Research on the Planning of Electric Vehicle Fast Charging Stations Considering User Selection Preferences

Abstract

The global energy and environmental crisis promotes the development of electric vehicles (EVs), and the rational planning of EV fast charging stations is an important influencing factor for their development. In this paper, for the EV fast charging station capacity planning problem, a joint-optimization model for optimal planning of EV fast charging stations and the economic operation of a distribution network is constructed, considering the impact of user preference selection and EV access on the regional distribution network. To address the problems of low efficiency and local convergence found in traditional heuristic optimization algorithms, an improved krill swarm optimization algorithm (CKHA) that introduces chaotic optimization parameters to make the initial population as uniformly distributed as possible is proposed to find the optimal planning scheme for EV fast charging stations. The case results show that the optimal planning model and its solution method are effective.

1. Introduction

1.1. Problem Statement

The global energy and environmental crises promote the development of electric vehicles. In October 2020, China’s State Council put forward the New Energy Vehicle Industry Development Plan (2021–2035) to promote the high-quality and sustainable development of China’s new energy vehicle industry. With China’s development goal of “carbon peaking and carbon neutral” and the State Grid Corporation’s proposal of “electricity instead of oil” for the transportation industry, the development of China’s vehicle electrification will be further accelerated. According to statistics from the Chinese Ministry of Public Security, by the end of March 2022, China had 8.915 million EVs, accounting for 2.9% of the total number of vehicles. According to the China Electric Vehicle Council 100, China’s EV (electric vehicle) fleet will reach 80 million units by 2030. For a long time to come, EV production will continue to grow at a high rate.

Charging network construction is an important foundation for the smooth promotion and application of electric vehicles. In January 2022, China’s National Development and Reform Commission and other departments issued the “Implementation Opinions on Further Improving the Service Guarantee Capability of Electric Vehicle Charging Infrastructure”, proposing to form a charging infrastructure system that is moderately advanced, balanced in layout, intelligent and efficient, and capable of meeting the charging needs of more than 20 million electric vehicles by the end of 2025. However, in China, the construction of charging stations is still slow. The unreasonable planning of the capacity of some charging stations and the failure to adequately consider the charging behavior of users are important constraints that limit the development of electric vehicles for them. In the current context, the number of electric vehicles will continue to increase and the charging demand of users will also increase, and the load of electric vehicles will further increase the pressure on the power supply of the distribution network. Therefore, reasonable capacity planning for charging stations to ensure user convenience and reduce the impact on the distribution network side has become a top priority in EV-related fields.

1.2. Literature Review

Rational planning of charging stations is a necessary foundation for the high-speed development of the electric vehicle industry. Scholars in China and abroad have carried out extensive research on issues related to EV charging station planning, mainly focusing on charging station operation constraints, planning decisions, algorithm improvement, etc.

With regard to the constraints of EV charging station planning, the literature [1] established a charging load estimation model based on the actual measured vehicle arrival hotspot map, fully considered the actual operational constraints of the distribution network, and introduced a multi-objective planning model. The literature [2] considers the constraints in the siting and capacity planning, including parking conditions, land use, traffic density conditions and user-side requirements, and focuses on quantifying the total cost and convenience of the user-side for the siting and capacity of charging stations. In the literature [3], a charging station planning model that takes into account the regional load, charging station construction and maintenance, and user losses is established, considering the impact of large-scale EV access on the regional distribution network, and an EV charging station planning method that takes into account the distribution network load is proposed. A method proposed in the literature [4] estimates the expected values of energy consumption and electricity demand of EV fast charging stations to reinforce the distribution grid, considering that EV charging may impact the existing low- and medium-voltage networks for a short period of time. A proposal in the literature [5] involves a unified approach to select a set of key indicators to measure the sustainability of EV charging stations, which supports the planning of sustainable EV charging stations in cities. Another proposal in the literature [6] used a multi-objective EV charging path planning framework to guide the path planning of charging stations considering the driving distance, total time consumption, energy consumption, and charging fees.

