Morphology-Oriented Layout Optimization for Enhancing Building-Cluster Photovoltaic Potential in Severe Cold Regions

Abstract

Under China’s carbon peaking and carbon neutrality goals, building-integrated photovoltaics (BIPV) are a key option for low-carbon urban transition. However, how urban morphology shapes effective PV potential in severe cold cities remains poorly understood. Previous work focuses on single buildings or citywide resource mapping and rarely yields actionable planning controls. Using Harbin as a case, this study integrates GIS with explainable machine learning to relate building-cluster morphology to effective PV generation potential. An XGBoost model is interpreted with SHAP and partial dependence analysis to quantify factor importance and response ranges. Building density (BD) and floor area ratio (FAR) are the dominant predictors, ranking above the other morphological indicators. PV density peaks at moderate BD (≈0.20–0.35) under medium-to-high development intensity, and it increases when building distribution is moderately even (NNI ≈ 1.3–1.5) with moderate height differentiation. These coupled responses define a Morphological Sweet Spot, indicating that higher PV performance depends on coordinated morphological configurations rather than on any single parameter. The framework provides an interpretable, data-driven basis for building-cluster BIPV assessment and for translating model outputs into morphology-based planning guidance for low-carbon renewal in severe cold regions.

1. Introduction

Global climate change and the energy transition have made the building sector a key field for achieving carbon reduction targets. In 2022, buildings and construction accounted for about 34% of global final energy demand and 37% of energy- and process-related CO₂ emissions [1,2]. The International Energy Agency notes that despite progress, much stronger action is needed for the sector to align with net-zero pathways [3]. In China, the carbon peaking and carbon neutrality strategy calls for improvements in building energy efficiency and the substitution of renewable energy, while the Action Plan for Carbon Dioxide Peaking Before 2030 identifies distributed photovoltaic systems as an important pathway for low-carbon transition in the building sector [4,5]. For severe cold cities, reducing operational energy use and integrating renewable energy into the built environment are key low-carbon urban strategies [6].

Building-integrated photovoltaics (BIPV) generate on-site clean electricity by integrating PV modules into roofs and facades, and are widely seen as a key technology for nearly zero-energy buildings [7,8]. Compared with conventional add-on rooftop photovoltaic systems, BIPV places greater emphasis on the systematic use of installable building surfaces [9]. With the development of urban-scale research, GIS-driven assessment methods have become increasingly mature and, in some studies, have been combined with three-dimensional urban models to support more refined evaluations of building surfaces. Through surface identification and solar radiation simulation, these approaches can estimate the solar potential of surfaces with different orientations [10,11]. Recent global-scale research further indicates that, in high-density cities, facade photovoltaic potential can equal or even exceed rooftop potential, underscoring the importance of integrated roof–facade assessments [12].

Building height, density, and spatial compactness affect solar accessibility. They alter sky view and mutual shading relationships. As a result, they influence solar potential at the urban block and courtyard scales [13,14,15]. Previous studies have shown that three-dimensional urban form is a key factor influencing spatial variation in photovoltaic potential at the block scale [16,17]. Climatic conditions in severe cold regions also affect photovoltaic system performance. The power output of photovoltaic modules is closely related to their operating temperature. Recent thermal-modeling and data-driven studies have shown that meteorological variables are important factors affecting module temperature and power generation efficiency. Among these variables, ambient temperature and solar radiation are especially important [18,19]. In high-latitude or cold regions, winter snow cover can cause persistent shading on photovoltaic modules. This can result in substantial generation losses [20]. Therefore, photovoltaic potential assessment in severe cold regions should consider the combined effects of shading, temperature, and snow cover.

Building on photovoltaic potential assessment, recent studies have used parametric modeling and evolutionary algorithms to optimize urban form. Their goal is to improve photovoltaic performance, solar utilization, and outdoor environmental quality [21,22]. Multi-objective evolutionary algorithms have been widely applied in building performance optimization and related built-environment design problems [23]. However, most conventional optimization studies focus on identifying optimal solutions. Their results are often difficult to translate directly into planning control indicators. In recent years, explainable machine learning methods have been increasingly used to identify variable contributions and critical influence ranges. Among these methods, SHAP can help quantify feature contributions. Partial dependence analysis can be used to examine the nonlinear response trends of variables [24].

Despite substantial progress in urban-scale photovoltaic potential research, several gaps remain. First, most studies still focus on rooftop photovoltaics. In contrast, facade potential has received limited attention in planning-scale research. Second, some urban assessment approaches adopt idealized irradiation assumptions. They also neglect snow-related losses and temperature corrections in cold climates. This can lead to overestimation of photovoltaic potential [20]. Meanwhile, shading estimation in urban environments often depends on detailed simulation workflows. Current calculation methods may face limitations in efficiency and scalability when applied to large urban models. This constrains their use in block-scale planning applications [16,25]. Existing studies also rarely report reproducible morphological thresholds. As a result, assessment results cannot easily be translated into guidance for urban renewal and design decision-making.

To address these gaps, this study took Harbin as a case study. Harbin is a severe cold and snow-prone city. Based on this case, the study developed a building-cluster-scale framework for assessing effective BIPV generation potential. The study integrated GIS-based analysis with morphological factor modeling. It considered solar irradiation, building shading, module temperature response, and snow-related losses. In this way, theoretical potential is translated into effective potential. It further identified key morphological factors, nonlinear response patterns, and critical threshold ranges that shape PV performance. The results provide a quantitative basis for morphology-oriented planning. They also support a shift in BIPV research from resource assessment to planning-oriented implementation in severe cold regions.

2. Materials and Methods

2.1. Study Area and Research Framework

Harbin, the capital city of Heilongjiang Province in northeastern China, was selected as the study area. Located at the southern end of the Songnen Plain and on the western foothills of the Lesser Khingan Mountains, Harbin is situated at 45°44′ N and 126°41′ E. Harbin belongs to the typical mid-temperate continental monsoon climate zone. It is characterized by long and severe winters. According to the Heilongjiang Provincial Standard for Energy Efficiency Design of Residential Buildings (DB23/1270-2019), the calculated heating period in Harbin is 167 days [26]. This indicates substantial heating demand. Previous studies have shown that Harbin has an annual total solar radiation of approximately 1426.18 kWh·m⁻² and an annual sunshine duration of 2641–2732 h [27]. These conditions are favorable for solar energy utilization.

Existing studies have shown that the built environment in Harbin exhibits pronounced differences in building height, massing, and spatial distribution [28]. These differences provide an important basis for analyzing variations in solar accessibility and photovoltaic utilization under different building-cluster morphological conditions. In addition, cold-climate characteristics such as prolonged low temperatures, snow cover, and winter icing have important effects on PV system operation. Low temperatures may improve the conversion efficiency of photovoltaic modules. In contrast, seasonal snow cover can significantly reduce solar exposure and cause electricity generation losses [29,30]. Therefore, Harbin represents a typical case for assessing the effective power generation potential of building-integrated photovoltaics (BIPV) at the building-cluster scale under cold-climate constraints.

Figure 1 shows the location and spatial extent of the study area. To further illustrate the climatic background of Harbin, Figure 2 presents the annual distributions of dry-bulb temperature, relative humidity, and solar radiation conditions. These radiation conditions include total, direct, and diffuse radiation. These climatic characteristics provide the environmental basis for subsequent cold-region correction and effective BIPV potential assessment.

On that basis, this study proposed an integrated framework for assessing the effective power generation potential of BIPV at the building-cluster scale. It also aimed to derive morphology-oriented planning implications. As shown in Figure 3, the framework consisted of four main steps. First, QGIS 3.34.1 and 3D building data were used to construct building-cluster units. They are also used to identify roof and facade surfaces suitable for PV installation. Second, theoretical photovoltaic potential was estimated under baseline radiation conditions. It is then corrected for temperature response, snow loss, and building-cluster-scale shading effects. In this way, effective generation potential is obtained. Third, urban morphological indicators were introduced to model and interpret the relationship between building-cluster form and photovoltaic performance. This helps identify key variables, critical response ranges, and coupled morphological effects. Finally, the interpreted results were translated into Morphological Sweet Spots and building-cluster typologies. These results support planning-oriented decision-making. In this way, the framework forms an integrated technical pathway. It includes problem identification, potential assessment, pattern extraction, and planning support. It also provides a quantitative methodological basis for urban renewal and building-cluster-scale BIPV deployment in cold regions.

