Optimizing EV Charging Station Carrying Capacity Considering Coordinated Multi-Flexibility Resources

Abstract

The rapid growth of electric vehicles (EVs) poses significant challenges to the safe operation of charging stations and distribution networks. Variations in charging power across different EV manufacturers lead to substantial load fluctuations at charging stations. In some tourist cities in China, charging loads can surge at specific times, yet existing research mainly focuses on optimizing station location and basic capacity configuration, neglecting sudden peak load management. To address this, we propose a method that enhances charging station carrying capacity (CSCC) by coordinating multi-flexibility resources. This method optimizes the configuration of soft open points (SOPs) to enable flexible interconnections between feeders and incorporates elastic load scheduling for data centers. An optimization model is developed to coordinate these flexible resources, thereby improving the CSCC. Case studies demonstrate that this approach effectively increases CSCC at lower costs, facilitates the utilization of renewable energy, and enhances the overall system economy. The results validate the feasibility and effectiveness of the proposed approach, offering new insights for urban grid planning and EV charging stations optimization.

1. Introduction

Compared with traditional gasoline vehicles, electric vehicles (EVs) are significantly characterized by reducing carbon dioxide (CO₂) emissions [1], leading to the trend that gasoline vehicles will gradually be replaced by electric vehicles [2]. By 2030, electric vehicles are expected to reduce CO₂ emissions by 28% [3]. The convenience of EV charging is a key factor influencing customers’ decisions to purchase EVs [4]. During charging peak periods, charging demand becomes highly concentrated, requiring careful design of EV charging stations to effectively meet user demands [5], which also presents a greater challenge to the charging station carrying capacity. If the charging station design does not match the charging demand, it could negatively impact both drivers and power quality [6].

Current research on EV charging stations primarily focuses on location selection and capacity design. For example, Ref. [7] comprehensively considers three major categories of factors—economic cost, environmental cost, and geographical demand distribution—in the siting of electric vehicle charging stations. Ref. [8] considers orderly charging behavior of EVs in the planning of charging station locations. Ref. [9] initially identifies potential locations for charging stations based on urban planning factors, then further confirms these locations from the perspective of driver convenience. Ref. [10] investigates charging station siting strategies by incorporating road-grid coupling information, wind/PV generation profiles, and related factors.

In this context, the charging station’s carrying capacity is defined as the maximum power output a charging station can provide. Refs. [7,8,9,10] do not consider how to maximize the carrying capacity of charging stations. Ref. [11] introduces a photovoltaic and energy storage charging station (PV-ESS-CS) model, which considers the uncertainty of EV charging demand and PV output. By utilizing PV and ESS, this model increases the designed charging station’s carrying capacity to some extent. Refs. [12,13,14,15] also consider integrating photovoltaic and energy storage systems during the construction of charging stations to mitigate the mismatch between charging pile loads and system loads. However, the configuration of photovoltaic and energy storage systems inevitably increases the initial investment costs of the charging station, which may affect the economic feasibility of new charging stations [16]. In urban core areas, there is a clear contradiction between charging demand and available land resources. The higher the population density, the greater the charging demand, but available land resources are more limited. Therefore, building charging stations in these areas presents a challenge: the need to maximize the charging station’s carrying capacity within a limited space.

With the advancement of technology, the penetration of renewable energy in modern power systems is continuously increasing, and the interaction of various flexible resources is becoming increasingly complex, having a significant impact on the entire distribution system [17,18]. In the past decade, the installation capacity of wind and solar power has rapidly increased, while the construction cost of energy storage remains high, leading to an increase in curtailment of wind and solar energy, resulting in the waste of flexible resources. Refs. [11,12,13,14,15,16] only consider the simultaneous construction of PV systems when building charging stations, but they do not account for the role of other potential PV systems in the network. To support the rapid development and application of renewable energy, optimizing the configuration and operational strategies of flexible resources across various segments of the new power system has become an urgent task [19,20]. The interconnection of adjacent distribution network subsystems enables broader accessibility to flexible resources throughout the integrated system [21]. Therefore, for surplus renewable energy output, it can be considered to utilize interconnection between distribution network subsystems to absorb it, such as using SOPs.

