VITALITY plugin. Section 3 analyzes the results for morphological indicators, clustering outcomes, the selection of representative block samples, PV simulation results under different materials and block types, and the construction of ridge regression prediction models. Section 4 provides a discussion covering seasonal generation patterns, spatial distribution of clusters, framework transferability, and limitations. Section 5 concludes the study by summarizing the main findings and proposing directions for future research.

2. Methods

2.1. Overview of the Workflow

This study establishes an urban block-scale rooftop PV potential assessment framework based on spatial morphology quantification and numerical simulation. As illustrated in Figure 1, the workflow consists of four main stages. First, building information for the sampled blocks is extracted and processed from geographic databases. Second, multiple spatial morphological indicators, including building area ratio, block site area, and floor area ratio, are calculated. PCA is then applied to reduce dimensionality and address potential multicollinearity among variables, followed by the classification of blocks using clustering algorithms. In the third stage, parametric models are constructed on the Grasshopper (version 1.0.0008) platform, and rooftop PV potential simulations are performed using the VITALITY plugin, generating outputs such as annual energy yield and payback period. Finally, based on the simulation results, the study conducts a comparative analysis across block types, evaluates the performance of different PV materials, and develops ridge regression prediction models to support material selection and deployment strategies tailored to various urban morphological contexts. The detailed methodology is presented in the following sections.

2.2. Data Preparation and Block Selection

This study mainly focuses on residential blocks in the central urban area of Jinan. Jinan is located in central Shandong Province (36°02′–37°54′ N, 116°21′–117°93′ E), with a total area of 10,244.45 km² and a permanent population of 9.515 million as of the end of 2024. According to the Jinan Energy Statistical Yearbook 2023, the average daily total solar radiation in the main urban area and the northern development region across the Yellow River reaches about 4 kWh/m², corresponding to an annual theoretical utilization of 1314–1398 h. This value reaches the upper limit of Category II areas in the national Classification of Climate Resource Utilization, and is clearly superior to neighboring regions in northwestern Shandong such as Dezhou and Liaocheng. The meteorological data used in this study were obtained from the China Standard Weather Data (CSWD) in the form of EPW files. These files provide typical-year hourly meteorological data, including temperature, humidity, wind speed, solar radiation, cloud cover, precipitation, etc., serving as a reliable basis for PV potential simulations.

As shown in Figure 2, Jinan has 10 districts and 2 counties (as of 2024). The city follows a “Core–Wings–Clusters” spatial development structure. The core area, composed of Lixia, Shizhong, Huaiyin, Tianqiao, and Licheng districts, serves key administrative, financial, and cultural functions, with Lixia District hosting provincial government offices. The eastern development area, located in the Tangye–Suncun region of Licheng, forms an innovation corridor connected to the Jinan Pilot Free Trade Zone. In the west, coordinated development between Huaiyin’s West Railway Hub and Changqing’s University Town supports integration between industry and academia.

This study focuses on 749 residential blocks within the five main districts of Jinan (Lixia, Shizhong, Huaiyin, Licheng, and Tianqiao), which together represent the city’s central business and cultural zones. As shown in

Table 2. Detail Information of 5 Districts in Jinan.

District	Location Within Urban Core	Area (km2)	Population (Year)	Key Functional Attributes
Lixia	Eastern core, adjacent to Licheng (E/N), Shizhong (S), Tianqiao (W)	100.89	0.82 million (2020)	Economic & cultural epicenter; Provincial government seat
Shizhong	South-central core; borders Lixia (E/N), Changqing (SW), Huaiyin (W)	281.49	0.91 million (2022)	Historic urban center with conserved traditional blocks
Huaiyin	Western core; connects Shizhong (E/S), borders Qihe County across Yellow River (W)	151.48	0.69 million (2022)	Emerging high-rise development zone
Tianqiao	Northern core: links Shizhong/Huaiyin (S), spans Yellow River (N)	261.92	0.73 million (2024)	Hybrid industrial-commercial cluster
Licheng	Eastern periphery; adjoins Lixia (W), Zhangqiu District (E)	1301.32	1.13 million (2024)	Dominant emerging residential-commercial expansion area

, the study area covers approximately 2117.58 km², accounting for 20.46% of Jinan’s total area and housing about 4.5 million residents, or 50% of the city’s population. This is a typical high-density urban area characterized by intense building energy consumption. The GIS data of sampled blocks were extracted from the 2024 Baidu Maps Geo-database, including building footprint geometries and height attributes.

2.3. Quantification of Urban Morphology Indicators

Urban block morphological indicators [40,41] provide quantitative descriptions of spatial configurations at the block scale. As shown in

Table 3. The 14 morphological indicators used in the study.

