Achieving accurate and balanced regional electric vehicle charging load forecasting with a dynamic road network: a case study of Lanzhou City

Abstract

Spatial and temporal predictions of electric vehicle (EV) charging loads provide a basis for further research on synergistic operation of road-vehicle-electricity networks with different attributes, which is important for siting and capacity building of urban road networks and charging stations, as well as for long-term planning and operation of power systems. However, some of the variables in EV charging load prediction are often given as random variables or constants, and to enhance the modeling and prediction accuracy for EV charging loads, data- and model-driven concepts were combined, and a novel model was proposed to achieve accurate balanced regional EV charging load forecasting with dynamic road networks: a case study of Lanzhou city. First, a road-vehicle-grid integration model was constructed, and an EV was used as an intermediate medium to initially integrate the flexible domains of the two layers of the road network and grid for establishing the actual road network topology in the city and for comparing static and dynamic road network models. Second, particle swarm optimization (PSO) was employed to optimize the backpropagation (BP) neural network for predicting future regional EV ownership. In addition, the PSO-BP-Monte Carlo (MC) model was refined for obtaining accurate spatial and temporal predictions of regional short-term charging loads through the introduction of an EV real-time unit mileage power consumption model with the use of M/M/c queue theory for determining charging waiting times. Finally, a simulation was conducted in the urban area of Lanzhou city as an example of actual traffic roads, and the results showed that the proposed model could be applied to reasonably effectively and more accurately predict the regional load conditions. The average growth in the peak load within the region over the next five years will reach 21.07$\%$, and accurately balances the occupancy rate of each charging pile of the charging station, and the dynamic road network will experience a decrease in the peak-valley difference between the loads of the static network of 5.92$\%$. Compared to those obtained with other methods, the single-day load distribution was more balanced, and the road access time better conformed with the actual road access conditions, which verifies the effectiveness and feasibility of the proposed method and lays a foundation for the next step of research on synergistic operation of road-vehicle-grid networks with different attributes.

Graphical abstract

1 Introduction

As energy and carbon dioxide emissions have become a growing concern, Article 2 of the Paris Agreement proposed the objective of limiting the increase in global average temperatures to 2 degrees Celsius ($^{\circ }$C) or even to 1.5 degrees Celsius ($^{\circ }$C). To this end, countries worldwide are aiming to build a beautiful Earth. As one of the nationally determined contributions (NDCs) [1] to the global response to climate change, in the general debate of the 75th United Nations General Assembly, China announced that it would implement more vigorous policies and measures [2] to achieve the goals of carbon dioxide emission peaking by 2030 and carbon neutrality by 2060 [3]. Among these issues, the discharge of greenhouse gases, the increase in air pollution, and the dependence on fossil fuels are important challenges affecting transportation development while promoting transportation electrification advancement. In recent years, transportation electrification has been recognized as an effective measure for achieving energy conservation, reducing emissions and improving the energy use efficiency. As a promising green transport option [4], electric vehicles (EVs) are an important means to explore the potential for carbon reduction in transport, to enhance the level of transport electrification, and to achieve the goals of carbon peaking and carbon neutrality [5]. At present, the energy crisis has created consumption pressure in China, and EVs have become an effective mode of transportation energy consumption to promote energy transition [6]. The Global Electric Vehicle Outlook 2023 published by the International Energy Agency (IEA), as shown in Fig. 1, reported more than 26 million EVs on the road in 2022, representing a 60$\%$ growth from 2021, with half of the world’s EVs observed in China.

Fig. 1

Global EV stocks from 2010-2022 Data sources: IEA, 2023. Global EVs Outlook 2023. https://iea.blob.core.windows.net/assets/dacf14d2-eabc-498a-8263-9f97fd5dc327/GEVO2023.pdf

China’s EV sales reached 9.495 million units in 2023, and a continued high-growth trend was observed. By the end of 2023, EV ownership in China reached 20.41 million units, which has created a high demand for charging and has accelerated the stimulation of full deployment and rapid growth in charging infrastructure. At present, China has built a total of 8,596,000 units of charging infrastructure and 3,567 power stations and has established the largest charging infrastructure network in the world. The vehicle-to-pile ratio has decreased, but compared with the continuous growth in the market demand, the integrated vehicle-to-pile ratio still exhibits a certain gap. A long charging time and poor charging experience are the main difficulties and challenges faced by existing EV charging technology. Due to the lack of data on the actual use of EVs at the initial stage, the construction of charging infrastructure lacks support and guidance, resulting in irrational planning of the location of charging stations and a mismatch between the construction of charging piles and the proportion of the actual demand, resulting in very high charging waiting rates in some areas and a large number of charging piles remaining idle in remote areas, a contradiction that has become a considerable challenge for the industry. Second, due to the limitations of power batteries and charging technology, the range of EVs is limited and will continue to decline, and the mileage anxiety problem limits the popularization and application of EVs. However, the limitations of the popularization and application of EVs have led to a reluctance among charging station operators to greatly invest in the construction of charging stations [7]. The above challenges faced by EV users and charging station construction create a vicious cycle. Computational intelligence has been significantly developed so far [8], and a much-needed solution to address EV users’ concerns about the limited range of EVs, improve EV charging experience, and increase the utilisation rate of regional charging stations is to employ computational intelligence to rationally and efficiently plan the layout and capacity of charging stations [9], so as to make them fit into the actual spatio-temporal distribution of charging load demand. This requires more accurate spatial and temporal forecasting of EV charging loads, which provides an important basis for determining the siting and capacity of EV charging stations.

As the number of EVs grows and the construction of charging networks improves, the uncontrolled charging of a large number of EVs can cause unstable operation of road network traffic conditions and power grids [10]. One aspect is that orderly charging of EVs could significantly reduce congestion within the road network and relieve road network scheduling operation. Another aspect of EVs, namely, flexible loads [11], could help to smooth loads, reduce costs, and result in the consumption of a high proportion of renewable energy in new power systems. To inhibit the negative impact of EVs on the road network grid, orderly cooperative operation of vehicle-road networks has become a research hotspot [12, 13]. Effective and reasonable spatial and temporal predictions of the charging loads of EVs as intermediate media in the case of road network-grid fusion provide the basis of cooperative operation while also constituting a key link.

It can be seen that for regional EVs more accurate and balanced charging loads prediction, the urban road network and charging station siting capacity construction, for the next step in the study of road-vehicle-grid different attributes of the synergy between the network, the long-term planning and operation of the power system is of great significance [14].

First, due to the different types of EVs, the driving and charging characteristics are very different, the road network-grid attributes vary, and a unified model is difficult to establish because EVs serve as an intermediate medium to integrate the two flexible domains of the road network and grid. Moreover, the road network model has been neglected in some of these studies. Second, with the growth in regional EV ownership, the security and stability of the regional power grid resulting from future large-scale EV access to the regional power grid should not be ignored. However, in most existing studies, it is assumed that the number of EVs is random and that the load prediction results are not sufficiently fine. Meanwhile, existing studies are not detailed enough in terms of modelling the dynamic network resistance, power consumption and queuing time during EV travel, which are often set as random variables or constants. Therefore, in this paper, the use of dynamic road networks was proposed to facilitate accurate and balanced regional EV charging load forecasting: a case study of Lanzhou city was conducted.

