An Analytical Framework for Assessing Equity of Access to Public Electric Vehicle Charging Stations: The Case of Shanghai

Abstract

With the unprecedented growth of electric vehicles usage, the equitable population-based provision of public charging services has become an important concern in high-density urban centers. To address sustainability concerns, this study explores an analytical framework for assessing the equity of access to public charging services. By comprehensively analyzing factors such as accessibility, the Gini coefficient, the correlation coefficient, and supply–demand matching, we investigated the unequal access to public charging stations within 24 types of sites in central Shanghai. The spatial distribution and accessibility were visualized to illustrate differences in service access. Subsequently, social equity was assessed by considering the population distribution and identifying areas of supply–demand imbalance. The results show that 81% of households share only 10% of public charging services, suggesting a generalized inequality within areas and facilities. Residents of large-scale, low-density, low-grade neighborhoods have difficulties accessing services. Nearly 66.96% of subdistricts have supply and demand conflicts. In addition, priority types of improvement were identified and directions for improvement were suggested, as well as recommendations for the integration of PCSs with exterior built places. We also found significant differences in accessibility and equity at both the district and subdistrict level. The findings of this study will help urban planners assess and locate unequal areas and provide insights and the basis for further expansion into the analysis methods adopted at different stages to achieve sustainable development.

1. Introduction

The transition from internal combustion engines to pure electric vehicles (EVs) is among the most effective methods for reducing fossil fuel consumption and air pollution. According to the International Energy Agency (IEA), the total number of EVs worldwide will increase from nearly 30 million in 2022 to 240 million in 2030, with an average annual growth rate of 30%. According to the Ministry of Public Security of China, by the end of 2023, the number of electric vehicles in China will reach 15.52 million. When compared against 2022, this growth rate is as high as 48.52%. By the end of 2023, Shanghai’s new energy vehicle ownership had reached 1.288 million, ranking first among global cities. Moreover, EVs had accounted for more than 50 per cent of new private vehicles. The widespread use of EVs requires a reliable public charging network, with a focus on deploying a sufficient number of public charging stations (PCSs) to meet the charging demand in each area [1]. McKinsey’s EV consumer survey suggests that “consumers are reluctant to buy an electric vehicle unless they can easily access and use a PCS”. As the number of electric vehicles increases, the demand for access to PCSs grows exponentially [2]. However, due to the high building coverage in the center of Shanghai, the high number of high-rise buildings, the high space saturation, and the scarcity of open space available for individual PCS construction, PCSs are generally small. Considering this limitation, it may be difficult for some residents to access adequate public charging services. Therefore, the adequate accessibility of PCSs has proven to be an essential criterion for the assessment of their configuration [3], particularly important for promoting EV use and urban sustainability.

While some countries have incentivized the development of such infrastructure by providing superior public charging facilities, this can also create horizontal and vertical inequities that “disenfranchise” certain groups by hindering their access to charging facilities [4]. In China, public charging posts are unevenly distributed as they are concentrated in public areas with high traffic density in first-tier cities, while gaps exist in other locations [5]. Taking central Shanghai as an example, the backbone expressway is patterned as a “circle”, and the inner-ring area serves as the distinctive city center. Compared with the peripheral areas, the central area has a higher population density and traffic concentration; accordingly, the number of required PCSs is higher, and their distribution will be more clustered. The distribution disparity in the number of stations may lead to inequity for residents in some areas. In the United States, many neighborhoods with large populations but low median household incomes suffer from so-called “charging deserts”, where any public charging facilities are few and far between [6]. Thus, even if the number of public charging facilities increases, some people may experience a lack of charging opportunities, leading urban planners to discuss transportation equity issues when deploying charging facilities [7].

The balance between the supply and demand of public resources is an important dimension of sustainable equity measurement [8]. The ultimate aim of evaluating charging pile allocation is achieving a balance between supply and demand [9]. In January 2022, the Chinese government proposed accelerating the construction of charging facilities in residential communities and prioritizing their allocation to enterprises, public utilities, commercial buildings sites, etc. By the end of 2020, more than 4800 PCSs will have been built across the city, and the 1 km radius coverage of public charging facilities in the central city will reach 93.5%. However, the average time utilization rate of stations around public buildings in areas such as Shanghai is less than 7%, and the service effectiveness of public piles around other types of building is even lower [10]. A plausible explanation is the mismatch between supply and demand caused by the misallocation of facility space [11]. Central Shanghai experiences a high population density, contains urban public resources and municipal facilities, and possesses a highly compact transport system, all in order to facilitate the intensive use of land. PCSs are no exception; they are often attached to building exteriors to provide a functional mix of public services. Therefore, PCSs, due to their urban function, appear in diverse forms, and the distribution of different PCS-types is likewise heterogeneous. Consequently, it is vital to explore and mitigate the supply–demand discrepancy that occurs because of diverse PCS allocation [12] to grant residents equitable access to these facilities.

In summary, urban planners and policymakers must assess spatial equity levels in PCS distribution and adjust their allocation strategies accordingly to achieve equitable distribution. To this end, an analytical framework examining whether residents’ access to PCS services is equitable, based on multiple PCS accessibility measures, is developed in this study. Moreover, we examine conflicts between service access and population needs, and we provide improvement recommendations. In particular, an effective PCS categorization scheme is proposed. In addition, inequitable areas in need of prioritized intervention are identified, and recommendations for improvements are also made. These measures will facilitate PCS accessibility in high-density urban areas, engender a better understanding of the inequity in the context of PCS development, and promote research on the classification and matching of PCS supply and population demand to various building types.

2. Literature Review

There have been three main aspects of PCS fairness studies: Firstly, differences in accessibility are compared between different regions or populations based on accessibility measures. The basic idea of the two-step floating catchment area method (2SFCA) [13] and the Gaussian-based two-step floating catchment area (G2SFCA) model are mainly used to assess PCS accessibility [14]. In the assessment process, the service capacity is reflected through indicators such as the number of charging piles within the PCS and the number of vehicle turnovers, but the proportion of the PCS’s facilities actually being utilized by users is not taken into account; the use of straight-line distances as a threshold makes it difficult to reflect the actual driving time required for residents to access the service, which leads to a bias in the calculation. In addition, residents have different needs for different types of PCSs. Therefore, the 2SFCA method needs to be optimized in terms of service capacity parameter formulation, time threshold measurement, and population allocation weights. Secondly, the relationship between the number of PCSs and deployment density (including per capita, per land, per vehicle, etc.) and the demographic attributes of the statistical unit has been modeled to quantify the variability of the configuration. Population attribute variables are mostly formulated in terms of background differences such as income, ethnicity, and education [12,15,16], with little attention paid to residential differences in the population. There is a need to further develop the system of population demand variables under different conditions of residential differentiation in order to gain a more comprehensive understanding of inequities that takes into account differences in population demand. Thirdly, using equitable access to PCSs as a constraint, the optimal set point for PCSs is proposed by taking into account the requirements of PCSs and the parking lots where they are located (e.g., cost, energy components, etc.). The key to these studies is to find the optimal solution to meet the EV charging demand (priority event counterpart demand, purchased power demand, etc.) as reflected in the status quo of the case area [17,18]. The current literature does not explore the mismatches that can occur under conditions of potential population demand, and this element can help urban planners to respond in advance. It is worth noting that the above studies are centered on three dimensions—the number of PCS configurations, the facilities within PCSs, and the internal and external linkages of PCSs—and the descriptions of PCSs are progressively more complete. However, the association between PCSs and building sites outside the stations is neglected. In particular, in high-density central urban areas with tight land use, PCSs are difficult to build independently and need to be dependent on multi-functional building sites to provide transport energy services.

To analyze the equity of access to public transportation facility services, current research uses various measures for quantification. Accessibility is widely used to assess the equity of urban public facility services [19], especially transportation infrastructure [20]. Measurement models such as the 2SFCA, the nearest distance method [21], and buffer analysis [22] have been developed. Currently, 2SFCA [23] and its extended method, which can incorporate factors such as supply, demand, and transportation costs into the calculation [24], are recognized as efficient models. Previous studies have applied accessibility to equity measurement using a variety of methods. Gini coefficients have been used to plot Lorenz curves aggregating accessibility with population data [25,26]. Correlation coefficients are used to examine the relationship between population and accessibility, reflecting the presence of inequality [26]. In addition, spatial autocorrelation that identifies spatial structures and mechanisms is gradually applied to the measurement of equity in public service facilities [27]. In order to identify patterns of supply and demand, bivariate spatial autocorrelation spatially supports the study of heterogeneity in service supply and demand [28]. Z-value normalization is a statistical method for calculating the “high value” and “low value” correspondences of service and demand variables [29]. In addition, further measures of the difference between supply and demand provide a more accurate picture of the level of inequality. Location entropy is used to quantitatively assess the degree of matching between resources and population demand in a cell [30]. The supply–demand coupling and coordination model, on the other hand, provides two-parameter calculations that support further delineation of coordinated development types [31]. In conclusion, the methodology of equity in access to public transport facility services mainly involves three stages: spatial accessibility calculation, social equity measurement, and spatial matching analysis.