As a typical representative of new flexible resources, data centers exhibit unique time–space characteristics. To provide highly reliable cloud computing services, large companies usually build distributed data centers in different locations, which can be interconnected and communicate with each other [22]. Data centers consume a large amount of energy and are often constructed in conjunction with renewable energy sources. Nevertheless, data centers remain heavily dependent on grid electricity supply [23]. As cloud-computing paradigms continue to evolve, managing workloads effectively across massive heterogeneous computing nodes to ensure the reliability and sustainability of the cloud is a crucial task [24]. Ref. [24] studies how to schedule data center computing tasks (workloads) based on renewable energy forecasts and dynamic electricity prices to match renewable energy supply. Refs. [25,26] explore the allocation of computing tasks between multiple data centers to maximize the absorption of green energy. Ref. [27] proposes a heuristic-based technique for scheduling workflows across multiple data centers, aiming to minimize electricity costs. Ref. [28] uses a heuristic algorithm for joint scheduling of computing tasks to minimize execution costs and completion times. It is clear that reasonable scheduling of data center computing tasks can have many positive impacts.

With the rapid growth of electric vehicles and the popularity of self-driving travel, tourism cities face increasing load pressure during peak seasons—charging loads may exceed ten times the normal level, posing a severe challenge to the safe operation of the power grid. If the charging station capacity is inadequately designed, it will lead to long waiting times, severely affecting user experience and the city’s image. On the other hand, overdesigning the capacity can lead to underutilization of resources and wasted investment during off-peak seasons. However, existing research often focuses on optimizing the location and basic capacity configuration of charging stations, neglecting how to address the sudden load peaks in tourism cities.

Therefore, researching methods to enhance charging station carrying capacity holds significant theoretical and practical importance. Although SOPs have been used in distribution networks for many years, studies combining SOP with data center task scheduling to improve charging station capacity remain limited. This paper proposes a method for enhancing charging station carrying capacity through the coordination of multiple flexible resources. The main innovations are as follows:

• Unlike traditional studies, this paper specifically addresses the characteristics of charging load fluctuations and high peak values in tourist cities, providing a practical solution to improve charging station carrying capacity;
• A multi-flexible resource coordination optimization method is proposed, which enhances charging station capacity at lower cost through the optimized configuration of SOPs and the coordinated scheduling of computational tasks in distributed data centers;
• The effectiveness of the proposed method is validated through a practical case study, offering new planning insights for the development of distribution networks in cities where charging loads exhibit significant seasonal variations.

The remaining content is structured as follows. Section 2 describes the background of the research problem. Section 3 introduces the charging station carrying capacity enhancement model considering multi-flexibility resources. Section 4 applies the proposed model to a practical case study. Section 5 summarizes the results of the proposed model and discusses its implications for grid development, while also offering suggestions for future research.

2. Problem Statement

Due to variations in the rated power of EVs from different manufacturers, even charging stations with the same number of charging guns experience significant fluctuations in load power. Therefore, this paper does not consider the load of each individual charging gun, but rather the total load of the entire charging station. The charging station carrying capacity studied in this paper is defined as the maximum power output that a charging station can sustain. This capacity must meet the following conditions: the station can continuously operate at this maximum output without negatively affecting the safe and stable operation of the distribution network.

This study focuses on existing, operational charging stations, where the location of the stations has already been determined. This paper primarily investigates enhancing the charging station carrying capacity through the optimized configuration of SOP and the task scheduling of data centers, with the goal of addressing sudden peak load demands. Due to practical constraints, the candidate installation locations for SOP switches have already been pre-determined. Additionally, data center loads, which have dual characteristics, are integrated into the distribution network. On one hand, their computational tasks can be optimized in terms of scheduling over time; on the other hand, with the help of high-speed fiber optic networks, tasks can be transferred spatially, enabling the time–space shifting of power loads. It is important to note that the data center load data used in this study has already accounted for its own renewable energy generation, presenting a net load value. As the power department lacks direct control over data centers, the proposed computational load scheduling strategy will be submitted as an optimization recommendation to the data center’s operational and maintenance team, aiming to enhance energy efficiency and power supply reliability. For other loads in the distribution system, load operation curves are constructed based on historical operating data using a typical scenario analysis method. The system’s overall operational framework is illustrated in Figure 1.

3. Coordinated Multi-Flexibility Resources CSCC-Enhancement Model

In the distribution network planning, our goal is to maximize CSCC within a given economic cost. Given that the location of the charging stations has already been determined, we consider multiple flexible resources in the distribution system to achieve the maximization of CSCC.