The novelty of this paper is that, first, a new model for accurately predicting dynamic spatiotemporal short-term EV charging loads on a regional scale was proposed, in which data- and model-driven methods are integrated to form a PSO-BP-MC model that accounts for the dynamic road network. Second, the charging behavior of EVs was exploited as an intermediary medium for the initial integration of two flexible domains, with the grid functioning as an electricity supplier and the road network encompassing charging stations, by generating the resulting electricity trading interactions. Third, the model driver was sufficiently improved to refine the characteristic quantities typically defined as random variables or constants in existing research models, such as the number of EVs and power consumption models. Fourth, it was verified whether the proposed hybrid model could provide dynamic spatiotemporal accurate short-term prediction of regional EV charging loads using real urban roads, and the proposed method was compared to other methods in the literature to verify its effectiveness and accuracy.

The remainder of this study is organized as follows: Related work is described in Section 2. The method is established in Section 3, which contains the overview of the proposed methodology, the regional EV charging load system model, the regional monolithic EV system model and the regional charging load distribution prediction methods. In Section 4, an arithmetic example analysis and discussion are provided to illustrate the effectiveness of our proposed model. Finally, conclusions and future research directions are outlined in Section 5.

Table 1 Literature review of EV charging load prediction

2 Related work

At present, researchers worldwide have extensively investigated the prediction of EV charging loads, which can be divided into two main categories: model- and data-driven methods. Data-driven methods are mainly oriented to historical charging load data and entail the use of machine learning to extract and screen local features of the data to optimize the accuracy of the combined machine learning model and thus improve the accuracy of data processing. The literature on data-driven modeling based on load forecasting [15,16,17,18,19] encompasses many studies on time-dimensional information, such as historical load and weather information, and abundant research results have been achieved. The difference is that this paper focused more notably on the road network model and the dual factors of the geographic distribution and time series to improve the EV charging load prediction accuracy.

Model-driven approaches mainly consider the driving and charging parameters of EVs, such as the daily driving distance, travel time distribution, travel habits of different vehicles, battery charge state, and energy consumption per kilometer, and charging loads are predicted spatiotemporally through mathematical models. Wu et al. [20] modified the optimal parameter values of the probability distribution within the fuzzy set based on the feedback from the EVs that have arrived at the microgrid to improve the stability of the prediction results and further regulate the charging of EVs in the microgrid. Zheng et al. [21] used the Monte Carlo (MC) method to extract a probability curve model for EV charging and validated the proposed method with a real city example. Goh et al. [22] proposed the use of a probabilistic load model to describe EV charging stochasticity and employed the MC simulation method to estimate the EV charging load demand. Niu et al. [23] established a multiscale EV load forecasting model using the Bass correction model for predicting EV retention considering seasonal characteristics. Huang et al. [24] constructed a charging user profile containing behavioral and attribute features, developed a MC simulation prediction model based on the established user profile, and generated charging load curves for a certain number of scales and a certain proportion of users. Xing et al. [25] proposed the GM(1, 1) model to estimate EV ownership and used the MC algorithm to establish a probability distribution model of travel patterns and charging characteristics for predicting the load demand when EVs are connected to a grid on a large scale. These studies focused on modeling and analyzing the characteristics of EV charging loads with relatively fixed EV locations. This paper further focused on demonstrating the impact of road network modeling on the charging stochasticity of EV users and charging station selection by considering the specific driving process of EVs and their mobility.

Liu et al. [26] proposed a spatial-temporal distribution prediction model for EV charging loads based on the gravity model considering vehicle-road-station-network fusion. Zhang et al. [27] established a spatial-temporal distribution prediction model for EV charging loads based on the travel origin-destination point matrix. Zhang et al. [28] developed an EV charging load prediction method that combines the real-time interaction between multisource information and user regret psychology. Mahmoudi et al. [29] used urban road networks and functional zones to simulate the daily travel trajectories of EVs and predicted the spatial and temporal demand for slow and fast charging power in cities. Cheng et al. [30] employed trip chain technology, the MC method and Markov decision process theory to establish a spatiotemporal transfer model for EVs, as well as an energy consumption model and a charging load prediction model for EVs under different scenarios considering the temperature, traffic conditions, and subjective willingness of vehicle owners. These studies were established to consider the impact of the road network on the EV charging load, on the basis of which the model details were refined in this paper to consider relevant factors such as node impedance, power consumption, charging queuing time, vehicle classification, and other factors influencing EV charging load prediction models. Moreover, the number of EVs was defined with data-driven models for retention prediction instead of the existing way of assigning hypothetical values.

Table 1 provides a summary of the above relevant papers on EV charging load forecasting, in ascending order of the year of publication.

Various model- and data-driven methods and combinations of modeling techniques and experimental studies have been used for EV charging load prediction. Among them, data-driven research remains at the stage of continuous exploration, and most of the literature on data-driven models for load forecasting only considers time-dimensional information, such as historical load and weather information, while ignoring the time series of the geographic distribution, which cannot provide detailed spatiotemporal predictions of EV charging loads. Whereas researchers have achieved more fruitful results in the application of model-driven research-based approaches, as indicated in Table 1, these approaches consider factors such as EV travel characteristics, electricity characteristics, and number of EVs. Because there are always unconsidered and assumed feature quantities in the model that can impact their prediction granularity. There are few combinations of model- and data-driven techniques in the literature, and the difficulty lies in how to fully and reasonably combine these two methods, how to accurately address the unconsidered and hypothetical feature quantities in model-driven mining available data-driven methods, and how to reasonably focus on key points under model-driven fusion.

Fig. 2

Fusion modeling framework for spatiotemporal prediction of EV charging loads

3 Method

3.1 Overview of the proposed method

The model framework constructed in this paper is shown in Fig. 2.

This spatiotemporal prediction fusion model framework is based on three main parts, namely, roads, EVs and grids; integrated modeling under data- and model-driven method fusion; and information, model and algorithm layers, to reach the final goal. The specific steps are as follows:

• 1. To establish a regional road-EV-grid integration model, the road network model was compared with two types of road networks, namely, static and dynamic road networks, in which the dynamic road network model introduces an improved speed-flow model and node impedance model.

• 2. The data-driven EV ownership prediction model (PSO-BP model) was used in the single EV model to estimate regional EV ownership over the next five years using five factors influencing EV ownership as inputs and their ownership as outputs.

• 3. The driving and charging characteristics of different types of EVs were analyzed and modeled, and the spatial and temporal distributions of the charging demand were obtained by combining the OD analysis method with the Dijkstra and Floyd algorithms for starting and stopping node allocation and path planning, respectively.

• 4. The standard IEEE33 distribution network model was selected for the grid model to calculate the total load.

• 5. The MC algorithm was employed to simulate the driving process and charging behavior, and an accurate PSO-BP-MC model was applied to predict and analyze the regional dynamic spatiotemporal short-term charging loads of EVs in Lanzhou city as an example, thereby using actual regional data.

3.2 Regional EV charging load system modeling

An EV is a type of transport vehicle, and its travel process is the same as that of other types of transport vehicles. Road network information and travel conditions exhibit interaction. Moreover, an EV represents a mobile load, and its charging and discharging behaviors jointly interact with grid information as an intermediate medium under the coupling of the road network and grid, which exhibits both transport and power properties. Thus, the establishment of a reasonable, effective and more accurate fusion model between the road-vehicle-grids of different networks, as shown in Fig. 3, can facilitate more accurate prediction of the spatial-temporal distribution of the EV charging load.