Each PCS belongs to a specific category, as PCSs require a “hosting” relationship with the building site in terms of parking, management, and electricity usage [32]. Although PCS programs are installed in several urban areas around the world, most lack a comprehensive analysis of building sites [33]. A review of off-station building site studies is necessary. Supported by the literature, there are three main categories of off-station building sites: home, work, and public services [34,35,36,37]. The building sites were further subdivided into a category system of “3 major categories, 10 medium categories, and 19 small categories” (

Table 1. Types of external building sites for PCSs.

Large Category	Medium Category	Small Category
Residence	/	Residential neighborhoods
		Apartment buildings
Workplace	/	Office development
		Industrial parks
		Enterprises and government organizations
		Factories
Public service place	Business	Shopping centers, supermarkets, malls, convenience stores
		Hotels
		Car rental stations
		Restaurants and cafés
	Recreation	Landscape areas, amusement parks, theme parks, zoos, aquariums, urban green spaces, tourist areas, etc.
		Sports grounds, recreational facilities, swimming pools, etc.
	Campus	Universities, primary and secondary schools, and other schools
	Public Buildings	Hospitals
		Cultural centers, libraries, stadiums, science and technology centers, museums, art galleries, etc.
	Car Parks	On-street parking, park-and-ride (P + R) car parks, public or private car parks on separate sites, and dedicated car parks for public services such as public transport, rentals, sanitation and logistics
	Traffic Hubs	Railway stations, airports, large metro stations, etc.
	Motorway	Intercity motorway service areas
	Others	Petrol stations, filling stations, etc.

). Since not all established residential communities have the conditions for installing private piles, and residents also generate public charging needs for office and service destination activities, PCSs have the value of being deployed around various types of building sites (such as residences, flats, and public buildings) in the center of the city. Therefore, PCSs can be categorized into three types accordingly: residential public charging stations (RPCSs), workplace public charging stations (WPCSs), and service public charging stations (SPCSs). This categorization will help to improve the accuracy of the equity and matching analysis.

Therefore, this study proposes a multi-stage analytical framework for measuring facility access equity based on PCS categorization to facilitate the improvement of inequalities in access to PCS services. Grounded in the status quo analysis of PCS service capacity, a map API was invoked to determine the time threshold, and a G2SFCA model was used to check the accessibility of PCSs by type in each subdistrict. Population needs were considered when assessing facility access equity. The Gini coefficient was calculated to determine horizontal equity for all populations, and Spearman’s rank correlation coefficient was calculated to determine vertical equity for specific populations. In order to differentiate between types of inequality areas, the Z-value standard deviation method was used to examine the mismatch relationship between service access and population, and the degree of mismatch was calculated using the coupled coordination degree model to prioritize improvements. Based on this, recommendations for improvement are made in relation to the current situation.

Additionally, the purpose of this study is to develop an analytical process for formulating a system of indicators for subdistricts’ demographic needs by integrating social and spatial attributes, examining the social equity and spatial matching between accessibility and demographic need correlations, and suggesting optimizations for areas of inequity. A methodology that balances social and spatial perspectives is provided for urban planners to assess and compare equity in access to public charging infrastructure.

3. Research Methodology

Figure 1 illustrates the analytical framework used in this study, which is divided into four phases: “analysis of the current situation”, “accessibility calculation”, “equity measurement”, and “matching analysis”. In this study, based on the status quo analysis of the distribution of multiple types of PCS, spatial accessibility is calculated using the G2SFCA method; using accessibility as an input, the Gini coefficient and Spearman’s rank correlation coefficient are applied to further superimpose the population demand in order to measure the equity in access to the PCS services; and finally, the supply–demand imbalance and the areas that need to be prioritized for improvement are identified through the Z-value standard deviation method and the coupled coordination degree model. Based on the results of the four-stage decision-making process and the current distribution of facilities, directions for improvement in PCS allocation are proposed.

3.1. Stage 1: Analysis of the Current Situation

First, it is necessary to provide an overview of the spatial distribution of PCSs in the central city in order to reflect the current status of PCS configuration. This is mainly analyzed from two perspectives: agglomeration and balance.

Facility agglomeration: This assesses the proportion of PCSs in each study unit distributed over 1% of the land area of the entire study area [38]. The formula is as follows:

$${AD}_i={\displaystyle \frac{R_i/R_n\times 100\%}{A_i/A_n\times 100\%}}={\displaystyle \frac{R_i/A_i}{R_n/A_n}}$$

(1)

where ${AD}_i$ is the degree of agglomeration of subdistrict i, $R_i$ is the number of PCSs in subdistrict i, $R_n$ is the number of PCSs in the central city, $A_i$ is the area of subdistrict i, and $A_n$ is the total area of the central city.

Facility coverage: Using the buffer tool of Arcmap 10.7, a buffer zone with a radius of 1000 m was delineated for the three types of PCS (according to the 14th Five-Year Plan for New Energy Charging (Switching) Facilities in Shanghai, the service radius of PCSs in the city center was calculated as 1000 m). Facility coverage is the ratio of households in the buffer zone to the total number of households in each subdistrict. The GIS visualization shows the differences in the agglomeration and coverage characteristics of each subdistrict, reflecting possible distributional inequities, but the actual access of residents to the service requires further precise calculations.

3.2. Stage 2: Calculation of Accessibility

Accessibility reflects how easy or difficult it is for residents to obtain services from PCSs. The 2SFCA methodology can be used to quantify accessibility through weighted calculations that translate the service capacity values of the PCSs into the service capacity values that the subdistrict actually receives within the threshold. The 2SFCA model was initially used to assess spatial inequality in healthcare services [39] and has since been widely applied to other urban planning and facility access issues [40]. In this paper, the G2SFCA model is used for analyzing accessibility. The G2SFCA model is derived from the traditional 2SFCA method. The traditional 2SFCA method considers undifferentiated spatial reachability within a certain threshold distance and unreachability outside the threshold distance, a representation which is quite different from the actual situation. In order to better simulate the distance-attenuation effect, scholars have developed multiple types of extended forms of 2SFCA, with the aim of improving the dichotomy which shows no difference in reachability within the search radius in the original form of 2SFCA into different types of segmented-type or continuous-type distance-attenuation functions. The segmented function is a rough simulation under the limitation of data accuracy as well as computational performance, and there is still a big gap with the realistic spatial relationship. The Gaussian function is a continuous-type function that can more realistically simulate the effect of spatial distance on spatial interaction forces, and its use as a distance-attenuation function for the 2SFCA is now widely used in the evaluation and analysis of the accessibility of various types of public service facilities. Therefore, the G2SFCA method, which is the integration of the 2SFCA model with the Gaussian function, was chosen for this study. By quantifying the distance decay effect using a Gaussian function, a more realistic spatial accessibility assessment is obtained by smoothly reflecting the reality that the influence of service facilities decreases with distance [41,42].

However, when using the G2SFCA model to effectively analyze spatial accessibility, multiple issues such as service and population parameter formulation, distance decay function use, threshold determination, facility selection weights, etc., need to be considered [43], and there is a need to calibrate the existing G2SFCA algorithms step by step in order to reduce the errors in the accessibility calculation process. Specifically, the following computational steps are included:

(1) Service parameter: The PCS service requires by both DC and AC chargers. Since DC charging piles are several times more powerful than AC charging piles, calculating the total PCS charging power can more accurately characterize the PCS service capability compared to the number of charging piles. At the same time, considering that not all charging piles are effectively used in the current situation, the following formula is obtained by combining the differences between the actual utilization rates of the three PCSs in the population:

$${\mathrm{CP}}_j= (\mathsf{\alpha }·N_{DC,j}+\mathsf{\beta }·N_{AC,j})·\lambda$$

(2)

where ${\mathrm{CP}}_j$ is the public charging service capacity of PCS j, $N_{DC,j}$ is the number of DC charging piles at PCS j, $N_{AC,j}$ is the number of AC charging piles, α is the DC charging pile power, and β is the AC charging pile power. According to the statistics of Shanghai’s official platform “Lianlian Charging” in 2021, DC charging piles are mainly 45 kW, while AC charging piles are mainly 7 kW; λ is the average utilization rate of the piles. According to the Charging Infrastructure Monitoring Report of Major Cities in China in 2022, the utilization rates of RPCSs, WPCSs, and SPCSs are 41.8%, 49.1%, and 57.7%, respectively.