In terms of planning decisions for EV charging station planning, the literature [7] provides an in-depth analysis of the EV demand space, classifies EV charging demand into static and dynamic demand according to lot characteristics, and uses density peak clustering to plan the location and capacity of EV charging stations. In the literature [8], a two-stage robust distribution planning model for coordinated optimization of EV charging stations and energy storage, considering new energy uncertainties, is proposed to mitigate the challenges brought by uncertainty of new energy output and disorderly charging of EVs to power-system security. The literature [9] introduced a new single-valued neutrophil information-additive ratio assessment (ARAS) method to assess and prioritize sustainable EV sites. This method developed a novel single-valued subjective and objective weighted integrated approach (SVN-SOWIA) to calculate criteria by aggregating objective weights generated by a similarity metric-based procedure. Subjective weights were given by experts to effectively address the information uncertainty in the EV charging station site evaluation and selection process. A method given in the literature [10] uses probability distributions to improve the gain and loss of dominance scores for group uncertainty modeling in subjective evaluation to mitigate the uncertainty caused by expert opinion disagreement in a multi-criteria decision problem like EV charging station planning. In the literature, a study [11] considers the charging demand response of EV users and proposes a method for planning PV energy storage fast charging stations considering charging demand response to maximize the social and economic benefits from fast charging services. Another study [12] proposes a joint modeling approach for user charging behavior decision and charging station planning, which clarifies the interaction mechanism between user behavior decision and charging station planning and is applicable to the planning problem of charging stations in urban areas. In another study [13], a model is proposed to optimize the capacity of charging station sites considering the economics of charging stations and customers in multiple scenarios, taking into account the economic benefits of distribution networks, charging stations, and customers. A further study [14] proposes an EV charging station planning model that considers the spatial and temporal distribution characteristics of the charging load, which can effectively achieve the organic unification of cost minimization for both EV charging stations and users from the perspective of user satisfaction.

In terms of algorithm improvement for electric vehicle charging station planning, a study [15] established a multi-objective charging station planning problem and combined the hybrid particle swarm optimization HPSO (hybrid particle swarm optimization) algorithm with an entropy-based preference technique for ordering the similarity of ideal solutions, named ETOPSIS (entropy technique for order preference by similarity to ideal solution), to solve such a problem. In another study [16], a multi-objective improved particle swarm algorithm is proposed to optimize the location of charging stations and the fast and slow charging ratios in charging stations; the inertia weight factor and scaling factor are improved for the shortcomings of the multi-objective particle swarm algorithm to improve the search capability of the algorithm and accelerate the convergence speed. Another study [17] considered the application of the six-party fuzzy multi-criteria decision making (MCDM) method in the site selection of electric vehicle charging stations, proposing a defusing and distance measurement method between two hexagonal fuzzy numbers (HFN) based on centroids, and proved that the method is stable and effective by example. A further study in the literature [18] presents an efficient planning method for a multi-objective binary version of fast charging stations for electric vehicles, using an atomic search optimization algorithm, which uses quantum operations to binarize the algorithm and achieves a higher convergence rate than existing binary ASO algorithms. In the literature [19], a two-tier planning framework was developed to develop an electric vehicle charging station route network design to improve the effectiveness and economy of the electric transportation route network.

1.3. Contribution to This Article

In summary, EV user charging behavior is an important factor to be considered in EV charging station planning, and some studies do not consider the interaction mechanism between the two. There are more studies on the impact of charging stations on distribution networks and construction costs. Therefore, this paper proposes an EV charging station planning method with user selection preference, and the main innovation points are as follows:

• Considering the interaction mechanism between EV user behavior and charging stations, which is missing in most current studies, a joint planning method with the objective of optimal planning of charging piles and optimal economic operation of the distribution network is constructed by quantifying EV user behavior as charging trips adding constraints.
• An improved chaotic optimized krill swarm algorithm is proposed, which introduces chaotic mapping in the initial search phase, updates the krill swarm positions, increases the randomness, optimizes the global search capability, takes into account the advantages of the robustness of the krill swarm algorithm, and improves the solution speed of the algorithm by reducing the number of algorithm parameters that need to be adjusted.
• Taking the planning area of fast charging stations and the actual distribution network in a region of Guizhou as the planning object, a case study is conducted with the characteristics of EV user demand satisfaction and the number of planned charging stations and the profitability of charging stations, etc. The results show that the joint planning and optimization method proposed in this paper, which aims at the optimal planning of charging piles and the optimal economic operation of the distribution network, effectively improves the economy and user charging efficiency when building charging stations.

2. Materials and Methods

The location and structure of charging stations are related to the purchase intention of electric car consumers. According to the field survey, cab owners in Guiyang generally reflect that there is a serious problem of electric vehicle charging in Guiyang, and the main reasons are that there are few electric vehicle parking spaces in residential areas and the distribution of charging piles is unreasonable. Based on the analysis of EV parking behavior, this paper proposes a joint optimization model for optimal planning of EV fast charging stations and economic operation of the distribution grid based on statistical data such as the distribution of user parking lots in the planning area, the number of vehicles arriving at the parking lots and the parking duration. The model takes minimizing socialization cost as the objective, considers the charging pile planning constraints as well as the distribution network safety operation constraints, and establishes the mixed integer nonlinear programming expression of this joint optimization model. The model is applied to the actual charging station planning area and the actual distribution network for testing. The test results show that the joint optimization model proposed in this study can obtain more accurate calculation results, and the calculation time is shorter.

