A Management Framework and Optimization Scheduling for Electric Vehicles Participating in a Regional Power Grid Demand Response under Battery Swapping Mode

Abstract

With the rapid development of new energy vehicle industry and battery technology, in addition to charging mode to supplement energy mode for electric vehicles, battery swapping mode is also about to become an important way for electric vehicles to recharge power. Therefore, in this context, this paper plans the demand response management framework of electric vehicles participating in the regional power grid under the battery swapping mode from the first time. On this basis, the time distribution of battery-swapping demand was proposed by the time series analysis model of different vehicle types of electric vehicles. Then, in order to reduce the peak-valley load difference in the regional power grid as the optimization management goal, the charging schedule optimization scheduling model of electric vehicles participating in the demand response of the regional power grid under the battery swapping mode was constructed. The case analysis shows that under the battery swapping mode, by participating in the demand response through the optimal management and scheduling of the charging load of the power battery, can help the grid balance the contradiction between supply and demand in the peak and valley and promote the full consumption of new energy.

1. Introduction

In recent years, new energy vehicles have become an important trend for the future development of the automotive industry. On 2 November 2020, the General Office of the State Council issued the “New Energy Automobile Industry Development Plan (2021–2035)”, which is the programmatic document for the development of new energy vehicles in China in the next 15 years [1]. At present, driven by policy and market demand, China‘s new energy vehicle ownership has increased rapidly in recent years, and the new energy vehicle ownership in China has shown a linear growth trend from 2015 to 2021. By the end of 2020, the national number of new energy vehicles stood at 4.92 million. Compared with 2019, the number of vehicles increased by 1.11 million, an increase of 29.18%. The increment of new energy vehicles is more than 1 million in three consecutive years, showing a sustained rapid growth trend. Specific growth is shown in Figure 1.

With the development of the new energy automobile industry and battery technology, in addition to the charging mode to supplement energy for electric vehicles [2], the battery swapping mode is also about to become an important way for electric vehicles to supply electricity [3,4]. The battery swapping mode has more advantages in reducing the cost of purchasing cars, eliminating mileage anxiety and improving the safety level. However, due to the uncertainty of time and space of electric vehicles as mobile loads, considering the large scale and random power battery switching load connected to the grid, it will have a very large negative impact on the safe and stable operation of the grid [5,6,7]. Therefore, studying how to optimize the charging load of power batteries under the battery swapping model not only improves the stability and efficiency of the regional power grid but also supports the sustainable integration of renewable energy. Additionally, it helps alleviate the challenges posed by peak-valley load differences, which is critical for the future development of smart grids and the promotion of low-carbon energy systems.

The contributions of this study can be summarized as follows:

(1)

Different time series analysis models for swapping mode states were constructed.

(2)

Optimal scheduling model for electric vehicles in the battery swapping mode was proposed.

(3)

The impact of power battery charging load on the regional grid was analyzed.

(4)

Research can help the grid balance the contradiction between supply and demand in peaks and valleys and promote the consumption of new energy.

2. Current State of Knowledge

At present, scholars at home and abroad have carried out some extensive research on the optimal scheduling management of electric vehicle power battery load. Niu et al. [8] proposes that electric vehicles in power stations can be used to replace batteries for B2G (power batteries to the grid) to participate in power grid regulation so as to achieve the goal of peak shaving and valley filling in the grid and stabilize the load of electric vehicles. Lu et al. [9] established a planning model based on the reliability of the distribution network from the perspective of the coordination between the power station and the distribution network. Zhang et al. [10] established a model of BSS cluster participating in the FR service and formulates a two-stage operation strategy. Tian et al. [11] constructed the orderly charging strategy of an EV-to-power station and proposed a multi-scenario coordinated planning method considering the distributed generation of an EV-to-power station as a whole with the construction and operation cost, load fluctuation and network loss as the objectives. Liu et al. [12] proposed a BSS energy exchange strategy based on photovoltaic power generation, including a battery swap service model and power allocation model, considering the battery swap demand. Sun et al. [13] analyzed the switching mode and the load characteristics of an electric vehicle switching station and pointed out that the orderly management and optimal scheduling of charging and discharging behaviors of switching station and power grid managers can not only improve the economic benefits of switching stations, but also play an obvious role in peak shaving and valley filling and improve the economy and security of power grid operations. Yang et al. [14] proposed a shared battery station (SBS) model. Based on the partitioned battery control method, a battery scheduling strategy is proposed to control the charging, discharging, sleeping and switching processes. From the operator’s point of view, an optimization objective function with the goal of maximizing the profit is established to optimize the number of batteries in each time slot. Liang et al. [15] established a linear programming model to maximize the daily operational profits of a battery swapping station (BSS) via considering the constraints of the battery swapping demands of users and the charge–discharge balance within the BSS. Liang et al. [16], from a systemic perspective, developed a real-time battery swapping pricing model for electric taxis, covering various stakeholders that significantly impact the pricing of battery exchanges in the charging and swapping system. Despite the extensive research on optimal scheduling and management of electric vehicle battery loads, current studies often lack a comprehensive approach that integrates the coordination between battery swapping stations, the power grid and renewable energy sources.

One of the most important factors restricting the development of electric vehicles is the high switching cost of electric vehicle batteries. Zhang et al. [17] used a Monte Carlo simulation of vehicle behavior to compare the service capacity and benefits of charging and battery swapping of electric vehicles in taxis and buses. The effects of vehicle battery size, vehicle moving speed and swap service price on service capacity were investigated. W F et al. [18] proposed a strategy model of an electric vehicle switching station, considering the frequency and distribution of electric vehicle user station access, user cooperation and power grid load demand curve. Zhang et al. [19] comprehensively considered five aspects of social benefit, economic benefit, technicality, security and network influence, and, using the method of classification and classification, constructed the index evaluation system including a target layer, criterion layer and index layer.