(2) Population parameter: The population size $p_k$ of each subdistrict k is the sum of the number of households $p_m$ in each residential neighborhood (RN) within that subdistrict. Using the number of households as a population size parameter is in line with the current practice of allocating EV purchase targets on a household basis. The calculation formula is as follows:

$$p_k=\sum _{m=1}^n{P}_m$$

(3)

In addition, to better represent reality, each RN’s population center of gravity within a subdistrict was used as the subdistrict center [44]. The coordinates of each subdistrict center were calculated as follows:

$$X_k={\displaystyle \frac{\sum _{m=1}^n{P}_m{x}_m}{\sum _{m=1}^n{P}_m}}(\mathrm{m}=1,2,\dots ,\mathrm{n})$$

(4)

$$Y_k={\displaystyle \frac{\sum _{m=1}^n{P}_m{y}_m}{\sum _{m=1}^n{P}_m}}(m=1,2,\dots ,n)$$

(5)

where there are n RNs in subdistrict k, m is any RN in the subdistrict, the latitude and longitude coordinates of each RN are ($x_m$, $y_m$), and ($X_k$, $Y_k$) are the coordinates of the center of the corresponding subdistrict k.

(3) Distance decay function: Since the traditional 2SFCA method classifies facilities’ ability to provide services into two categories based on the threshold time, it does not consider the fact that it constantly decays with increasing distance. For this reason, we chose to improve it by selecting a Gaussian distance decay function. In addition, the service catchment weight calculation through the distance decay function ignores the actual spatial impedance by using the linear distance between the facility and the population center instead of the trajectory distance. Therefore, the actual traveling time was used in the decay function to make it more realistic. The calculation formula is as follows:

$$G\left(t_{kj},t_0\right)=\left\{\begin{array}{c}{\displaystyle \frac{e^{-\left(\frac{1}{2}\right)\times \left(\frac{t_{kj}}{t_0}\right)}-e^{-\left(\frac{1}{2}\right)}}{1-e^{-\left(\frac{1}{2}\right)}}}, if{t}_{kj}\le t_0 \\ 0, if t_{kj}>t_0\end{array}\right.$$

(6)

where $G\left(t_{kj},t_0\right)$ is the value of the Gaussian distance decay function, $t_{kj}$ is the time cost between subdistrict center k and PCS j, and $t_0$ is the time threshold.

(4) Time threshold determination: through our analyses, we chose 8 min as the time threshold $t_0$. We derived a time threshold from our analyses that allows most demand locations to have at least one PCS accessible, but prevents them from accessing too many PCSs. This is in line with people’s willingness to travel in order to access services. If there is no PCS nearby, people may travel further; conversely, if there is an abundance of PCSs nearby, people may not waste additional time searching for them. In this paper, we introduce AutoNavi API route planning to calculate the actual traveling time and determine the time thresholds. AutoNavi API route planning is the result of real-time navigation measurements based on map data, with the option of time measurements in the private car traffic mode, which is more closely related to the actual situation of residential users who are driving in search of PCS. The service time thresholds for the three types of PCS are based on the time cost corresponding to capturing at least one PCS at more than 95% of the demand points [14]. Specifically, we used the AutoNavi API Route Planning 2.0 module via the Datamap tool to calculate the start and end time cost matrices required for each subdistrict center with all three types of PCS. We analyzed the minimum critical travel time that would allow most subdistrict centers to visit at least one PCS in increments of 1 min. The results show that the proportion of zonal centers that can capture at least one RPCS, WPCS and SPCS within the 8 min time threshold is greater than 95% of all zonal centers at 100, 95.65, and 100% respectively.

(5) Facility weight setting: Since users will choose to visit different PCSs in different building sites for charging according to their preferences, it is necessary to set weight values for different PCS types. In this paper, the weight $w_j$ is set to indicate the influence of different types of PCS on users’ preferences, referring to the research results of the 2022 China Electric Vehicle Users’ Charging Behavior White Paper. Moreover, RPCS, WPCS, and SPCS weights are set to 0.1, 0.15, and 0.75, respectively.

(6) Calculation by type: The first step of the search is as follows: centered on PCS j, search each subdistrict center k within the time threshold, calculate the service population $p_n$, and combine the Gaussian function and weights to determine the service-to-population ratio $R_j$. The formula is as follows:

$$R_j={\displaystyle \frac{{\mathrm{CP}}_j}{{\sum }_{k\in \left\{t_{kj}\le t_0\right\}}G{\left(t_{kj},t_0\right)P}_n{w}_j}}$$

(7)

where $R_j$ is the service-to-population ratio of PCS j; ${\mathrm{CP}}_j$ is the public charging service capacity of PCS j; $G\left(t_{kj},t_0\right)$ is the value of the Gaussian distance decay function between subdistrict center k and PCS j; $P_n$ is the potential service population; and $w_j$ is subdistrict center k’s residents’ willingness to use PCS j.

The second search step is as follows: Centering on subdistrict center i, search each PCS j within the time threshold range, and combine a Gaussian function with residents’ willingness to wait and sum the PCS service to population ratio to derive the accessibility of each subdistrict center $A_i$. The formula is as follows:

$$A_i={\displaystyle \sum _{j\in \left\{t_{ij}\le t_0\right\}}}G\left(t_{ij},t_0\right)R_j{w}_j$$

(8)

where $A_i$ is the accessibility of subdistrict center i, $R_j$ is the service-to-population ratio of PCS j, $G\left(t_{ij},t_0\right)$ is the value of the Gaussian distance decay function between subdistrict center i and PCS j, and $w_j$ is the subdistrict center i’s residents’ willingness to use PCS j.

Calculations can obtain $A_{rpcs,i}$ (RPCS accessibility), $A_{wpcs,i}$ (WPCS accessibility), and $A_{spcs,i}$ (SPCS accessibility). Summing these three accessibility scores yields $A_{pcs,i}$ (total accessibility).

The above calculations may reflect gaps in users’ current access to PCS services; however, further analysis of the underlying population’s size and characteristics is needed to determine whether and to what extent inequalities exist.

3.3. Stage 3: Equity Measurement

Horizontal equity: This measures whether the overall distribution of PCS service access is equitable across all populations. The Gini coefficient helps assess the overall level of inequality in a population and is used in transportation equity studies to quantify inequality in automobile transit accessibility [45]. The Gini coefficient reflects the ratio of the area of the gap between the Lorenz curve and the line of perfect equality to the total area under the line of perfect equality [46,47]. The formula is as follows:

$$G_p=1-\sum _{i=1}^n\left({\mathrm{Y}}_i+{\mathrm{Y}}_{i-1}\right)·\left({\mathrm{X}}_i-{\mathrm{X}}_{i-1}\right)$$

(9)

where $G_p$ is the Gini coefficient, ${\mathrm{Y}}_i$ is the cumulative percentage of PCS accessibility, and ${\mathrm{X}}_i$ is the cumulative percentage of a subdistrict population.

The Gini coefficient is between 0 and 1. The larger the value, the more the Lorenz curve bends, and the higher the inequality. A Gini coefficient of less than 0.2 indicates a very high average, 0.2–0.3 a high average, 0.3–0.4 a reasonable level, 0.4–0.5 an excessive gap, and 0.5 a very excessive gap.

Vertical equity: This measures equity in PCS service access for people with different characteristics. Urban facilities studies have used Spearman’s rank correlation coefficient as an indicator of vertical equity [48,49]. This coefficient has been used to assess vertical equity in accessibility as a scale-independent indicator [50,51], with the advantage of being easy to interpret by policymakers [48]. The formula is as follows:

$$\mathrm{V}\mathrm{E}={\rho }_{r{A}_i,r{X}_i}={\displaystyle \frac{cov(r{A}_i,r{X}_i)}{{\sigma }_{r{A}_i}{\sigma }_{r{X}_i}}}$$

(10)

where VE denotes the vertical equity indicator; ${\rho }_{r{A}_i,r{X}_i}$ is Spearman’s rank correlation coefficient; $r{A}_i \mathrm{and} r{X}_i$ correspond to the accessibility class and the subdistrict population class of each subdistrict, respectively; $cov(r{A}_i,r{X}_i)$ is the covariance between the accessibility class and the population class of the subdistrict; and ${\sigma }_{r{A}_i}$ and ${\sigma }_{r{X}_i}$ are the standard deviations. The values of VE range from −1 to 1, indicating that accessibility decreases completely or increases completely, respectively, as the subdistrict demographic index increases.

The measurements suggest that there may be both horizontal and vertical inequities in access to PCS services. The uneven distribution of PCS accessibility and maladjustment to population are among the main causes of inequality in public charging services. To improve inequality, further matching analysis is needed to identify mismatched areas.