Nomenclature	Formula	Describe	Unit
$BA$	$BA={\displaystyle \frac{\sum _{i=1}^n{BA}_i}{N}}$	${BA}_i$$\mathrm{is} \mathrm{the} \mathrm{footprint} \mathrm{area} \mathrm{of} \mathrm{the} i$ building. $N$ is the number of buildings in the block.	${\mathrm{m}}^2$
${BA}_{sd}$	${BA}_{sd}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{({BA}_i-BA)}^2}{N}}}$	$BA$ is the average building area in the block.	${\mathrm{m}}^2$
$BSC$	$BSC={\displaystyle \frac{\sum _{i=1}^n(\frac{F_i}{V_i})}{N}}$	$F_i$$\mathrm{is} \mathrm{the} \mathrm{exterior} \mathrm{surface} \mathrm{area} \mathrm{of} \mathrm{the} i$ building. $V_i$$\mathrm{is} \mathrm{the} \mathrm{volume} \mathrm{of} \mathrm{the} i$ building.	None
$MBS$	$MBS={\displaystyle \frac{\sum _{i=1}^n\min d_{ij}}{N}}$	$min{d}_{ij}$ is the minimum spacing value between a single building and all its adjacent buildings.	m
$BTC$	$BTC={\displaystyle \frac{\sum _{i=1}^n{BTC}_i}{N}}$	${BTC}_i$$\mathrm{is} \mathrm{the} \mathrm{distance} \mathrm{from} \mathrm{the} i$ building to the block center.	m
${BTC}_{sd}$	${BTC}_{sd}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{({BTC}_i-BTC)}^2}{N}}}$	$BTC$ is the average distance from buildings within the block to the block center.	m
$BH$	$BH={\displaystyle \frac{\sum _{i=1}^n{BH}_i}{N}}$	${BH}_i \mathrm{is}$$\mathrm{the} \mathrm{height} \mathrm{of} \mathrm{the} i$ building.	m
${BH}_{sd}$	${BH}_{sd}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{({BH}_i-BH)}^2}{N}}}$	$BH \mathrm{is}$ the average height of buildings in the block.	m
$OAS$	$OAS={\displaystyle \frac{\sum _{i=1}^n\left|{OAS}_i\right|}{N}}$	${OAS}_i$$\mathrm{is} \mathrm{the} \mathrm{angle} \mathrm{between} \mathrm{the} \mathrm{main} \mathrm{facade} \mathrm{of} \mathrm{the} i$ building and true north.	°
${OAS}_{sd}$	${OAS}_{sd}=\sqrt{{\displaystyle \frac{\sum _{i=1}^n{({OAS}_i-\mathrm{OAS})}^2}{N}}}$	$OAS$ is the average angle between the main facades of buildings and true north.	°
$BAR$	$BAR={\displaystyle \frac{\sum _{i=1}^n{BA}_i}{BSA}}$	$BSA$ is the block site area.	None
$FAR$	$FAR={\displaystyle \frac{\sum _{i=1}^n{(BA}_i \times \frac{{BH}_i}{FH})}{BSA}}$	$FH$ is the floor height of buildings, set at 3 m.	None
$BSA$	None	None	${\mathrm{m}}^2$
$BN$	None	None	None

, considering the multidimensional nature of built environments, this study selected 14 morphological indicators categorized into five dimensions.

Building geometry was described using the average building area ($BA$), its standard deviation (${BA}_{sd}$), the average building shape coefficient ($BSC$), and the minimum spacing between buildings ($MBS$). Spatial arrangement was captured through the average building-to-block-center distance ($BTC$) and its standard deviation (${BTC}_{sd}$). The vertical profile included the average building height ($BH$) and its standard deviation (${BH}_{sd}$), while orientation patterns were described by the average orientation angle of buildings to the south ($OAS$) and its standard deviation (${OAS}_{sd}$). Finally, block-level information was captured through block site area ($BSA$), number of buildings ($BN$), building area ratio ($BAR$), and floor area ratio ($FAR$).

To address potential multicollinearity among these parameters, PCA was applied to extract key morphological features [42]. This classical dimensionality reduction algorithm projects original variables into orthogonal eigenvectors maximizing variance retention. The resulting principal components were subsequently used for cluster analysis to identify prototypical blocks.

2.4. Morphological Clustering Framework

Based on PCA-derived morphological features, unsupervised clustering algorithms were applied to classified blocks [43]. As shown in

Table 4. The 4 clustering algorithms used in the study.

Algorithm	Type	Key Mechanism	Limitations
K-means	Centroid-based	Optimized centroid initialization via seeding	Spherical cluster assumption
GMM (Gaussian mixture model)	Probabilistic	Expectation-Maximization fitting of Gaussian distributions	Requires predefined component count
DBSCAN Density-based cluster algorithm	Density-based	Eps-neighborhood connectivity with noise filtering	Sensitive to density parameters
SC Spectral clustering	Graph-based	Laplacian eigen-decomposition for manifold separation	Computational complexity

, four clustering algorithms were benchmarked to mitigate methodological bias. The study uses Silhouette Coefficient [44] and Davies-Bouldin Index [45] to evaluate the clustering results. Silhouette Coefficient (S∈ [−1,1]):

$$S(i)={\displaystyle \frac{b(i)-a(i)}{\max \left(a(i),b(i)\right)}}$$

(1)

where $a(i)$ denotes the mean intra-cluster distance for sample $i$, and $b(i)$ represents the mean nearest-cluster distance. Higher Silhouette values approaching 1 indicate better-defined and well-separated clusters.

Davies-Bouldin Index (DBI > 0):

$$DB={\displaystyle \frac{1}{k}}\sum _{i=1}^k\underset{j\ne i}{\max }\left({\displaystyle \frac{{\sigma }_i+{\sigma }_j}{d_{ij}}}\right)$$

(2)

where ${\sigma }_i$ is the mean intra-cluster distance of cluster $i$ and $d_{ij}$ is the centroid distance between clusters $i$ and $j$. Lower DBI values indicate improved cluster compactness and separation.

2.5. Urban-Scale PV Potential Modeling

In terms of radiation modeling, this study employs the Perez sky model [46] to calculate solar radiation, which accurately captures circumsolar brightening and horizon glow effects. Under partially cloudy conditions, the model achieves a root-mean-square error of less than 7% for diffuse irradiance estimates. Building surfaces in urban blocks receive four primary radiation components: 1. beam radiation ($G_b$), representing direct irradiance from the solar disc; 2. diffuse radiation ($G_d$) arising from anisotropic atmospheric scattering; 3. ground-reflected radiation ($G_r$), driven by terrain albedo; and (4) inter-building reflected radiation ($G_{adj}$), which includes specular and diffuse contributions from surrounding façades.