Fig. 3

Road-EV-Grid fusion model

The fusion model comprises a grid layer, an EV layer and a road network layer from top to bottom. Among them, the grid layer is based on the IEEE33 standard distribution network model. The EV layer is categorized into commuter private cars, taxis, and city function vehicles. The bottom road network layer is categorized into work, downtown, and populated areas as an example of part of Lanzhou city, Gansu Province, China, and each area contains road network intersection nodes represented by squares and triangles. The main reason for area functional division at the road network level is that there are notable differences in the distribution of the initial locations among different types of EVs; for example, the initial locations of private cars are more common in populated areas. Second, different types of EVs involve the use of various charging methods in different areas during different periods; for example, the proportion of private cars engaged in fast charging is greater in work areas during daytime working hours. The distribution grid functions as an electric energy supplier, while the road network layer encompasses charging stations, through the intermediary medium of the charging behavior of EVs for generating electric energy transactions and determining interactions. The use of the aforementioned EV intermediary medium in grid-road network initial fusion can enable more accurate prediction of the spatial and temporal distributions of EV charging loads.

3.2.1 Regional road network model

With the rapid development and increasing popularity of EVs, fast charging stations are favored by EV users due to their short charging time, and it was proposed that the topology of regional road networks containing fast charging stations must be considered. To provide a better description of the actual road traffic network and travel planning for EVs, the topology of the regional road network in Lanzhou city was obtained, as shown in Fig. 4.

The squares and triangles represent intersections within the road traffic network. Notably, the triangles denote fast charging station nodes, which function as both traffic network nodes and grid nodes with both traffic and electrical attributes. Moreover, the light blue enlarged area with two-way arrows denotes two-way streets. The road network structure can be expressed by (1):

$$\begin{aligned} {\left\{ \begin{array}{ll} G^{L} =\left\{ V^{L},R^{L},C^{L},D^{L} \right\} \\ V^{L}=\left\{ v_{i} \mid v_{i}=1,2,\cdots ,n \right\} \\ R^{L}=\left\{ r_{ij} \mid i\ne j \right\} \\ T^{L}=\left\{ t_{ij} \mid i\ne j \right\} \\ C^{L}=\left\{ c_{k} \mid v_{i}=1,2,\cdots ,x \right\} \\ D^{L}=\left\{ d_{ij} \mid \left\langle v_{i},v_{j} \right\rangle \in R^{L} \right\} \end{array}\right. } \end{aligned}$$

(1)

where $G^{L}$ is the transport network; $V^{L}$ denotes all nodes in the road network; n is the total number of nodes, e.g., $v_{1}$, $v_{2}$, ..., in the light blue enlarged area; $R^{L}$ is the set of connected road segments between the nodes; $r_{ij}$ denotes the length of each road segment, such as road segment $r_{12}$ connected by nodes $v_{1}$ and $v_{2}$; $T^{L}$ is the set of passage times of the connected road segments between the nodes; $t_{ij}$ denotes the current passage time of each road segment; $C^{L}$ is the number of fast charging stations within the road network; x is the total number of charging stations, e.g., $c_{8}$ and $c_{9}$; and $D^{L}$ is the road network adjacency matrix, e.g., $d_{12}$ denotes the section between nodes 1 and 2.

The influencing factors related to accurate regional dynamic spatiotemporal EV charging load prediction are complex and encompass multiple angles, and based on the macrolevel of the overall load distribution, the choice of traveling paths can be overlooked. Moreover, based on the microlevel of the specific spatial load distribution, the choice of traveling paths must be optimized. Second, the perceived state of EV users with respect to the road network is generally distance, which is constant in space and time, but for actual roads, the passage time dynamically varies. Therefore, of the proposed static road network model and dynamic road network model, the speed-flow model and road node impedance model are introduced into the dynamic road network model.

Fig. 4

Regional road network topology in Lanzhou city

Table 2 Road planning indicators

The static and dynamic road network adjacency matrix are denoted as $D_{s}^{L}$ and $D_{d}^{L}$, respectively, where INF indicates that the two nodes are not directly connected. In determining charging stations, after the charging demand of the EV user was calculated, Dijkstra’s and Floyd’s algorithms were used to obtain optimal results, the static road network was employed to determine the shortest traveling distance $R_{sd}$, and the dynamic road network was adopted to determine the shortest traveling time $T_{sd}$.

$$\begin{aligned} D_{s}^{L}=\begin{bmatrix} 0& r_{12}& \cdots & r_{1i}& \cdots & r_{1n}\\ r_{21}& 0& \cdots & \cdots & \cdots & r_{2n}\\ \vdots & \vdots & 0& r_{ji}& \vdots & \vdots \\ r_{i1}& \vdots & r_{ij}& 0& \vdots & r_{jn}\\ \vdots & \cdots & \cdots & \cdots & 0& \vdots \\ r_{n1}& r_{n2}& \cdots & r_{nj}& \cdots & 0 \end{bmatrix} \end{aligned}$$

(2)

$$\begin{aligned} d_{ij}=d_{ji}=\left\{ \begin{matrix} 0& i=j & \\ r_{ij} & i\ne j & ij\ directly\ connected \\ INF& i\ne j & ij\ not\ directly\ connected \end{matrix}\right. \end{aligned}$$

(3)

$$\begin{aligned} R_{sd}=\sum r_{ij} \end{aligned}$$

(4)

$$\begin{aligned} D_{d}^{L}=\begin{bmatrix} 0& t_{12}& \cdots & t_{1i}& \cdots & t_{1n}\\ t_{21}& 0& \cdots & \cdots & \cdots & t_{2n}\\ \vdots & \vdots & 0& t_{ji}& \vdots & \vdots \\ t_{i1}& \vdots & t_{ij}& 0& \vdots & t_{jn}\\ \vdots & \cdots & \cdots & \cdots & 0& \vdots \\ t_{n1}& t_{n2}& \cdots & t_{nj}& \cdots & 0 \end{bmatrix} \end{aligned}$$

(5)

$$\begin{aligned} t_{ij}=t_{ji}=\left\{ \begin{matrix} 0& i=j & \\ t_{ij} & i\ne j & ij\ directly\ connected \\ INF& i\ne j & ij\ not\ directly\ connected \end{matrix}\right. \end{aligned}$$

(6)

$$\begin{aligned} T_{sd}=\sum t_{ij} \end{aligned}$$

(7)

Here, the road classes classified by urban road traffic planning and design code GB50220-95 were introduced to obtain the capacity $N_{ij}$ and zero-flow velocity $V_{ij-m}$ of each road section, which yielded the following speed-flow utility model [31]:

$$\begin{aligned} {\left\{ \begin{array}{ll} S=q_{ij}\left( t \right) /N_{ij} \\ V_{ij}=V_{ij-m}/\left( 1+S^{\beta } \right) \\ \beta =a+b\cdot \left( q_{ij}\left( t \right) /N_{ij} \right) ^{n} \end{array}\right. } \end{aligned}$$

(8)

where S denotes the saturation degree of each road section, $q_{ij}\left( t \right)$ denotes the traffic flow passing through node ij of the road section at moment t, $V_{ij}$ denotes the passing speed of each road section, and a, b, and n are adaptive coefficients. The specific values are listed in Table 2.