Battery swapping mode (BSM) is an important method to provide energy to electric vehicles. In the battery swapping mode, if the battery swapping station does not have a sufficient reserve battery margin, the battery swapping behavior of electric vehicle users will directly affect the charging load generated by the battery swapping station [20]. Yang et al. [21] proposed the dynamic operation prediction model of battery swapping stations in the electricity market and constructed the swapping strategy based on short-term battery management. Zhong et al. [22], based on battery swapping technology and considering the variance of the battery charging rate, established a binary integer programming model to balance the contradiction between the bypass cost and the total cost of battery charging in the shared battery swapping mode and realized the benign interaction between the electric vehicle charging station and the power grid. Gan et al. [23] used the Monte Carlo random sampling method to collect the battery charging state in one day. Considering the constraints of charging and discharging times of charging stations, the operation model of the electric vehicle charging station was established, and the interior point optimization method was used to realize the orderly charging and discharging of electric vehicles. Zhang et al. [24] introduced the distribution planning requirements of the electric vehicle-to-power station and proposed an optimization model to meet various requirements when selecting station sites. The model aims to minimize the overall construction and transportation costs and meet the charging needs of drivers [25], changing the substation service type and operation characteristics into constraints. Yang et al. [26] considered the smooth charging load curve and constructed a two-stage optimal charging model to optimize the charging load with the goal of minimizing the energy cost. Many studies tend to focus on specific technical aspects or localized scenarios without considering the broader implications of integrating BSM with smart grid technologies and renewable energy sources. Additionally, the existing models often lack a comprehensive evaluation of user behavior dynamics and economic interactions, which are crucial for developing effective and sustainable battery swapping strategies.

Through the research of the above scholars, the current research mainly focuses on the location planning of the power station, the price strategy of the power station and the optimal operation. The dispatching mode participating in the demand response of the regional power grid under the battery swapping model and the optimal management decision of the charging load of different types of vehicle power batteries need to be further improved. Under this background, this paper first plans the demand response management framework of electric vehicles participating in the regional power grid under the battery swapping mode. On this basis, this paper analyzes the battery swapping timing and battery swapping demand of the electric bus in the bus power station, the electric taxi in the public power station and the distribution based on the mobile battery swapping mode. Then, with reducing the peak-valley difference in load as the optimization management objective, the optimal scheduling model of the charging plan participating in the demand response of power grid under the switching mode was constructed.

The remainder of this paper is organized as follows: Section 3 proposes a demand response management framework for electric vehicles participating in the regional power grid under the battery swapping mode. Section 4 analyzes and models the battery swapping state time series of non-passing electric vehicles. Section 5 constructs the optimal scheduling decision model of electric vehicles participating in the demand response of the regional power grid under the battery swapping mode. Section 6 takes the actual operation data of a regional power grid in China as the simulation object for analysis and verification, and Section 7 gives the main conclusions of the study.

3. Framework Design

In order to better explore the effect of electric vehicles on the accurate demand response of the regional power grid load under the battery swapping model, this paper plans the operation demand response management framework of centralized charging and swapping power stations, bus swapping power stations, public swapping power stations and mobile swapping energy vehicles with photovoltaic power generation. The specific participation in the demand response management framework is shown in Figure 2.

Under this operation management framework, this paper deeply integrates electric vehicles, power batteries, photovoltaic power generation and power stations, and uses the cloud platform of the vehicle power station and power grid demand response platform to realize information interaction to participate in power grid demand response. In order to make full use of the land resources of the power battery centralized charging station and promote the consumption of clean energy, the photovoltaic power generation system was planned as a supplement to the power grid in the operation architecture. The swapping stations were mainly divided into bus swapping stations and public swapping stations, and the distributed mobile swapping energy vehicles provided more accurate spot-based swapping services. This operation mode can achieve the purpose of large-scale management of power batteries, peak shaving and valley filling and promoting new energy consumption.

4. Time Series Analysis Model of Electric Vehicle Battery Swapping State

4.1. Time Series Analysis of Bus Switching State

According to the relevant rules and regulations, the driving time and driving line of the bus were regular every day. Starting from the bus center, the bus was driven in a circle according to the prescribed path and then returned to the bus parking lot. When the power battery on the bus was depleted or not enough to run for another cycle, it was necessary to replace the battery to supplement electricity. In this paper, considering the influencing factors such as the cycle mileage of electric buses, the first and last vehicle time of operation, the interval departure time and the time required for battery replacement, the time series analysis model of electric buses’ switching state was constructed. The whole process of analysis and simulation of each electric bus’s departure, return time and the state of charge of the power battery was carried out. Finally, the time series distribution of the switching demand of the bus at different times of the day was calculated.

4.1.1. Constraint of Required Driving Mileage

The electric bus ran periodically according to the specified path. In order to more accurately control the running state of electric buses and the demand distribution for battery swapping, we divided the electric bus in the operation process into three states to analyze, namely, the state of waiting for the bus to start in the bus center, the state of driving in the specified route and the state of needing to supplement electric energy for battery swapping in the power station. The specific state transition scenario is shown in Figure 3.

It can be seen from Figure 3 that there were mainly four scenarios in the state transition of electric buses. Scenario 1: when the first bus of the electric bus started to leave, the state of waiting to leave was converted from the state of waiting to leave according to the time interval of leaving to the state of driving on the route; Scenario 2: when the first vehicle returned to the bus concentration area after a cycle, the state of charge of the power battery could still meet the mileage of the next cycle needs to be directly into the waiting state; Scenario 3: when the first vehicle returned to the bus center one after another after a cycle, the state of charge of the power battery could not meet the mileage needs of the next cycle, so it needed to enter the state of battery swapping; and Scenario 4: when the first vehicle replaced the power station to replenish the electric energy, it entered the queue state of the waiting vehicle again and repeated the process of Scenario 1 [27].