2.1. Analysis of Electric Vehicle Parking Behavior

EV parking behavior is often considered to be the dominant factor directly affecting the distribution of EV charging demand. According to existing studies, EV parking behavior can be jointly described as the distribution curve of the number of EV arrivals versus parking time. However, due to the relatively low penetration rate of EVs at this stage, the historical data of their parking behavior is limited and cannot accurately describe their statistical characteristics. The data in this paper comes from the number of parking spaces by time period counted by the Qiannan State Big Data Development Authority, using fossil fuel vehicle data as an analogy to EV user parking behaviour.

Figure 1 shows the distribution curves of the number of vehicles arriving at the parking lot and the parking duration in a typical day for residential, work and other zones, where the vertical coordinates are based on the maximum number of parking in each type of zone. In this paper, the concept of the standardized value (p.u., actual value/base value) is introduced to facilitate the calculation, and the same is done below. The time span of the horizontal coordinate in the figure is 4 days, divided into 96 periods (15 min is 1 period). The distribution curve of the number of vehicles arriving at the parking lot shows that the distribution pattern of the residential area and the work area is more obvious, i.e., the number of vehicles arriving at the residential area is more in the period from 48th to 68th, which is more in line with the travel pattern of users returning home for rest during this period. The arrival of vehicles in the work area is mainly concentrated in the period from 32nd to 40th, because the users mainly commute to work during this period. The distribution pattern of other zones is less obvious, reflecting only the basic travel characteristics of users who travel during the day and rest at night. In addition, observing the distribution curve of the parking duration of vehicles, we can find that the parking time of vehicles in the work area is mostly around 32 time periods, which is more in line with the working hours of a day. The vehicle parking duration in the residential area is mainly divided into 28th and 64th, which mainly shows the night or a non-working time period. Other zones are mainly composed of service institutions, such as shopping malls or hospitals, where users mainly handle temporary business, and most of the vehicle stopping time is only 8–12 time periods.

It is important to note that when EVs arrive at the parking lot, their charging demand is mainly related to the state of charge (SOC) of the battery at the current time. Since the current charging history data of EVs are limited, this paper adopts a normal distribution in the interval of [0, 1] (the expected value is 0.5 and the standard deviation is 0.2) to simulate the SOC condition of each EV in each time period, then generates a set of SOC data of each EV in 96 time periods by sampling. In this paper, it is assumed that when the SOC of EVs exceeds 0.9, they are not selected for charging, and all other cases are selected for charging. By analyzing the above EV user parking behavior statistics and charging demand law, it can provide strong data support for the subsequent seeking of EV fast charging station load.

2.2. Joint Optimization Model for Optimal Planning of Charging Stations and Economic Operation of Distribution Networks

In the joint optimization model of this paper, it is assumed that there are several charging station candidates connected to a distribution network that can cover different types of areas, and each candidate can be installed with several charging piles to meet the local charging demand, each with the same configuration and specifications. Meanwhile, we use the regular load and EV charging demand data of a typical day to simulate the operation scenario for 365 days a year. Based on this, we can construct the following optimization problem.

2.2.1. Optimization Goals

In this paper, the overall objective of minimizing the social cost of building EV charging stations according to the equal annual value method can be written in the form of the expression equation:

$$\min \hspace{1em}{C}^{total}=C^I+C^R+C^M+365{\displaystyle \sum _{t=1}^{96}{C}^L\left(t\right)},$$

(1)

in the formula, $C^I$ denotes the equivalent annual value investment cost of building charging piles; $C^R$ denotes the grid reinforcement cost after the distribution grid is connected to the EV charging load; $C^M$ denotes the operation and maintenance cost of charging piles; and $C^L\left(t\right)$ denotes the network loss cost during $t$ time period.

The specific formula for calculating each cost is as follows:

• Charging piles and other annual value investment costs

The investment cost of the charging pile is mainly related to the number of charging piles installed, and the specific expression is as follows:

$$C^I=r_d{\displaystyle \sum _{i\in {\Omega }_c}\left(c_{FCF}^I\cdot I_i^{FCF}\right)},$$

(2)

$$r_d=\frac{d{\left(1+d\right)}^Y}{{\left(1+d\right)}^Y-1},$$

(3)

in the formula, $c_{FCF}^I$ denotes the construction cost of a single charging post (in dollars); $I_i^{FCF}$ denotes the number of charging piles installed at charging station candidate node $i$ of the charging station, which is an integer variable to be optimized; ${\Omega }_c$ denotes the set of charging station candidate nodes; $r_d$ denotes the equal annual value factor; $d$ denotes the depreciation rate; and $Y$ denotes the economic lifetime of the charging post (in years).