The traveling time $t_{r_{ij}}$ of each road segment under the consideration of the speed-flow model is expressed in (9), where $x_{ij}$ is the path decision variable, which is 1 if the EV travels from nodes i to j of the road network and 0 otherwise, i.e.:

$$\begin{aligned} t_{r_{ij} } =\sum _{i,j\in n}\left( d_{ij} /V_{ij} \right) x_{ij} \end{aligned}$$

(9)

In the urban road network, in addition to the road flow affecting the vehicle travel time, cross-node intersections more than the existence of signals for road travel control, in the intersection nodes subject to signal control generated by the delay time $t_{v_{ij}}$ to the node impedance model [32] is introduced, that is:

$$\begin{aligned} {\left\{ \begin{array}{ll} t_{v_{ij} }\left\{ \begin{matrix} 9/10\left( c\left( 1-\lambda \right) ^{2} /2\left( 1-\lambda S \right) +S^{2}/2q\left( 1-s \right) \right) & 0< S\le 0.6\\ c\left( 1-\lambda \right) ^{2}/2\left( 1-\lambda S \right) +1.5S\left( S-0.6 \right) /\left( 1-S \right) & 0.6< S \end{matrix}\right. \\ \lambda =t_{green,yellow} /c \end{array}\right. } \end{aligned}$$

(10)

Where c is the signal period; $\lambda$ is the green letter ratio, refers to the effective green light hours, that is, the total length of the green light and yellow light $t_{green,yellow}$, and the ratio between the signal period; q is the arrival rate of the roadway vehicles, in this paper, respectively, are set to $c=30$, $\lambda =0.7$, $q=0.8$. then after the introduction of the dynamic roadway network model of the speed-flow model as well as the roadway node impedance model the passage time $t_{ij}$ is:

$$\begin{aligned} t_{ij}=t_{r_{ij} }+ t_{v_{ij} } \end{aligned}$$

(11)

3.2.2 Regional power grid model

An IEEE33 standard-based distribution network model was chosen to focus on the impact of the regional EV charging behavior on the spatial and temporal distributions of grid loads and the occupancy of charging stations and charging piles within the context of the continuous growth in EV ownership. The interaction between the distribution grid (as the electrical energy supplier) and the charging stations occurs through the intermediate medium of the EV whose charging behavior generates the transaction of electrical energy. The regional grid model parameters are provided in Table 3.

Table 3 Regional distribution network modeling parameters

A Regional power grid topology

Under the condition that the EV is used as an intermediate medium to integrate the road network with the power grid, the $G^{D}$ regional power grid model must be spatially matched with the road network model, and the regional power grid topology is expressed in (12).

$$\begin{aligned} {\left\{ \begin{array}{ll} G^{D} =\left\{ V^{D}\left( G \right) ,E^{D}\left( G \right) ,\psi ^{D}_{G}\right\} \\ V^{D}\left( G \right) =\left\{ s_{i} \mid s_{i}=1,2,\cdots ,s_{G} \right\} \\ E^{D}\left( G \right) =\left\{ \left\langle s_{i} ,s_{j} \right\rangle \mid s_{i},s_{j}\in V^{D} \right\} \\ \psi ^{D}_{G}=\left\{ \left( r_{i},x_{i},c_{i},P_{i}^{l}\right) \mid \left\langle s_{i} ,s_{j} \right\rangle \in E^{D} \right\} \\ B^{D}_{G}=\left\{ \left( P_{i}^{D},Q_{i}^{d} \right) \mid i=1,2,\cdots ,s_{G} \right\} \\ F^{D}_{G}=\left\{ f_{i} \left( t \right) \mid t=1,2,\cdots ,T \right\} \end{array}\right. } \end{aligned}$$

(12)

B Road-vehicle-grid interaction structure

The road-vehicle-grid interaction structure mainly comprises the driving and charging behaviors of the intermediate medium of the EV, in which the charging station functions as an interface, which is the interaction medium between the road network and the power grid. In this paper, the road network nodes and power grid nodes were connected accordingly, and the location of the road network in the urban area determines the construction of the regional power grid. Regarding the division of the three functional areas of the city with the road network as the boundary, the base load of the charging station nodes in each functional area and the EV charging power of the access nodes were accumulated as the total load, as expressed in (13).

$$\begin{aligned} {\left\{ \begin{array}{ll} P_{total,t}^{C_{L} } =\sum _{x\in C_{L} }\left[ P_{B,t}^{x}+P_{EV,t}^{x} \right] \\ P_{EV,t}^{x}=\sum _{n=1}^{N_{x} }P_{n,x,t} \end{array}\right. } \end{aligned}$$

(13)

3.2.3 Regional EV retention forecasting model

A Regional EV ownership influences

The data related to EV ownership are all based on annual statistics, and the main factors influencing the data are as follows [33]: first, with respect to economic factors, both the GDP per capita and car ownership growth rate are relatively high, and in regard to the economic environment and consumption level, the GDP per capita is one of the factors impacting regional EV ownership. Second, consumer factors, growth or, otherwise, regional EV ownership, depend on the degree of consumer purchasing, which can be defined by EV penetration. Third, by providing notable support and government subsidies to reduce consumer spending, which affects consumers’ judgment of the cost-effectiveness of EVs and indirectly enhances their purchase rate, the policy factor of EVs as a green transport mode with broad development prospects can resolve both energy and environmental problems. Fourth, technical factors and EV technology maturity determine the fundamental development of EVs, but consumers also decide to purchase key EV factors, the range of which directly affects EV mileage anxiety among consumers. Fifth, the infrastructure factor, namely, charging infrastructure, continues to improve to ensure consumer recognition of the EV driving experience and eliminate mileage anxiety among EV users. The number of regional public charging piles, which is representative of infrastructure construction, is one of the important factors in EV ownership prediction.

B PSO-BP prediction model

Based on the above analysis of the five factors influencing EV ownership, the particle swarm optimization (PSO) algorithm [34] was used to optimize the BP neural network prediction model [35]. The initial weights and thresholds are not optimized, so the BP neural network typically falls into local minima and converges slowly. The PSO algorithm was used to optimize the initial weights and thresholds herein to improve the prediction accuracy of the BP neural network and overcome the shortcomings of its tendency to fall into local minima and exhibit slow convergence.