The complexity of urban morphology introduces three critical challenges for modeling urban radiation distribution: 1. multi-orientation effects, where surfaces with varying tilts from 0° rooftops to 90° façades necessitate per-plane calculations; 2. height-induced heterogeneity, with vertical shadow casting causing over 70% irradiance loss on lower floors (validated via LiDAR observations); and 3. non-uniform distribution, where simple area-scaling methods underestimate fluxes by 18–34% compared to ray-traced simulations.

Architectural diversity (e.g., pitched versus flat roofs, articulated façades) and inter-building interactions (mutual shading and reflections) produce highly non-linear radiation patterns. Traditional two-dimensional horizontal-plane models exhibit mean absolute errors exceeding 42% in dense urban environments, highlighting the need for three-dimensional radiative transfer algorithms incorporating Monte Carlo ray tracing. The total surface irradiance is defined as:

$$G_i=G_{bi}+G_{di}+G_{ri}+G_{adji}$$

(3)

where $G_i$ is the total irradiance (W/m²), $G_{bi}$ is the beam component, $G_{di}$ is the diffuse component, $G_{ri}$ is the ground reflected component, and $G_{adji}$ represents inter-building reflections.

In the 3D urban modeling framework, individual buildings were abstracted as rectangular prisms. This geometric simplification necessitates conversion of horizontal irradiance data from standard typical meteorological year (TMY) datasets to arbitrary surface orientations, including vertical façades (90° inclination). The beam irradiance component on tilted surfaces is calculated using the following geometric transformation:

$$G_{bi}=G_{b,TMY}\times {\displaystyle \frac{\cos {\theta }_i}{\sin {\alpha }_s}}$$

(4)

where $G_{b,TMY}$ represents the beam irradiance from TMY data (W/m²), ${\theta }_i$ is the surface tilt angle (0° ≤ ${\theta }_i$ ≤ 90°), and ${\alpha }_s$ is the solar altitude angle.

The ground-reflected irradiance component on tilted surfaces is quantified through albedo-driven formulation:

$$G_{ri}=(G_{bi}+G_{di})\times \rho \times {\displaystyle \frac{1-\cos \beta }{2}}$$

(5)

where $\rho$ = 0.2 denotes the urban terrain albedo as recommended by the (ASTM E1918 [47]) standard, and $\beta$ represents the surface tilt angle.

For diffuse radiation, the Reindl model [48] resolves circumsolar and horizon brightness effects:

$$G_{di}=G_d\left[\left(1-{\displaystyle \frac{G_b}{G_o}}\right)\left(1+\sqrt{{\displaystyle \frac{G_b}{G}}}\sin \left({\displaystyle \frac{\beta }{2}}\right)\right){\displaystyle \frac{1+\cos \beta }{2}}+{\displaystyle \frac{G_b}{G_o}}{R}_b\right]$$

(6)

where $G_d$ is the global horizontal diffuse irradiance (W/m²), $G_o$ is the extraterrestrial irradiance (ASTM E490 [49]), $R_b$ is the geometric factor ${\displaystyle \frac{\cos {\theta }_i}{\cos {\theta }_z}}$, and $\beta$ is the surface tilt angle.

The Perez sky model was implemented to resolve urban radiation complexities, demonstrating enhanced accuracy in obstructed environments through its tri-component sky luminance distribution.

In terms of PV conversion, the optimal tilt angle for standalone PV systems should approximate the local latitude, as specified in GB50797-2012 [50] (Code for Design of Photovoltaic Power Stations). For Jinan (36.01°N), the recommended fixed tilt angle is 41.01°. For building-integrated PV systems, GB/T51368-2019 [51] (Technical Standard for Application of Building Integrated Photovoltaic) suggests seasonal adjustments: 1. Summer: Latitude −15° (21.01°); 2. Winter: Latitude +15° (51.01°). Considering the focus on annual-scale evaluation of urban PV potential, a compromise fixed tilt angle of 40° was adopted for rooftop panels to balance seasonal variations.

According to the National Standards Information Public Service Platform, standard 182 mm silicon modules (60-cell configuration) measure 2.278 m × 1.134 m. For computational efficiency, these dimensions were simplified to 2 m × 1 m in this study. Rooftop perimeter zones lacking sufficient space were excluded from PV deployment. GB/T51368-2019 mandates true south orientation (azimuth 0°) for maximum energy yield, with >15% efficiency reduction observed at azimuth deviations exceeding ±15°. In this study, all flat rooftops were modeled with south-facing PV arrays and North-facing building surfaces (azimuth 180° ± 45°) were excluded due to negligible direct irradiance exposure.

Conventional PV yield analysis employs the Ladybug Tools (version 1.8.0) parametric plugin [52], which calculates irradiance components (beam, diffuse, ground-reflected) from EnergyPlus weather data using the Perez sky model. For district-scale simulations, the CPU-based Ladybug workflow requires prohibitive computational resources. This study instead implements the VITALITY plugin (version 2.3), a simulation tool embedded in Grasshopper within Rhino (version 8), which maintains identical algorithms but leverages NVIDIA CUDA parallelization to reduce simulation time cost.

VITALITY requires three types of input data: target buildings, surrounding buildings and ground platforms, and the EPW weather file of the study city. As shown in Figure 3, VITALITY calculates the solar potential of building rooftop in urban blocks through the following steps: (1) input the target buildings; (2) input the surrounding buildings and the ground, with the target buildings also included so that mutual shading effects among them are considered; (3) input the corresponding city EPW file; (4) mesh the target buildings, surrounding buildings, and ground platforms; (5) calculate the solar radiation on each building surface, taking shading effects into account; (6) generate 3D visualization results based on the radiation; (7) export the solar radiation values of each building surface; and (8) calculate the PV power generation of building surfaces according to the settings of different PV modules. This workflow provides a systematic approach for estimating rooftop solar potential at the urban block scale.