2.2. Data Sources and Effective Photovoltaic Potential Assessment

This study used three main types of data: spatial data, solar radiation data, and meteorological data. The spatial data include the study area boundary, road network, building footprints, and building height information. Road and building vector data were primarily extracted from OpenStreetMap. They were then further processed in a GIS environment to construct building-cluster analytical units. Specifically, the road network of the study area was first extracted. A 10 m buffer was then generated from the road centerlines. The buffered road network was used as the spatial boundary to subdivide continuous built-up areas into building-cluster units. This treatment reflects the urban block structure defined by roads. It also makes the analytical units more consistent with the spatial scale of block renewal and planning control. Building height data were used to identify installable roof and facade surfaces. They were also used to extract building-cluster morphological indicators and support subsequent shading-related analysis. After projection unification, spatial clipping, and attribute matching, building height data and building footprint data were combined to form a building-level database. The database was then aggregated to the building-cluster scale. To ensure spatial consistency among different data sources, all spatial data were transformed into a unified coordinate reference system. They were also cleaned within the study boundary. Samples with missing attributes, geometric errors, or invalid aggregation results were removed before modeling.

Annual cumulative solar radiation in 2024 was used as the input for theoretical photovoltaic potential estimation. The radiation data were obtained from the China 1 km Surface Solar Radiation Dataset (CN_2000–2024_1km_SSR). This dataset provides monthly surface solar radiation values. The monthly values were summed to obtain annual radiation. The annual radiation was then converted into kWh·m⁻² for theoretical PV generation calculations at the building-cluster scale. The dataset was generated from ERA5-Land solar radiation data using the Delta downscaling method. WorldClim v2.1 was used as the reference baseline. Meteorological data were mainly used for cold-climate correction. These data included monthly mean air temperature and snow-related information. Monthly mean temperature data were obtained from publicly available NOAA/NCEI station records. They were organized at the monthly scale to support temperature correction. Snow data were used to construct monthly snow-loss coefficients. These coefficients were then aggregated into an annual snow-loss factor. Together, these datasets were used to convert theoretical photovoltaic potential into effective photovoltaic potential under severe cold-climate constraints.

At the stage of installable-surface identification, both roofs and facades were included in the assessment. This integrated rooftop–facade treatment is consistent with recent studies. These studies suggest that BIPV assessment in dense urban environments should move beyond rooftop-only approaches. They also emphasize the need to consider the full building envelope [8]. Roofs are the primary surfaces for urban photovoltaic deployment. Their installable area was calculated from the roof projection area. It was then reduced by an engineering constraint coefficient. For the $i$-th building, the installable roof area can be expressed as follows:

$$A_{roof,i}=A_{footprint,i}\times r_{roof}$$

(1)

where $A_{roof,i}$ is the installable roof area of building $i$, $A_{footprint,i}$ is the building footprint area of building $i$, and $r_{roof}$ is the roof utilization coefficient.

In actual projects, roofs cannot be fully covered by PV panels. Space must be reserved for equipment placement, maintenance access, and fire safety setbacks. Therefore, based on previous studies and engineering practice, the roof utilization coefficient was set to 0.7. This value has been widely adopted in urban-scale photovoltaic potential assessments. It helps avoid overestimation caused by the assumption of full coverage. The total installable roof area at the building-cluster scale was obtained by summing the installable roof areas of all buildings within the cluster:

$$A_{roof}={\displaystyle \sum _{i=1}^n}{A}_{roof,i}$$

(2)

where $A_{roof}$ is the total installable roof area of the building cluster, and $n$ is the number of buildings within the cluster.

Compared with roofs, facades are an important supplementary PV resource in high-density urban environments. Recent studies further indicate that facade-level potential can become comparable to rooftop potential in some dense urban contexts. In some cases, it may even exceed rooftop potential. This reinforces the need for integrated surface assessment [31]. The installable facade area was calculated from building geometry using building height and perimeter:

$$A_{facade,i}=P_i\cdot H_i\cdot r_{facade}$$

(3)

where $A_{facade,i}$ is the installable facade area of building $i$, $P_i$ is the building perimeter, $H_i$ is the building height, and $r_{facade}$ is the facade utilization coefficient. In this study, $r_{\mathrm{facade}}$ was set to 0.4 as an engineering assumption based on previous facade-PV studies. These studies indicate that the practically utilizable fraction of the facade area is substantially reduced by the window-to-wall ratio, facade articulation, shading, and other architectural constraints. As a result, the usable facade fraction commonly falls within an approximate range of 10–40% [32,33].

In high-latitude severe cold regions, solar radiation shows strong directional differences. Facade orientation therefore has a decisive influence on photovoltaic generation potential. This is also supported by recent urban-scale BIPV studies. These studies show that orientation-sensitive facade assessment is critical for improving the realism of building-surface photovoltaic evaluation [34]. Because the winter solar altitude angle is low, north-facing and near-north-facing facades remain under weak-radiation conditions for long periods. Their PV efficiency is therefore much lower than that of south-facing and side-facing facades. To improve the reliability of the assessment, facades were classified by the azimuth of the external building edges using an eight-direction system (N, NE, E, SE, S, SW, W, NW). Based on this classification, the installable facade area was filtered by orientation. Only orientations with relatively high solar radiation potential were retained:

$$A_{facade,i}^{valid}=\left\{\begin{array}{cc}{A}_{facade,i}^{*},& orientation\in \{E,SE,S,SW,W\}\\ 0,& orientation\in \{N,NE,NW\}\end{array}\right.$$

(4)

where $A_{facade,i}^{*}$ is the corrected facade area, and orientation is the facade orientation category.

To represent the effect of inter-building shading on photovoltaic generation within each building cluster, this study did not use time-dynamic three-dimensional solar shadow simulation. Instead, a morphology-based proxy method was introduced for shading correction. This choice was made because the study aims to conduct a comparative analysis across a large number of building clusters at the planning scale. At this scale, computational efficiency and morphological interpretability are more important than highly detailed dynamic simulation at the individual-building level. Similar planning-oriented studies have also emphasized the need to balance computational efficiency and practical applicability in large-sample urban assessments of morphology-related PV effects [22].

First, a shading-intensity indicator was constructed based on the internal height contrast within each building cluster:

$$S{I}_{shd}={\displaystyle \frac{H_{cluster,max}-H_{cluster,mean}}{H_{cluster,max}}}$$

(5)

where $S{I}_{shd}$ is the shading-intensity indicator, $H_{cluster,max}$ is the maximum building height within the cluster, and $H_{cluster,mean}$ is the mean building height within the cluster. This indicator reflects a basic condition: larger internal height differences make lower buildings more likely to be shaded by taller ones. Therefore, a larger $S{I}_{shd}$ value indicates a stronger potential shading effect.

Based on this indicator, the compactness variable was further introduced to calculate the final shading correction coefficient:

$$k_{shading}=clamp(1-0.25\cdot S{I}_{shd}-0.15\cdot compact, 0.65, 1.00)$$

(6)

where $k_{shading}$ is the building-cluster-scale shading correction coefficient, and $compact$ is the compactness indicator of the building cluster. This formulation means that larger internal height differences and a more compact spatial arrangement correspond to stronger shading. As a result, the $k_{\mathrm{shading}}$ value becomes lower. To avoid unrealistically large reductions, the value of $k_{\mathrm{shading}}$ was constrained to the range of 0.65–1.00. This ensures that it remains a reasonable correction parameter at the planning scale.

This method follows a morphology-proxy logic. Denser, more compact, and internally more uneven building clusters tend to experience stronger mutual shading. Although simplified, this approach is suitable for comparative analysis at the building-cluster or block scale. It also remains consistent with the subsequent morphology-based analysis. This proxy-based treatment is intended for planning-scale comparative assessment rather than detailed time-dynamic solar simulation.

The theoretical photovoltaic generation potential was calculated under a unified baseline scenario without considering cold-climate losses. Annual theoretical generation is expressed as

$$E_{theoretical}=G\cdot A_{install}\cdot \eta$$

(7)

where $E_{theoretical}$ is the annual theoretical electricity generation (kWh), $G$ is annual solar radiation (kWh·m⁻²), $A_{install}$ is the total installable photovoltaic area (m²), and $\eta$ is the nominal PV module efficiency. In this study, $\eta =0.18$ was adopted to ensure the comparability of theoretical potential estimates among different building clusters. It does not represent the operating efficiency of a specific engineering system.

To estimate effective photovoltaic generation under cold-climate conditions, temperature correction, snow-loss correction, and shading correction were introduced. Temperature correction was modeled as

$$f_T=1+\gamma \left(T_{ref}−T_m\right)$$

(8)

where $f_T$ is the temperature correction coefficient, $\gamma$ is the module temperature coefficient, $T_{ref}$ is the reference temperature, and $T_m$ is the monthly mean air temperature.

Snow-cover loss was represented by a monthly snow-loss fraction. For month $m$, the snow-loss coefficient was defined as

$$f_{snow,m}={\alpha }_m$$

(9)

where $f_{snow,m}$ is the snow-loss fraction in month $m$, and ${\alpha }_m$ is the monthly coefficient determined by the average snow-cover conditions in that month. A larger $f_{snow,m}$ value indicates a stronger reduction in photovoltaic generation caused by snow cover. This treatment is consistent with recent studies. These studies show that snow cover can cause substantial PV output losses in cold and snowy climates. They also suggest that snow effects should be explicitly incorporated into performance modeling [35].