3.4. Stage 4: Matching Analysis

Mismatch types: A Z-value standardization method is introduced to analyze the match between PCS service access and population. This is a statistical method that effectively distinguishes between high and low values of a variable [29]; it can be used to show the correspondence between high and low values of two variables, and it is widely used in urban planning and geography studies, such as for measuring the gap between the supply and demand of transportation services [24,52]. The formula is as follows:

$$Z_{A_i}=(A_i-\overline{A})/{\delta }_A$$

(11)

$$Z_{D_i}=(D_i-\overline{D})/{\delta }_D$$

(12)

To avoid the influence of accessibility (kW/household) and population unit (household) on the calculation results, the normalized values are taken separately, where $\overline{D}$ and ${\delta }_D$ are the mean and standard deviation of the normalized values of the population of each subdistrict, respectively, while $A_i$ and ${\delta }_A$ are the mean and standard deviation of the normalized values of accessibility, respectively. The x-axis denotes $Z_{A_i}$ and the y-axis denotes $Z_{D_i}$.

Four quadrants were formed to classify the matching relationship into four types: high supply–high demand (Quadrant I), low supply–high demand (Quadrant II), low supply–low demand (Quadrant III), and high supply–low demand (Quadrant IV) [53]. The PCS accessibility–population matching relationship was calculated for each category in turn to identify mismatched subdistrict s with “oversupply” and “undersupply” phenomena.

Improving prioritization: Due to limited resources, it is important to identify the types of PCS that need to be prioritized for improvement. In order to make accurate comparisons, the degree of coordination between supply and demand needs to be quantified. The more uncoordinated a subdistrict is, the more it should be prioritized for improvement. The coupled coordination degree model is thus introduced. This model has been applied to studies related to transportation, travel [54], and accessibility to public service facilities [55,56], reflecting the interactions between the systems and the level of coordinated development, and helping us to effectively measure and compare the development of different regions [57]. The calculation method is as follows:

$$\mathrm{C}={\displaystyle \frac{2\sqrt{{\mathrm{A}}_{\mathrm{i}}^{\prime }{·\mathrm{D}}_{\mathrm{i}}^{\prime }}}{{\mathrm{A}}_{\mathrm{i}}^{\prime }+{\mathrm{D}}_{\mathrm{i}}^{\prime }}}$$

(13)

$$\mathrm{T}=\mathsf{\alpha }{\mathrm{A}}_{\mathrm{i}}^{\prime }+\mathsf{\beta }{\mathrm{D}}_{\mathrm{i}}^{\prime }$$

(14)

$$\mathrm{D}=\sqrt{\mathrm{C}·\mathrm{T}}$$

(15)

where ${\mathrm{A}}_{\mathrm{i}}^{\prime }$ and ${\mathrm{D}}_{\mathrm{i}}^{\prime }$ are the normalized values of the indicators of the PCS service access subsystem and the PCS population demand subsystem, respectively; C denotes the degree of coupling between the two subsystems; T denotes the integrated development indicator of the subsystems; and α and β stand for the contribution rates of service access and population demand, respectively. Since the two subsystems are equally important, both α and β are set to 0.5, where D represents the degree of coupling coordination—0 ≤ D < 0.2: severe imbalance; 0.2 ≤ D < 0.4: moderate imbalance; 0.4 ≤ D < 0.5: mild imbalance; 0.5 ≤ D < 0.6: barely balanced; 0.6 ≤ D < 0.8: well balanced; and 0.8 ≤ D < 1.0: superior balance.

Comparing the coupling coordination degree of RPCS-, WPCS-, and SPCS-mismatched subdistricts, the largest value is the type of intervention that is prioritized. Based on this, mismatched subdistricts can be classified into six types of areas: RPCS-undersupplied priority improvement areas, RPCS-oversupplied priority improvement areas, WPCS-undersupplied priority improvement areas, WPCS-oversupplied priority improvement areas, SPCS-undersupplied priority improvement areas, and SPCS-oversupplied priority improvement areas.

4. Research Data

4.1. Research Area: The Central Urban Area of Shanghai

This study takes the central urban area of Shanghai as the research object. Shanghai has three important elevated ring roads: the Inner Ring Road, the Central Ring Road, and the Outer Ring Road. The central urban area is the area within the outer ring road, including 11 districts and 115 subdistricts (Figure 2). This area has many EVs and frequent external transportation links. The results of this study have important implications for future PCS construction in Shanghai.

4.2. Datasets

4.2.1. PCS Data

The PCS data were obtained from “Lianlian Charging” (www.evchargeonline.com (accessed on 13 June 2022)). This platform is the only official PCS data platform designated by the Shanghai Municipal Government. Firstly, we wrote two programs in Python, including a crawler and a merge and de-duplication program. After initially inputting the names of Shanghai’s municipal districts into the crawler for the data acquisition of PCSs in different districts, the merge and de-duplication procedure was initiated to form the final PCS dataset. A total of 10,597 PCS data points were collected across the city, including 5258 dedicated stations and 5339 PCSs (as of June 2022) using the crawler. Secondly, the corresponding latitudinal and longitudinal coordinates were obtained according to the formatted address rules using the forward geocoding function of AutoNavi Map (lbs.amap.com (accessed on 25 November 2022)), and the PCS and RN data were transformed into spatial point elements using the Display XY tool of Arcmap 10.7. Finally, the Intersect tool was used to extract the point data within the boundary of the central city. Through the aforementioned data acquisition and processing process, a total of 2971 PCSs within the central urban area had their data extracted. Each PCS data item contains the number of charging piles and other basic information.

Currently, there are no official city-level statistics on EV charging stations [13]. However, data comparison is possible through policy and planning documents issued by the Shanghai Municipal Government. The 14th Five-Year Plan for the development of new energy charging (switching) facilities in Shanghai shows that by the end of 2020, 4800 PCSs and 63,000 public charging piles had been built in the city. The data obtained are accurate as of June 2022, and include 5339 PCSs with a total of 67,303 charging piles. Based on the growth target set by the Shanghai Municipal Government (6500 PCSs by 2025), assuming a projection based on an average year-on-year growth, 5480 PCSs will be built in 2022, which is very close to the data obtained in this case (5339 PCSs). Additionally, to further verify data credibility, the number of PCSs of the mainstream operator “TELD” was selected for verification. The total number of PCSs in the relevant jurisdictions in both the urban and central city areas is close to 90 per cent of the number of PCSs displayed on the operator’s APPs, which is a high level of data coverage.

The PCSs in the central urban area were classified into three categories according to the building site classification listed in the Section 2. Two urban planning engineers with more than 10 years of planning and design experience independently performed a manual reading of each building function at the PCS address. The results were cross-verified to form the current classification result. Considering the reality of Shanghai, four new items—namely, villas, talent apartments, research institutions, and funeral facilities—were added, and enterprises and institutions were subdivided into two types. As a result, PCSs in central Shanghai were divided into 24 subcategories. Among them, those in building sites 1–4 are RPCSs, those in building sites 5–10 are WPCSs, and located in building sites 11–24 are SPCSs (

Table 2. Classification of PCSs in Shanghai.

Type of PCS	Type of External Building Site	Number of PCS (pcs)	Percentage
RPCS	Residential neighborhoods	591	19.89%
	Villa	31	1.04%
	Commercial and Residential Apartments	74	2.49%
	Talent Apartments	4	0.13%
WPCS	Office buildings	703	23.63%
	Industrial Parks	286	9.61%
	Enterprises and Institutions	47	1.58%
	Government and Social Organizations	31	1.04%
	Factories	12	0.40%
	Research Institutions	11	0.37%
SPCS	Shopping	501	16.81%
	Hotels and Hostels	193	6.47%
	Automotive	130	4.36%
	Dining	19	0.64%
	Scenic Spots	48	1.61%
	Sports and Leisure	25	0.84%
	Education and Training	52	1.74%
	Medical	49	1.64%
	Culture, Sports, Science and Technology Venues	42	1.41%
	Public Car Parks	81	2.71%
	Traffic Hubs	22	0.74%
	Highway Service Areas	2	0.07%
	Petrol (Gas) Stations	12	0.40%
	Funeral	5	0.17%

). Using IBM SPSS Statistics 23′s complex sampling tool, stratified sampling by district was conducted from 2971 PCS samples with a 1% sampling ratio, resulting in 30 PCS samples. We searched for these PCSs online, and site pictures were obtained to verify the authenticity and reliability of the PCS information (

Table A1. Photographs of 30 sampled PCSs.