2.

Annual value of grid, etc., reinforcement costs

When the charging pile is connected to the grid, the grid needs to reinforce some of its own hardware facilities, such as expanding the capacity of the transformer or increasing the transmission capacity of the line, the cost of which can be calculated according to the following formula:

$$C^R=r_d{\displaystyle \sum _{i\in {\Omega }_c}\left(c_{FCF}^R\cdot P^{FCF}\cdot I_i^{FCF}\right)},$$

(4)

in the formula, $c_{FCF}^R$ denotes the cost of grid reinforcement per unit of charging power increased (in yuan/kW); $P^{FCF}$ denotes the rated charging power of a single charging post (in kW).

3.

Annual operation and maintenance costs of charging piles

During the daily operation of the charging pile, certain operating costs and labor maintenance costs need to be considered, which can be calculated according to the following formula:

$$C^M={\displaystyle \sum _{i\in {\Omega }_c}\left(c_{FCF}^M\cdot I_i^{FCF}\right)},$$

(5)

in the formula, $c_{FCF}^M$ denotes the annual operation and maintenance cost of a single charging post (in dollars).

4.

Network wear and tear costs

With the access of EV charging piles, the system load will be significantly increased, so it is necessary to consider its impact on the system network loss, which can be calculated by the following equation:

$$\begin{array}{l}{C}^L\left(t\right)=c^L{\displaystyle \sum _{\left(i,j\right)\in {\Omega }_L}\mathrm{Re}\left\{y_{ij}\right\}\cdot ({\left(e_i\left(t\right)-e_j\left(t\right)\right)}^2}\\ \hspace{1em}\hspace{1em}\hspace{1em}+{\left(f_i\left(t\right)-f_j\left(t\right)\right)}^2)\Delta t\end{array},$$

(6)

in the formula, $C^L$ denotes the unit cost of network losses (in $/kWh); ${\Omega }_L$ denotes the set of lines in the network; $e_i$ and then $f_j$ denote the real and imaginary parts of the voltage vector at node $i$, respectively; and $y_{ij}$ denotes the conductance between node $i$ and node $j$.

2.2.2. Binding Conditions

The constraints in this paper are mainly considered in terms of the trip limit of EVs, the charging demand of EVs, and the safe operation of the distribution network.

• Overall balance constraint of EV charging stroke

All EVs driving to the destination node need to have enough charging posts to meet their charging needs, as shown in the following equation:

$$N_i^{arFCV}\left(t\right)={\displaystyle \sum _{j\in {\Omega }_c}{I}_{ij}^{FCV}\left(t\right)},\hspace{1em}\forall i\in {\Omega }_N,$$

(7)

in the formula, $N_i^{arFCV}\left(t\right)$ denotes the number of EVs whose destination at time $t$ is node $i$ and need to be charged; $I_{ij}^{FCV}\left(t\right)$ denotes the number of EVs whose destination at time $t$ is node $i$ but need to be charged at charging station candidate node $j$, an integer variable to be optimized; and ${\Omega }_N$ denotes the set of all nodes.

2.

Distance constraint of EV charging stroke

For the above-mentioned EVs whose destinations are nodes requiring charging at node j, the distance traveled should not exceed the maximum limit of their additional trips, as expressed below:

$$I_{ij}^{FCV}\left(t\right)=0,\hspace{1em}\forall \left(i,j\right)\in \left\{\left(i,j\right)|d_{ij}>d_{\lim }\right\},$$

(8)

in the formula, $d_{ij}$ denotes the distance between node $i$ and node $j$ (in km); $d_{\lim }$ denotes the maximum distance traveled by the EV to make additional trips.

3.

Charging pile demand constraint

For the number of charging posts installed at charging station candidates, the EV charging demand for each time period should be met, as expressed below:

$$I_j^{FCF}\ge {\displaystyle \sum _{i\in {\Omega }_N}{I}_{ij}^{FCV}\left(t\right)},\hspace{1em}\forall i\in {\Omega }_c,$$

(9)

4.

Charging power constraint

The charging power of a candidate point of a charging station is determined by the number of EVs to be charged installed at that point and the rated power of the charging post, which is expressed as follows:

$$P_j^{FCV}\left(t\right)=P^{FCF}\cdot {\displaystyle \sum _{i\in {\Omega }_N}{I}_{ij}^{FCV}\left(t\right)},\hspace{1em}\forall j\in {\Omega }_c,$$

(10)

5.