3.1. Constraints Related to SOPs

For SOPs, the following constraints must be satisfied:

$$P_{s,t,i}^{\mathrm{SOP}}+P_{s,t,j}^{\mathrm{SOP}}=0,\forall ij\in {\mathrm{\Omega }}_{\mathrm{branch}},$$

(1)

$$-P_{\mathrm{capacity},i}^{\mathrm{SOP}}·X_{ij}^{\mathrm{SOP}}\le P_{s,t,i}^{\mathrm{SOP}}\le P_{\mathrm{capacity},i}^{\mathrm{SOP}}·X_{ij}^{\mathrm{SOP}},\forall i\in {\mathrm{\Omega }}_{\mathrm{SOP}},$$

(2)

$$-Q_{\mathrm{capacity},i}^{\mathrm{SOP}}·X_{ij}^{\mathrm{SOP}}\le Q_{s,t,i}^{\mathrm{SOP}}\le Q_{\mathrm{capacity},i}^{\mathrm{SOP}}·X_{ij}^{\mathrm{SOP}},\forall i\in {\mathrm{\Omega }}_{\mathrm{SOP}},$$

(3)

where $X_{ij}^{\mathrm{SOP}}$ is a binary variable indicating whether an SOP is installed on line-$ij$. If $X_{ij}^{\mathrm{SOP}}=1$, it means an SOP is installed on line-$ij$; otherwise the variable takes the value 0. The subscripts s and t represent the time moment-t of scenario-s, respectively. $P_{s,t,i}^{\mathrm{SOP}}$ ($P_{s,t,j}^{\mathrm{SOP}}$) represents the active power flowing from line-$ij$ to node-i (j) if an SOP is installed. Equation (1) states that for lines equipped with an SOP, the SOP only adjusts the power flow distribution without absorbing or injecting power. Equations (2) and (3) represent the capacity constraints of SOPs.

3.2. Constraints Related to Data Centers

For data centers, the transfer of computational tasks enables the time–space shifting of electricity loads. The modeling of the data center is as follows:

$$\sum _{k=1}^{k_n}\sum _{t=1}^{t_n}{P}_{s,t,i}^{\mathrm{L}}=\sum _{k=1}^{k_n}\sum _{t=1}^{t_n}{P}_{s,t,i}^{\mathrm{ADL}},\forall s\in {\mathrm{\Omega }}_{\mathrm{S}},$$

(4)

$$P_{s,t,i}^{\mathrm{ADL}}\ge \delta P_{s,t,i}^{\mathrm{L}},$$

(5)

$$-\beta P_{s,t-1,i}^{\mathrm{L}}\le P_{s,t,i}^{\mathrm{L}}-P_{s,t-1,i}^{\mathrm{L}}\le \beta P_{s,t-1,i}^{\mathrm{L}},$$

(6)

where ${\mathrm{\Omega }}_{\mathrm{S}}$ is the set of scenarios. Equation (4) indicates that the loads among data centers can be shifted in both time and space, and the total load should be conserved. Here, n represents the number of data centers in the system, and m denotes the time-shifting scale. If m is set to 4, it means that computing tasks can be delayed or advanced for up to 4 h. For example, $P_{s,t,i}^{\mathrm{L}}$ represents the initial load corresponding to computing tasks before scheduling, while $P_{s,t,i}^{\mathrm{ADL}}$ represents the actual load of data center i at moment t of scenario s after scheduling. Equation (5) indicates that each data center has a fixed power consumption during normal operation, and a portion of the basic computing tasks cannot participate in load scheduling, where $\delta$ represents the proportion of basic computing tasks. Equation (6) means that the computational task scheduling should involve an orderly transfer. $\beta$ represents the upper limit of the transfer rate.