4.1.2. Bus State Transition Process Analysis Model

Based on the scenario analysis of electric bus state transition and considering the constraints of different scenarios, this paper focuses on the analysis and modeling of each state transition process and calculates the distribution of electric bus demand at different times.

Step 1: According to the scenario analysis of the state transition of the electric bus, in order to maintain the closed-loop operation state of the electric bus according to the fixed interval in a specified line, the number of the electric bus should be limited first. Therefore, the minimum number of electric buses required in the driving line $N_{min}^b$ is expressed in Equation (1):

$$N_{min}^b={\displaystyle \frac{T_r^b+T_c^b}{T_g^b}}$$

(1)

where $N_{min}^b$ is the minimum number of electric buses required in the line. When the value is a decimal, in order to ensure the departure interval of electric buses, it should be processed by rounding up to an integer. The parameter $T_r^b$ is the time required for an electric bus running cycle on the line; $T_c^b$ is time required for an electric bus to replace a battery at a power station; and $T_g^b$ is the departure interval between every two electric buses on the line.

Step 2: Determine the departure time $t$ of electric bus. According to the vehicle scheduling plan of the electric bus, the starting time of the electric bus and the departure time of the end bus and the departure interval $T_g$ are set, then when $\varphi$ in Equation (2) is an integer greater than or equal to 0, $t$ is the departure time of the line.

$${\displaystyle \frac{t-T_s^b}{T_g^b}}=\varphi$$

(2)

where $t$ is the departure time of the electric bus; $T_s^b$ is the starting time of the first electric bus; and $\varphi$ determines the electric bus departure time coefficient.

Step 3: Determine the departure vehicle of electric buses. According to the setting in Scenario 1, the electric buses in the waiting state depart in order of waiting. Therefore, the $i$-th electric bus to be departed is selected as the one with the longest waiting time for departure $t_i^w$. Equation (3) is expressed as follows:

$$\max f(t_i^w)=w_i^b\times t_i^w$$

(3)

where $t_i^w$ is the waiting time of the $i$-th electric bus if it is long and the initial value is set to 0; $w_i^b$ is the state of electric bus waiting for departure; $i$ = 1, 2, 3, ……$N_{min}^b$; when $w_i^b$ is 1, it indicates that the electric bus is in the state of waiting for departure; and when $w_i^b$ is 0, it indicates that the vehicle is not in the waiting queue.

When the $i$-th electric bus leaves, the vehicle state has been converted to the driving state on the line, and the arrival time of the $i$-th electric bus and the state of charge of the power battery at the arrival time are calculated, as shown in Equations (4) and (5):

$$T_{e,i}^b=T_r^b+t_i$$

(4)

$$SO{C}_{e,i}^b=SO{C}_{s,i}^b-{\displaystyle \frac{M^b\times {\phi }^b}{{\omega }^b}}$$

(5)

where $T_{e,i}^b$ is the arrival time of the $i$-th electric bus after a cycle of operation; $T_r^b$ is the time required for an electric bus running cycle on the line; $t_i$ is the departure time of the $i$-th electric bus; $SO{C}_{e,i}^b$ is the state of charge of the power battery when the $i$-th electric bus arrives at the station after a cycle; $SO{C}_{s,i}^b$ is state of charge of power battery before departure of electric bus $i$; $M^b$ denotes the miles traveled by the $i$-th electric bus for one cycle of operation; ${\phi }^b$ is electric bus unit mileage power consumption; and ${\omega }^b$ is the rated capacity of the electric buses at full power.

Step 4: When the $i$-th electric bus returns to the centralized parking lot after a cycle, it is judged whether the vehicle enters the state of waiting for departure again in Scenario 2 or the state of switching power in Scenario 3. The judgment is based on whether the battery charge state $SO{C}_{e,i}^b$ of the first electric bus when it reaches the station after a cycle can support the next cycle, so it can be expressed in Equation (6):

$$SO{C}_{e,i}^b-({\displaystyle \frac{M^b\times {\phi }^b}{{\omega }^b}}+SO{C}_{min})\ge 0$$

(6)

where $SO{C}_{min}$ is the $i$-th electric bus needs to maintain the minimum state of charge.

When Equation (6) is greater than or equal to 0, it indicates that the electric quantity of the $i$-th electric bus can support the end of the next cycle, and then the vehicle enters the state of waiting for departure again in Scenario 2. The $w_i^b$ value is set to 1 and the waiting time of the vehicle is calculated.

When Equation (6) is less than 0, it shows that the $i$-th electric bus needs to enter the battery swapping state of Scenario 3, then the number of power battery sequence $\lambda$ of the electric bus battery swapping demand is generated. The initial value of $\lambda$ is set to 0, and there is no power battery required to charge at the beginning. Each time a new electric bus enters the state of the third scenario, set $\lambda =\lambda +1$, corresponding to the number of power batteries. The switching demand time is set to $\lambda$, then the end time $T_{\gamma }^b$ of the $i$-th electric bus can be expressed as follows:

$$T_{\gamma }^b=t_e$$

(7)

$$T_{ce,i}^b=T_c^b+t_e$$

(8)

where $T_{\gamma }^b$ is the switching time corresponding to the $\lambda$-th switching demand; $T_{ce,i}^b$ is the end of the battery swapping of the $i$-th electric bus; and $t_e$ is the $i$-th electric bus arrives at the public bus parking lot after a cycle.

Step 5: When the electric bus $i$ is switched over, update the state of charge $SO{C}_{s,i}^b$ of the electric bus, and then the electric bus enters Scenario 4 from the state of exchange to the state of waiting for departure. Set $w_i^b$ to 1 and begin to calculate the waiting time of the vehicle.