To obtain an annual snow-loss factor, the monthly snow-loss fractions were aggregated using the number of days in each month as weights:

$$f_{snow}={\displaystyle \frac{{\displaystyle {\sum }_{m=1}^{12}}{f}_{snow,m}\cdot d_m}{365}}$$

(10)

where $f_{snow}$ is the annual snow-loss factor, $f_{snow,m}$ is the monthly snow-loss fraction for month $m$, and $d_m$ is the number of days in month $m$. This treatment converts monthly snow-cover effects into an annual correction term. This term can be directly integrated into building-cluster-scale photovoltaic potential assessment.

After accounting for temperature, snow, and shading effects, the final effective electricity generation was calculated as

$$E_{effective}=E_{theoretical}\cdot f_T\cdot (1-f_{snow})\cdot k_{shading}$$

(11)

where $E_{effective}$ is the annual effective electricity generation after cold-climate and shading corrections, $E_{theoretical}$ is the annual theoretical electricity generation, $f_T$ is the temperature correction coefficient, $f_{snow}$ is the annual snow-loss factor, and $k_{shading}$ is the building-cluster-scale shading correction coefficient. This approach takes into account the computational efficiency required at the planning scale. It also considers the major physical effects associated with severe cold-region constraints.

To reduce scale effects caused by differences in building-cluster size, photovoltaic generation density was adopted as the core indicator:

$$P{V}_{density}={\displaystyle \frac{E_{eff}}{A_{cluster}}}$$

(12)

where $P{V}_{density}$ is the effective PV generation density (kWh·m⁻²), $E_{eff}$ is corrected annual generation, and $A_{cluster}$ is the building-cluster area. This normalization allows the analysis to focus on morphology-related differences rather than only on differences in total size. Recent studies on morphology-oriented photovoltaic assessment have reached a similar conclusion. They show that planning-relevant interpretation benefits from normalized indicators and interpretable morphology–response analysis. It does not benefit as much from total-potential comparison alone [24,36].

2.3. Morphological Indicators at the Building-Cluster Scale

To quantitatively describe building-cluster spatial morphology, this study established a six-indicator system with three dimensions: development intensity, vertical height organization, and spatial configuration. This framework is consistent with recent studies. These studies show that urban morphology should be described through multiple dimensions rather than by a single density-related indicator. This is especially important when solar access, PV performance, or energy-related environmental responses are considered [13]. The development-intensity dimension includes building density (BD) and floor area ratio (FAR). The vertical-height-organization dimension includes building height fluctuation (BHF) and building height dispersion (BHD). The spatial-configuration dimension includes building compactness (BC) and nearest neighbor index (NNI). These variables jointly reflect how much has been built, how building height is organized, and how buildings are distributed in space. These are all key aspects in recent morphology-based analyses of solar access, block energy performance, and urban environmental response [13]. This indicator system captures not only how much has been built but also how height is organized and how buildings are spatially distributed. It is therefore suitable for photovoltaic response analysis at the building-cluster scale. Recent studies have shown that development intensity, height organization, and spatial distribution jointly affect solar access, PV yield, and block-level energy performance [13,34].

All indicators were first extracted at the building scale. They were then aggregated to the building-cluster scale.

Table 1. Morphological indicators at the building-cluster scale and their calculation methods.

Indicator	Formula	Meaning	Unit	Tool
BD	$BD={\displaystyle \frac{\sum B_i}{S_b}}$	Building footprint area ratio within the block	_	QGIS
FAR	$FAR={\displaystyle \frac{\sum S_i}{S_b}}$	Total floor area-to-block area ratio	_	QGIS
BHF	$H_{max}-H_{min}$	Building height fluctuation within the block	m	QGIS
BHD	$\sqrt{{\displaystyle \frac{1}{n}}\sum {(H_i-H_{avg})}^2}$	Standard deviation of building heights	m	QGIS
BC	$BC={\displaystyle \frac{1}{n}}\sum {\displaystyle \frac{4\pi A_i}{P_i^2}}$	Building compactness index representing the geometric compactness of building footprints within the cluster	_	QGIS
NNI	$NNI={\displaystyle \frac{D_o}{D_g}}$ $D_o={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n}{d}_i, D_g={\displaystyle \frac{0.5}{\sqrt{n}}}$	Nearest neighbor index reflecting the spatial distribution pattern of buildings within the cluster	_	QGIS

summarizes the formulas, meanings, units, and processing tools for each indicator.

2.4. Morphology–Photovoltaic Relationship Modeling and Validation

After obtaining effective photovoltaic density at the building-cluster scale, this study employed XGBoost to model the relationship between morphological indicators and photovoltaic response. The output variable was corrected $P{V}_{density}$, and the input variables were BD, FAR, BHF, BHD, BC, and NNI. XGBoost was selected because it can effectively capture nonlinear relationships and variable interactions. It is also well suited to tabular spatial datasets with a moderate sample size and a limited number of features. Recent studies on urban energy and morphology-related modeling have shown that tree-based models are effective for identifying nonlinear built-environment response patterns [24,36]. Their performance is especially strong when they are combined with interpretable methods such as SHAP. Studies on interpretable machine learning and morphology-based photovoltaic assessment have shown that tree-based models combined with SHAP can effectively identify dominant built-environment variables and their response ranges. This approach has already been applied in recent morphology–PV studies at the building-cluster scale. It has also been used in urban BIPV assessment under local climate constraints [36]. Model training, validation, and interpretation were implemented in Python 3.10.19 using pandas 2.3.3, scikit-learn 1.7.2, XGBoost 3.2.0, SHAP 0.49.1, and Matplotlib 3.10.8.

To reduce the risk of bias from relying on a single model, multiple linear regression was introduced as a baseline model. The use of a simpler baseline helps distinguish approximately linear relationships from more complex nonlinear response structures. The dataset was divided into training and testing sets using a fixed random seed. The split ratio was 80% to 20%. A five-fold cross-validation procedure was then carried out on the training set. Model performance was evaluated using R², RMSE, and MAE. In addition, the key hyperparameters of XGBoost are explicitly reported in

Table 2. Key hyperparameter settings of the XGBoost model.

Parameter	Name in Code	Value	Description
Objective function	objective	reg:squarederror	Squared-error loss function for regression
Number of trees	n_estimators	300	Total number of boosted trees
Maximum tree depth	max_depth	4	Controls the complexity of each tree and helps prevent overfitting
Learning rate	learning_rate	0.05	Step size of each boosting iteration
Row subsampling ratio	subsample	0.8	Randomly samples 80% of training instances in each boosting round
Column subsampling ratio	colsample_bytree	0.8	Randomly samples 80% of features for each tree to improve generalization
L1 regularization term	reg_alpha	0.0	Controls weight penalization to reduce overfitting
L2 regularization term	reg_lambda	1.0	Controls L2 regularization to reduce overfitting
Random seed	random_state	42	Ensures reproducibility of data splitting and model training
Number of parallel threads	n_jobs	4	Number of CPU threads used for model training

Note: XGBoost denotes eXtreme Gradient Boosting. The parameter names in the “Name in code” column are reported as used in the Python XGBoost package.

to improve reproducibility. These hyperparameters include $n\_estimators$, $max\_depth$, $learning\_rate$, $subsample$, $colsample\_bytree$, the regularization terms, and the random seed. Recent reviews of explainable and data-driven urban energy modeling have also emphasized the importance of transparent parameter reporting and reproducible modeling workflows [24].

Before model interpretation, collinearity diagnostics were conducted. Pearson correlation matrices were used to identify linear correlations among variables. Variance inflation factors (VIFs) were calculated to assess potential multicollinearity. Although tree-based models are less sensitive to collinearity than linear regression models, explicit reporting of Pearson and VIF results improves the transparency of model interpretation. To further assess robustness, uncertainty analysis was also conducted. Key parameters related to facade-orientation correction, snow-loss correction, and shading correction were moderately perturbed. The resulting changes in corrected PV density were then compared. This was carried out to determine whether the core morphology–photovoltaic relationships remained stable. For planning-oriented machine-learning applications, model interpretation should be complemented by robustness or uncertainty assessment. It should not rely solely on model fit.

2.5. Interpretable Analysis and Planning Translation Framework

To avoid treating the model as a black-box predictor, this study further employed SHAP and partial dependence analysis for interpretation. First, mean absolute SHAP values were used to rank the importance of morphological variables. SHAP beeswarm plots were used to visualize the positive and negative contributions of each variable across different value ranges. They were also used to show the degree of dispersion among samples [36]. Finally, SHAP dependence plots and partial dependence plots (PDPs) were combined to identify the nonlinear response trends and threshold-like ranges of key morphological variables. This combination of global and local interpretation has been increasingly used in recent built-environment studies. It helps reveal nonlinear effects, interaction structures, and response intervals that cannot be captured by simple coefficient-based models [24,36]. This workflow extends the analysis beyond identifying which variables are important. It also helps explain how they influence photovoltaic performance and within which ranges they do so at the building-cluster scale. Such a shift from variable ranking to response-structure identification is increasingly regarded as necessary for turning data-driven urban performance models into actionable planning knowledge [37].