3.3. Constraints Related to Distribution Network

Although peak loads of charging stations may only occur during certain periods, to ensure that the safety operation constraints are not violated during the operation of the charging station, we assume that the load of the charging station remains at its peak value at all times. This conservative assumption is particularly relevant in scenarios such as the Spring Festival in China, where large-scale population inflows to tourist cities can cause sustained charging demand surges over several days. Modeling peak load continuously allows us to evaluate system robustness under the most critical and high-risk operating conditions. Based on ref. [29], and combined with the specific context of this paper, the linearized distFlow model can be formulated as Equations (7)–(15). Therefore, the node power balance constraint is shown as Equations (7) and (8):

$$\sum _{j\in {\mathrm{\Omega }}_i^{-}}{P}_{s,t,ij}^{\mathrm{Flow}}+P_{s,t,i}^{\mathrm{L}}+P_{s,t,i}^{\mathrm{EV}}=P_{s,t,i}^{\mathrm{MT}}+P_{s,t,i}^{\mathrm{DG}}+\sum _{j\in {\mathrm{\Omega }}_i^{+}}{P}_{s,t,ki}^{\mathrm{Flow}}+P_{s,t,i}^{\mathrm{SOP}},\forall i\in N,\forall s,t,$$

(7)

$$\sum _{j\in {\mathrm{\Omega }}_i^{-}}{Q}_{s,t,ij}^{\mathrm{Flow}}+Q_{s,t,i}^{\mathrm{L}}+Q_{s,t,i}^{\mathrm{EV}}=Q_{s,t,i}^{\mathrm{MT}}+Q_{s,t,i}^{\mathrm{DG}}+\sum _{j\in {\mathrm{\Omega }}_i^{+}}{Q}_{s,t,ki}^{\mathrm{Flow}}+Q_{s,t,i}^{\mathrm{SOP}},\forall i\in N,\forall s,t,$$

(8)

where $P_{s,t,ij}^{\mathrm{Flow}}$ and $P_{s,t,ki}^{\mathrm{Flow}}$ represent the active power flowing into and out of node-i, respectively. ${\mathrm{\Omega }}_i^{+}$ is the set of parent nodes of the lines that supply power to node-i, and ${\mathrm{\Omega }}_i^{-}$ is the set of child nodes of the lines through which power flows out of node-i. $P_{s,t,i}^{\mathrm{MT}}$ and $P_{s,t,i}^{\mathrm{DG}}$ represent the active power received by node i from the main transformer and the active power output from distributed generation (DG), respectively. If node i is not directly connected to a main transformer, then $P_{s,t,i}^{\mathrm{MT}}=0$, and the same applies to the DG output. Variables represented by the letter Q represent the corresponding reactive power. Besides, $P_{s,t,i}^{\mathrm{EV}}$ satisfies Equation (9):

$$P_{s,t,i}^{\mathrm{EV}}=\left\{\begin{array}{cc}{c}^{\mathrm{Charger}}\left(i\right),\hfill & i\in {\mathrm{\Omega }}_{\mathrm{C}}\hfill \\ 0,\hfill & i\notin {\mathrm{\Omega }}_{\mathrm{C}}\hfill \end{array}\right.,$$

(9)

where ${\mathrm{\Omega }}_{\mathrm{C}}$ is the set of nodes where charging stations are constructed, and $c^{\mathrm{Charger}}\left(i\right)$ is the carrying capacity of charging station i. The charging station carrying capacity is obtained by solving the model.

In addition, the following operational constraints of the distribution network must also be satisfied:

$$P_{s,t,i}^{\mathrm{MT}}\ge 0,\forall i\in {\mathrm{\Omega }}_{\mathrm{MT}},$$

(10)

$$0\le P_{s,t,i}^{\mathrm{DG}}\le P_{s,t,i,\mathrm{real}}^{\mathrm{DG}},$$

(11)

$$-0.8·P_{max,ij}^{\mathrm{Flow}}\le P_{s,t,ij}^{\mathrm{Flow}}\le 0.8·P_{max,ij}^{\mathrm{Flow}},\forall ij\in {\mathrm{\Omega }}_{\mathrm{branch}},$$

(12)

$$-0.8·Q_{max,ij}^{\mathrm{Flow}}\le Q_{s,t,ij}^{\mathrm{Flow}}\le 0.8·Q_{max,ij}^{\mathrm{Flow}},\forall ij\in {\mathrm{\Omega }}_{\mathrm{branch}},$$

(13)

$$U_{s,t,i}-U_{s,t,j}-(r_{ij}{P}_{s,t,ij}^{\mathrm{Flow}}+x_{ij}{Q}_{s,t,ij}^{\mathrm{Flow}})/U_{\mathrm{R}}=0,\forall ij\in {\mathrm{\Omega }}_{\mathrm{branch}},$$