Step 6: Step 1 to Step 5 completed the whole process analysis of the electric bus from waiting for departure to the state of running on the line and the state of battery swapping. Finally, judge the end time of the last bus every day and calculate the total number of demand for battery swapping and the corresponding distribution of battery swapping time.

$$t_i-T_e^b\ge 0$$

(9)

where $t_i$ is the departure time of the $i$-th electric bus and $T_e^b$ is last departure time of electric bus.

When Equation (6) is less than 0, it indicates that the departure time of the first electric bus has not reached the end of the operation time, and it is necessary to continue the cycle of Steps 1 to 5. When Equation (6) is greater than or equal to 0, it indicates that the last electric bus has been issued and that the day of operation can be concluded. Then, the total demand times and the time distribution of the corresponding switching time are calculated as shown in Equation (10):

$$T^b=(T_1^b,T_2^b,T_3^b\cdots T_{{\lambda }_{\max }}^b)$$

(10)

where is the time distribution of electric bus switching time; ${\lambda }_{max}$ is the total number of electricity swapping requirements per day for electric buses, which is obtained via generating electricity swapping requirements $\lambda =\lambda +1$. The timing analysis process of bus state transition and power change demand is shown in Figure 4.

4.2. Time Series Analysis of Battery Swapping Status of Public Power Station

In the current electric vehicle segmentation market, private electric vehicles mainly use charging piles to supplement electric energy via slow charging [28,29]. The electric bus has been analyzed in detail above, mainly through centralized battery swapping to supplement the electric energy. However, the travel of electric taxis has more obvious randomness, and there is a high demand for operating efficiency. The brand of cars is relatively concentrated, and there is a strong demand for battery asset preservation. For electric taxis, the requirements for the operating efficiency of electric taxis do not have a long time to wait for charging via slow charging, and the fast charging mode has a great impact on the service life of the battery pack. Fast charging will significantly reduce the use efficiency of the battery pack and greatly reduce the sustainable mileage of electric taxis [28].

Therefore, in this paper, the electric vehicles in the public power station of electric vehicles were mainly analyzed using electric taxis. According to the characteristics of the continuous operation mode of two people and one car for electric taxis, this paper focuses on the analysis of the switching demand sequence and load situation of electric taxis and calculates the switching demand distribution of electric taxis in different periods.

Step 1: To calculate the electricity exchange demand of electric taxis in different periods, the total number of electricity exchange demand $N_c^T$ of electric taxis per day in the region should be calculated first. The total number of electricity exchange demand of electric taxis in the region can be calculated as shown in Equation (11):

$$N_c^T={\displaystyle \frac{M_d^T}{M_{em}^T}}\times M^T\times {\eta }^T$$

(11)

where $N_c^T$ is total electricity demand for electric taxis per day; $N_c^T$ is total electricity demand for electric taxis per day; $M_d^T$ is average daily mileage of electric taxis in the area; $M_{em}^T$ is average mileage of electric taxis operated in the region; $M^T$ is total number of electric taxis operated in the region; and ${\eta }^T$ is the operating rate of electric taxis operating in the region, the proportion of actual daily departures and the total number of electric taxis operating in the region.

Step 2: Calculate the electricity exchange demand of electric taxis. Next, it is necessary to analyze the distribution function of the start time of electric taxis arriving for electricity exchange, since the behavior time of electric taxis reaching the public battery swapping station is random and relatively independent. Therefore, in this section, we assume that the switching behavior of electric taxis arriving at the public switching station in turn conforms to the Poisson distribution and describes the demand of electric taxis for switching to the public switching station within a certain time interval through the Poisson distribution, as shown in Equation (12):

$$P(k)={\displaystyle \frac{m^k\times e^{-m}}{k!}}$$

(12)

where $P(k)$ denotes the duration of each counting interval. The probability of reaching the electric taxi $k$ of the public power station within the counting interval $t$; $m={\lambda }^T\times t$ denotes the duration of each counting interval. Count the average number of electric taxis arriving at public swap stations within interval $t$; ${\lambda }^T$ denotes the average frequency of electric taxis reaching the public power station in unit time; and $t$ denotes the duration of each count interval.

Step 3: Calculate the ${\lambda }^T$ value of the Poisson distribution function of the electric taxi reaching the power station. The specific calculation is shown in Equation (13):

$${\lambda }^T={\displaystyle \frac{N_c^T}{T_{sum}^T/T_c^T}}$$

(13)

where ${\lambda }^T$ is the average frequency of electric taxis reaching the public power station in unit time; $N_c^T$ is the time required for a public power station to complete an electric taxi battery replacement; $T_c^T$ is the time required for the public power station to complete the battery replacement of an electric taxi; and $T_{sum}^T$ is the public power station daily switching operation time.

Step 4: Using Monte Carlo simulation sampling based on the Poisson distribution function, the power demand distribution of public power station at different times in a day is calculated as shown in Equations (14) and (15):

$$T^T=(N_1^T,N_2^T,N_3^T\cdots N_j^T)$$

(14)

$$N_j^T\le N_{max}^T$$

(15)

where $T^T$ is the time distribution of electric taxi switching time; $N_j^T$ is the number of electric taxis with battery replacement at the same time in period $j$ of the public power station; and $N_{max}^T$ is the maximum number of electric taxis in a public power station that are switched simultaneously.

4.3. Time Series Analysis of Power Change State of Mobile Power Change Vehicle

With the development and improvement of electric vehicle technology, vehicle networking technology and electric vehicle related equipment and management systems, the advantages of power conversion mode will become increasingly prominent. The point-to-point distribution power conversion mode based on mobile power conversion vehicles is an extension and development of the current power conversion mode in service. In the environment of “Internet + Transportation” sustainable development, the Internet of Vehicles will be more mature, and the spot distribution and battery swapping mode of mobile battery swapping vehicles will be more timely and personalized. In this mode, it can also better play its advantages of flexibility and mobility. The implementation path of the point-to-point distribution power conversion mode of the mobile power conversion energy vehicle is shown in Figure 5.