The five factors influencing EV retention were selected as the input values of the neural network, and EV retention was considered the output value. Then, the number of input units i of the network was set to 5, the number of output units o was set to 1, and the number of hidden layer units l is expressed in (14), where c is an integer within [1,10].

$$\begin{aligned} l=\sqrt{i+o}+c \end{aligned}$$

(14)

The PSO algorithm originates from bird flock foraging behavior patterns, and the foraging behavior process is simulated by particles. A certain number of particle swarms are randomly generated at the initial stage. In the initial weight and threshold optimization problem of the BP neural network, the spatial dimensionality of each particle exhibits a number of vectors set to represent a potentially optimal solution, and the total number of weights and thresholds in the BP network structure to be optimized determines its dimensionality. Individual and global optimal solutions are saved throughout the optimization process, and velocity and position parameters are updated to obtain the optimal solution, as expressed in (15) and (16), respectively.

$$\begin{aligned} {\left\{ \begin{array}{ll} v_{is}^{k} =\delta v_{is}^{k}+e_{1}r\left( p_{is}^{k} -x_{is}^{k}\right) +e_{2}r\left( g_{is}^{k} -x_{is}^{k}\right) \\ \delta =\delta _{\max } -k\left( \delta _{\max }-\delta _{\min } \right) /k_{max} \end{array}\right. } \end{aligned}$$

(15)

$$\begin{aligned} x_{is}^{k+1} =x_{is}^{k}+v_{is}^{k+1} \end{aligned}$$

(16)

where $i=1,2,3,...M$, M is the total number of particle swarms, $v_{is}^{k}$ is the velocity of the ith particle in iteration step k and spatial dimension s; $e_{1}$ and $e_{2}$ are learning factors, both of which are set to 2 in this paper, $p_{is}^{k}$ and $g_{is}^{k}$ are the individual optimal solution and global optimal solution, respectively, $x_{is}^{k}$ is the position of the ith particle in iteration step k and spatial dimension s, and r is a random constant within (0, 1). The inertia factor $\delta$ was determined using a typical linearly decreasing strategy [36], where $\delta _{\max }=0.9$ and $\delta _{\min }=0.4$. The fitness value F of each particle was determined by the fitness function, which can be expressed as:

$$\begin{aligned} {\left\{ \begin{array}{ll} F=1/N\left( \sum _{m=1}^{N}\sum _{i=1}^{S} \left( Y_{mi} -Y_{mi}^{'} \right) \right) \\ S=o+l+il+ol \end{array}\right. } \end{aligned}$$

(17)

where S is the spatial dimension in which the particle swarm is located, which can be combined with (14) to obtain l within [4, 13], eventually obtaining a value of 10; N is the number of samples; $Y_{mi}$ is the BP model-predicted output value; and $Y_{mi}^{'}$ is the BP model-expected output value. Through comparison experiments for optimizing the initial parameters of the neural network with different numbers of particle swarms, the most reasonable particle swarm size and number of iterations were obtained, as shown in Fig. 5.

Fig. 5

Results of iterative experiments with different sizes of particle swarms

The experimental results can be seen, when the particle swarm size is 200, such as Fig. 5 left Y-axis pointed to the red bar and the blue curve indicates the two experiments adaptation fluctuation value and the average value, which verifies that the particle swarm size of the case of the BP neural network of the initial weights and thresholds of the optimization of the best effect. There will always be small-range fluctuations when the adaptation process reaches convergence, but it is not possible to determine a certain number of iterations, so the number of iterations was expressed as an interval. As shown by the red-blue three-dot graphical interval indicated by the right Y-axis in Fig. 5, the number of iterations in the two experiments occurs within the [425, 475] interval. Based on the above results, to ensure that the PSO algorithm is sufficiently optimized for the BP neural network, the size of the particle swarm was set to 200, and the number of iterations was set to 450.

A flowchart of the PSO-BP model is shown in Fig. 6, where the PSO algorithm is optimized by adding adaptive variants.

Fig. 6

Flowchart of the PSO-BP prediction model

The steps of the PSO algorithm for optimizing the BP neural network are as follows:

Step 1: Initialize the BP neural network with the population and parameter structure of the PSO algorithm.

Step 2: Calculate the global optimal solution and local optimal solution according to (15) and (16), respectively.

Step 3: Update the velocity and position of each particle according to the global optimal solution and local optimal solution.

Step 4: Repeat steps 2 and 3 until the maximum number of iterations is reached.

Step 5: Extract the optimal solution of the PSO algorithm to obtain the optimal weights and thresholds of the BP neural network.

Step 6: Perform BP neural network training.

3.3 Regional monolithic EV system model

The main state parameters of the regional EV model include battery power and travel location information, which are characterized by the state parameter ensemble $EV=\left\{ L_{o},L_{c},S_{EV}^{i},S_{EV}^{c},S_{EV}^{t},B_{e},B_{c},B_{t},P_{c},E_{p},\eta ,\zeta \right\}$. The meanings of the parameters are provided in Table 4.

Table 4 State parameters of EVs

3.3.1 Regional EV classifications

The vigorous development of EVs in China in recent years can be divided into five types, as summarized in Table 5. In addition to the four types of basic commuting private cars, taxis, official cars, and buses [37], accompanied by the rapid development in the economy, the industrial clustering effect of the enhancement in the consumer demand of people has gradually shifted to diversity and individuality, and with this shift, logistics activities have dramatically enhanced the increase in the number of triggered logistics vehicles; in contrast, purely electric logistics vehicles are still at the development stage [38]. The number and scale of future EV charging loads cannot be ignored.

Table 5 Types of EVs

The daily mileage amounts of official vehicles and pure electric logistics vehicles are similar, their parking locations are fixed, the charging mode is fast charging during the day and slow charging at night, and the initial position occurs in the working area. hence, they are subsequently referred to as urban functional vehicles uniformly. As pure electric bus models in Lanzhou city encompass fewer specific driving routes and designated charging piles, the charging time is mostly 12:00-5:00 at night, which exerts less impact on the grid load, and at the same time, its charging characteristics are less notably affected by traffic, so pure electric buses were subsequently not classified as a research object.

3.3.2 Regional EV travel and power characteristics

A Regional EV travel characteristics

Notably, regional EV initial travel moment $t_{s}$ and return moment $t_{f}$ probability distribution curves can be obtained by fitting the statistical parameters and be employing techniques provided by the National Cooperative Highway Research Program (NCHRP) Report 716, as shown in Fig. 7.

Fig. 7

Probability distribution of EVs during initial and return trips Data sources: Travel Demand Forecasting: Parameters and Techniques (2012), NCHRP 716 Rep. http://nap.nationalacademies.org/14665

The probabilities of traveling are highest at 6:00 a.m., when taxis occur at the transition stage between night and day shifts, and at 7:00 a.m., when commuter private cars and city functional vehicles start working.

To better describe regional EV travel characteristics, origin-destination (OD) analysis was used to obtain the travel characteristics of different types of EVs [39]. The OD analysis method is often used in traffic planning and simulation, and the OD matrix is at the center of the matrix, where the traffic flow in the real road network during each period can be used to invert the OD starting and stopping matrices. Moreover, the random sampling MC algorithm was used to assign starting and stopping points to each type of EV, with the probability matrices expressed as follows:

$$\begin{aligned} {\left\{ \begin{array}{ll} P_{ij}^{T}= Q_{ij}^{T}/\sum _{j=1}^{n}P_{ij}^{T} & 1\le i\le n\\ 1\le T\le 7& \end{array}\right. } \end{aligned}$$

(18)

where $Q_{ij}^{T}$ denotes the number of EVs traveling from start node i to end node j during period T and $P_{ij}^{T}$ denotes the probability of an EV traveling from start node i to end node j. If i and j are equal, the EV remains stationary.