PV modules exhibit distinct power conversion efficiency thresholds due to material variations. This study evaluates four prevalent PV technologies: 1. Monocrystalline silicon (m-Si); 2. Polycrystalline silicon (p-Si); 3. Amorphous silicon (a-Si); 4. Cadmium sulfide/cadmium telluride (CdS/CdTe). For systems where capacity cannot be predetermined, the area-based estimation model is adopted:

$$E_p=H_A\times A_{pv}\times {\eta }_{pv}\times PR$$

(7)

where $E_p$ is the annual energy yield (kWh), $H_A$ is the annual solar irradiation (kWh/m²), $A_{pv}$ is the available installation area (m²), ${\eta }_{pv}$ is the module efficiency at standard test conditions (%), and $PR$ is the system performance ratio (%).

The Performance Ratio (PR), a dimensionless parameter ranging from 0 to 1, serves as a crucial indicator for evaluating the operational performance of grid-connected PV systems. As demonstrated by Kumar et al. [53] through statistical analysis of 23 utility-scale PV plants across 15 countries, the global PR distribution follows a normal distribution with mean value of 85.2%, while top-performing systems can achieve PR values above 90% through optimized design. Since the focus of this study is on the impact of block morphology on PV potential, a fixed PR value of 90% was adopted to simplify calculations and ensure comparability across block types. This value represents the performance level of optimized PV systems. As shown in

Table 5. The four PV panel material used in the study.

Module Type	Installation Cost (¥/m2)	Cost Benchmark (¥/m2)	Threshold Irradiance (W/m2)	Irradiance Benchmark (W/m2)	${\mathit{\eta }}_{\mathit{p}\mathit{v}}$(%)	${\mathit{\eta }}_{\mathit{p}\mathit{v}}$ Benchmark (%)
m-Si	1050–1500	1275	100	100	18–24	22
p-Si	400–600	500	120	120	15-20	17
a-Si	140–560	350	50–100	75	6–10	8
CdS/CdTe	250–300	275	50–80	65	9–16	13

, the study sets the Irradiance benchmark and ${\eta }_{pv}$ benchmark.

While energy yield serves as a direct indicator of PV module efficiency, determining the optimal PV system for urban blocks requires comprehensive economic analysis considering (i) capital expenditure disparities among different PV technologies, and (ii) local electricity market dynamics. As presented in Table 5, the total system costs were calculated based on 1. Current market prices of PV modules, 2. Balance-of-system components (inverters, mounting structures, etc.) and 3. Installation labor costs. The study adopts China’s electricity market trading rules where: 1. Price ceiling = 1.2 × base rate (0.49932 CNY/kWh); 2. Annual revenue = $P_E\times E_p$, where $E_p$ represents annual energy yield (kWh) and $P_E$ denotes electricity price (CNY/kWh). The payback period ($P_y$) was derived:

$$P_y={\displaystyle \frac{C_{PV}\times A_{PV}}{P_E\times E_p}}$$

(8)

where $C_{PV}$ is the PV module cost per square meter (CNY/m²), and $A_{PV}$ is the available building surface area (m²).

3. Results

3.1. Morphology Indicators Selection

The study calculated 14 morphological indicators for 749 urban blocks, filtering a validated dataset of 731 blocks after excluding incomplete records (data completeness = 97.6%). PCA was employed to address multicollinearity among these indicators and reduce dimensionality. As shown in Figure 4, the loading matrix reveals significant heterogeneity in variable contributions across components, highlighting differences in explanatory power. The scree plot (Figure 5) indicated that six principal components accounted for 82.3% of the total variance (PC1 = 22.7%, PC2 = 20.3%, PC3 = 11.4%, etc.). Since the first six principal components already provide strong explanatory power, this study focuses on these six components and calculates the composite importance score of each morphological indicator for selection. Choosing too few indicators may lead to information loss, while choosing too many may marginally improve model interpretability but with diminishing returns and increased model complexity. Therefore, six key indicators with composite importance scores greater than 0.3 were ultimately selected, namely $BAR$, $BSA$, $MBS$, $FAR$, ${OAS}_{sd}$ and $BTC$ (Figure 6). Together, they capture distinct dimensions of block morphology and serve as representative variables for subsequent analysis.

3.2. Morphology Clustering

Utilizing the six key morphological indicators identified through PCA, the study conducted comprehensive clustering analysis on 731 residential blocks. Due to the unsupervised feature of clustering algorithms, the study implemented a multi-algorithm verification approach to ensure robust classification. The study used Density-based cluster algorithm (DBSCAN) [54], Centroid-based cluster algorithm (K-means and K-means++) [55], Probabilistic cluster algorithm (GMM) [41] and Graph-based cluster algorithm (SC) [56].

To ensure optimal performance, the study performed 1000 iterative runs to adjust algorithm hyperparameters, including ε-neighborhood and minimum samples for DBSCAN, initial centroid selection for K-means and K-means++, and covariance type selection for the GMM. Clustering results from each iteration were evaluated using the Silhouette Coefficient and Davies-Bouldin Index, with the best-performing results selected for further analysis.

This study presents visualizations of the optimal clustering results obtained from each algorithm by t-SNE method [57]. As shown in Figure 7, the DBSCAN method failed to achieve effective clustering of urban block morphology. As shown in Figure 8, a comprehensive evaluation was conducted on the clustering performance of GMM, K-means, K-means++, and SC algorithms using Silhouette Score and Davies-Bouldin Index.