Based on model interpretation results, this study further developed a building-cluster typology and planning-translation framework. Specifically, building clusters were classified according to corrected PV density and the dominant variables identified by the model. Particular attention was given to variables related to development intensity and spatial configuration. On this basis, a Morphological Sweet Spot framework was proposed. It summarizes the combinations of morphological conditions associated with relatively favorable photovoltaic performance. Recent studies have reached a similar conclusion. They show that translating machine-learning outputs into typologies and planning-oriented recommendations is a key step in moving BIPV research from resource assessment to practical implementation. This is especially important when the goal is to support block renewal, morphology regulation, and low-carbon urban design, rather than only to report theoretical resource levels [37,38].

3. Results

3.1. Descriptive Statistics and Model Validation

3.1.1. Descriptive Statistical Characteristics of Variables

After building-cluster units were delineated, effective photovoltaic potential was calculated, and morphological indicators were extracted. Descriptive statistical analysis was then conducted on the modeling samples. After removing missing values and screening valid samples, a total of 2406 building clusters were retained for modeling. These samples cover building-cluster types with different levels of development intensity, vertical height organization, and spatial distribution. They therefore adequately reflect the morphological differences in the built environment of central Harbin.

The descriptive statistics show that corrected photovoltaic generation density ($P{V}_{density}$) varies substantially across building clusters. This indicates clear spatial heterogeneity in effective photovoltaic potential at the building-cluster scale. At the same time, the six morphological indicators also differ markedly in both range and dispersion.

Development-intensity indicators (BD and FAR) show wide value ranges. Vertical-organization indicators (BHF and BHD) reveal pronounced differences in building height structure among samples. Spatial-configuration indicators (BC and NNI) vary less overall. However, they still exhibit identifiable structural differences. These results indicate that the study area differs not only in photovoltaic potential but also in built-form characteristics. This provides a statistical basis for analyzing morphology–photovoltaic relationships.

In terms of distribution, $P{V}_{density}$ and some morphological indicators exhibit a certain degree of skewness and long-tail behavior. This suggests that the study area contains a large number of low- and medium-value building clusters. It also contains a small number of high-value or high-intensity samples. Such distributions imply that subsequent analysis should not rely solely on linear relationships. Nonlinear models should also be used to identify variable response patterns. Overall, the descriptive statistics confirm that the sample set has sufficient morphological diversity and variation in the target variable. This provides a basis for subsequent correlation diagnosis, model training, and interpretive analysis. The descriptive statistics of all variables are reported in

Table 3. Descriptive statistics of the variables used in the model.

Variable	N	Mean	Std.	Min.	Q1	Median	Q3	Max.
$\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$	2406	71.2877	40.4171	0.5830	44.5893	65.5385	92.4400	527.1710
BD	2406	0.2885	0.1270	0.0030	0.2020	0.2760	0.3638	1.0850
FAR	2406	2.1878	1.2517	0.0080	1.3113	2.0435	2.9035	10.6660
BHF	2406	28.8345	24.4433	0.2280	12.3825	19.8775	38.5458	152.3370
BHD	2406	7.8441	6.2253	0.1610	3.9723	5.8345	9.6968	53.0610
BC	2406	0.6682	0.1320	0.0490	0.6110	0.7150	0.7670	0.9260
NNI	2406	1.3804	0.2847	0.1753	1.2314	1.3566	1.5058	3.8348

Note: N denotes sample size; Std. denotes standard deviation; Min. and Max. denote the minimum and maximum values, respectively; Q1 and Q3 denote the first and third quartiles, respectively. $P{V}_{density}$ denotes corrected cluster-scale photovoltaic generation density; BD, building density; FAR, floor area ratio; BHF, building height fluctuation; BHD, building height dispersion; BC, building compactness; NNI, nearest neighbor index.

.

3.1.2. Pearson Correlation and Multicollinearity Diagnosis

To preliminarily identify the linear relationships between morphological variables and effective photovoltaic generation density, Pearson correlation analysis and variance inflation factor (VIF) diagnostics were conducted. These methods were also used to examine potential collinearity among the explanatory variables. The results show that $P{V}_{density}$ is strongly positively correlated with BD and FAR. The Pearson correlation coefficient between $P{V}_{density}$ and BD is 0.82, while that between $P{V}_{density}$ and FAR is 0.81. By contrast, $P{V}_{density}$ has a moderate positive correlation with the nearest neighbor index (NNI), with a coefficient of 0.31. Its linear correlations with BHF, BHD, and BC are relatively weak. These results suggest that development-intensity indicators are likely to be the main linear factors explaining differences in effective photovoltaic potential at the building-cluster scale. By contrast, height and spatial-configuration indicators may act in a more conditional or nonlinear manner.

The relationships among the explanatory variables also show clear structural patterns. BHF and BHD are strongly positively correlated, with a coefficient of 0.92. This indicates that both variables partly describe the vertical morphological differences in building clusters. They may therefore contain overlapping information in the interpretation stage. By contrast, BC has correlations close to zero with most variables. This suggests that its linear explanatory power is limited. NNI has moderate positive correlations with both BD and FAR. This indicates that the degree of spatial regularity is coupled with development intensity to some extent. However, it does not simply duplicate the intensity indicators. The detailed correlation coefficients are reported in

Table 4. Pearson correlation coefficients and variance inflation factor (VIF) diagnostics.

Panel (A). Pearson Correlation Matrix
Variable	$\mathit{P}{\mathit{V}}_{\mathit{d}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{y}}$	BD	FAR	BHF	BHD	BC	NNI
$P{V}_{density}$	1.0000	0.8173	0.8084	−0.1209	−0.0067	−0.0475	0.3132
BD	0.8173	1.0000	0.7631	−0.2621	−0.2033	−0.0264	0.3245
FAR	0.8084	0.7631	1.0000	0.0826	0.2201	−0.0028	0.3590
BHF	−0.1209	−0.2621	0.0826	1.0000	0.9164	−0.0315	−0.1616
BHD	−0.0067	−0.2033	0.2201	0.9164	1.0000	−0.0005	−0.0650
BC	−0.0475	−0.0264	−0.0028	−0.0315	−0.0005	1.0000	−0.0717
NNI	0.3132	0.3245	0.3590	−0.1616	−0.0650	−0.0717	1.0000
Panel (B). VIF diagnostics
Variable	VIF
BD	3.7298
FAR	4.1197
BHF	7.2285
BHD	8.4160
BC	1.0166
NNI	1.2175

Note: Panel (A) reports Pearson correlation coefficients among the variables. Panel (B) reports variance inflation factor (VIF) values for the explanatory variables to diagnose potential multicollinearity. $P{V}_{density}$ denotes corrected cluster-scale photovoltaic generation density. BD denotes building density; FAR, floor area ratio; BHF, building height fluctuation; BHD, building height dispersion; BC, building compactness; and NNI, nearest neighbor index.

, Panel A. The VIF results are reported in Table 4, Panel B.

The VIF results further show that some variables are correlated, especially the height-related indicators. However, the overall level of multicollinearity remains within an acceptable range and does not prevent subsequent modeling. Because tree-based models are more robust to multicollinearity than linear regression models, all six morphological indicators were retained in the XGBoost model. This was carried out to preserve a complete representation of building-cluster morphology [24]. Overall, the Pearson and VIF results not only confirm the importance of development-intensity indicators. They also suggest that subsequent model interpretation should pay particular attention to nonlinear effects and variable interactions. It should not rely solely on linear correlations [36].

3.1.3. Baseline Model Comparison and Cross-Validation Results

Based on the descriptive statistics and correlation diagnosis, the morphology–photovoltaic relationship model was further validated. To avoid relying on a single model, multiple linear regression was introduced as the baseline model. It was then compared with the XGBoost regression model. Test-set results show that the multiple linear regression model achieved an R² of 0.6695, an RMSE of 26.5538, and an MAE of 10.5938. The corresponding values for the XGBoost model were 0.6479, 27.4063, and 10.7371, respectively. Overall, the two models show a similar fitting performance on the test set. Linear regression performs slightly better on some metrics. The comparison results are reported in

Table 5. Comparison of baseline models (multiple linear regression vs. XGBoost).

Model	R2	RMSE	MAE
Multiple Linear Regression	0.6695	26.5538	10.5938
XGBoost	0.6479	27.4063	10.7371

Note: R² denotes the coefficient of determination, RMSE denotes the root mean square error, and MAE denotes the mean absolute error. All metrics were calculated on the held-out test set.

. This indicates that the relationship between building-cluster morphology and photovoltaic generation density is not dominated entirely by complex nonlinear effects. It still contains a certain linear component.