The point-of-arrival distribution battery swapping mode of mobile battery swapping vehicle mainly serves the private vehicle users who have higher requirements on the time and place of battery swapping and approve the battery swapping mode. According to the actual attribute information of the vehicle, the electric vehicle users determine the driving path and the mileage of the electric vehicle. Then, the Internet-connected mobile phone and the cloud platform of the vehicle power station are used to interact with the information such as the state of charge of the vehicle, the specification number of the power battery and the geographical location, and then the satellite positioning system is used to select the appropriate power change location for agreement. Then, the power centralized charging station will respond to the user’s demand information through the vehicle power station cloud platform, dispatching the mobile battery-changing energy vehicle to carry a certain number of batteries with appropriate specifications to replace the battery service for the vehicles that need to be replaced at the agreed location.

Next, according to the random characteristics of electric private cars’ electricity demand, this paper analyzes the time sequence of electric private cars’ electricity demand and its influence on load and calculates the distribution of electric private cars’ electricity demand in different periods.

Step 1: In the point-to-point distribution battery swapping mode of mobile battery swapping vehicles, the current battery swapping demand of electric private vehicles is mainly due to the requirements for the convenience of the time and place of power supply. Each electric private vehicle is relatively independent of this demand and the probability of generating battery swapping demand is the same. On the other hand, the average time from the mobile battery swapping vehicle to the predetermined battery swapping location within the corresponding service range is also relatively fixed. Therefore, this paper first conducts simulation sampling according to the probability density function of battery swapping when the electric private car reaches the destination stop and determines the target data set of electric private car battery swapping users. The specific probability density function fitted by the survey data conforms to the normal distribution function, as shown in Equation (16):

$$f_p(t^p)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_c}}\exp (-{\displaystyle \frac{{(t^p+24-{\mu }_c)}^2}{2{\sigma }_c^2}})& 0<t^p\le {\mu }_c-12\\ {\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_c}}\exp (-{\displaystyle \frac{{(t^p-{\mu }_c)}^2}{2{\sigma }_c^2}})& {\mu }_c-12<t^p\le 24\end{array}\right.$$

(16)

According to the data fitting, ${\mu }_c=17.1$; ${\sigma }_c=3.3$ and $t^p$ is the parking time of electric private car changers.

Step 2: Determine the number of electric vehicles that can be exchanged in the target data set of electric private vehicle users. According to Equation (16), we obtain the vehicles that may be scheduled for battery swapping, and then determine whether the scheduled battery swapping service is needed according to the mileage of each electric private car. According to the survey data, fitting electric private car daily mileage approximately obeys lognormal distribution. Therefore, the daily mileage probability density function of electric vehicles is shown in Equation (17):

$$f_r(M_d^p)={\displaystyle \frac{1}{\sqrt{2\pi }{\sigma }_r{M}_d}}\exp (-{\displaystyle \frac{{(\mathrm{l}\mathrm{n}{M}_d^p-{\mu }_r)}^2}{2{\sigma }_r^2}})$$

(17)

where expected mileage ${\mu }_r=3.31$ is based on data fitting; standard deviation ${\sigma }_r=0.87$; and $M_d^p$ is the daily mileage of electric private cars.

Step 3: To determine whether the electric private car generates electricity exchange demand, when the charged state $SO{C}_i^p$ after a certain mileage of the electric private car is lower than the set critical value of the electricity exchange state, it is necessary to make an appointment for electricity exchange service. The specific expression is shown in Equation (18):

$$SO{C}_{s,i}^p-{\displaystyle \frac{M_d^p\times {\phi }^p}{{\omega }^p}}\le SO{C}_{e,i}^p$$

(18)

where $SO{C}_{s,i}^p$ is the initial state of charge of electric private cars; ${\phi }^b$ is the electric private car unit mileage power consumption; ${\omega }^p$ is the rated capacity of electric private car battery; and $SO{C}_{e,i}^p$ is the electric private cars’ need to change the charge state threshold.

Step 4: Determine whether the time that the electric private car users may change electricity meets the requirements of the mobile electric energy car to provide electricity change service. In order to improve the working efficiency of the mobile power-changing energy vehicle, the operating time of its work is limited. The electric private vehicle mainly recharges and supplements electric energy at night, so the operating time under the point-of-arrival power-changing mode was temporarily set to provide services in the daytime. Therefore, the time when the electric private car power changer makes an appointment for power change needs to meet Equation (19), which is expressed as follows:

$$t_s^p\le t^p\le t_e^p$$

(19)

where $t^p$ is any time of battery swapping under the spot distribution battery swapping mode of mobile battery swapping vehicle; $t_s^p$ is the start time of the mobile energy vehicle to point distribution mode; and $t_e^p$ is the end running time of the mobile electric energy vehicle to point distribution mode.

Step 5: Determine the minimum number of mobile power-exchange vehicles in the region. According to the above analysis, the total demand number of mobile power-exchange vehicles for power-exchange in the region within a day is determined. Then, the number of mobile power-exchange vehicles $N^p$ is determined based on the daily operation time, the operation time of battery replacement and the average time to reach the agreed location. The specific Equation is shown in Equation (20):

$$N^p\ge {\displaystyle \frac{N_c^p}{(t_e^p-t_s^p)/(T_c^p+T_{ca}^p)}}$$

(20)

where $N^p$ is the number of schedulable mobile battery swapping vehicles in the region; $T_c^p$ is the time required for a single mobile energy vehicle to complete a battery replacement for an electric vehicle; $T_{ca}^p$ is the average time required for a single mobile battery swapping vehicle to reach the reservation battery swapping location; and $N_c^p$ is the total demand for electricity exchanged by mobile energy vehicles in the region per day.