[Star Charge] DC Charging Station for Box Office (New Aloe City Store)	Johnson Rental Yindu Road	Fenxiang Charging (Lane 958 Xin Song Road)
Longhu Huajing Tianjie Charging Station, Xuhui District, Shanghai, China	Foreshore Corporate World II 2	Spring Dawn in Shilong
Shanghai Longyang Road Charging Station	Shanghai Red Star Macalline Wuzhong Store Charging Station	Changning Raffles (Hotel Chain)
Shanghai Fuxing Longyi Charging Station	Hengjie Building	Electric Vehicle Charging Point at Kingboard Property, Changning District, Shanghai
Lane 945, Kwai Chung New Town	[Star Charge] Xiangshan Market Charging Station	BMW Charging Station in Jing’an Joy City, Shanghai
Home Inn Group and Yi Hotel Jinqiao Branch	Charging Station, 399 Xinfu Road, Shanghai	Platinum Bay Residence
Gonghua New Village	Li Zi Yuan Building Charging Station	Shanghai Dragon Motor Co.
Xinpu Hui Commercial Plaza	Chenghong-Shibei Hi-Tech Park	Shanghai Cable Technology Park
Qixiuayuan, BaoShan District	Charging station in Shanghai Xinjinbo Building	Fung Po Court
D8 Park	No. 208 Datong Road	Fenxiang Charging (No. 2, Lane 201, Tongtai North Road)

in Appendix A).

4.2.2. Subdistrict Population Data

The data for each RN contain the number of households and other community building information. We counted the quartiles of the data related to the attributes of the RNs. In

Table 3. Demographic attributes of subdistricts.

Serial Number	Variables	Explanation of RN Characteristics
X1	Population living in multi-building RNs	RNs larger than 15 buildings
X2	Population living in multi-family RNs	RNs larger than 700 homes
X3	Population living in large RNs	RNs larger than 6 hectares
X4	Population living in completely small- and medium-sized type of flat	RNs with no large-sized type of flat
X5	People living in low greening residential RNs	RNs with greening ratio less than or equal to 30%
X6	Population living in RNs with high floor area ratio (FAR)	RNs with FAR greater than 2.4
X7	People living in RNs with high housing costs	RNs with house price higher than CNY 90,000/m2
X8	People living in RNs with high property costs	RNs with property tax above CNY 1.6/month·m2
X9	People living in newer RNs	RNs up to 20 years old
X10	People living in RNs with adequate parking	RNs with parking ratios greater than 0.8/household

, the high values of the characteristics of the variables are formulated above the 3/4 quartile and the low values below the 1/4 quartile. On this basis, a system of subdistrict demographic attribute indicators reflecting the characteristics of residential differentiation was formulated (Table 3). Among them, X1, X2, and X3 reflect the spatial scale differentiation of the RNs; X4, X5, and X6 reflect the construction intensity differentiation of the RNs; and X7, X8, X9, and X10 reflect the quality grade differentiation of the RNs. In addition, the variables are all characterized by the number of households in the subdistrict that meet specific criteria as a percentage of the total sample.

Figure 3a illustrates the distribution of the different types of PCS in the subdistricts. Figure 3b shows the distribution of the subdistrict population and subdistrict centers.

The distribution of RPCSs may be related to where EV owners live. Since not all established RNs are equipped to install private piles, the primary purpose of RPCS deployment is to supplement the private pile layout, focusing on being used to address the charging needs of EV owners in their RNs. Moreover, even if RPCSs are open to all users, EV owners living in their RNs are likely to be the main beneficiaries. This means that we can observe the current spatial distribution characteristics of some EV owners from the distribution of RPCSs. We calculated the distribution density of RPCSs in each subdistrict and used Natural Breaks (Jenks) to classify the subdistricts into five categories from high to low density. We also counted the mean values of the five subdistrict categories’ demographic variables. As shown in

Table 4. Comparison of mean values of demographic attributes for subdistricts with different RPCS density classes.

Density Level	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10
Extremely high	32.12%	31.70%	7.73%	26.18%	51.39%	36.12%	48.58%	26.87%	24.48%	11.57%
High	43.60%	55.41%	10.83%	22.13%	49.99%	30.36%	28.57%	19.96%	27.86%	6.65%
Medium	46.37%	59.13%	17.65%	22.51%	41.57%	31.64%	27.62%	25.54%	36.17%	8.66%
Low	49.12%	59.32%	20.35%	22.26%	39.39%	22.82%	30.80%	26.48%	40.11%	9.76%
Extremely low	54.51%	64.30%	15.59%	21.38%	44.14%	21.25%	12.21%	15.80%	42.67%	5.57%

, the higher the percentage of residents in high-density, high-quality RNs within the central city, the higher the likely distribution density of EV owners. Conversely, areas with a higher percentage of residents in large RNs are likely to have a lower distribution density of EV owners. It is worth noting that, to accurately determine the distribution of EV owners, a comprehensive assessment needs to be made in conjunction with the distribution of RPCSs as well as other relevant data and analyses, such as EV sales data, registration data, and traffic flow.

5. Results

5.1. Current Distribution of PCSs

We used Excel 2016 to count the agglomeration and visualized the results using ArcGIS 10.7, with the darker areas indicating higher PCS agglomeration. The spatial clustering of PCSs is shown in Figure 4d. The subdistricts with high clustering of PCSs are all distributed in the area west of the Huangpu River, while the areas east of the Huangpu River are generally low in clustering. In particular, more PCSs are highly concentrated in the city center area within the inner ring, resulting in one significant clustering area in the western area within the inner ring. Figure 4a–c show the distribution of the spatial agglomeration of the three types of PCS. RPCSs are distributed in all districts, with varying degrees of clustering at the edges or centers of the districts. WPCSs are mainly concentrated in the border areas of the two districts of JA and HP, and they stretch from east to west to form a continuous zone. There is also a significant regional clustering of the distribution of SPCSs, which are mainly located in the central area of HP. More WPCSs and SPCSs are highly concentrated in the downtown area, although they are also found in other areas.

We used the buffer tool in ArcGIS 10.7 to map PCS coverage areas, count population coverage, and display the results overlaid with RN point elements. Darker-colored areas indicate higher PCS coverage and different colored points indicate different build date. Figure 5 shows the differences in PCS population coverage, with high-coverage units located around the city center, which is largely covered. However, there are still multiple low-coverage areas on the periphery (marked with a red line in Figure 5). Spatial differences in population demand under residential differentiation were analyzed by further overlaying RNs in these areas. In areas with later residential construction, the population’s need for charging may not be as pressing. As a result, large-scale protected housing communities that started construction after 2000 are not well covered by PCS services, such as the Gucun residential community (Zone 6) and the Caolu residential community (Zones 5 and 7). There are also blind spots in the coverage of some high-quality neighborhoods under construction and their surrounding areas, such as Senlan International Community (Zone 8) and Qiantan International Community (Zone 1). In addition, there is a lack of PCS service in residential areas supporting industrial parks, such as the neighborhoods surrounding Kangqiao Industrial Park (Zone 10), Yangpu Electric Industrial Park (Zone 2), and Zhangjiang Hi-Tech Park (Zone 4). In particular, the Lingqiao community near Waigaoqiao Free Trade Zone (Zone 14) is not covered by any PCSs; even though it is located in the suburbs, with sufficient land conditions, it fails to provide sufficient access to PCSs. Some scattered old residential areas and welfare communities (Zones 3, 9, 12, and 13) are also excluded from the coverage area. By analyzing the current situation, the phenomenon of PCS aggregation and coverage blindness can be identified to provide a basis for exploring PCS service acquisition.

5.2. Spatial Variation in PCS Accessibility

Accessibility varies by service capacity, time threshold, and population. We used the Data map for Excel V6.9.2 plug-in to use the AutoNavi API Route Planning 2.0 Module to count and compare the time spent between the PCS and subdistrict centers, which was performed using Excel 2016 in order to determine the time thresholds and to calculate accessibility by combining the service capacity with the population. The accessibility was visualized with the help of ArcGIS 10.7. Darker-colored areas indicate higher PCS accessibility. The spatial layout of accessibility is shown in Figure 6. The results show that the mean value of accessibility for RPCSs is the lowest among the three categories, with a continuous unequal distribution in the area west of the Huangpu River. The continuous distribution of high values in the area east of the Huangpu River suggests that the RPCSs may fulfill most of the needs at the zoning level in terms of service capacity, except for a few areas with lower accessibility, such as the riverfront area west of the PD (Figure 6a). In contrast, WPCS accessibility (Figure 6b) is locally dotted, suggesting that WPCS services are centrally provided in internal subdistricts in multiple subareas (MH, CN, CH, HP, BS, YP). Compared to the other two types of facilities, SPCSs have the highest average accessibility of the three categories, but the distribution of their accessibility is more concentrated, showing a localized block distribution dominated by HP and MH (Figure 6c). As shown in Figure 6d, PCS services are more accessible in the central and southern MH areas. These are areas of high population concentration and mobility in Shanghai. In summary, the overall spatial distribution of PCS accessibility in downtown Shanghai is unbalanced. Determining the variability in access to public charging services based on the results of the accessibility analysis supports the ability to focus on difficult areas with inequitable access to facilities in a timely manner.