B Regional EV power characteristics

According to the regional EV classification, the battery capacity and specific parameters of the different types of EVs obey the gamma or normal distribution [40], as expressed in (19).

$$\begin{aligned} {\left\{ \begin{array}{ll} f\left[ B_{c}^{k}\left( i \right) ;\alpha _{k},\beta _{k}\right] =\frac{1}{\beta _{k}^{\alpha _{k} }\tau \left( \alpha _{k} \right) } B_{c}^{k}\left( i \right) ^{\alpha _{k}-1 }e^{-\frac{B_{c}^{k}\left( i \right) }{\beta _{k} } } \\ g\left[ B_{c}^{k}\left( i \right) ;\mu _{k},\sigma _{k}\right] =\frac{1}{\sigma _{k}\sqrt{2\pi } } e^{-\frac{\left( B_{c}^{k}\left( i \right) -\mu _{k} \right) ^{2}}{2\sigma _{k}^{2} } } \end{array}\right. } \end{aligned}$$

(19)

The various regional types of EV daily charging pattern parameters are detailed in Table 6, and the initial battery charge ($B_{e}$) can be obtained by the initial state of charge (SOC), as expressed in (20).

$$\begin{aligned} B_{e}=S_{EV}^{i}\cdot B_{c} \end{aligned}$$

(20)

Table 6 Parameters of the daily charging behavior patterns for the different types of EVs

Table 7 Charging constraints for the different types of EVs

The regional EV power consumption has been set to a fixed value in some studies, but it is influenced by many factors in reality. First, the traveling speed of vehicles varies due to road saturation changes; the higher the saturation is, the lower the speed and the higher the power consumption [41]. According to the different road classes classified in the Urban Road Traffic Planning and Design Code GB50220-95, the power consumption on class I/II roads under the influence of the traveling speed varies [42]. Second, the temperature of the environment directly affects the relative capacity of the battery, which decays nonlinearly with decreasing temperature [43], while temperature change leads to the use of air conditioning in the vehicle to generate an additional power consumption. Therefore, the power consumption should not be set to a constant value, which can cause errors in the prediction results. As indicated in (21), a regional real-time unit mileage electric consumption model [27] for EVs was introduced, in which the vehicle traveling speed and ambient temperature are accounted for.

$$\begin{aligned} {\left\{ \begin{array}{ll} E_{P}=E_{P,T}^{K} +E_{P1\left( 2 \right) }^{V} \\ E_{P,T}^{K}={\left\{ \begin{array}{ll} P_{k}^{c}r_{ij}/v_{ij} & T> T_{k-\text {max}} \\ P_{k}^{h}r_{ij}/v_{ij} & T> T_{k-\text {min}} \end{array}\right. } \\ E_{P1}^{V} \!=\!0.247\!+\!1.52/v_{ij} \!-\!4^{-3}v_{ij}\!+\!2.993\cdot 10^{-5} v_{ij} \\ E_{P2}^{V} =-0.179+4^{-3}v_{ij}+5.492/v_{ij} \end{array}\right. } \end{aligned}$$

(21)

where $E_{P,T}^{K}$ is the power consumption of the air conditioner when driving across distance $r_{ij}$ at a speed of $v_{ij}$ and an ambient temperature of T, $P_{k}^{c}$/$P_{k}^{h}$ is the cooling/heating power of the air conditioner, and $T_{k-\text {max}}$/$T_{k-\text {min}}$ is the limit of the cooling/heating temperature. Moreover, $E_{P1\left( 2 \right) }^{V}$ is the power consumption of the vehicle under the influence of the driving speed on roads of class I/II, and $E_{P}$ denotes the total power consumption of the vehicle under the influence of these two factors. The residual charge state of the vehicle at time t is expressed in (22), where the battery efficiency coefficient $\eta _{EV}$ is 0.9.

$$\begin{aligned} {\left\{ \begin{array}{ll} B_{t}=\eta _{EV}S_{EV}^{t}B_{c}\\ S_{EV}^{t}=S_{EV}^{i}-d_{ij} E_{p} /B_{c} \end{array}\right. } \end{aligned}$$

(22)

C Regional EV charging time

Fig. 8

Flowchart of the MC charging load temporal and spatial distribution prediction process

The regional EV charging time comprises two parts: the time $T_{c}$ needed for EVs to be charged to the desired level of charge, as expressed in (23), and the queuing time needed for EV charging when the occupancy rate of charging piles at the charging station is greater than 1. The EV charging waiting time can be described according to M/M/c queuing theory [44]. The arrival of the vehicle at the charging station is assumed to obey a Poisson distribution, and the average regional EV queuing waiting time $T_{w}$ is expressed in (24).

$$\begin{aligned} T_{c}=\left( S_{EV}^{c} -S_{EV}^{t} \right) B_{c}/P_{c}\eta \end{aligned}$$

(23)

$$\begin{aligned} {\left\{ \begin{array}{ll} T_{w} =P_{0} \left( m\rho _{m} \right) ^{m}\rho _{m}/m!\left( 1-\rho _{m} \right) ^{2}\lambda \\ P_{0}=\left( \sum _{k=0}^{m-1} \left( 1/k! \right) \left( \lambda /k \right) ^{k}+\left( 1/m! \right) \left( 1/\left( 1-\rho _{m} \right) \right) \left( \lambda /\mu \right) ^{m} \right) ^{-1} \\ \rho _{m}=\lambda /m\mu \end{array}\right. } \end{aligned}$$

(24)

where $\eta$ is the charging efficiency, which is 0.9. Moreover, $P_{c}$ can be determined according to Connection Devices for Conductive Charging of Electric Vehicles (GB/T 20234.1-2023) and statistics of the actual charging facilities in Qilihe District and Anning District of Lanzhou city. Notably, the slow-charging power of different nodes was set to 7 kW, and the fast-charging power of the charging stations was set to 60 kW. In addition, m is the number of charging piles at the charging station, $\lambda$ is the number of charging demands served at the charging station during each period, $\rho _{m}$ is the number of EVs served per unit time per charging pile, and $\mu$ is the intensity of charging pile services. Then, the total charging time of EVs in the region can be obtained as:

$$\begin{aligned} T_{total}^{EV} =T_{c} +T_{w} \end{aligned}$$

(25)

D Regional EV charging constraints

To prevent EV batteries from being fed or overcharged and to maintain the battery life, charging constraints were defined for all types of EVs, as expressed in (26).

$$\begin{aligned} {\left\{ \begin{array}{ll} S_{EV-\text {min}}^{i}\ge 10 \% \\ S_{EV-\text {max}}^{c}\le 90 \% \end{array}\right. } \end{aligned}$$

(26)

For the different types of EVs, the fast charging mode or slow charging mode can be selected under different circumstances, as different types of EVs provide different functions and generate varying charging demand constraints. The specific settings in this paper are detailed in Table 7.

3.4 Regional charging load distribution prediction methods

The regional road network model, grid model, EV retention prediction model, regional EV model are considered to enable charging load spatiotemporal distribution prediction, a flowchart of which is shown in Fig. 8.

The flowchart is divided into two main parts. The predicted regional EV holdings were first utilized to obtain the spatial and temporal distributions of the EV charging demand, as shown in the blue subplot on the right side of Fig. 8. Then, the number of EVs at each charging station was obtained based on the spatiotemporal distribution of the charging demand, and the spatiotemporal distribution of the regional accurate charging load was determined, as shown in the green part on the left side of Fig. 8. The precise regional spatiotemporal distribution of the charging load could be predicted as follows:

• 1. The PSO-BP prediction model combines the above five factors influencing EV ownership to predict regional EV ownership and introduces the number of different types of EVs at the transportation nodes in a certain proportion.