Step 6: Calculate the distribution of charging time when the mobile energy vehicle returns to the light storage centralized charging station. Since it takes a certain time, $T_{rca}^p$, for the mobile power-changing energy vehicle to return to the centralized charging station from the agreed power-changing site, the time distribution for the centralized charging load is equivalent to a period of delay at the end of the power-changing. Therefore, the time distribution of specific charging requirements is shown in Equation (21):

$$T^p=(N_1^p,N_2^p,N_3^p\cdots N_j^p)$$

(21)

$$N_j^p\le N_{max}^p$$

(22)

where $T^p$ is the inter-distribution of charging when the mobile energy vehicle returns to the centralized charging station; $N_j^p$ is at the time $j$, the number of batteries carried by the mobile battery changer that needs to be charged in the centralized charging station is returned; and $N_{max}^p$ is the maximum number of batteries brought back to the centralized charging station by the mobile energy vehicle.

5. Optimal Management Decision-Making Model Is Established for Participating in Demand Response Charging Plan under Battery Swapping Mode

Firstly, the number of batteries is the key factor affecting the optimization level of charging load when participating in the demand response of the power grid under the switching model. The number of batteries configured in different power conversion modes should at least meet the needs of bus scheduling plans on different lines, power conversion needs of electric taxi public power stations and battery distribution needs of mobile power conversion vehicles. Only when the battery configuration scale is greater than the minimum requirement can there be a certain margin for optimizing the charging load in the management decision-making so as to realize the demand response of peak shaving and valley filling for the regional power grid load.

5.1. Quantity Analysis of Batteries in Battery Swapping Modes

In the switching mode, in order to ensure that all the switching vehicles can carry out timely switching services, a certain number of circulating batteries are needed. That is to say, no matter when any type of vehicle generates electricity exchange demand, it can ensure that at least one battery is provided to provide electricity exchange service. Therefore, it is necessary to prepare a certain number of battery backups for the power station. The minimum number of backup batteries for the power station needs to meet the number of batteries that meet other switching needs before the first battery that is replaced at the daily switching operation is completed. Therefore, it is assumed that the total number of spare batteries for electric vehicles participating in the grid demand response management framework under the switching mode is $Q_{sum}$, and the minimum number of batteries is $Q_{min}$, then $Q_{min}$ is expressed in Equation (23):

$$Q_{min}=Q_{min}^b+Q_{min}^T+Q_{min}^p$$

(23)

where $Q_{min}$ is the minimum number of standby batteries in the area under switching mode; $Q_{min}^b$ is the minimum number of bus standby batteries provided by the bus power station in the battery swapping mode; $Q_{min}^T$ is minimum number of spare batteries for electric taxis provided by public power stations in electricity exchange mode; and $Q_{min}^p$ is the minimum number of standby batteries provided by mobile battery swapping energy vehicles for electric private cars in the power conversion mode.

The minimum number of bus standby batteries $Q_{min}$ for bus switching operation is mainly determined by the timing of each switching demand, the time required to replace the battery and the time required to complete the charging of the replaced battery, as shown in Equations (24) and (25):

$$T_{\lambda }^b<T_1^b+T_c^b+T_{char}^b$$

(24)

$$Q_{min}^b=\max (\lambda )$$

(25)

where $T_{\lambda }^b$ is each day the electric bus produces the corresponding time of the $\lambda$ power change demand; $T_c^b$ is the time required for an electric bus to replace a battery at a power station; $T_{char}^b$ is the time needed for electric buses to replace batteries to complete charging; and $\lambda$ is the number of electric buses generating electricity demand.

According to Equation (23), when the battery replaced by the electric bus is not charged for the first time, all the new demand for battery replacement needs to be supplemented by standby batteries.

In terms of the minimum reserve number $Q_{min}^T$ of taxi batteries in the public power station, it is different from the bus power station. It is mainly because in the public power station, we assume that it does not have a certain charging capacity, and the replaced batteries need to be uniformly distributed to the centralized charging station to supplement the required electric energy, so the round-trip time of battery distribution needs to be considered. This is shown in Equations (26) and (27):

$$T_{\delta }^T<T_1^T+T_c^T+T_{char}^T+2T_{rea}^T$$

(26)

$$Q_{min}^T=\max (\delta )$$

(27)

where $T_{\delta }^T$ is the corresponding time when the electric taxi generates the $\delta$-th battery swapping demand in the public power station; $T_{rca}^T$ is The time needed for the public power station to return to the centralized charging station; $T_c^T$ is the time required for the public power station to complete the battery replacement of an electric taxi; $T_{char}^T$ is the time required for the battery of an electric taxi to complete charging at a centralized charging station; and $\delta$ is the order number of electric taxis generating electricity exchange demand in public power stations.

The minimum number of spare batteries for electric private cars in mobile energy vehicles is similar to that in public power stations, and additional battery distribution round-trip time is needed, and the battery parameters can also be calculated according to the average value. The details are shown in Equations (28) and (29):

$$t_{\gamma }^p<T_1^p+T_c^p+T_{char}^p+2T_{rea}^p$$

(28)

$$Q_{min}^p=\max (\gamma )$$

(29)

where $t_{\gamma }^p$ is the time when electric private cars generate electricity demand corresponding to the point-to-point distribution mode of mobile energy vehicles; $T_{rca}^p$ is the time required for the mobile power-changing energy vehicle to return to the centralized charging station from the agreed power-changing location; $T_c^p$ is the time needed to replace a battery in a mobile energy vehicle; $T_{char}^p$ is the time required for the battery of electric private cars to complete charging at the centralized charging station; and $\gamma$ is the number of electric private cars generating electricity demand.

When the minimum number of batteries required in this mode of operation is $Q_{min}$, the batteries returned to the photovoltaic storage centralized charging station will be charged and recharged to provide the next cycle. In this case, there is no optimal adjustment margin for demand response. Therefore, only when the number of spare batteries exceeds the minimum demand $Q_{min}$ can they have the ability to participate in the adjustment of grid load by grid demand response, and the greater the value of $Q_{sum}$ is, the stronger the adjustment ability will be.