5.3. Equity in Access to Public Charging Services

The Gini coefficient was calculated to reflect the overall equity of PCS service access in the central city. We calculated the Gini coefficient using Excel 2016 and plotted the Lorenz curve graphs using the charting tool. When considering the population factor, the Gini coefficient of all PCS service access is 0.86, which shows significant inequality. As shown in Figure 7, the Lorenz curve shows that 81% of households share only 10% of PCS accessibility, compared to 25% of RPCS accessibility. There is a distributional difference between RPCSs and the other two types of PCS. The inequitable distribution of WPCSs and SPCSs (0.88) is more serious than that of RPCSs (0.72). However, this severity needs to be considered in context. Usually, cities prioritize the allocation of a sufficient number of utility piles in public buildings and offices, because these are the areas where short-duration vehicular activity is concentrated (resulting in higher facility turnover).

The Lorenz curves were also constructed separately for each of the three types of PCS, in order to assess the distributional fairness of access to PCS services in each subarea. Figure 8 shows the Lorenz curves, where the horizontal axis represents the cumulative percentage of households and the vertical axis represents the cumulative percentage of accessibility. We use different line types, colors, and data point shapes to distinguish the curves in each district. In particular, we use dashed lines to indicate marginal areas and solid lines to indicate central areas. As shown in Figure 8d, seven districts have PCS Gini coefficients above 0.5, indicating widespread and significant inequality. Only the distribution of facilities in PT and CN (less than 0.4) is “relatively reasonable”, while the rest of the districts have “large disparities”. As can be seen in Figure 8a, the spatial distribution of RPCSs is more uneven in PD (0.75) than in the other regions, and the distribution of WPCSs in BS (0.86), XH (0.84), HP (0.85), and MH (0.83), and of SPCSs in BS (0.66), MH (0.68), and JA (0.67), is extremely uneven (Figure 8b,c), but the high-level units in these areas are important city-level or regional centers, and the moderate concentration of facility services in these areas helps to ensure the necessary utilization rates, which is consistent with the findings of the spatial analysis of accessibility. Therefore, exploring the absolute balance of services in relation to the overall population is more conducive to reflecting the inequality of services across all PCSs, and further exploration of the relative fit between the population and the various types of PCS services is necessary.

We used IBM SPSS Statistics 23′s bivariate correlation analysis tool for Spearman’s rank correlation coefficients between demographic variables and accessibility, and the results of the calculations were plotted using Excel 2016′s plotting tool. Figure 9 illustrates the adaptability of PCS service access to populations with residential differentiation characteristics, where the more positively the vertical rectangle deviates from the central horizontal line, the more adaptable the service is to a certain type of population. The more negatively the vertical rectangle deviates from the central horizontal line, the less adaptive the service is to a certain type of population. Residents of multi-building (X1) and multi-household (X2) neighborhoods generally find it more difficult to access all types of PCS. In contrast, residents of large-acreage (X3) neighborhoods have greater difficulty in accessing WPCSs and SPCSs, but they have easier access to RPCSs. Residents of low-green-ratio (X5) and high-FAR (X6) neighborhoods have easier access to all types of PCS, and, in particular, residents of high-FAR (X6) neighborhoods have the easiest time accessing WPCSs. Residents of upscale neighborhoods with high home prices (X7), high property taxes (X8), and ample parking (X10) have less difficulty accessing PCSs than residents of lower-end neighborhoods. Interestingly, residents of neighborhoods with high property rates (X8) are able to access significantly more RPCSs. In addition, there is a contrast in access to PCSs for residents of new (X9) neighborhoods, who are able to access RPCSs more easily but have difficulty in accessing SPCSs.

We measured the significance of Spearman’s rank correlation coefficients between demographic variables and various types of accessibility (p-value less than 0.05 or p-value less than 0.01). There were more significant results for the X1–X8 variables than for the X9–X10 variables, which implies that residents characterized by the X1–X8 variables in terms of access to multiple types of PCS services showed more pronounced inequality (

Table 5. Frequency of occurrence of correlation coefficient significance results.

Significance	X1	X2	X3	X4	X5	X6	X7	X8	X9	X10
p-value < 0.01	3	3	0	0	1	2	3	1	0	0
p-value < 0.05	0	1	3	3	2	1	1	2	0	1
Total frequency	3	4	3	3	3	3	4	3	0	1

). The social equity analysis captures the equalization and adaptability of the distribution of PCS services among the population. For urban planners and policymakers, there is a need to further understand the areas of supply and demand between the current services and the potential population.

5.4. Areas of Unequal Access to Public Charging Services

However, given the demand generated by different subdistrict population sizes, higher capacity may not be needed. In contrast, lower services do not always imply a significant shortage. Improving the adaptability of supply to demand is crucial to mitigating inequity. We used Excel 2016 to calculate the Z-value standardization and the coupling coordination and used the pivot table function to cross-tabulate the supply–demand matching and coupling coordination results.

Table 6. Percentage of number of unequal subdistrict types.

Classification	Matching	Severe Imbalance	Moderate Imbalance	Mild Imbalance	Barely Balanced	Well Balanced	Excellent Balance
RPCS	Low supply–low demand	13.91%	29.57%	0.00%	0.00%	0.00%	0.00%
	Low supply–high demand	9.57%	22.61%	0.87%	0.00%	0.00%	0.00%
	High supply–low demand	0.00%	9.57%	3.48%	0.87%	0.87%	0.00%
	High supply–high demand	0.00%	0.00%	4.35%	4.35%	0.00%	0.00%
RPCS	Low supply–low demand	33.91%	11.30%	0.00%	0.00%	0.00%	0.00%
	Low supply–high demand	28.70%	9.57%	0.00%	0.00%	0.00%	0.00%
	High supply–low demand	0.00%	12.17%	0.00%	0.87%	0.00%	0.00%
	High supply–high demand	0.00%	2.61%	0.87%	0.00%	0.00%	0.00%
SPCS	Low supply–low demand	33.04%	16.52%	0.00%	0.00%	0.00%	0.00%
	Low supply–high demand	22.61%	15.65%	0.00%	0.00%	0.00%	0.00%
	High supply–low demand	0.00%	6.96%	0.00%	1.74%	0.00%	0.00%
	High supply–high demand	0.00%	0.87%	0.87%	0.00%	0.87%	0.87%
PCS	Low supply–low demand	25.22%	20.87%	0.00%	1.74%	0.00%	0.00%
	Low supply–high demand	18.26%	20.00%	0.00%	0.00%	0.87%	0.00%
	High supply–low demand	0.00%	8.70%	0.87%	0.00%	0.00%	0.87%
	High supply–high demand	0.87%	0.87%	0.87%	0.00%	0.00%	0.00%

shows the results of the supply–demand matching as well as the coupled coordination statistics for the 115 subdistricts. We found 77 supply–demand mismatch subdistricts, accounting for 66.96% of the total. Under the current PCS distribution conditions, there are more “undersupplied” subdistricts than “oversupplied” subdistricts. Of these, RPCSs have an unequal number of “undersupplied” and “oversupplied” subdistricts (38 and 17, respectively). This number of “oversupplied” subdistricts exceeds that of WPCSs (15) and SPCSs (10). There are also fewer “undersupplied” subdistricts than for WPCSs (44) and SPCSs (44). Combined with the supply–demand balance analysis, the main problem faced by all three types of PCS is of being “undersupplied”, with varying degrees of severity, and with WPCSs and SPCSs having more severe issues than RPCSs.

Since resources are very limited, prioritizing in which building sites to improve PCS placement needs to be a choice made in relation to the severity of the imbalance. Combined with the results of the comparison of imbalance severity, we used ArcGIS 10.7 to highlight the different mismatched subdistrict types. Figure 10 shows the spatial distribution of PCS inequity areas. The categorization highlights where different types of PCS are “undersupplied” and “oversupplied”. A total of 77 mismatched units were grouped into six categories. WPCSs have the highest number of subdistricts in need of improvement, with 29 undersupplied subdistricts for improvement and 13 oversupplied subdistricts prioritized for improvement. They are mainly concentrated in the northern part of BS, the northern part of YP and Gaoqiao Town, the “Qibao-Xinzhuang” area in MH, and the “Beicai-Kangqiao” area in PD (Figure 10c,d). For SPCSs, there are 15 undersupplied subdistricts prioritized for improvement (the southern part of PT and Jiangqiao town, the fringe areas of Zhangjiang and Sanlin towns in PD, the center of PD, and the junction of YP, BS, HK, and JA), as well as 4 oversupplied subdistricts prioritized for improvement (West Nanjing Road in the city center and the fringe areas of MH) (Figure 10e,f). The smallest number of subdistricts in need of improvement is for RPCSs, with 4 undersupplied and 4 oversupplied subdistricts prioritized for improvement, including 4 oversupply-prioritized improvement units (Bund area in HP, Wusong subdistrict and Miaohang subdistrict in BS, and city center areas in HK, CN, and XH) and 12 oversupply-prioritized improvement subdistricts (border areas in PT and JA, and Hanamu subdistrict in PD) (Figure 10a,b).