Despite this, XGBoost remains more suitable for capturing potential nonlinear relationships and interaction effects among morphological variables. It was therefore retained as the main model for subsequent interpretation. Cross-validation results indicate that XGBoost performs with reasonable stability within the training samples. The five-fold cross-validation results are reported in

Table 6. Five-fold cross-validation results of the XGBoost model.

Metric	Mean_CV	Std_CV
R2	0.7673	0.0829
RMSE	18.5235	4.7341
MAE	9.1223	0.9231

Note: Mean_CV denotes the average value across the five folds, and Std_CV denotes the standard deviation across folds. R² denotes the coefficient of determination, RMSE denotes the root mean square error, and MAE denotes the mean absolute error. Together, these metrics reflect model stability within the training dataset.

. In the five-fold cross-validation, the mean ${\mathrm{R}}^2$ was 0.7673, with a standard deviation of 0.0829. The mean RMSE was 18.5235, with a standard deviation of 4.7341. The mean MAE was 9.1223, with a standard deviation of 0.9231. Among these metrics, the relatively small fluctuation in MAE suggests a stable average prediction error. The standard deviation of ${\mathrm{R}}^2$ also remains within an acceptable range. This indicates that the model captures the overall trend with reasonable robustness. By contrast, the larger variation in RMSE suggests that the model is still sensitive to some high-value or highly heterogeneous samples.

A further comparison between the cross-validation means and the independent test-set results shows that the test-set R² is lower than the cross-validation mean. RMSE and MAE are also slightly higher than the corresponding cross-validation values. This suggests that the model fits and validates well within the training samples. However, its generalization performance on the independent test set is somewhat weaker. This suggests that the model fits and validates well within the training samples. However, its generalization performance on the independent test set is somewhat weaker. This indicates that some heterogeneity remains within the sample set. On this basis, the main role of XGBoost in this study is to identify complex response structures. It is not simply to improve predictive accuracy on the test set [36]. Subsequent analysis therefore combined SHAP and partial dependence analysis. These methods were used to further interpret the marginal contributions, response ranges, and interaction effects of key morphological factors.

To further visualize model performance, an observed-versus-predicted scatter plot was produced (Figure 4). The results show that most samples are distributed around the 1:1 reference line. This indicates that the model captures the overall trend reasonably well. However, some dispersion remains in the high-value range. This is consistent with the relatively large variation in RMSE noted above. It also suggests that high-potential building clusters often have more complex morphological combinations and stronger local heterogeneity. This also provides a basis for the subsequent nonlinear analysis using SHAP and PDP.

3.1.4. Sensitivity and Uncertainty Analysis

The estimation of effective photovoltaic potential depends not only on building-cluster morphology itself but also on parameter settings such as facade-orientation correction, snow-loss correction, and shading correction. Therefore, a sensitivity and uncertainty analysis was further conducted. Key correction parameters were perturbed, and the resulting changes in corrected photovoltaic generation density at the building-cluster scale were compared. In this way, the study examined whether the main conclusions depended on a specific parameter setting. Using the baseline scenario (Base) as the reference, the results of the perturbed scenarios are reported in

Table 7. Sensitivity and uncertainty analysis results.

Scenario	$\mathbf{Mean} \mathit{P}{\mathit{V}}_{\mathit{d}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{y}}$	$\mathbf{Median} \mathit{P}{\mathit{V}}_{\mathit{d}\mathit{e}\mathit{n}\mathit{s}\mathit{i}\mathit{t}\mathit{y}}$	Mean Change vs. Base (%)	Median Change vs. Base (%)
Base	71.5482	65.5923	0.0000	0.0000
Orientation_low	73.2878	67.2296	2.4314	2.4962
Orientation_high	69.8086	63.9867	−2.4314	−2.4478
Shading_low	74.9756	68.9780	4.7903	5.1616
Shading_high	68.1208	62.1451	−4.7903	−5.2555
Snow_low	73.6917	67.5574	2.9959	2.9959
Snow_high	69.4047	63.6272	−2.9959	−2.9959

Note: Base denotes the baseline scenario. Orientation_low and Orientation_high indicate reduced and increased facade-orientation weighting, respectively. Shading_low and Shading_high indicate weaker and stronger shading correction, respectively. Snow_low and Snow_high indicate reduced and increased snow-loss correction, respectively.

.

The results show that the relative differences among building-cluster samples remain broadly stable after reasonable perturbations to facade-orientation weighting, snow-loss coefficients, and shading correction coefficients. This indicates that the spatial differentiation of effective photovoltaic potential is not driven entirely by any single correction parameter. At the same time, development-intensity indicators retain strong explanatory power across different perturbation scenarios. This suggests that the conclusion that BD and FAR are the dominant factors is relatively robust. By contrast, the marginal effects of some secondary variables show a certain degree of fluctuation under the perturbed scenarios. This implies that the roles of spatial-configuration and height-structure indicators are more sensitive to local conditions and parameter settings.

Overall, the main morphology–photovoltaic relationships remain consistent across different perturbation scenarios. However, some variability persists in local high-value samples and in the responses of certain secondary variables. This suggests that the high-value response patterns identified in this study are reasonably stable. However, they still involve some uncertainty at the level of specific ranges and local samples. Accordingly, the following discussion of morphology–response characteristics focuses on trends and ranges. It emphasizes the identification of stable high-value response intervals rather than the presentation of a single fixed optimum [22,34].

3.2. Spatial Pattern of Effective PV Potential and PV Composition

3.2.1. Spatial Distribution of Effective PV Potential

Figure 5 shows the spatial distribution of effective photovoltaic potential at the building-cluster scale. Overall, photovoltaic generation density varies substantially across building clusters in the study area. This indicates pronounced spatial heterogeneity. Based on the classification results, low- and medium–low-value clusters dominate the study area. By contrast, high-value clusters are relatively few, but they show clear local clustering. This suggests that the effective photovoltaic potential of urban building clusters in severe cold regions is not evenly distributed. It is strongly influenced by local built-environment conditions.

In terms of the overall pattern, building clusters with medium photovoltaic generation density are the most widely distributed. They form the main background of central Harbin. The lowest-value clusters are found more often in peripheral areas or in places with relatively limited installable surface conditions. By contrast, higher-value and highest-value clusters are mainly concentrated in several local areas within the urban core. A small number of point-like or patch-like occurrences is also found in outer groups. This indicates that high-potential clusters are not distributed continuously over large areas. Instead, they are associated with particular combinations of built form, installable surface conditions, and relatively favorable local solar-access environments.

A closer look at the spatial pattern shows that high-value clusters are concentrated in the central part of the urban area and in some locally high-intensity built-up zones. By contrast, peripheral areas are dominated by low- and medium-value clusters, with only a few scattered high-value samples. This pattern of “local clustering with sparse high-value patches” suggests that effective photovoltaic potential at the building-cluster scale does not follow a simple center-to-periphery linear decline. Rather, it reflects a more complex spatial structure. This structure is shaped jointly by development intensity, vertical height organization, spatial configuration, and cold-climate correction. As a result, building clusters located in similar areas may still exhibit different levels of effective generation because of differences in morphology.

The classification results further show that the highest-value clusters account for only a small proportion of the study area. However, they have strong spatial visibility and form distinct high-potential patches. Medium-high-value clusters are distributed mainly around these patches. They create a gradient from the high-value core areas to the surrounding zones. Medium-low- and low-value clusters occupy a much larger area. This pattern is consistent with the skewed distribution of $P{V}_{density}$ described earlier. Most samples are concentrated in the low- and medium-value range. Only a small number of high-value samples form the long tail of the distribution.

Overall, Figure 5 indicates that effective photovoltaic potential at the building-cluster scale in central Harbin is characterized by strong local variation and clear spatial heterogeneity. These results suggest that, in severe cold urban environments, effective photovoltaic potential is not determined solely by solar radiation. It is also jointly associated with building surface resources, local shading conditions, cold-climate correction, and building-cluster morphology. This provides a spatial basis for the subsequent interpretation of morphology–photovoltaic relationships. The following analysis focuses on variable importance, single-variable response, and coupling effects.

3.2.2. Relative Contributions of Rooftop and Facade PV

Figure 6 shows the statistical distribution of rooftop and facade contributions to effective electricity generation. Overall, the median contribution of facades is clearly higher than that of rooftops. The interquartile range of facade contribution is also located at a higher level. By contrast, the median contribution of rooftops is lower. Its distribution is concentrated more in the low- and medium-value range. These results indicate that, at the building-cluster scale, the contribution of facades to effective photovoltaic generation is generally higher than that of rooftops.

In terms of distribution characteristics, rooftop contribution shows strong dispersion. Its values range from near zero to relatively high levels. This indicates substantial variation among building clusters. By contrast, facade contribution is concentrated mainly in the higher range. Its median is about 0.7, and its upper quartile is close to 1. This means that facades are an important source of effective generation in a considerable number of building clusters. Some samples even show clear facade-dominant characteristics.