Network tide equation

The common AC current equation for power systems is shown in the following equation:

$$P_i^L\left(t\right)+P_i^{FCV}\left(t\right)=\mathrm{Re}\left\{V_i\left(t\right){\displaystyle \sum _{k\in i}{y}_{ik}^{*}}{V}_k^{*}\left(t\right)\right\},\hspace{1em}\forall i\in {\Omega }_N,$$

(11)

$$Q_i^L\left(t\right)=\mathrm{Im}\left\{V_i\left(t\right){\displaystyle \sum _{k\in i}{y}_{ik}^{*}}{V}_k^{*}\left(t\right)\right\},\hspace{1em}\forall i\in {\Omega }_N,$$

(12)

in the formula, $P_i^L\left(t\right)$ and $Q_i^L\left(t\right)$ denote the regular active load and reactive load at node $i$ in $t$ time period, respectively; $V_i\left(t\right)$ denotes the voltage vector at node $i$ in $t$ time period.

6.

Nodal voltage magnitude constraint

The voltage of each node in the network should be kept within the limits, i.e., the upper and lower limits of the voltage of each node are constrained to satisfy the following constraints:

$$V_{\min }\le \left|V_i\left(t\right)\right|\le V_{\max },\hspace{1em}\forall i\in {\Omega }_N,$$

(13)

in the formula, $V_{\min }$ and $V_{\max }$ denote the upper and lower limits of the voltage amplitude at node $i$, respectively.

7.

Branch circuit current constraint

In order to ensure the safety of line operation, this paper sets the upper and lower limits for the current flowing through the line, as shown in the following equation:

$$\begin{array}{l}{\left|y_{ij}\right|}^2\left({\left(e_i\left(t\right)-e_j\left(t\right)\right)}^2+{\left(f_i\left(t\right)-f_j\left(t\right)\right)}^2\right)\le {\overline{I}}_{ij}^2,\\ \forall (i,j)\in {\Omega }_L\end{array},$$

(14)

in the formula, ${\overline{I}}_{ij}^{}$ denotes the maximum allowable line current between the node $i$ and the node $j$.

2.3. Improved Krill Swarm Algorithm

The joint optimization model considering the optimal planning of charging stations and the economic operation of the distribution network often has to consider several aspects, including economy and reliability, and the calculation is extremely complicated. The traditional intelligent optimization algorithms often fall into local optimal solutions, long computation time and complicated adjustment parameters, which are not conducive to planning solutions. In this paper, an improved krill swarm algorithm is proposed to improve the krill swarm algorithm in the following two aspects.

2.3.1. A Krill Swarm Algorithm Based on Chaos Optimization

The initial population data of traditional krill swarm algorithms are generated by using random numbers, which may lead to sparse populations near the optimal solution and insufficient global search capability.

In this paper, chaos optimization parameters are introduced in the traditional krill swarm algorithm to make the initial population as uniformly distributed in the data space as possible, to improve the krill swarm diversity and the uniform distribution of individuals, and to achieve the purpose of improving the global search and convergence speed of the krill swarm, by optimizing the random numbers in the first step of the krill swarm algorithm through chaos optimization:

$$\lambda =(\frac{p}{4})\times \sin (\pi \times {\lambda }_{r-1}),$$

(15)

$$x_i=x_{\min }+\lambda (x_{\max }-x_{\min }),$$

(16)

in the formula, $\lambda$ is the sinusoidal mapping of [0, 1] and $x_{\max }$, $x_{\min }$ are the upper and lower boundaries of the position of the initial krill population.

2.3.2. Introduction of Variation Factors

In this paper, the variation factor is introduced in the study of individual position update, which can expand the search range and avoid falling into local optimum. In the early stage of the algorithm, a larger variation factor can expand the search space and improve the sample diversity, and in the later stage, it should take a smaller value in order to improve the convergence speed and accuracy, and the probability density function of the variation factor is as follows:

$$F=\{\begin{array}{c}\frac{F^{\ast }arccot\theta }{\pi },\hspace{1em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\theta ⩽\frac{\pi }{4}\\ 1-\frac{F^{\ast }arccot\theta }{\pi },\hspace{1em}\theta >\frac{\pi }{4}\end{array},$$

(17)

$$\begin{array}{l}{x}_i{}_{best}(t)=x_i(t)+x_i(t)F\\ x_i(t+1)=\{\begin{array}{l}{x}_i{}_{best}(t),f(x_i{}_{best}(t))>f(x_i(t))\\ x_i(t),f(x_i{}_{best}(t))\le f(x_i(t))\end{array},\end{array}$$

(18)

in the formula, $f(x_i{}_{best}(t))$ is the fitness of krill $i$ at the $t$ th iteration, and by introducing the variation factor $F$, the improved krill swarm algorithm removes the local optimum, expands the search range and improves the accuracy.