The key findings can be summarized as follows. In terms of Silhouette Score, both K-means and K-means++ demonstrated consistent performance, achieving scores exceeding 0.245 when k = 6, and outperforming the best clustering results from GMM and SC. The K-means algorithm with k = 6 showed marginally better Silhouette Scores compared to K-means++. In terms of the Davies-Bouldin Index, the K-means algorithm achieved the lowest value (below 1.15) when k = 6, indicating superior clustering quality relative to the best-performing cases of GMM, K-means++, and SC.

Based on the comparative evaluation of clustering indicators, the K-means clustering result with k = 6 was selected as the optimal solution. The analysis revealed that one cluster contained only 4 urban blocks (0.54% of the total dataset), which were deemed statistically insignificant and non-representative; these blocks were removed from further analysis.

The remaining five clusters were systematically analyzed through normalized average morphological indicators to facilitate comparative observation. Significant inter-cluster variations were identified in urban form characteristics, as shown in the Figure 9:

Cluster 1 exhibited distinctive features with $BSA$ significantly larger than other clusters, achieving 129.56% higher than the average value, and $BTC$ also substantially larger with 65.95% above the average. Cluster 2 demonstrated unique characteristics in ${OAS}_{sd}$, with values 107.66% higher than the average, and showed diverse building alignments without consistent perpendicularity to southern orientation. Cluster 3 was characterized by a much lower $BAR$ (46.28% lower than average) and a substantially greater $MBS$ (78.89% higher than average). Cluster 4 showed marked differentiation in $FAR$, with an average value 55.76% higher than the average. Cluster 5 displayed prominent features in $BAR$, which was higher than other clusters and achieved 40.79% above the average value.

Due to the imbalance in the number of blocks after clustering, Cluster 2 contained 235 blocks, accounting for 32.1% of the total, while Cluster 4 had only 80 blocks, accounting for 10.9%. If all blocks were used for modeling, large clusters would dominate the model and weaken the representativeness of smaller clusters. In addition, conducting detailed simulations for all blocks would result in extremely high computational costs. Against this background, this study selected representative samples for modeling while ensuring diversity coverage. Specifically, 10 blocks closest to each cluster center were chosen, giving a total of 50 blocks, which were then used for PV potential simulations and ridge regression analysis.

To further validate the representativeness of the selected samples, each cluster’s typical blocks were parametrically visualized with the following color-coded scheme: red curves for urban street networks, blue curves for target block boundaries, green arrows for the southern orientation, and a grayscale gradient for building height (darker shades indicating shorter buildings). As demonstrated in Figure 10, the selected representative blocks effectively capture the distinctive morphological characteristics of their respective clusters. This visualization confirms that the centroid-proximity selection criterion successfully identifies prototypical examples.

3.3. Block PV Power Result

As shown in Figure 11, PV simulations were conducted for typical blocks selected from each cluster, followed by comparative analysis of energy generation and economic indicators (Figure 12). Under identical m-Si PV panel conditions, significant variations in annual energy yield were observed among clusters. Clusters 1 (48,065,400 kWh) and 4 (36,603,850 kWh) exhibited superior generation capacities—61.76% and 23.19% higher than the average (29,713,264 kWh), respectively—while Cluster 3 (14,274,313 kWh) recorded the lowest output, 51.96% below average. The high performance of cluster 1 was attributed to its large $BSA$, which allowed for more buildings and thus larger cumulative roof surfaces. In contrast, the low $BAR$ (0.2087 vs. average 0.3885) in Cluster 3 restricted viable installation potential.

Investment costs also differed significantly among clusters. Cluster 1 required 75.08% higher investment than the average, while cluster 3 showed 54.52% lower costs. These differences were primarily due to system scale, as larger roof areas increased system size and cost, whereas a smaller number of buildings reduced overall investment needs.

Economic feasibility, as measured by payback period, also varied across clusters. When m-Si panels were employed, Clusters 4 and 5 achieved the shortest payback times (2.91 and 2.97 years), representing reductions of 8% and 6% compared with the average, respectively. In contrast, cluster 1 and cluster 2 had longer payback periods (3.54 and 3.37 years), corresponding to 11.8% and 6.4% above the average. These results suggest that although cluster 1 offers high energy yield, the large capital requirement offsets the benefit, while cluster 2 shows moderate investment but insufficient annual revenue.

In terms of urban block deployment using standardized m-Si panels, clusters 4 and 5 demonstrated the most balanced outcomes—achieving moderate energy yields, controlled investment costs, and short payback periods (2.91–2.97 years), making them suitable for priority PV deployment. Cluster 1 delivered the highest energy yield (61.76% above average) but required substantial capital (75.08% higher than average), suggesting its applicability in large-scale, long-term institutional or commercial projects. In contrast, cluster 3 presented the lowest rooftop PV potential due to low building density ($BAR$ = 0.208), indicating the need for alternative renewable strategies.

The study revealed substantial differences in energy performance and investment metrics across four PV panel materials (Figure 12). While p-Si (25,369,021 kWh) exhibited 14.62% lower energy output than m-Si (29,713,263 kWh), it significantly outperformed a-Si (11,461,642 kWh) and CdS/CdTe (19,880,199 kWh) by 121.34% and 27.61%, respectively. Moreover, p-Si offered a 32.43% cost reduction and a 19.58% shorter payback period compared to m-Si, highlighting its suitability for investment-sensitive contexts. In contrast, a-Si showed the lowest energy output (42.35–61.43% lower than other materials) and the longest payback periods (25.93–56.59% longer), making it the least viable option. The CdS/CdTe material outperformed a-Si by 73.45% in energy output and offered 16.43–34.24% lower investment costs than m-Si and p-Si. However, its performance remained 21.64–33.09% below that of the crystalline silicon variants.