These results indicate that, in severe cold and high-density urban environments, building-cluster photovoltaic potential is not determined mainly by rooftops alone. Facades also represent an important surface resource that should not be neglected [31]. This is especially true for building clusters with higher development intensity and larger facade areas. In these clusters, facades make a more substantial contribution to overall effective generation. Therefore, subsequent morphology analysis should consider not only total installable area. It should also consider the conditions under which facade potential can be better released and coordinated with rooftop use.

3.3. Effects of Building-Cluster Morphology on Effective PV Potential

3.3.1. Identification of Key Morphological Factors

To identify the key morphological factors affecting effective photovoltaic potential at the building-cluster scale, this study further interpreted the variables using XGBoost feature-importance ranking and the SHAP summary plot. The results show that the contributions of different morphological indicators to $P{V}_{\mathrm{density}}$ differ markedly. Development-intensity-related variables show the strongest explanatory power.

The feature-importance ranking shows that floor area ratio (FAR) contributes the most, followed by building density (BD). Both variables are clearly more important than the remaining indicators. By contrast, the contributions of the nearest neighbor index (NNI), building height dispersion (BHD), building height fluctuation (BHF), and building compactness (BC) are lower overall. However, they still influence model output to some extent (Figure 7). The SHAP summary plot further shows that different value ranges of the variables correspond to different contribution directions. High values of FAR and BD are mainly distributed in the positive SHAP range. By contrast, low values are more often associated with negative contributions. High values of BHF appear more often in the negative SHAP range. The effect direction of BHD is weaker overall. However, some variation is still visible in part of the samples. The overall influence of NNI and BC is relatively limited. NNI still shows some fluctuation in local samples. By contrast, the contribution of BC is concentrated mostly around zero (Figure 8).

Overall, the contribution ranking of the variables shows a clear gradient. FAR and BD form the first tier. By contrast, NNI, BHD, BHF, and BC form the second tier.

3.3.2. Single-Variable Response Characteristics

After identifying the key morphological factors, SHAP dependence plots were used to analyze the response characteristics of individual variables with respect to $P{V}_{density}$. The results show that the response patterns differ among morphological variables. FAR and BD exhibit relatively clear monotonic trends. By contrast, NNI shows a more nonlinear response.

The dependence plot for BD shows that SHAP values increase continuously as BD increases. They gradually shift from negative to positive values. Low-BD samples are mainly associated with negative contributions. By contrast, samples in the medium-to-high BD range are more often associated with positive contributions. At the same time, dispersion becomes stronger in the higher BD range. This indicates greater variation among high-density building clusters (Figure 9a).

The dependence plot for FAR shows an even clearer upward trend. As FAR increases, SHAP values continue to rise. Low-FAR samples are concentrated mainly in the negative contribution range. By contrast, medium- and high-FAR samples are more often associated with clearly positive contributions (Figure 9b).

The response pattern of NNI is clearly different from those of FAR and BD. Its SHAP values do not change monotonically as NNI increases. Instead, they fluctuate across different value ranges. Relatively high positive SHAP values appear in the low-NNI range. In the middle range, SHAP values are more often distributed near zero or are slightly positive. In the high-NNI range, the effect gradually weakens. Some negative fluctuations also appear (Figure 9c).

Taken together, the single-variable response results show that FAR and BD have relatively clear response trends. By contrast, NNI shows stronger interval-based variation [34]. The differences in response direction, magnitude, and dispersion among the variables indicate that photovoltaic generation density does not respond equally to all dimensions of morphology.

3.3.3. Coupled Morphological Effects and High-Value Response Ranges

Based on the single-variable response analysis, two-dimensional partial dependence plots were further used to identify coupling effects among key morphological variables and their high-value response ranges. The results show that photovoltaic generation density is not determined by any single variable alone. Instead, it reflects different response levels under the joint effects of multiple variables (Figure 10).

The two-dimensional partial dependence results for BD and BC show that the predicted $P{V}_{\mathrm{density}}$ increases overall as BD increases. By contrast, the variation along the BC axis is relatively limited. The contour lines are distributed mainly in a near-vertical pattern. This indicates that the response gradient in this variable pair is driven mainly by BD. The effect of BC is relatively weak (Figure 10a).

The coupling relationship between FAR and BD is the most evident. The two-dimensional partial dependence plot shows that the predicted $P{V}_{density}$ continues to increase as FAR and BD increase together. The high-value response zone is concentrated mainly in the combination range of medium-to-high FAR and medium-to-high BD. Compared with the low-FAR–low-BD combination, this region corresponds to substantially higher predicted values (Figure 10b).

The two-dimensional partial dependence results for FAR and NNI show that the overall gradient of $P{V}_{\mathrm{density}}$ is mainly aligned with the FAR axis. As FAR increases, the predicted value rises continuously. At the same time, NNI still exerts some local modulation on the response level. Relatively higher responses appear in part of the middle-NNI range. By contrast, changes are more limited at the lower and higher ends of the NNI range (Figure 10c).

Taken together, the two-dimensional partial dependence results show that higher responses of $P{V}_{\mathrm{density}}$ occur mainly under variable combinations associated with higher development intensity. By contrast, BC and NNI act more as local modulation variables. The differences among variable combinations indicate that the high-value zone of effective photovoltaic potential at the building-cluster scale has a clear combinational character. It does not correspond simply to the change in a single variable [34].

3.4. Morphological Sweet Spot and Building-Cluster Typology

3.4.1. Identification of the Morphological Sweet Spot

Based on the identification of key morphological factors, the analysis of single-variable responses, and the two-dimensional partial dependence results, this study further identified the high-response combination zones of effective photovoltaic potential at the building-cluster scale. The results show that higher responses of $P{V}_{density}$ do not correspond to extreme values of a single variable. Instead, they occur mainly within specific ranges formed by the joint action of multiple variables.

The single-variable response results show that increases in FAR and BD are both associated with clear increases in $P{V}_{\mathrm{density}}$. Low-value ranges are mainly linked to negative contributions, whereas medium- and high-value ranges are more often associated with positive contributions. In comparison, the response of NNI shows clearer interval-based variation. The two-dimensional partial dependence results further indicate that high-value zones of $P{V}_{\mathrm{density}}$ are concentrated mainly in the combination region of medium-to-high FAR and medium-to-high BD. In this combination, NNI and BC act more as local modulation variables.

Based on the single-variable response patterns shown in Figure 9 and the two-dimensional partial dependence results shown in Figure 10, a relatively stable high-response range can be identified. This range generally corresponds to higher development intensity, higher or medium-to-high building density, and a relatively moderate spatial distribution pattern. Under these combined conditions, building clusters tend to show relatively high $P{V}_{\mathrm{density}}$. Compared with low-response zones, these high-response samples are more concentrated in parameter space.

Accordingly, this study defines the above parameter-space zone as the “Morphological Sweet Spot” of effective BIPV potential at the building-cluster scale. This zone is relatively concentrated and corresponds to high $P{V}_{\mathrm{density}}$. Here, the Morphological Sweet Spot refers to a high-response combination zone rather than an absolute optimum defined by any single variable.

3.4.2. Typology Construction and Spatial Expression

Based on the identification of the Morphological Sweet Spot, the building clusters in the study area were further classified according to $P{V}_{\mathrm{density}}$ and the dominant morphological variables. The results show that building clusters differ clearly in both photovoltaic generation density and morphological combinations. They can be grouped into four representative types. The classification rules and characteristic summary of these types are presented in

Table 8. Typological classification rules and characteristic summary of building clusters.

Type	Typology	Classification Characteristics (Relative Rules)	PV Performance Characteristics	Spatial Pattern
T1	High-potential synergy	High $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$; relatively high FAR; medium-to-high BD; NNI within a favorable range; both rooftop and facade contribute strongly	Highest effective $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$ with strong roof–facade synergy	Mainly clustered in localized high-value patches
T2	High-potential constrained	Relatively high $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$; high FAR and/or BD; but one or more unfavorable conditions in NNI, BHF, or BHD; facade contribution is often prominent	High PV potential, but constrained by local spatial organization or height variation	Mainly distributed in or around high-intensity built-up areas, often as fragmented high-value patches
T3	Balanced optimization	Moderate $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$; FAR and BD in medium ranges; relatively moderate NNI; relatively balanced rooftop and facade contributions	Stable intermediate PV performance; the most representative type in the study area	Most widely distributed and forms the dominant background type
T4	Low-potential extensive	Low $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$; relatively low FAR; relatively low BD or insufficient surface utilization; either rooftop or facade contribution remains weak	Lowest effective $\mathrm{P}{\mathrm{V}}_{\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}$ and generally weak PV performance	Mostly distributed in peripheral areas or locally unfavorable built-form conditions

.