(14)

$$0.95U_{\mathrm{R}}\le U_{s,t,i}\le 1.05U_{\mathrm{R}},$$

(15)

where ${\mathrm{\Omega }}_{\mathrm{MT}}$ is the set of transformer nodes. Equations (10) and (11) indicate that when the output of renewable energy exceeds the distribution network’s absorption capacity, the transformers cannot reverse the active power flow to the feeders, and partial renewable energy output must be curtailed. Equations (12) and (13) represent the line power limit constraints. Equations (14) and (15) correspond to the voltage drop constraint and the node voltage constraint, respectively.

3.4. Objective Function

In the planning of the distribution network, we need to consider the construction and operational costs of SOPs, as well as the cost of purchasing electricity from the upper-level grid, as shown in Equations (16)–(18):

$$C_{\mathrm{inv}}^{\mathrm{SOP}}=\sum _{ij\in E}{X}_{ij}^{\mathrm{SOP}}·c_{\mathrm{inv}}^{\mathrm{SOP}}\left(ij\right),$$

(16)

$$C_{\mathrm{operation}}^{\mathrm{SOP}}=\sum _{s\in {\mathrm{\Omega }}_S}\sum _{ij\in E}\left|P_{s,t,i}^{\mathrm{SOP}}\right|·c_{\mathrm{operation}}^{\mathrm{SOP}}·X_{ij}^{\mathrm{SOP}},$$

(17)

$$C_{\mathrm{buy}}=\sum _{s\in {\mathrm{\Omega }}_S}\sum _{m\in {\mathrm{\Omega }}_{\mathrm{MT}}}\sum _{t=1}^{t_n}{c}_{\mathrm{buy}}·P_{s,t,m}^{\mathrm{MT}},$$

(18)

where $C_{\mathrm{inv}}^{\mathrm{SOP}}$, $C_{\mathrm{operation}}^{\mathrm{SOP}}$, $C_{\mathrm{buy}}$ represent the costs for constructing SOPs, operating SOPs, and purchasing electricity from the upper-level grid, respectively. $c_{\mathrm{inv}}^{\mathrm{SOP}}\left(ij\right)$ is the cost of constructing an SOP on line $ij$; the SOP operating cost is determined by the active power flow, and $c_{\mathrm{operation}}^{\mathrm{SOP}}$ is the cost per kW when the SOP is running. As shown in Equation (1), the active power of the SOP during operation can be represented by $P_{s,t,i}^{\mathrm{SOP}}$.

Besides, the lines of charging stations may need to be upgraded to accommodate higher loads. Therefore, the cost of upgrading the lines is also considered, as shown in Equation (19):

$$C^{\mathrm{Charger}}=\sum _{c\in {\mathrm{\Omega }}_C}\beta ·c^{\mathrm{Charger}}\left(c\right),$$

(19)

where $c^{\mathrm{Charger}}\left(c\right)$ is the charging station carrying capacity, and $\beta$ is the conversion factor between the capacity of the upgraded lines and their corresponding cost.

In addition, the method for calculating the renewable energy absorption rate is shown in Equation (20), which represents the proportion of the actual absorbed distributed generation relative to the total generation.

$$\alpha =\left(\sum _{s\in {\mathrm{\Omega }}_S}\sum _{t=1}^{t_n}{P}_{s,t,i}^{\mathrm{DG}}\right)/\sum _{s\in {\mathrm{\Omega }}_S}\sum _{t=1}^{t_n}{P}_{s,t,i,\mathrm{real}}^{\mathrm{DG}},$$

(20)

The goal is to maximize the charging station carrying capacity under a given economic cost. Therefore, when setting the objective function, we can consider either a single-objective optimization method or a multi-objective optimization method. The objective function for the single-objective optimization method is shown as Equation (21):

$$minF={\lambda }_1\left(C_{\mathrm{inv}}^{\mathrm{SOP}}+C_{\mathrm{operation}}^{\mathrm{SOP}}+C^{\mathrm{Charger}}+C_{\mathrm{buy}}\right)-{\lambda }_2\sum _{c\in {\mathrm{\Omega }}_{\mathrm{C}}}{c}^{\mathrm{Charger}}\left(c\right),$$

(21)

where the second term means the total charging station carrying capacity.