5.2. Objective Function and Constraints of Charging Load Optimization in Battery Swapping Modes

5.2.1. Objective Function

The above analysis of the number of standby batteries shows that in the switching mode, only when the configuration scale of the standby battery exceeds the minimum demand $Q_{min}$ can the charging time of the replaced battery have a certain adjustment margin. As the managers of charging plan arrangement, they can choose a reasonable charging time to respond to the demand of the grid. Therefore, this chapter combines the number of standby batteries in the switching mode to achieve the minimum impact on the peak-valley difference in the regional power grid load as the optimization management objective and optimizes the charging load of the replaced batteries. The specific objective function Eq. is shown in Equation (30):

$$\min {\eta }_s={\displaystyle \frac{P_{s,max}-P_{s,min}}{P_{s,max}}}$$

(30)

where ${\eta }_s$ is the peak-valley difference rate of the regional power grid load; $P_{s,max}$ is the peak daily load of the regional power grid; and $P_{s,min}$ is the daily load valley value of the regional power grid.

In the battery swapping mode, in order to make better use of land resources and promote the consumption of clean energy, the photovoltaic power generation system is planned in the centralized charging station as a supplement to the power grid. Therefore, the calculation Equation of the regional power grid total load $P_s$ is shown as (31):

$$P_s=P_o+P_b+P_T+P_p-P_v$$

(31)

where $P_s$ is the regional power grid load; $P_o$ is conventional load outside the battery swapping mode in the regional power grid; $P_b$ is charging load caused by replacing electric bus battery in bus replacement power station; $P_T$ is charging load caused by replacing electric taxi battery in public power station; $P_p$ is charging loads caused by battery replacement of electric private cars for mobile electric energy vehicles; and $P_v$ is power of the photovoltaic power generation system in centralized charging station.

Among them, in order to achieve the purpose of prioritizing the consumption of new energy, the photovoltaic power generation system is first used to charge the battery during the charging plan arrangement, and then interacts with the grid. Therefore, in Equation (31), the photovoltaic power generation output is optimized after deduction.

5.2.2. Constraint

(1)

Constraints on Configuration Number of Electric Buses on Lines

According to the operation requirements of the public transport management department and the corresponding scheduling plan, in order to maintain the closed-loop operation state of the electric bus according to the fixed interval in a specified line, the number of electric buses in the line should be greater than the minimum number. The specific requirements are shown in Equation (32):

$$N_{min}^b\ge {\displaystyle \frac{T_r^b+T_c^b}{T_g^b}}$$

(32)

where $N_{min}^b$ is when the minimum number of electric buses required in the line is small; in order to ensure the departure interval of electric buses, the integer is taken up.

(2)

Constraints on configuration number of mobile electric energy vehicles

In order to better meet the diversified and personalized demand for electricity exchange of electric vehicle users, under the condition of a certain radius of electricity exchange service and battery replacement operation time there should be the minimum number of mobile electricity exchange energy vehicles in the region to ensure the waiting time of electric vehicle electricity exchange service and improve the operation efficiency of electric vehicles and the service efficiency of electricity exchange. The specific requirements are shown in Equation (33):

$$N^p\ge {\displaystyle \frac{N_c^p}{(t_e^p-t_s^p)/(T_c^p+T_{ca}^p)}}$$

(33)

where $N^p$ is the number of schedulable mobile battery swapping vehicles in the region and $N_c^p$ is total demand for electricity exchanged by mobile energy vehicles in the region per day.

(3)

Constraints on the number of spare batteries for different vehicles

According to the operation scenario designed in Section 5.1 under the battery swapping mode, in order to ensure that different vehicles can enjoy the battery swapping service in a timely manner, when the battery swapping demand is initiated, the corresponding spare battery should be replaced. Therefore, according to the travel behavior and number setting of vehicles in existing scenarios, the reserve of each battery must have a minimum number of constraints, as shown in Equation (34):

$$Q_{min}\ge Q_{min}^b+Q_{min}^T+Q_{min}^p$$

(34)

where $Q_{min}$ is the minimum number of standby batteries in the area under switching mode; $Q_{min}^b$ is the minimum number of bus standby batteries provided by the bus power station in the battery swapping mode; $Q_{min}^T$ is the minimum number of spare batteries for electric taxis provided by the public switching power station under the switching mode; and $Q_{min}^p$ is the minimum number of standby batteries provided by mobile battery swapping energy vehicles for electric private cars in the power conversion mode.

(4)

Replace the battery to charge the maximum number of constraints at the same time

Under the switching mode, when the battery is replaced for different switching scenarios, and when the operator responds to the demand through unified management and optimization of the charging plan, due to the limitation of the number of charging equipment in the centralized charging station, it is impossible to supplement the power of a large number of power batteries at the same time even in the low load period. Therefore, the maximum number of simultaneous charging constraints need to be considered when participating in the demand response of the power grid, as shown in Equation (35):

$$E{Q}^b+E{Q}^T+E{Q}^p\le E{Q}_{sum}$$

(35)

where $E{Q}^b$ is the number of electric bus batteries replaced by the bus replacement power station charging at the same time; $E{Q}^T$ is the number of electric taxi batteries replaced by public power stations charged simultaneously; $E{Q}^p$ is the number of electric private car batteries charged at the same time replaced by mobile energy vehicles; and $E{Q}_{sum}$ is the total number of charging equipment in the centralized charging station.