In terms of typological characteristics, the high-potential synergy type (T1) corresponds to the highest level of $P{V}_{\mathrm{density}}$. It is also morphologically the closest to the high-response zone. The high-potential constrained type (T2) also shows relatively high photovoltaic generation density. However, its overall level is lower than that of T1. The balanced optimization type (T3) represents a medium level of $P{V}_{\mathrm{density}}$. It is the most common building-cluster type in the study area. The low-potential extensive type (T4) corresponds overall to a lower level of generation density. These four types differ not only in their numerical levels but also in their morphological combinations.

Figure 11 shows the spatial distribution of the four building-cluster types. T1 is the least common type. However, it shows the strongest clustering in the urban core and forms several dense high-value patches. T2 is more widely distributed and is located mainly around T1. It forms a relatively continuous transition belt within the urban core. T3 is the most widespread type in the study area. It covers much of the urban core and part of the outer area. It forms the main background of the overall spatial pattern. T4 is concentrated mainly in peripheral areas and some edge groups. It forms the low-value background of the building-cluster typology pattern.

At the overall level, the building-cluster typology shows a clear spatial hierarchy. The urban core is dominated by T1 and T2. T1 forms locally clustered high-value areas, whereas T2 forms the outer transition zone. Over a broader area, T3 constitutes the main background type. By contrast, T4 is distributed mainly in peripheral and edge areas. This pattern indicates that differences in effective photovoltaic potential at the building-cluster scale are reflected not only in value levels. They are also reflected in a clear core–transition–background spatial structure.

Taken together, the high-potential types are relatively limited in number. However, they are spatially distinctive. The medium type is the most numerous. It forms the main building-cluster background of the study area. The low-potential type is concentrated mainly in peripheral areas. The spatial differentiation among these types jointly forms the overall pattern of effective photovoltaic potential at the building-cluster scale in the study area.

4. Discussion

4.1. Main Findings and Interpretation of Results

This study developed a framework for assessing effective BIPV potential and analyzing morphology–PV responses at the building-cluster scale in severe cold regions. Based on the results, three main findings can be identified. First, effective photovoltaic potential at the building-cluster scale shows clear spatial heterogeneity. High-value clusters are relatively limited in number. However, they are strongly concentrated in several local areas of the urban core. Low- and medium-value clusters are more widely distributed. They form the main background of the study area. Second, rooftops and facades jointly constitute the main surfaces contributing to effective generation. Facade contribution is generally higher than rooftop contribution. This finding is consistent with recent studies. These studies show that facade PV can provide a substantial share of BIPV potential in dense urban environments. In some cases, it may approach or exceed rooftop potential [12]. This indicates that, in high-latitude severe cold cities, facades are not merely supplementary surfaces. They are also an important component of building-cluster-scale BIPV assessment. Third, morphological variables show differentiated effects on effective photovoltaic potential. Among them, FAR and BD are the most important explanatory variables. NNI shows a clear nonlinear pattern. The effects of BHF, BHD, and BC are relatively weaker.

In spatial terms, effective photovoltaic potential does not show a simple center-to-periphery pattern. Instead, it presents a composite structure. In this structure, locally clustered high-value areas coexist with a broad background of low- and medium-value clusters. This suggests that building-cluster-scale photovoltaic potential is not determined by radiation alone. It is also related to development intensity, surface resource conditions, spatial configuration, and cold-region corrections. Building clusters with higher potential usually correspond to a relatively high or medium-to-high development intensity and more favorable surface-use conditions. By contrast, low-value clusters are more common in areas with limited usable surface resources or less favorable spatial conditions.

The rooftop–facade contribution results further show that effective photovoltaic potential is not formed mainly by a single surface type. As indicated by the boxplots in Figure 6, both the median and the overall distribution range of facade contribution are higher than those of rooftop contribution. This suggests that facades are an important source of effective generation for many building clusters in the study area and should be explicitly considered in severe cold and high-density urban environments.

In terms of morphology–response patterns, FAR and BD show the strongest effects in both the feature-importance ranking and the SHAP results. This indicates that development intensity is the dominant dimension explaining differences in effective photovoltaic potential at the building-cluster scale. The single-variable response results show that FAR and BD both have clear positive relationships with $P{V}_{\mathrm{density}}$. By contrast, the response of NNI varies across different ranges. The two-dimensional partial dependence results further show that higher-response zones are concentrated mainly in the combination range of medium-to-high FAR and medium-to-high BD. In this combination, NNI and BC act more as local modulation variables. These findings suggest that high-value zones of effective photovoltaic potential are not the result of changes in any single variable alone. Rather, they reflect the combined effects of multiple morphological parameters.

Overall, effective BIPV potential at the building-cluster scale in severe cold regions shows clear spatial differentiation, surface-composition differences, and morphology-dependent response patterns. Development intensity acts as the dominant factor. Rooftop–facade coordination forms an important structural feature. High-response zones exhibit clear combinational characteristics. These findings provide the basis for the following comparison with previous studies, the discussion of methodological reliability, and the derivation of planning implications.

4.2. Comparison with Previous Studies and the Contributions of This Study

Previous studies on urban photovoltaic potential have mainly followed three lines of research: integrated PV use in buildings, multi-scale rooftop–facade BIPV assessment, and city-scale hybrid workflows that combine physical simulation with machine learning [12,31,39]. The first line uses GIS or remote sensing data to identify building surface resources and estimate the theoretical photovoltaic potential of rooftops or other building surfaces. The second line applies machine learning methods to identify relationships between built-environment morphology and photovoltaic potential. The third line focuses on high-latitude or cold-region contexts. It introduces climate correction, installation-angle optimization, or integrated BIPV assessment frameworks to analyze photovoltaic performance under cold conditions. Overall, these studies have made substantial progress in photovoltaic resource estimation, building-surface identification, and city-scale potential evaluation.

However,

Table 9. Comparison between representative previous studies and this study.

Study	Analytical Scale	PV Object	Cold-Region Correction	Method	Planning Translation	This Study’s Contribution
Li et al. (2024) [41]	District/sub-district scale	Rooftop PV	No systematic consideration of low-temperature or snow-related corrections	Deep learning + GIS	Limited	Extends rooftop PV to integrated rooftop–facade BIPV with cold-region and cluster-scale shading corrections
Chen et al. (2024) [42]	City scale	PV object: Buildings (3D building-based PV potential)	Cold-region climate correction not explicitly incorporated	Multi-source remote sensing + 3D building extraction	Limited	Advances the analysis to the building-cluster scale with interpretable morphology–PV response identification
Ruan et al. (2024) [43]	Module/installation optimization scale	Mainly installation angle and power-generation performance	Snowfall and snowmelt effects explicitly considered	Historical weather data + optimal tilt-angle model	Weak	Introduces cold-region correction into building-cluster-scale BIPV assessment and links it to urban morphology
Liu et al. (2025) [36]	Building-cluster/settlement scale	Rooftop and facade PV	Cold-region correction not emphasized	XGBoost + SHAP	Yes	Applies XGBoost + SHAP to severe-cold urban building clusters with added snow-loss and shading corrections
Yu et al. (2025) [12]	Multi-scale (building, block, city)	BIPV (rooftop + facade)	Comprehensive consideration of different climates and meteorological datasets	3D building footprints + multi-source spatiotemporal datasets	Limited	Focuses on the building-cluster/block scale and strengthens morphology-based identification of effective BIPV potential in severe-cold regions
Tang et al. (2025) [39]	City scale	BIPV	Climate factors considered	Physical simulation + machine learning + 3D building models	Moderate	Emphasizes the building-cluster scale, severe-cold-region correction, and interpretable morphology-response analysis
This study	Building-cluster scale	Rooftop–facade integrated	Severe-cold correction	GIS + XGBoost + SHAP + PDP	Yes	Develops an effective BIPV potential assessment and morphology-based typology framework at the building-cluster scale in severe-cold regions

Note: PV denotes photovoltaic; BIPV denotes building-integrated photovoltaics; GIS denotes geographic information system; SHAP denotes SHapley Additive exPlanations; PDP denotes partial dependence plot; XGBoost denotes eXtreme Gradient Boosting; and 3D denotes three-dimensional.

shows that several limitations remain in the existing literature. In terms of analytical scale, most studies focus on individual buildings, entire cities, or large districts. By contrast, relatively less attention has been paid to the intermediate scale of building clusters. This scale connects building surface resources with block-level spatial organization. In terms of deployment objects, many studies still focus mainly on rooftops. Even when building surfaces or BIPV are included, the coordinated role of rooftops and facades in dense urban environments is rarely discussed in a systematic way. In terms of constraints, low temperature, snow, and shading in cold regions are often treated separately. They are rarely integrated within a unified building-cluster-scale framework. In terms of result expression, many studies remain at the level of potential identification or method validation. Typological expression and planning-oriented translation remain limited [40].