In multi-objective optimization, the $ϵ$-constraint method is a commonly used approach. It effectively transforms a multi-objective problem into a series of single-objective optimization problems, thereby obtaining the Pareto optimal solution set.

Specifically, given an optimization problem with multiple objective functions, it can be represented as Equation (22):

$$min{f}_1\left(x\right),f_2\left(x\right),\dots ,f_k\left(x\right),$$

(22)

where x represents the decision variables, and $f_1\left(x\right)$, $f_2\left(x\right)$,..., $f_k\left(x\right)$ are the objective functions, with k being the number of objective functions. To transform the multi-objective problem into a single-objective problem, the $ϵ$-constraint method selects one objective function as the primary optimization objective and treats the remaining objective functions as constraints [30]. The specific steps are as follows: First, select an objective function $f_1\left(x\right)$ as the main optimization objective. Then, transform the other objective functions $f_2\left(x\right)$,..., $f_k\left(x\right)$ into constraints. The value of each objective function $f_i\left(x\right)$ is constrained within a given threshold ${ϵ}_i$, where ${ϵ}_i$ is a tunable parameter representing the allowable deviation for that objective function. Finally, by adjusting the thresholds ${ϵ}_i$, different optimization solutions are obtained, forming the Pareto frontier. The flowchart for this process is shown as Figure 2.

In this paper, the multi-objective function can be expressed as Equation (23) and (24):

$$min{F}_1=C_{inv}^{SOP}+C_{operation}^{SOP}+C^{Charger}+C_{buy},$$

(23)

$$min{F}_2=-\sum _{c\in {\mathrm{\Omega }}_C}{c}^{\mathrm{Charger}}\left(c\right).$$

(24)

4. Case Studies

This study analyzes a real-world case from a specific region in China. The typical load scenarios and their associated probabilities are illustrated in Figure 3. These scenarios include representative curves for both conventional load and renewable energy output. Specifically, renewable generation in each scenario considers both photovoltaic (PV) and wind power outputs. The output profiles of PV and wind are constructed using typical generation curves derived from historical or forecast data.

4.1. Case Study of the Dual-Feeder System

This section first analyzes a specific dual-feeder system. The penetration rate of renewable energy of this system is 35.43%, and its topology is shown in Figure 4. The red dashed lines represent potential locations for the installation of SOPs, while nodes 13 and 22 are the nodes with a charging station. The gray circles (nodes 11 and 30) represent data centers, which allow for flexible time–space shifting of loads.

At this stage, the system is relatively simple, and a single-objective optimization method is applied. The objective function is shown as Equation (21). The optimization results show that it is more economical to improve the charging station carrying capacity through the time–space shifting of flexible loads rather than installing SOPs. This is because, with a lower penetration rate, the existing conventional loads can absorb a higher proportion of renewable energy, and the additional charging stations can achieve full absorption of renewable energy. Operating SOPs would incur higher costs in this scenario.

Table 1. Comparison of charging station carrying capacity using different methods.

Methods	Without Considering Flexible Resources	Considering Flexible Resources
Carrying capacity (kW)	454	513
Utilization rate	100%	100%

compares the difference in charging station carrying capacity with and without considering flexible resources. From the table, it can be seen that, by considering flexible resources, the charging station carrying capacity can be increased by 13%.

Taking scenario 3 as an example, the computational task scheduling plan curves for data centers are shown in Figure 5. From 1:00 to 9:00, data center 30 on feeder 2 originally has fewer computational tasks. During this period, computational tasks for Node 30 are appropriately increased, while those for data center 11 are reduced, thereby alleviating the power demand on feeder 1 and supporting the charging station carrying capacity during this time. After 13:00, the conventional load on feeder 1 is higher, so the computational tasks of data center 11 are appropriately reduced, transferring the load pressure to feeder 2.

4.2. Case Study of the Four-Feeder System

Next, the planning scope is expanded to include two additional feeders with higher penetration rates near the original double-feeder system, forming a four-feeder system. The topology is shown in Figure 6.