• 2. The MC method is used to generate EV power characteristic parameters and travel characteristic parameters for each randomly sampled EV to obtain the spatial and temporal distributions of the EV charging demand, and Dijkstra’s and Floyd’s algorithms are utilized to determine the shortest travel distance $R_{sd}$ in the static road network and the shortest travel time $T_{sd}$ in the dynamic road network, respectively.

• 3. The number of EVs $X_{EV}$ at each charging station is determined, the power of each EV $x_{EV}$ charging in the charging station area is computed via summing, the regional distribution network node load is calculated, and the example test distribution network is analyzed on the basis of the IEEE33 standard distribution network to appropriately adjust the line parameters so that its capacity matches that in the test area, and the spatial-temporal distribution of the regional accurate charging load is predicted.

4 Example analysis and discussion

4.1 Regional EV ownership forecasts

4.1.1 Indicators for evaluating the prediction model

To verify the effectiveness and accuracy of the model predictions, the root mean square error (RMSE) and mean absolute percentage error (MAPE) [45, 46] were adopted as evaluation indices of the regional EV retention prediction model, and these metrics can be calculated are as follows:

$$\begin{aligned} {\left\{ \begin{array}{ll} E_{RMSE}=\sqrt{\left( 1/n \right) \sum _{k=1}^{n}\left( \hat{y_{k} }- y_{k}\right) ^{2} } \\ E_{MAPE}=\left( 100/n \right) \sum _{k=1}^{n} \left| \left( \hat{y_{k} }- y_{k} \right) / y_{k}\right| \end{array}\right. } \end{aligned}$$

(27)

Fig. 9

Factors influencing EV regional holdings Data source: National Bureau of Statistics, Ministry of Finance of the Central People’s Government of the People’s Republic of China, China Electric Vehicle Charging Infrastructure Promotion Alliance, China Automobile Industry Yearbook, China Association of Automobile Manufacturers, Lanzhou Municipal Bureau of Statistics, Lanzhou Public Security Traffic Police Detachment Statistics, Lanzhou Municipal Statistical Bulletin on the National Economy and Social Development, as well as Lanzhou Municipal Relevant Statistical Yearbooks data collation

Fig. 10

Regional EV ownership forecast from 2013-2028

In the above equations, the MAPE and RMSE are related to the prediction performance of the model, and a lower MAPE indicates that the model performs better in capturing the overall outcome.

4.1.2 Analysis of the projected results

Data on the five factors impacting EV ownership in the Lanzhou region of Gansu Province from 2013-2023, namely, the GDP per capita, EV penetration rate, government subsidies, average sustainable EV range, and number of public charging piles, are shown in Fig. 9.

The five influencing factors shown in the figure are employed as the independent variables, regional EV ownership is adopted as the dependent variable, and the constructed PSO-BP prediction model of regional EV ownership is introduced. Due to the limited number of samples, data augmentation is employed to increase the number of effective samples for reducing the direct prediction error. To verify the prediction enhancement resulting from the optimization of the BP neural network model by different algorithms, GA-BP, PSO-BP and unoptimized BP neural networks are modeled and compared. Moreover, the modeling methods in this paper are compared with the convolutional neural network-long short-term memory (CNN-LSTM) and convolutional neural network-gated recurrent unit (CNN-GRU) models. Based on the historical data of EV ownership in the region from 2013-2023, EV ownership in the region from 2024-2028 is predicted, and specific data are obtained, as shown in Fig. 10. The evaluation of the errors of the all prediction models is provided in Table 8.

As shown in the graphs, the prediction accuracy of the optimized BP algorithm is significantly improved, and the deviation between the predicted and actual curves decreases. Under the conditions of the sample data in this paper, the CNN-LSTM and CNN-GRU models are prone to overfitting during sample training, resulting in inaccurate prediction data and a high degree of discretization, while the PSO-BP prediction error is significantly reduced, with better prediction performance and a more lightweight model structure. The PSO-BP model achieves a better fit between the EV ownership forecasts and actual values than the other models from 2013-2023, and the increase in 2027 as technology advances and charging facilities continue to improve can be captured, with a forecast of 64,302 EVs in the region in 2028.

Table 8 Regional EV retention forecast errors

4.2 Prediction of the dynamic spatial and temporal distributions of the regional EV charging load

The path planning in this paper consists of two cases: static road network path planning and dynamic road network path planning. The considered road network information is mainly based on the regional map information provided by ArcGIS Pro software, and the 5 km$\times$10 km regional road network in Qilihe District of Lanzhou city is adopted as an example. The number of roads is 51, and the average road length is 1.21 km, of which 33 are trunk roads I and 18 are secondary roads II. Notably, the blue line shown in Fig. 3 is a trunk road, the black line denotes a secondary road, and the saturation degree of each road section of the trunk and secondary roads within a day by period is shown in Fig. 11.

Fig. 11

Saturation of the road sections by time of day

Fig. 12

Percentage of EVs at the different traffic nodes

The number of road network nodes is 33, of which 4 nodes are both road network nodes and fast charging points, while the remaining nodes provide slow charging with dual attributes. In this region, with the statistical data of Lanzhou Public Security Traffic Police and the PSO-BP model-predicted results of regional EV ownership from 2013-2023, the EV penetration rate in the region is set to 20$\%$, and the numbers of corresponding EVs introduced in 2024, 2026 and 2028 are 8756, 9793 and 12860, respectively, of which the proportions of commuter private vehicles, urban functional vehicles and taxis are 40$\%$, 30$\%$, and 30$\%$, respectively. Moreover, the proportion of the number of vehicles at each node is shown in Fig. 12, the simulation time is 24h (all day), as shown in Fig. 13, is the spatial and temporal distribution of the charging demand of the road section, which is involved in the charging of vehicles introduced according to the different time periods.

The above figure reveals there is a significant difference in the time of day when the demand for EVs charging occurs, with the peak distribution occurring between 11:00-13:00 and 16:00-18:00, the spatial distribution of the peak charging demand is mainly concentrated in the commercial and residential areas of the road network branch (roads r4/5/r13/15/r24/25/r6/7/r7/13/r30/31), and unevenly distributed in both time and space. With the driving experience in the region, the above roads are easily congested during the daily peak period, so the charging demand coincides with the actual situation, which also verifies the rationality of the method proposed in this paper.

The single-day charging load profiles of different superimposed types of EVs in the region from 2024-2028 obtained from the forecast results are shown in Fig. 14(a). The prediction method in this paper is compared with the prediction methods proposed by Xing [25] and Zhang [27], and the single-day charging load curve in 2024 is obtained, as shown in Fig. 14(b).