Overall, the study recommends against using a-Si due to poor economic performance, and advises caution with CdS/CdTe due to environmental and recycling concerns. For practical implementation, m-Si is recommended for long-term applications, while p-Si is better suited for urban-scale solar deployment with limited budgets.

3.4. Regression Predict Model

This study develops predictive models linking the morphological indicators of typical urban blocks to objective functions, including power generation, system cost, and payback period. Regression algorithms are employed to establish these models using Python (version 3.9.10) and the Scikit-learn library (version 1.5.1). Given the observed correlations among selected morphological indicators, ridge regression is employed to mitigate multicollinearity issues [58]. The ridge regression is a modified linear regression technique incorporating L2 regularization (penalty term: λ∑β²) to compress coefficients and enhance model stability. The ridge regression can eliminate over-fitting while retaining all predictor variables. The values of hyperparameter (λ) in the ridge regression will be optimized via 5-fold cross-validation (k = 5). Based on previous analysis, a-Si and CdS/CdTe PV materials were excluded due to their limited suitability for urban rooftop PV systems in Jinan.

In terms of PV power generation, the study established two ridge regression models predicting power generation capacity for m-Si and p-Si using morphological indicators. As shown in Figure 13, the study found that the ridge regression demonstrates robust predictive capacity (p < 0.001) for rooftop energy yield (The values of R² in m-Si and p-Si ridge regression models are 0.6489 and 0.6314).

The formulation of m-Si PV Power Generation prediction model is:

$$\begin{gathered} {Energy}_{m-Si} = (2.8445 + 1.2100 \times BAR + 3.9782 \times BSA + 0.9683 \\ \times MBS + 0.4776 \times FAR + 0.4096 \times {OAS}_{sd}-2.6694 \times BTC) \times {10}^7 \end{gathered}$$

(9)

The formulation of p-Si PV Power Generation prediction model is:

$$\begin{gathered} {Energy}_{p-Si} =(2.9754 + 0.0715 \times BAR + 4.3646 \times BSA + 0.2601 \\ \times MBS + 0.3199 \times FAR + 0.0323 \times {OAS}_{sd}-2.8873 \times BTC) \times {10}^7 \end{gathered}$$

(10)

As illustrated in Figure 13, regression analysis identified $BTC$ and $BSA$ as the dominant urban morphology indicators affecting block PV power generation. Both indicators showed strong and consistent effects across the m-Si and p-Si models. $BTC$ exhibited significant negative correlations (β = −2.67 for m-Si and −2.89 for p-Si), as larger $BTC$ values indicate a more dispersed building layout, which reduces the cumulative rooftop area and thereby lowers the PV power generation potential. Conversely, $BSA$ showed the strongest positive effect (β = 3.98 for m-Si and 4.37 for p-Si), because larger block site areas can accommodate more or larger buildings, providing more rooftop area for PV installation. Secondary indicators, such as $BAR$ and $MBS$, also contributed positively to the m-Si model (β = 1.21 and 0.97, respectively). Larger $BAR$ represents larger rooftop surfaces, increasing the potential PV capacity, while higher $MBS$ reduces mutual shading between buildings, improving the effective generation efficiency. Both effects lead to an overall increase in solar power generation.

In terms of PV system investments, the study established two ridge regression models. As shown in Figure 14, the ridge regression shows robust predictive capacity (p < 0.001) for investments (The values of R² in m-Si and p-Si ridge regression models are 0.6718 and 0.6596).

The formulation of m-Si PV system investment prediction model is:

$$\begin{gathered} {Investment}_{m-Si} = (3.7599 + 1.2594 \times BAR + 4.7418 \times BSA + 0.8439 \\ \times MBS + 0.4189 \times FAR + 0.4556 \times {OAS}_{sd}-2.623 \times BTC) \times {10}^7 \end{gathered}$$

(11)

The formulation of p-Si PV system investment prediction model is:

$$\begin{gathered} {Investment}_{p-Si} =(2.7835 + 0.2768 \times BAR + 3.8318 \times BSA- 0.5100 \\ \times MBS + 0.0125 \times FAR + 0.4210 \times {OAS}_{sd}-2.7105 \times BTC) \times {10}^7 \end{gathered}$$

(12)

As shown in Figure 14, the regression analysis identified $BTC$ and $BSA$ as the most influential morphological indicators affecting PV system investment. $BTC$ exhibited a strong negative influence in both models (β = –2.62 for m-Si and –2.71 for p-Si), suggesting that larger $BTC$ values reduce available rooftop space due to more dispersed building layouts, thereby lowering total installation costs. In contrast, $BSA$ showed strong positive correlations (β = 4.742 for m-Si and 3.832 for p-Si). Larger $BSA$ values typically indicate blocks with broader development footprints and greater cumulative roof area, enabling larger PV system deployment but also driving up equipment and installation expenses. Secondary indicators such as $BAR$ contributed modestly (β = 1.259). Higher $BAR$ reflects a denser rooftop configuration, which increases the effective installation surface but also leads to greater system capacity and corresponding investment. Meanwhile, $MBS$ exerted a weak negative influence (β = –0.51), implying that wider building separation could reduce usable roof area and lower investment demands.

In terms of PV System payback period, the study established two ridge regression models. As shown in Figure 15, the ridge regression shows good predictive performance (p < 0.001) (The values of R² in m-Si and p-Si ridge regression models are 0.6344 and 0.5843).