6. Discussion

This study presents a multi-stage framework to analyze the equity of PCS accessibility. The findings provide some new perspectives on social equity and spatial matching, with implications for categorizing PCS allocations to better achieve clean energy sharing and promote equal rights for sustainable development. In this section, new findings and their usefulness based on the analytical framework are discussed, along with the value of the framework, as well as limitations and areas for further research.

6.1. Accessibility and Equity of PCSs

The analysis of the central city of Shanghai shows that, among the three facility categories, RPCSs, while generally in less urgent need of improvement than the other two PCS categories, still have a number of inequitable areas of under- or oversupply. For WPCSs and SPCSs, inequitable areas are predominantly “undersupplied”. Improving supply is crucial to mitigating inequities. However, social equity and spatial matching analysis show that good spatial accessibility does not necessarily imply high service equity. To further explore this discrepancy, we first used the Ordinary Least Squares (OLS) model in ArcGIS 10.7, which was used to determine the statistical association between the dependent variable (accessibility) and the independent variables (influencing factors). Through the analyses in Section 5.3, we used the X1–8 variables as independent variables. In this model, the VIF values of all independent variables did not exceed 7.5, and the Geographically Weighted Regression (GWR) model was used afterward.

Table 7. Variables and OLS/GWR model results.

Variable		OLS			GWR
		Coefficient	R2	AICc	Coefficient (Average)	R2	AICc
RPCS	X1	0.0099	0.0624	−674.1226	0.0099	0.3547	−687.6872
	X2	−0.0186 *			−0.0180
	X3	−0.0010			0.0003
	X4	−0.0184			−0.0148
	X5	0.0037			0.0013
	X6	0.0079			0.0114
	X7	−0.0124			−0.0095
	X8	0.0179			0.0073
WPCS	X1	0.1993	0.1053	−126.1259	0.1993	0.1053	−126.1068
	X2	−0.3841 *			−0.3843
	X3	−0.0914			−0.0914
	X4	0.0962			0.0963
	X5	−0.0502			−0.0503
	X6	−0.0674			−0.0674
	X7	0.0215			0.0215
	X8	0.1227			0.1228
SPCS	X1	−0.1977	0.1814	123.8444	−0.2020	0.2430	122.9436
	X2	−0.4567			−0.4169
	X3	0.8676 *			0.9199
	X4	0.6000			0.6460
	X5	−0.4285			−0.3681
	X6	0.1526			0.1734
	X7	0.7307 *			0.7971
	X8	−0.9876			−1.0291
PCS	X1	−0.1060	0.1783	133.6009	−0.1073	0.2107	133.1750
	X2	−0.6411			−0.6207
	X3	0.7690			0.8014
	X4	0.5740			0.6073
	X5	−0.4098			−0.3759
	X6	0.1118			0.1188
	X7	0.6894 *			0.7292
	X8	−0.8445			−0.8604

* p-value (probability) < 0.05.

compares the summary statistics of the independent variables used in the OLS and GWR models, as well as the results of these two models, and it can be observed that the RPCS, WPCS, and PCS GWR models outperform the OLS model according to R². Moreover, it can be seen that all four GWR models’ results have slightly lower Akaike Information Criterion-corrected (AICc) values compared to the OLS model. Both model results suggest that a larger proportion of multi-dwelling (X2) community residents may negatively affect RPCS and WPCS use. Additionally, a greater proportion of residents in higher-priced (X7), upscale neighborhoods may promote SPCS and PCS use. However, a greater proportion of residents in large (X3) neighborhoods may promote SPCS use, which differs from the correlation analysis results and may be caused by controlling for other variables.

Therefore, based on the regression analysis results, we selected the three most salient indicator categories for the RPCSs, WPCSs, SPCSs, and PCSs (RPCS and WPCS significance variables are the same), including X2 (population living in multi-family RNs), X3 (population living in large RNs), X7 (people living in RNs with high housing costs). These indicators were used to capture vertical equity across districts. In Figure 11, the horizontal axis indicates the degree of horizontal inequality (Gini coefficient for the district), the vertical axis indicates the degree of vertical inequality (absolute value of Spearman’s rank correlation coefficients within the district), and the size of the circle reflects the degree of accessibility. We can see that there are significant differences between the service capacity and spatial equity of the three types of PCS. For the RPCS configuration in HK and WPCS configuration in MH, higher horizontal inequity reflects stronger demand, and higher vertical inequity reflects the special needs of multi-household neighborhoods, which show great inequality even though they do not have low accessibility levels (Figure 11a,b). In MH, while there is easy access to PCS services, the need for WPCSs and SPCSs for small-acreage and low-house price neighborhoods is overlooked (Figure 11c,d).

In addition, the spatial distribution of the estimated coefficients of the GWR can further reflect this variation at the subdistrict scale. Figure 12 shows the spatial distribution of the estimated coefficients of the significant factors across all PCS types; the darker the color, the more significant the spatial divergence, implying greater inequality. In particular, a darker blue color indicates a more pronounced negative correlation between a particular independent and dependent variable, while a darker red color indicates a stronger positive correlation. The RPCS accessibility level in Zhangjiang Town (Region 1) and the WPCS accessibility level in Xinhong Street (Region 2) are both relatively high, but residents of multi-dwelling neighborhoods in these areas are likely to face serious inequality in PCS access, which may be related to the many newly developed large-scale residential developments in these areas, and supporting facilities lag behind in terms of development (Figure 12a,b). Although the level of SPCS accessibility is high in Meilong Town (Region 3), residents of small neighborhoods have difficulties accessing adequate SPCS services, which may be due to small residential areas in this region being located in urban–rural areas, mostly mixed with factories and lacking services, which is not conducive to SPCS installation in the neighborhoods (Figure 12c). The PCS accessibility level is not low in Jinqiao Town (Region 4); however, residents of low-household neighborhoods experience significant PCS access inequalities, which may be because of the area’s concentration of high-end industrial parks, with a large number of supporting high-quality neighborhoods, and a more adequate number of PCSs being allocated earlier (Figure 12d). The results of the subdistrict- and district-level differences reflect that there is considerable scope for optimal PCS allocation encompassing everything from spatial accessibility to service equity. If PCS facility allocation is determined solely on the basis of accessibility results after project completion, the facilities constructed will not equitably meet the needs of all.

6.2. Directions for Improvement in Areas of Inequality

We combined the identified supply–demand imbalance areas with the current distribution of PCSs in the central city of Shanghai. We used the alluvial plot template of Origin 2021 to show the correspondence between different configuration characteristics and the type of supply–demand imbalance at the zoning level using different colored curves, with the width of the curves reflecting the number of subdistricts that fit into a certain correspondence (Figure 13). The purpose is to provide a direction for improving the inequality, which consists of four types: First, subdistricts with low service level configurations for RPCSs, along with a lack of volume agglomeration and low coverage, which greatly contribute to the undersupply (Figure 13a). In addition, some subdistricts with low levels of service configurations for SPCSs have similar problems even with high coverage (Figure 13c). We recommend expanding the PCS capacity in areas with appropriate land conditions, and the scale should be expanded in available locations, with appropriate increases in fast charging equipment to enhance service capacity, while simultaneously moderately increasing the number of small RPCSs to weave a dense RPCS network. Secondly, some subdistricts with WPCSs and SPCSs are obviously insufficient in terms of quantity density, although the service levels and spatial coverage are relatively adequate (Figure 13b,c). In particular, some subdistricts with high SPCS service levels have a “low supply and high demand” situation due to the lack of clustering of facilities (Figure 13c). It is recommended that suitable work and service locations be chosen to further enhance the delivery of new sites, either by finding new locations or by building additional sites where there are already existing ones. Thirdly, in some subdistricts there is a highly balanced allocation of small RPCSs with low levels of service at high levels of agglomeration, which may have created an oversupply (Figure 13a). In these areas, it is recommended that smaller, more dispersed RPCSs be consolidated where appropriate, and that RPCSs with extremely limited levels of service (and especially low usage) should be closed where appropriate to minimize unused facilities. Fourth, although WPCSs and SPCSs in some areas have low service levels and low input density, they have strong population coverage capacity, which may result in the phenomenon of “oversupply” (Figure 13b,c). We recommend optimizing the number of fast and slow charging piles at PCSs according to the actual demand, while simultaneously reducing the duplication of stations in the same location in order to avoid wasting resources.