Compared with single-objective optimization, which can be heavily influenced by weight coefficients, multi-objective optimization better aligns with the practical situation of the utility company, as it allows for the selection of a reasonable method from multiple options. The optimization objective is to maximize the charging station carrying capacity while minimizing costs, as shown in Equations (23) and (24). According to previously mentioned method, the $ϵ$-constraint method is employed for multi-objective optimization. By comparing different penetration rates, the Pareto frontier is obtained and shown in Figure 7 and Figure 8. For ease of observation, the negative values of Obj-2 in the figure are converted to positive values, where the cost is minimized (shown on the horizontal axis) and the carrying capacity is maximized (shown on the vertical axis).

From the Pareto front, it can be observed that as the penetration rate increases, the carrying capacity of the charging station also increases. The analysis is conducted with the $ϵ$ value is set to 0.1. In this case, the locations for SOP installation under different penetration rates are shown in Figure 9 and Figure 10, and the designed capacities are listed in

Table 2. SOP installation for different penetration rates.

Penetration Rate	Line Configuration	Capacity
	Line Details	(kW)
41.2%	Line-72 (Node 12–44)	500
	Line-74 (Node 32–73)	400
52.4%	Line-71 (Node 9–26)	500
	Line-72 (Node 12–44)	400
	Line-74 (Node 32–73)	300

.

As shown in

Table 3. CSCC and renewable energy utilization rate under different penetration rates.

Penetration Rate	41.2%		52.4%
	Method 1	Method 2	Method 1	Method 2
Carrying capacity (kW)	454	1215	513	1440
Utilization rate	95.2%	100%	91.0%	100%

, when flexible resources are not considered, each feeder operates independently, resulting in the same carrying capacity for both the double-feeder and four-feeder systems, which fails to fully utilize the available resources. When flexible resources are considered, the system can make full use of generation resources, significantly improving the charging station carrying capacity.

When the penetration rate is lower, renewable energy output exceeds the original load of the system only during a few moments, leading to some wind and solar energy curtailment. As the system penetration rate increases (especially for feeders 3 and 4), the renewable energy utilization rate decreases. In this case, by installing SOPs, not only can the charging station carrying capacity be increased, but the utilization of renewable energy can also be improved, reducing the cost of purchasing electricity from the upper-level grid.

At higher penetration rates, when flexible resources are not considered, the renewable energy utilization rate curve for feeders 3 and 4 under scenario 3 is compared, as shown in Figure 11. In this case, the system’s overall utilization rate is only 91%. However, by installing SOPs, the charging station carrying capacity can be increased while achieving full utilization of renewable energy.

In summary, when the planning scope is small and the penetration rate is low, the cost of installing and operating SOPs is relatively higher. In this case, adjusting flexible loads and appropriately curtailing solar energy is a more economical choice. However, as the planning scope expands and the penetration rate increases, building SOPs becomes a more cost-effective and flexible option. It allows for both enhancing the charging station carrying capacity and promoting the utilization of renewable energy.

4.3. Sensitivity Analysis

We perform a sensitivity analysis on a four-feeder system under high penetration conditions. A multi-objective optimization method is employed, consistent with the previous setup, where the $ϵ$ value is fixed at 0.1. In this analysis, we first investigate the regulation capabilities of the data center. The parameter $\delta$ denotes the proportion of basic computing tasks, with lower values indicating greater flexibility.

As shown in Figure 12, the CSCC values vary with different $\delta$ levels, under the assumption that each data center maintains a minimum operational load ratio of 20%. It can be observed that when the regulation capability of the data center has not exceeded a certain threshold, reducing the value of $\delta$—i.e., enhancing the center’s flexibility—has a significantly positive impact on the CSCC. However, once this threshold is surpassed, the marginal improvement in CSCC becomes negligible. This is because, at this point, the main limiting factors are physical constraints, such as the capacity limits of distribution lines and transformers. Therefore, further improvement in CSCC would require infrastructure upgrades, such as line reinforcement or transformer expansion.

Next, a sensitivity analysis is conducted on the economic cost of SOPs. Using the initial cost coefficient $c_{\mathrm{inv}}^{\mathrm{SOP}}\left(ij\right)$ as a baseline, we investigate how variations in SOP installation costs affect the planning results. The corresponding outcomes are shown in the Figure 13 and

Table 4. SOP installation schemes and CSCC under different cost scenarios.