The model formulation of m-Si PV system payback period is:

$$\begin{gathered} {Period}_{m-Si} = 3.1823 + 0.1199 \times BAR + 0.2583 \times BSA-0.0916 \\ \times MBS + 0.0296 \times FAR-0.0372 \times {OAS}_{sd} + 0.1490 \times BTC \end{gathered}$$

(13)

The model formulation of the p-Si PV system payback period is:

$$\begin{gathered} {Period}_{p-Si}=2.5636-0.2542 \times BAR-0.3189 \times BSA-0.3865 \\ \times MBS-0.3056 \times FAR + 0.001 \times {OAS}_{sd} + 0.2731 \times BTC \end{gathered}$$

(14)

As illustrated in Figure 15, the ridge regression analysis identified $BTC$ and $BAR$ as two critical morphological indicators strongly influencing the payback period of rooftop PV systems. $BTC$ showed positive β values (0.1490 for m-Si and 0.2721 for p-Si), suggesting that as $BTC$ increases, the available rooftop area decreases, leading to lower power generation and an extended payback period. Conversely, $BAR$ exhibited negative coefficients (−0.1199 for m-Si and −0.2542 for p-Si), indicating that a greater building area ratio shortens the payback period by enhancing roof utilization.

In addition, $FAR$ was found to be an important predictor in the p-Si regression model, with a β value of −0.3056. Although an increase in $FAR$ may lead to higher costs, it simultaneously expands rooftop space for PV deployment, improving generation efficiency and ultimately shortening the payback period due to the lower unit cost of p-Si panels.

Similarly, $MBS$ showed high importance in p-Si models, particularly in the polycrystalline regression model (β = −0.3865). Greater $MBS$ values reduce shading effects between buildings, thereby improving solar access and reducing the payback period.

$BSA$ emerged as a significant factor in both models, particularly in the m-Si model, where the value of β reaches the highest value of 0.2583. On the other hand, in the p-Si model, β reaches −0.3189. An increase in $BSA$ means an increase in available roof PV panels area. Due to the significant difference in costs between the two materials, $BSA$ affects the payback periods differently. Since m-Si is more expensive than p-Si, an increase in PV panel area will greatly increase investment, leading to payback period extension. On the other hand, p-Si is less expensive and has reasonable power generation efficiency. An increase in PV panel area will increase costs but will also increase power generation, resulting in a decrease in the payback period value.

4. Discussion

4.1. Impacts of Seasonal Generation Patterns on Urban PV Utilization

The study analyzed the monthly average power generation of four PV materials across 50 urban blocks. As shown in Figure 16, all panel types exhibited consistent seasonal patterns, with noticeable variations across the year. For m-Si panels, underperformance was observed in January (1,829,790 kWh), April (1,821,231 kWh), and May (1,851,981 kWh), where generation was 26.85–27.19% lower than the annual average (2,501,360 kWh). Output began to increase steadily from June (2,129,260 kWh) onwards, with monthly gains ranging from 4% to 8%. Compared with m-Si, p-Si panels generally produced 13.68–22.65% less power, though they exhibited comparable or slightly higher output (0–2.4%) from February to April. In contrast, a-Si panels recorded the lowest performance across all months, with output falling 57.32–63.57% below m-Si, 52.59–58.50% below p-Si, and 38.44–47.80% below CdS/CdTe, indicating limited viability under real-world conditions.

Further analysis of monthly deviations from the annual average (Figure 17) highlighted distinct periods of underperformance and overperformance, revealing pronounced seasonal differences among the four PV materials. In January, all materials recorded substantially lower generation than the mean, with reductions ranging from 26.8% to 35.3%. In contrast, February and March showed above-average performance for most materials, with p-Si (13.7–20.7%) and CdS/CdTe (15.4–20.1%) exhibiting the highest increases, while a-Si also showed improvements (4.4–14.9%), and m-Si remained approximately at the average level. During April to June, all materials consistently underperformed (–27.2% to –11.0%), indicating a seasonal trough. In July and August, generation was close to the mean (–8.5% to 3.4%), reflecting relative stability but limited advantage. The period from September to December was the most favorable, with all materials significantly exceeding the annual mean: m-Si increased by 14.0–29.8%, p-Si by 8.5–20.4%, a-Si by 10.7–26.3%, and CdS/CdTe by 8.3–21.0%.

These findings indicate two annual peak periods for PV generation: late winter to early spring (February–March) and autumn to early winter (September–December). Therefore, grid integration planning and operation and maintenance strategies should prioritize these critical months to ensure the efficient operation and stable energy supply of urban PV systems.

4.2. Spatial Distribution and Morphological Characteristics of Block Clusters

The study conducted systematic clustering and spatial analysis of the 749 urban blocks using the following methodology: (1) Blocks were categorized based on cluster identification numbers; (2) Blocks were grouped using a proximity-based method with a threshold distance of 600 m; (3) Only blocks containing more than three buildings were considered for further analysis; (4) Group boundaries were delineated based on the geometric centroids of the included blocks.

As shown in Figure 18, the spatial distribution of the resulting groups across administrative districts reveals the following patterns: Cluster 1 groups are entirely located in Licheng District (2 groups). Cluster 2 includes 7 groups, of which 4 are situated on the district borders of Tianqiao and Shizhong, and 3 on the border between Licheng and Lixia. Cluster 3 comprises 9 groups, mainly distributed across Lixia District (5 groups), Huaiyin District (2 groups), and Shizhong District (2 groups). Cluster 4 consists of 4 groups, including 1 in Huaiyin District and 3 along the border of Lixia District. Cluster 5 includes 9 groups, with 4 groups located in Tianqiao District, 4 groups in Lixia District, and the remaining 1 group situated in Huaiyin District.