The proposed framework will not only help formulate the direction of improvement in areas of inequality but can also inform efficient PCS integration with external built places in the future. Six typical subdistricts were selected for analysis. These subdistricts are notable areas selected by combining the current PCS allocation levels and the results of matching supply and demand. For comparison, the agglomeration, coverage, and service capacity levels are ranked in a hierarchical order from lowest to highest, assigned a score of 1–5, and the summed total score is defined as the current configuration level. For undersupply, areas with low configuration level scores require extra attention; for oversupply, areas with high scores require extra attention.

Among these areas, results are as follows: Ban Songyuan (RPRS oversupply, total score = 13): duplicate construction exists in the Zhongfu Garden RN, and it is recommended that RPCSs be considered in a unified manner by combining the energy system transformation in the existing community’s central basement (Figure 14a). Shimen Er Road (WPCS oversupply, total score = 13): the very small and scattered WPCSs in the southeastern district should be closed down as appropriate, and the focus should be on combining with 688 Plaza to form a high-rise office building charging energy service center (Figure 14b). West Nanjing Road (SPCS oversupply, total score = 12): encourage the establishment of public charging energy sharing zones in large commercial centers such as Jing’an Kerry City and Taikoo Hui, and guide the multi-operators to cooperate in an orderly manner and compete in a benign manner (Figure 14c). Huamu (RPCS undersupply, total score = 6): expand the scale of the existing single-pile RPCSs where possible, particularly in the case of the several newer residences built after 2000, which tend to have adequate space and energy-loading conditions relative to older neighborhoods (Figure 14d). Gumei Road (WPCS undersupply, total score = 4): add WPCSs in conjunction with small job centers along the Hechuan Road, especially among newly built public services (Figure 14e). Changqiao (SPCS undersupply, total score = 3): take advantage of the area’s public service facilities, such as campuses and hospitals, and explore the connection between SPCS and campus energy systems using the smart campus construction of the Shanghai Sports Institute and Shanghai High School (Figure 14f).

6.3. Value and Limitations of the Multi-Stage Analysis Framework

The value of the multi-stage analysis framework is reflected in four aspects: First, using the framework as an analytical tool to categorize inequality in the 115 subdistricts in the central city helps to more accurately identify inequality, the areas where it occurs, and the types of PCS that should be prioritized for improvement, while also providing a reference for decision-making on the implementation of targeted improvements in each area. Second, the methodology can be used to analyze the accessibility and equity of PCSs at different types of sites, especially for important sites of policy interest (e.g., residential areas, supermarkets and stores, and business buildings), allowing for more in-depth categorized assessments and comparisons, and suggesting differentiated directions for improvement. Third, the proposed framework provides several indicators, including PCS spatial agglomeration, PCS population coverage, and PCS service capacity, which can be combined to reflect the current subdistrict-level PCS distribution level. Further, using the results of the supply–demand matching analysis, it is possible to anticipate the extent to which the level of PCS installations will need to be increased or contracted within subdistricts, which can help policymakers and urban planners to make quick decisions at the earliest stages of facility planning and upgrading. Finally, the PCS external building site classification, PCS classification, temporal threshold measurements, and supply–demand relationship tests provided by the framework provide an analytical basis for further optimization of the spatiotemporal relationship between population, station external building site, and PCSs. As shown in Figure 15, a good charging service supply–demand relationship should form a “public charging service circle” centered on “home”, while coordinating various PCS allocations in an orderly manner in different time zones around the residence. Based on this, in the future, emphasis should be placed on systematically scheduling individual PCSs to participate in clean energy management optimization together with building energy systems [58], and further strengthening the linkages between multiple PCSs and building energy systems, public transport hubs, or renewable energy sources in the neighboring areas, in order to create a more cohesive and efficient network of urban energy infrastructures.

The limitations of the multi-stage decision-making framework and the scope for further research are reflected in four aspects: Firstly, finer accessibility calculations for specific area networks or square grid scales are meaningful and help concentrate the matching analysis as well as the optimization strategy proposals to a specific location. Secondly, the development of service capability indicators requires further consideration of factors such as charging speed, charging cost, and charging operator. In addition, the potential number of EVs can be calculated by combining the demographic characteristics of potential EV consumers with a survey of their willingness to purchase a vehicle. Based on this, the relevant parameters for accessibility measurement are further calibrated. Again, census data and online review data are introduced to expand the system of potential user variables, and a regression model of user variables and degree of accessibility is established to quantitatively measure the degree of equity in each research unit, which can reveal the causes of inequalities. Finally, time is introduced as a new dimension of analysis: we count the changes in the potential number of EVs over a given period of time and analyze the changes in the matching of supply and demand in the case of the dynamic growth of EVs, which is closely related to the current rapid development of EVs and the updated construction of charging facilities.

To summarise, a diagram is drawn to represent possible future extensions to the proposed framework, with the aim of being able to predict future PCS installations based on the increase in EVs at a given location (Figure 16). Firstly, taking the grid center as the demand point and the PCS as the service point, an initial assessment is carried out using the multi-stage framework based on the calculation of the potential number of EVs and PCS service capability indicators within the grid; and then, with the help of the results of the assessment of the configuration level and supply–demand matching, the initial PCS configuration optimization level for the specific grid location is proposed with the aim of improving the equity of the PCS acquisition and solving the supply–demand matching problem. The multi-stage assessment framework is then iterated in conjunction with the changes in the potential number of EVs in each grid region until the configuration optimization level reaches a steady state, where each mismatch grid is equipped with key decision-making information such as the type of mismatch, the type of PCS to focus on improving, and the degree of improvement level, ultimately enabling the prediction of the future installation of PCSs in a specific location.

In addition, the iterative computation process involves different types of PCSs and different management regions; meanwhile, PCS data involves the privacy of personal information, operational data, and geolocation information. The Adaptive Alternating Direction Multiplier Method (ADMM) [59] can be introduced in the future to address the data privacy and computational efficiency issues of multi-agent energy systems. Specifically, the ADMM can solve a part of the optimization problem independently instead of centralizing all the data. This helps promote privacy preservation while reducing the latency caused by centralized data processing. At the same time, the ADMM ensures that the entire system is consistent and the optimization goal is achieved, despite each agent solving the problem independently. Notably, the distributed nature of the ADMM enables each agent to effectively participate in the overall optimization even when the PCS system scales up. This helps improve the scalability of the system.

7. Conclusions

For cities with high EV penetration, recognizing the inequitable distribution of PCSs is an important step in optimizing the distribution of clean energy. This study proposes a multi-stage analytical framework for assessing the social equity of access to PCSs and identifying areas of inequity that need to be prioritized for improvement.

The researchers collected information from publicly available data and categorized PCSs into 3 major categories and 24 subcategories. Subdistricts were used as the basic unit for calculating population needs. First, a status analysis and an accessibility analysis were conducted to determine the spatial distribution and service accessibility of the PCSs. Horizontal equity and vertical equity were assessed for each of the three PCS categories using the Gini coefficient and Spearman’s rank correlation coefficient, respectively. Finally, the Z-value normalization method and the coupled coordination degree model were used to comprehensively determine the types of subdistricts with supply–demand imbalances, as well as the priorities for improvement. An empirical study was conducted in central Shanghai to test the applicability of the framework. By identifying the locations and types of inequitable areas, the direction of PCS allocation improvement associated with the current level of PCS allocation was discussed.

The results show that access to PCS services is unevenly distributed in downtown Shanghai. PCS services are more readily available in downtown and localized areas; 80% of households share only 10% of PCS accessibility. Residents of large-scale, low-density, and low-grade neighborhoods generally have greater difficulty accessing all types of PCS. Nearly 66.96% of the subdistricts had an imbalance between supply and demand, and the main problem faced by all three types of PCS was “undersupply”, which was more serious for WPCSs and SPCSs than for RPCSs. In addition, the 77 unequal subdistricts were classified into six priority improvement types, comparing the current situation of different types of PCS, and four directional improvements are proposed based on current configuration levels. In addition, we propose six possibilities for the effective future integration of PCS with external built places for subdistricts with significant mismatch problems. We found significant differences in accessibility and equity at both the district and subdistrict levels, with particular attention to Xinhong and Meilong Town, which are located in MH.

The proposed framework can be used to assess whether the distribution of PCSs is equitable or not, and to propose priority areas for improving inequities in order to facilitate the planning and construction of different types of PCS in an integrated manner. The proposed framework can be extended with further calibration and data support, adapted to carry out PCS future configuration prediction and optimization more accurately, in order to improve the equitable distribution of clean energy facilities and contribute to the achievement of sustainable urban mobility goals.