Cost Change	SOP Installation (Line and Nodes)	CSCC (kW)
−30%	Line-71 (Node 9–26) Line-72 (Node 12–44) Line-74 (Node 32–73) Line-76 (Node 48–87)	1870
−20%	Line-71 (Node 9–26) Line-72 (Node 12–44) Line-74 (Node 32–73)	1440
−10%
0%
10%
20%	Line-72 (Node 12–44) Line-75 (Node 33–46)	1276
30%

.

The analysis reveals that when the SOP cost decreases by 30%, the optimal planning scheme includes an additional SOP installed on line 48-74, resulting in a CSCC increase to 1870 kW. This improvement occurs because the surplus transmission capacity from the third feeder (i.e., the feeder starting from node 34) can be redirected to feeder 4, thereby enhancing the overall system CSCC.

Conversely, when the cost increases by 20%, the optimal configuration excludes the SOP on lines 33–46, causing the CSCC to drop to 1276 kW. As shown in the table, the SOP installation scheme exhibits discrete changes under varying cost conditions. This is attributed to the integer nature of the SOP deployment decision variables, which inherently leads to non-continuous transitions in the solution.

In summary, the final CSCC is jointly influenced by the value of $\delta$ and the installation cost of SOPs. The SOP deployment plan is particularly sensitive to cost variations. However, once $\delta$ exceeds a certain threshold, further improvement in CSCC is primarily constrained by physical hardware limitations within the distribution system. Therefore, to achieve additional gains in CSCC, it is necessary to consider potential upgrades to existing infrastructure. This insight constitutes one of the key findings of this study.

5. Discussion

While the proposed method shows clear technical and economic benefits in enhancing the charging station carrying capacity (CSCC) through the coordination of SOP configurations and data center load scheduling, several practical barriers to implementation must be acknowledged.

First, the operational integration between the power grid and data centers presents coordination challenges. Although the model assumes that computing tasks can be elastically scheduled, in practice, transferring workloads between data centers may involve non-negligible costs or lead to operational disruptions. Factors such as data latency, service-level agreements, and computational continuity must be carefully considered to avoid negative impacts on data center performance.

Second, from the grid operator’s perspective, the installation and deployment of Soft Open Points (SOPs) entail capital investment, planning permissions, and maintenance responsibilities. Decisions regarding SOP placement are influenced not only by technical feasibility but also by regulatory compliance and cost-effectiveness.

Moreover, stakeholder alignment is a critical factor. The interests of power utilities and data center operators may not always be aligned, especially when cost-sharing or operational adjustments are involved. Effective implementation of the proposed strategy would require institutional mechanisms that incentivize collaboration between these parties, possibly through regulatory support, contractual agreements, or market-based coordination frameworks.

These practical issues highlight the importance of complementing technical optimization with policy, regulatory, and stakeholder considerations. Future research should explore collaborative business models and policy incentives that facilitate the real-world deployment of such coordinated flexibility strategies.

6. Conclusions

This paper addresses the issue of charging load surges at certain times in some tourist cities in China and proposes a method for enhancing the charging station carrying capacity through the coordination of multiple flexible resources. The research results indicate that by integrating the elastic scheduling of data center computational tasks and SOP into the system optimization model, not only is the charging station carrying capacity significantly improved while maintaining economic efficiency, but the renewable energy utilization rate is also increased to 100%. Additionally, the study uncovers an important pattern: under the same penetration rate, the number of feeders involved in joint planning is positively correlated with the economic feasibility of SOP construction. That is, through multi-feeder coordinated optimization, fewer SOP installations can achieve better economic benefits.

This finding has practical implications for the construction of urban power grids in China. Given the unique characteristics of charging loads in China (such as the surge load during the Spring Festival or the sharp increase in regional load during peak tourist seasons), some regions may experience charging loads exceeding ten times those of off-peak hours during certain periods. Traditional responses mainly rely on passive measures, such as manual load monitoring, rolling blackouts, or temporary power generation vehicles. These methods not only incur high operational and maintenance costs but also have limited response times. The research presented in this paper offers a new approach to addressing this issue: through SOPs, active optimization of the distribution system’s power flow can be achieved, effectively alleviating the impact of charging load peaks on the power grid.

Moreover, the proposed model is adaptable to different urban environments and distribution network conditions. By adjusting regional parameters such as SOP candidate locations, data center flexibility levels, and electricity pricing mechanisms, the strategy can be customized for various application scenarios, providing broad applicability beyond the studied case.