2.3.3. Joint Planning and Optimization of Charging Stations and Distribution Networks Based on Improved Krill Swarm Algorithm

The above improved krill swarm algorithm is applied to the joint optimization model proposed in this paper, and the solution process is as follows; the algorithm flow chart is shown in Figure 2:

Step 1: initialization of model data, inputting known parameters such as various costs and user parking behavior.

Step 2: initialization of the krill population for time period T according to chaotic optimization.

Step 3: generating the location X of the initial population in time period T, recording the location of the best krill and the adaptation degree f.

Step 4: iterative solution, where each of the obtained solutions is substituted into the constraints for judgment and the krill population food center location is updated.

Step 5: Execute the variation factor to update the krill location and fitness.

Step 6: After a certain number of iterations, complete the data processing work and output the optimal solution for planning the number of charging stations at each node in the current stage, otherwise return to step 3.

3. Results

3.1. Basic Data

In order to verify the effectiveness of the joint optimization model proposed in this paper, a certain fast charging station planning area in Guizhou is selected for simulation tests by combining the charging post planning of the government department, the actual operation range of charging stations in Guizhou (see Figure 3 for details) and the actual distribution network (see Figure 4 for details). The planning of the number of charging stations is carried out after the station site is determined. Among them, there are 41 nodes in the distribution network, containing 14 charging station candidates, which are represented by red nodes in the figure. The green circles indicate the charging service area with the charging station candidate points as the center of the circle. The letter mark corresponding to each distribution node indicates the charging area corresponding to that node, where H indicates residential area, W indicates office area, and O indicates other areas, and the maximum number of parking in each block can be detailed in

Table 1. Maximum number of parking spaces in each block.

Block	Maximum Number of Parking Spaces	Block	Maximum Number of Parking Spaces	Block	Maximum Number of Parking Spaces
H1	41	W1	19	O1	14
H2	15	W2	20	O2	10
H3	22	W3	67	O3	6
H4	61	W4	9	O4	30
H5	25	W5	9	O5	34
H6	21	W6	53	O6	5
H7	33	W7	27	O7	7
H8	20	W8	28	O8	39
H9	86	W9	14	O9	18
H10	19	W10	16	O10	22
H11	22	W11	12	O11	29
H12	11	W12	52	O12	9
		W13	84	O13	23
		W14	41
		W15	11

, and the relevant parameters of the optimization model are detailed in

Table 2. Example parameter values.

Parameters	Numerical Value
$d$	0.03
$Y$	10
$P^{FCF}$	60
$c_{FCF}^I$	40,000
$c_{FCF}^R$	750
$c_{FCF}^M$	4000
$c_{FCF}^M$	560
$c_L$	0.6
$d_{\lim }$	0.95
$V_{\min }$	1.05
$V_{\max }$	1.8187
${\overline{I}}_{ij}^{}$	0.03

.

Figure 5 shows the conventional load profile of this distribution network on a typical day, and the maximum peak value of each type of load in 96 periods is used for the load reference value. For example, for the residential area load, the peaks occur mainly in the midday and evening tine (e.g., periods 48 to 56 and 76 to 84), when customers are more likely to be at home and have higher demand for electricity. As for the work area load, its peak is mainly concentrated in the daytime working time (periods 40 to 68), as customers mainly work during this time period.

3.2. Optimal Planning Results for Charging Stations

Based on the above statistics, the optimal number of charging piles to be installed at each charging station candidate point is given in Figure 6 using the joint optimization model of optimal planning of charging stations and economic operation of the distribution network proposed in this paper. It can be found that enough charging piles are allocated at each candidate node in order to meet the EV trip and charging demand. Among them, node 22 is equipped with 94 charging posts, which is the largest number in the whole network. Combining with Figure 3 and Figure 4, it can be seen that this is mainly because node 22 is located in block W2, whose maximum number of local outage vehicles is 20, while its charging service area also covers node 23(O9), node 24(O8), node 25(H4) and node 38(H3), corresponding to the maximum number of outage vehicles of 18, 39, 61 and 22, respectively. In addition, node 25(H4) and node 38(H3) can only choose the charging post at node 22 to provide charging service for them, so the demand of charging post at node 22 is very high.