Fig. 13

Spatial and temporal distributions of the regional EV charging demand

Fig. 14

Overlaying the predicted results of the single-day charging load profiles for the different types of EVs

As shown in the figure, as regional EV ownership increases year by year, the superimposed maximum charging load increases year by year; for example, regarding the test distribution network access to EVs, the total peak loads in 2026 and 2028 increase by 12.144$\%$ and 45.786$\%$, respectively, compared to that in 2024, and the average growth in the peak load within the region over the next five years is 21.070$\%$. The peak charging load in a single day occurs between 11:00-14:00 and 17:00-20:00, while the remainder of the charging load distribution is more uniform. Second, fast charging is mainly distributed at charging stations during the day, while slow charging largely occurs in the evening, namely, 17:00-20:00. Notably, due to the superposition of slow charging and fast charging, the peak load is 5.759$\%$ higher than that during the daytime on average, and safe operation of the distribution network at night should not be ignored. Simultaneous, the charging power curve obtained with this method is shown in Fig. 14(b), which shows that the charging power curve is more balanced, with peaks during the midday and afternoon hours, whereas the curve obtained with the comparison method exhibits only one peak during the afternoon hours. The reason for this finding is that the method in this paper enables more fine-grained dynamic path simulations, and the user’s charging choices and charging time within the road network are relatively decentralized, so that the charging load distribution in a single day is more balanced than that of the comparative method, whereas the charging time obtained by the comparison method is more fixed and thus relatively centralized.

During the evening peak hours from 17:00-19:00, when the spatial and temporal distributions of the charging demand are not considered, with starting points (1, 33) and (30, 21), according to the optimal objective in the static/dynamic road network model, Dijkstra’s algorithm and Floyd’s algorithm are employed to solve the best result. With increasing amount of computational data, the Floyd algorithm becomes more time-consuming than the Dijkstra algorithm, as shown in Fig. 15. The evaluation indices of the two road network path searches are provided in Table 9.

Both algorithms can be used for optimal path solving, and the time consumption levels of the two algorithms are similar when the data size is small. With increasing data size, Floyd’s algorithm requires more time than Dijkstra’s algorithm because it calculates the multisource shortest paths, thereby recording the shortest paths between all nodes.

Fig. 15

Comparison of algorithm time consumption

The dynamic road network entails path planning based on real-time road conditions, which reduces the travel time by 26.23$\%$ compared to that of the static road network, avoids congested road sections in time, and alleviates the traffic pressure on the road network. However, to avoid traffic congestion, the mileage of the planned path traveling increases by 9.35$\%$ compared to that of the static road network. Under static and dynamic road network driving conditions, the occupancy rate of charging piles in each charging station when in use on a single day in 2024 is illustrated in Fig. 16(a), the spatial and temporal distribution of loads in the area of charging stations on a single day is illustrated in Fig. 16(b), and the waiting rate of EVs while charging and the peak load changes are illustrated in Table 10.

As shown in the graphs, the overall charging load remains within the charging station planning thresholds, with the peak EV numbers at each charging station concentrated at approximately 12:00, while the number of vehicles during the daytime is greater than that at night. In the static road network driving situation, it can be seen that the number of charging vehicles in each charging station is more unevenly distributed, 10:00, 11:00, 12:00, 13:00, 14:00, 15:00, 17:00 have demanded charging but need to wait for the vehicle, the dynamic road network driving situation, the number of charging vehicles in each charging station has demanded charging is more evenly distributed, only at 11:00 and 12:00, there are vehicles that need charging but have to wait. The charging wait rate under static road network driving conditions during the daytime peak period decreased from 30.714$\%$ to 18.571$\%$ under dynamic driving conditions, with charging wait rate decreased during the remaining hours. The peak loads under static and dynamic road network conditions at charging station No. 9 at 12:00 were 1.016 and 0.957 MW, respectively, the trough load under both road network conditions at charging station No. 8 at 4:00 was 0.019 MW, and the peak-valley difference in the load within the dynamic road network was reduced by 5.92$\%$ compared with that within the static road network.

Table 9 Static and dynamic road network path search evaluation indicators

Fig. 16

Number of EVs and load distribution by charging station

5 Conclusion

Based on the temporal non-deformation of road travelling distances in real situations, but the dynamic variability of travelling times, a dynamic road network was introduced into the model, and refined model-driven charging load prediction was achieved, which combines EV retention with a data-driven methodology. Moreover, a new model could be helpful for using the dynamic road network to achieve accurate and balanced regional EV charging load prediction. A case study of Lanzhou city was conducted. The model integrates data-driven and model-driven methods to form a PSO-BP-MC model that accounts for the dynamic road network. The new model initially integrates two layers of flexible domains, namely, the grid as the electrical energy supplier and the road network with charging stations, by generating electrical energy trading interactions due to the charging behavior of EVs. The feature quantities in the new model were also refined by replacing the unconsidered and assumed feature quantities present in previous research models with corresponding models. Finally, the actual roads in the urban area of Lanzhou city, Gansu Province, China, were introduced, and the effectiveness of the proposed strategy was verified through simulation and comparison, which provides practical references for constructing urban road networks and determining charging station siting and capacity in this region. The conclusions obtained in this paper are as follows:

Table 10 Charge wait rate and load peak-to-valley differences between the static and dynamic road networks

• 1. The proposed static/dynamic road network considers the practical invariance of the actual road travelling distance and the dynamic variability of the travelling time, with the shortest driving distance/driving time as the objective function, which agrees with the spatial perception of EV users of the distance and congested roadway avoidance behavior, and the actual driving needs to reach the destination quickly, and has a comparative nature.

• 2. The weights and thresholds of the BP algorithm are optimized by the PSO algorithm, and regional EV retention prediction allows for more accurate regional load forecasting. As EVs continue to develop, they will readily aggravate the burden on the distribution network during peak load hours, forming two peak-on-peak phases during the daytime and at night, with an average increase in the peak load in the region of 21.07$\%$ over the next five years.

• 3. The refined PSO-BP-MC charging load prediction model is compared with previous models. Notably, in contrast to previous studies, more refined dynamic path simulation could divide one peak period into two peak periods throughout the day, which could effectively reduce the load peak-valley difference and alleviate charging congestion and queuing and waiting time during peak hours. The spatial and temporal distributions of the charging loads at fast charging stations under two road network conditions are compared, and charging congestion in the region can be effectively alleviated, the occupancy rate of charging piles at each fast charging station can be equalized, and the charging waiting rate during the peak period can be reduced from 30.714$\%$ under the condition of a static road network to 18.571$\%$ under the condition of a dynamic road network. Moreover, the dynamic road network decreases the peak-valley difference in the loads within the static road network by 5.92$\%$.

In the model, EV driving and charging characteristics are used as an intermediate medium to initially integrate the flexible domains of the two layers of the road network and power grid for accurate regional dynamic spatiotemporal short-term charging load prediction, which lays a foundation for further research on synergistic operation of road-vehicle-grid networks with different attributes. Nevertheless, there are still several limitations. First, EVs are considered to exhibit the same travel patterns as those of fuel-powered vehicles in the simulation process, and the charging demand is estimated based on NCHRP data. The other limitation is the lack of analysis and discussion of the potential load impacts on the distribution network during peak load hours. Future research can start from the following two aspects: one is to fully account for the data-driven idea, combined with big data technology, to collect historical data of charging stations or facilities in the region, corresponding to the date type of the time series, temperature conditions, etc., and to employ more advanced neural network data mining technology for historical data processing [47] to establish a purely data-driven prediction model relying on historical charging load data. Another objective is to study and analyze the potential load impact of regional EV charging loads on the distribution network during peak load hours in greater depth.