Compared with previous studies, this study makes four main contributions. First, it takes the building cluster as the core analytical unit. This links building-surface PV assessment with block-level spatial organization. Second, it develops an integrated rooftop–facade framework for effective BIPV potential assessment under severe cold conditions. This framework combines temperature correction, snow-loss correction, and building-cluster-scale shading correction within one unified workflow. Third, it adopts a GIS + XGBoost + SHAP + PDP analytical framework to identify key morphological variables, nonlinear response patterns, and coupled effects among variables. Fourth, it moves beyond potential estimation by introducing the Morphological Sweet Spot and a building-cluster typology framework. In this way, model outputs can be translated into clearer morphology-based planning guidance.

Taken together, these advances provide an interpretable framework for linking effective BIPV potential assessment with morphology-oriented planning support at the building-cluster scale.

Overall, this study does not merely add a severe-cold case to the existing body of urban photovoltaic research. Instead, it advances previous work in terms of analytical scale, assessment object, methodological framework, and result expression. In this way, it links effective BIPV potential assessment in severe cold urban building clusters with the identification of morphology-dependent photovoltaic responses. It also provides a basis for subsequent typological expression and planning-oriented discussion.

4.3. Method Reliability, Applicability, and Limitations

This study combines GIS with interpretable machine learning to analyze effective BIPV potential and morphology–response relationships at the building-cluster scale in severe cold regions. Compared with approaches that rely only on linear models, XGBoost is better suited to capturing nonlinear relationships and interaction effects. These effects involve development intensity, spatial organization, building surface conditions, and cold-region correction factors. SHAP and partial dependence analysis further provide information on variable importance, effect direction, and response intervals. This improves the interpretability of model results.

The validation results indicate that the method is reasonably reliable. The baseline comparison shows that multiple linear regression and XGBoost perform similarly on the test set. This suggests that the relationship between building-cluster morphology and photovoltaic generation density contains a certain linear component. At the same time, XGBoost is better suited to identifying variable responses and nonlinear structures. The five-fold cross-validation results show that the model is relatively stable within the training samples. Although test-set performance is slightly lower than the cross-validation mean, the overall error level remains acceptable. Pearson correlation analysis and VIF diagnostics further show that some variables are correlated, especially the height-related indicators. However, the input variable system remains usable overall. In terms of robustness, the sensitivity and uncertainty analysis shows that the relative pattern of $P{V}_{\mathrm{density}}$ among building clusters remains broadly stable after reasonable perturbations to facade-orientation weighting, snow-loss coefficients, and shading correction coefficients. The dominant roles of FAR and BD also do not change substantially. This suggests that the main morphology–response patterns are reasonably robust. However, some local high-value samples and secondary variables still show variation. Therefore, the identification of high-response zones in this study is presented in terms of intervals and combinations rather than as a single fixed optimum.

The time-scale treatment adopted in this study is also consistent with the research objective. Because the study focuses on identifying and comparing overall effective potential at the building-cluster scale, annual radiation, together with monthly temperature and snow data, was used for integrated correction. This treatment is intended to reflect relative differences among building clusters under long-term average conditions rather than short-term operational dynamics. As a result, the method is more suitable for overall potential identification and typological expression at the scale of urban renewal or block planning. It is less suitable for detailed engineering design at the single-building scale or for hourly operational simulation [12,39].

Several limitations should also be acknowledged. First, shading was represented by a simplified building-cluster-scale correction rather than by time-dynamic three-dimensional solar simulation. The method is therefore limited in its ability to capture highly detailed local shading relationships. Second, the temperature, snow, and orientation corrections were implemented through parameterized expressions. These corrections reflect the general direction of cold-region effects. However, they cannot fully replace more detailed physical simulation. Third, this study is based on a single severe-cold city, Harbin. The transferability of the identified response ranges and typologies to other cities and climate contexts still requires further verification. Fourth, the current analysis focuses on technical–morphological potential. It does not incorporate economic feasibility, retrofit cost, grid access, policy constraints, or other implementation conditions. In addition, SHAP and partial dependence analysis are used here to interpret model-learned response patterns rather than to establish strict causal relationships.

Overall, the method developed in this study has good applicability and reasonable reliability for identifying effective BIPV potential, analyzing nonlinear morphology–response patterns, and interpreting results at the building-cluster scale. Its main advantage is that it can incorporate cold-region correction, shading correction, and morphology–response identification within a relatively limited data environment. Its main limitations lie in shading precision, parameterized approximation, and the incomplete inclusion of real-world implementation constraints.

4.4. Planning Implications

The results of this study show that effective BIPV potential at the building-cluster scale in severe cold regions exhibits clear typological and spatial differences. Therefore, planning and renewal practice should avoid applying a single deployment mode to all building-cluster types. Instead, differentiated strategies should be adopted according to the morphological characteristics and surface-resource conditions of each type.

For the high-potential synergy type (T1), $P{V}_{\mathrm{density}}$ is the highest. Both rooftops and facades contribute strongly. These clusters can be treated as priority deployment areas. In these areas, coordinated rooftop–facade use can be promoted during renewal or retrofitting to improve overall surface-resource efficiency. For the high-potential constrained type (T2), effective photovoltaic potential is also high. However, local spatial organization, height differences, or shading conditions may limit performance. In this case, a more suitable strategy is to maintain relatively high development intensity while improving local unfavorable conditions. For the balanced optimization type (T3), generation levels remain moderate. As the most numerous and most widespread type, it can serve as the main target for large-scale promotion. Emphasis should be placed on the gradual improvement of integrated rooftop–facade use. For the low-potential extensive type (T4), effective photovoltaic potential is relatively low. Therefore, a more conservative deployment strategy is more appropriate. Priority should be given to improving basic conditions.

From the perspective of morphological parameters, FAR and BD are the dominant factors affecting effective photovoltaic potential at the building-cluster scale. By contrast, NNI shows a clear interval-based effect. This suggests that, at the block-planning scale, development intensity, building density, and spatial distribution pattern are the key morphological dimensions that require attention. Higher or medium-to-high development intensity is associated with higher photovoltaic generation density. However, high-response zones are not produced by extreme values of any single variable. Instead, they result from the joint action of multiple morphological combinations. Therefore, BIPV planning at the building-cluster scale should move from a single-surface use perspective to a morphology–surface coordinated configuration perspective. At the same time, it should balance intensity control, surface-resource release, and spatial organization.

In addition, the differences in rooftop–facade contribution indicate that photovoltaic deployment in severe cold urban renewal should not be limited to rooftops. Facade potential should also be considered. This is especially important in building clusters with high density, tall buildings, or large facade areas. In these clusters, facades often provide an important source of effective generation. Therefore, during building-cluster renewal and the retrofit of existing buildings, the configuration mode should be selected according to the surface-composition characteristics of different types. Possible options include rooftop-priority, facade-enhanced, and coordinated rooftop–facade deployment.

It should be noted that the planning implications proposed here are mainly intended for overall potential identification and typological expression at the building-cluster scale. They are meant to provide quantitative support for block renewal and spatial optimization. In actual implementation, they still need to be refined in combination with existing building conditions, retrofit cost, grid access, and engineering feasibility.

5. Conclusions

Using Harbin as a case study, this study developed a building-cluster-scale framework for assessing effective BIPV potential and analyzing morphology–response relationships in severe cold regions. By integrating GIS-based spatial analysis with interpretable machine learning, the framework incorporates rooftop–facade surface identification, temperature correction, snow-loss correction, and building-cluster-scale shading correction to evaluate effective BIPV potential under cold-climate constraints.

The results show that effective BIPV potential at the building-cluster scale exhibits clear spatial heterogeneity. High-value clusters are limited in number but show distinct local clustering in the urban core, whereas low- and medium-value clusters form the main background of the study area. Rooftops and facades jointly contribute to effective generation, and facade contribution is generally higher than rooftop contribution, indicating that facades are an essential component of building-cluster-scale BIPV assessment in high-latitude severe cold cities.

Morphology–response analysis further shows that FAR and BD are the dominant variables affecting effective photovoltaic potential, while NNI exhibits a clearer nonlinear pattern. Higher-response zones are concentrated mainly in the combination range of medium-to-high FAR and medium-to-high BD, suggesting that high-value effective photovoltaic potential is shaped by the combined effects of multiple morphological parameters rather than by any single variable alone. On this basis, the study identified a Morphological Sweet Spot and classified building clusters into four representative types.

Overall, this study contributes in four respects: analytical scale, assessment object, methodological framework, and result expression. It takes the building cluster as the core analytical unit, develops an integrated rooftop–facade framework for severe cold conditions, adopts GIS + XGBoost + SHAP + PDP to identify interpretable morphology–response patterns, and translates the results into Morphological Sweet Spots and building-cluster typologies. These findings provide quantitative support for BIPV deployment, morphology regulation, and low-carbon spatial optimization in severe cold urban renewal. Nevertheless, limitations remain in shading precision, parameterized correction, and the consideration of economic and implementation constraints. Future research should strengthen shading simulation, cross-city validation, and the integration of techno-economic factors.