Similarly, node 23 is equipped with 13 charging posts, which is the lowest number in the whole network, mainly because its charging service range covers node 20 (O7), node 24 (O8) and node 26 (W3), which overlap with the service range of other charging station candidate nodes and can be provided by other candidate nodes, so there is no need to install more charging posts.

3.3. Sensitivity Analysis

3.3.1. Difference between Electricity Purchase and Charging

The spread in this paper is mainly the spread after averaging the power purchase prices during the peak and valley periods. Figure 7 shows that the dynamic break-even point tends to decrease exponentially as the magnitude of the price differential increases. Overall, when the average charging service price is higher than about $0.45, the break-even point 89 of the charging station is lower than its maximum daily load of 448, and thus has the possibility of profitability; when the average charging price is higher than the electricity purchase price of about $0.45, the break-even point 89 of the charging station is lower than the current average daily number of charging vehicles at the charging station 112, and thus can realize profitability. Thus, it can be concluded that the charging station can be profitable when the difference between charging and electricity purchase price needs to be greater than or equal to 0.45 yuan, with other parameters remaining unchanged.

3.3.2. Charging Time and Charging Requirements

The length of charging time will directly affect the total load of charging stations and thus their potential profitability. Excessive charging time affects both the utility satisfaction of consumers purchasing EVs and the profitability of charging station operators. This is currently a key factor affecting EV proliferation and business model innovation. A key difference in the charging and swapping business model is the charging and swapping time. With the improvement of battery technology and charging technology, the charging time of electric vehicles will drop significantly in the future.

As can be seen from

Table 3. Example parameter values.

Charging Time (h)	Total Load of Charging Stations (Vehicles/Day)	Elasticity Factor
12	56	/
10	20	0.7
8	25	1.25
6	29	0.64
4	36	0.72
2	89	2.94

and Figure 8, the decrease in charging time causes the load level of the charging station to rise rapidly, and the total load elasticity of the charging time increases as the charging time decreases.

Although the decrease in charging time increases the total charging station load, the increase in the degree of charging station load still has a more limited impact on the profitability of the project if the total demand for charging is low, thus the increase in the total demand for charging is critical to the profitability of charging station operators. As the marketization of electric vehicles accelerates and the replacement of traditional fuel vehicles strengthens, the demand for charging at charging stations will rise significantly in the future, thus increasing the expected profit level of charging stations.

3.3.3. Initial Investment Cost of Charging Station

The decrease in the initial investment cost of charging stations will reduce the cost outlay of charging station operators, which will lead to a decrease in the break-even point. According to Figure 9, when the initial investment cost is $3.2 million, only 89 vehicles are charged, which is lower than the average number of charging vehicles per day. It can also be concluded that the initial investment cost of charging stations has been decreasing, the break-even point has been decreasing, and the profitability of charging stations has been increasing.

3.3.4. Labor Wages and Site Share

After research, it is learned that the cost of site share of charging stations is an important cost item in the operation of charging stations. Figure 10 shows that when the site share ratio increases, the break-even point also increases, and when the site share ratio reaches 28% and other conditions remain unchanged, the break-even point of charging stations is lower than 112 vehicles, and charging stations can still be profitable at this time.

With the current increasing cost of human resources, the labor cost of charging stations is also a major factor affecting the profitability of charging stations. Figure 11 analyzes the impact of labor wages on the break-even point of charging stations; it can be seen that the labor cost of charging stations in this case is within 300,000 yuan, and when other conditions remain unchanged, the break-even point of charging stations is lower than 112 vehicles, and charging stations can still be profitable at this time.

3.3.5. Project Cycle

The change in the project cycle will affect the overall operation time of the project and thus the overall profitability of the project. In the initial parameter setting, the project cycle is assumed to be 5 years, but in the actual operation process, the operation time of charging stations may exceed 10 years. Therefore, the project cycle is assumed to be 3 to 10 years in different cases, as shown in Figure 12. As can be seen in Figure 12, when the project cycle is increased from the initial 5 years to 10 years, the break-even point of the charging station decreases from 89 to about 68 vehicles, which is a small change, but the break-even point is lower than the estimated average number of charging vehicles per day at the charging station, and the charging station is able to maintain its commercial operation with the other initial parameters unchanged.

Based on the above analysis, it can be concluded that the charging station operators are able to achieve profitability according to the initially set parameter values. The charging service fee (the cost difference between charging and electricity purchase) and the daily charging time of electric vehicles have a more significant impact on the break-even point. The initial investment cost, labor wage cost and site sharing cost, and the project cycle of charging stations have a relatively low impact on the profitability of charging stations.