The study systematically calculated the minimum average distances between each cluster boundary and key urban functional elements in Jinan, including: (1) Commercial land (CL); (2) Industrial zones (IZ); (3) Forest areas (FA); (4) Park spaces (PS); (5) River networks (RN); (6) Highway networks (HN).

As shown in Figure 19, the spatial analysis revealed clear differentiation among clusters. Cluster 4 exhibited the best commercial accessibility, with its groups located closest to commercial land (mean distance: 365.68 m), whereas cluster 1 was the farthest (mean distance: 1545.98 m), suggesting that cluster 4 blocks are better suited for retail or service-oriented development. In terms of industrial zone adjacency, cluster 2 groups were nearest to industrial areas (mean distance: 649.81 m), reflecting their mixed-use industrial–residential context, while cluster 3 was the farthest (mean: 1738.56 m). Regarding forest area proximity, cluster 3 blocks were generally closer to forest land (mean: 1021.03 m), whereas cluster 5 was the farthest (mean: 1565.46 m). River network connectivity also varied: cluster 2 was the nearest (530.06 m) and cluster 3 the farthest (1075.57 m). Finally, in terms of access to highway networks, cluster 2 again ranked the closest (541.61 m), while cluster 1 had the least accessibility (mean distance: 1322.52 m). These spatial relationships offer insights into the environmental and infrastructural contexts shaping each cluster’s development potential.

Based on the distance between group boundaries and urban functional elements, the study reveals several significant morphological patterns. Cluster 1 primarily consists of suburban residential blocks. Being located far from the city center, these blocks exhibit the highest $BSA$ among all clusters. Cluster 2 demonstrates notable morphological diversity; the irregular shape of its blocks, influenced by their proximity to highway networks or river systems, has led to substantial variations in building orientations, resulting in high orientation angle standard deviations (${OAS}_{sd}$). Cluster 3 is situated in a peri-urban transition zone. These blocks, mainly positioned along the urban periphery, feature significantly lower $BAR$ and higher $MBS$ than other clusters. Cluster 4 is mostly located in the Central Business District and is characterized by high-density mixed-use development with elevated $FAR$ values. Lastly, cluster 5 is also situated in central urban areas, but shows a different density pattern: it exhibits high $BAR$ but relatively low $FAR$, reflecting its composition of traditional residential blocks with mid-rise housing typologies, typically ranging from four to six stories.

4.3. Applicability of the Framework to Diverse Urban Typologies

This study proposes a framework that is not only applicable to the case of Jinan but also shows potential for application in other urban contexts, warranting further exploration. First, the energy simulation component can be adapted to different climatic conditions by substituting local meteorological data, thereby enabling PV potential assessments across diverse climate zones.

Second, the six key morphological indicators adopted in this study were identified through a combination of literature review and PCA. For PV potential studies in cities across regions such as Asia and Europe, local literature can be consulted and PCA employed to extract indicators suited to the specific urban morphological context, ensuring scientific and context-sensitive classification and evaluation, followed by clustering to identify representative prototype blocks.

Furthermore, the economic evaluation component can be flexibly adjusted to reflect local market conditions. Parameters such as PV module prices, installation costs, electricity tariffs, and policy incentives can be updated accordingly, allowing the framework to adapt to different economic environments and policy settings.

Overall, after adjustments to climate, morphology, and market conditions, the framework holds potential for application across diverse urban types and merits further validation and refinement in additional city contexts.

4.4. Limitations and Future Work

Despite the positive results achieved in this study, several limitations remain and warrant further investigation in future research. First, the proposed PV potential assessment method was applied only to residential blocks in Jinan, China, and its applicability to cities or regions with different morphological and climatic contexts requires further validation. The analysis was based on building footprint and height information; incorporating higher-resolution rooftop morphology and building geometry data in future work could enhance simulation accuracy. Second, for the sake of simplifying the simulation process, the performance degradation of PV modules over time was not considered in this study. Future work will enhance the reliability of generation forecasts by incorporating appropriate linear degradation models. In addition, subsequent studies could integrate PV deployment strategies into broader urban energy system planning, including considerations of battery storage, grid integration, and load management, to support more comprehensive low-carbon transition goals. Finally, with the continuous progress of PV and storage technologies, anticipated improvements in efficiency and reductions in cost are likely to influence both the technical and economic outcomes of urban PV deployment. Future studies will continue to monitor these developments and refine the framework accordingly.

5. Conclusions

This study evaluated the rooftop PV potential of residential blocks in Jinan by combining morphological indicators, clustering, and numerical simulation. The main conclusions are as follows:

(1)

Block differences: Six key morphological indicators effectively characterized block features, and clustering divided the samples into five typical types. Significant differences in PV potential were observed among different block types. Cluster 1 achieved the highest annual generation (61.76% above the average) but required 75.08% higher investment with a payback period of 3.54 years. Clusters 4 and 5 generated moderate output and achieved the shortest payback periods (2.91–2.97 years), showing better coordination between energy and economic performance.

(2)

Material selection: In terms of materials, m-Si is most suitable for scenarios pursuing maximum energy yield, while p-Si produced slightly lower output but reduced costs by 32.43% and shortened the payback period by 19.58%, making it more suitable for investment-sensitive projects.

(3)

Seasonal patterns: PV generation showed two peak periods throughout the year, namely February–March and September–December. These critical months should be the focus of grid operation and maintenance to ensure stable PV supply in cities.

(4)

Policy implications: The proposed assessment framework is applicable to the Jinan case and shows potential for application in other cities. With appropriate adjustment of local climate data, morphological indicators, and market conditions, it may serve as a reference for planners and contribute to urban energy transition and sustainable development.