4. Discussion

4.1. Impact on the Grid before and after EV Access

The maximum peak value of the total system load before the introduction of EV charging load is 8.59 MW, and Figure 13 shows the standardized curve of the total system load before and after the introduction of EV charging load (the base value is 10 MVA). It can be found that the maximum system load can reach 16.35 MW after the introduction of EV charging load, which indicates that the load level of the system will be significantly increased when the number of EVs connected to the distribution network is large enough, and the distribution network operators need to reserve enough access capacity and line transmission capacity when planning charging stations.

Figure 14 compares the changes in the currents of some branches in the network before and after accessing the EV charging load, where the dashed line indicates before consideration and the solid line indicates after consideration. It can be found that after connecting a sufficient number of charging posts to the distribution network, the current of each branch is significantly increased, among which, the current of branches 1–2 is most significantly increased with a maximum value of 1.645 p.u. (the benchmark value is 549.85 A). Since node 1 is the balance node of the distribution network and the distribution network is a radial distribution network, the currents of branches 1–2 are the gateway currents of the network and their amplitudes should be the maximum of the whole network. The above results show that EV load access will have a large impact on the branch currents in the network, and the grid company also needs to consider sufficient line transmission capacity in the process of charging station construction and planning.

4.2. Comparative Analysis of Algorithms

In order to compare the superiority of using the improved krill swarm algorithm (CKHA), this paper compares and contrasts three algorithms, namely, the ant colony algorithm (ACO), simulated annealing algorithm (SA) and particle swarm algorithm (PSO), on the basis of using the improved krill swarm algorithm for data processing, and derives the results of their respective runs.

The final optimal solution results, number of iterations, solution time, and global search capability using different algorithms for data processing are shown in

Table 4. Comparison of the results of four optimization algorithms.

Algorithm	Number of Charging Piles	Number of Iterations to Find the Optimal Solution	Number of Iterations into Local Optimum	Optimal Annual Total Cost/Billion	Solving Time/Sec
CKHA	771	32	About 2 times	1.38	1.39
ACO	762	36	About 15 times	1.42	1.52
SA	842	48	About 13 times	1.54	1.73
PSO	801	39	About 11 times	1.43	1.66

.

The results show that, in terms of total annual cost, the optimal solution obtained by CKHA has the lowest comprehensive total cost, followed by ACO; among them, the solution corresponding to CKHA still has the lowest total cost even though the number of charging piles is significantly more than that of ACO, indicating that the solution corresponding to this algorithm greatly saves the user’s usage cost and the economic loss of distribution network load; in addition, CKHA requires 19.65% less time than the traditional SA algorithm to In addition, CKHA reduces the solution time by 19.65% compared with the traditional SA algorithm, which greatly improves the operational efficiency; and CKHA is more efficient and basically does not fall into local convergence.

5. Conclusions

In this paper, a joint optimization model for optimal planning of EV fast charging stations and economic operation of distribution network is constructed by considering user selection preferences, and an example simulation is conducted for a region in Guizhou. The results and sensitivity analysis prove the effectiveness of the model proposed in this paper, and the following conclusions are obtained:

• In order to meet the demand for EV trips and charging in the area, as well as the economic operation of the distribution network, the candidate nodes for each charging station were planned and the specific number of charging pile configurations for each node was obtained.
• A sensitivity analysis of the factors affecting the operation of charging stations reveals that the main factors affecting the profitability of charging stations are charging service charge (the cost difference between charging and electricity purchase), the daily charging time of electric vehicles, initial investment cost, labor wage cost and site sharing cost. The project cycle of charging stations has a relatively low impact on the profitability of charging stations.
• Through the analysis of EV access to the grid, it is found that EV load access will have a large impact on the branch currents in the network, and the grid company also needs to consider sufficient line transmission capacity in the process of building and planning charging stations.
• A krill swarm algorithm based on chaos optimization proposed in this paper demonstrated significant improvement in terms of computational time and computational accuracy. Compared with the traditional intelligent optimization algorithm, the computational time is reduced by 19.65% compared with the traditional SA algorithm, it basically does not fall into local convergence, and has higher solution efficiency.

This paper considers the selection preferences of users in choosing charging, including distance and time, which effectively improves the economy and user charging efficiency when building charging stations. However, there are still the following points to be further improved: on the one hand, the factors of EVs in choosing charging are often diverse and need to be considered by a combination of subjective and objective factors; on the other hand, with the rapid development of EVs, EV switching stations will also be studied in depth, which is one of the main directions of this topic in the future.