(5)

Constraints of regional power grid load

At any time interval of the daily load of the regional power grid, the maximum number of batteries in the centralized charging station should be less than the maximum load limit that the regional power grid can withstand after the superposition of the charging load generated by the supplementary electric energy and the conventional load of the regional power grid. The specific requirements are shown in Equation (36):

$$P_j^o+P_j^b+P_j^T+P_j^p\le P_j^{sm}$$

(36)

where $P_j^{sm}$ is the maximum load value that the regional power grid can withstand in any $j$ period; $P_j^o$ is the conventional load other than the switching mode in the regional power grid in any $j$ period; $P_j^b$ is the charging load generated by replacing the electric bus battery in the bus replacement power station at any $j$ period; $P_j^T$ is the charging load generated by replacing the electric taxi battery in the public power station in any $j$ period; and $P_j^p$ is the charging loads caused by battery replacement of electric private cars for mobile electric energy vehicles at arbitrary phase $j$.

5.3. Model Optimization Based on Particle Swarm Optimization in Battery Swapping Mode

This section uses the particle swarm optimization algorithm to solve the above model. Particle swarm optimization is a swarm intelligence algorithm designed via simulating the predation behavior of birds [30,31]. There are different food sources in the region. The task of birds is to find the largest food source, and we regard it as the global optimal solution of the problem. Birds throughout the search process, through passing on each other’s location information, let other birds know the location of the food source, and ultimately the whole flock can gather around the food source to, as we would say, find the optimal solution to the problem.

In the process of problem optimization, the initial random position and initial random velocity are assigned to all particles in the space. The particle moves in the solution space. The individual position is updated via tracking the best value Pbest and the group extreme value Gbest of each particle. The fitness function value is calculated once the particle updates the position. With the increase in the number of calculations, the position of the new individual extreme value Pbest and the group extreme value Gbest is determined via comparing the fitness function value of the new particle with the fitness function value of the individual extreme value and the fitness function value of the whole extreme value. Finally, through continuous iteration, the particles gather or aggregate around one or more optimal advantages so as to obtain the optimal solution of the problem. The updating methods of particle velocity and position in each iteration are shown in Equations (37) and (38):

$$v_{id}^k=w\ast v_{id}^{k-1}+c_1{r}_1\left(p_{id}-x_{id}^{k-1}\right)+c_2{r}_2\left(p_{gd}-x_{id}^{k-1}\right)$$

(37)

$$x_{id}^k=x_{id}^{k-1}+v_{id}^{k-1}$$

(38)

where $v_{id}^k$ is the $d$-dimensional component of the velocity vector of particle $i$ in the $k$th iteration; $x_{id}^k$ is the $d$-dimension component of the $i$-position vector of the $k$-iteration particle; $c_1,c_2$ are the cognitive coefficients adjusting the learning maximum step size; $r_1,r_2$ is two random numbers, value range [0, 1], to increase the search randomness; and $w$ the is inertia weight, non-negative number adjustment for the search range of solution space.

In the particle swarm optimization algorithm, inertia weight $w$ is the most important parameter. Larger inertia weight is conducive to global search, while a smaller inertia weight is more conducive to local search. In order to better balance the global and local search ability of the algorithm, a linear decreasing weight method is proposed, that is, inertia weight decreases linearly from large to small, as shown in Equation (39):

$$w(k)=w_s-(w_s-w_e)\times {\displaystyle \frac{k}{k_{\max }}}$$

(39)

where $w(k)$ is the inertia weight value of the $k$th iteration; $w_s$ is the initial inertia weight; $w_e$ is the inertia weight value when iterating to the maximum number; $k$ is current iterations; and $k_{\max }$ is the total number of iterations.

In the process of solving via the particle swarm optimization method, the charging conditions of different types of power batteries are coded in matrix form. Let $X={\left[x_{ij}\right]}_{Q\times j_{\max }}$ be the decision matrix of the power battery charging plan. In this matrix, the number of rows is the total number $Q$ of power batteries that need to be charged, and the number of columns is the total number of periods divided in a day. According to the interval of one period per 10 min, $j_{\max }=144$. The main solving steps are as follows:

Step 1: According to the bus battery swapping state time series analysis model in Section 4.1, Section 4.2 and Section 4.3, the public power station electric taxi battery swapping state time series analysis model and the electric private car battery swapping state time series analysis model based on mobile battery swapping energy, as well as the battery swapping demand time distribution of different types of vehicles, are calculated.

Step 2: According to the time distribution of battery swapping demand of different types of vehicles, the charging schedule load of the battery is calculated and the high-dimensional load matrix of ${\left[x_{ij}\right]}_{Q\times j_{\max }}$ is generated. In the matrix, 1 denotes the time when the battery is being charged, and 0 denotes the time when the battery is not charged.

Step 3: Initialize the particle swarm, including the size of the population, the number of iterations, the initial position of the particle, the speed and the range of its changes, and randomly generate the charging plan scheme population under constraints.

Step 4: Set the peak-to-valley difference rate of the regional power grid load as the fitness function and calculate the individual optimal fitness function value and the group fitness function value.

Step 5: Use Equations (37) and (38) to update the position and velocity of particles iteratively. Compare the fitness function value again after the update.

Step 6: Determine whether the end condition of the iteration is satisfied. If not, $k=k+1$ is repeated, iteratively optimized. If the end condition is satisfied, the optimized charging load scheme is output. The flow chart of model solution is shown in Figure 6.

6. Case Analysis

6.1. Data and Parameter Settings

In terms of the operation of electric buses, a certain bus line in the region was taken as the object for analysis and research. The operation time $T_s^b$ of the first bus was 6:00 a.m. and the departure time of the last bus was 22:00 p.m. In the line, the time $T_e^b$ needed for the electric bus to run a cycle was 60 min, the departure interval $T_g^b$ between each two electric buses was 10 min, the time $T_c^b$ needed for the electric bus to replace the battery in the power station was 10 min, the mileage $M^b$ of the electric bus running a cycle was 20 km, the power consumption per unit mileage ${\phi }^b$ was set to 80 kWh/100 km, and the rated capacity of the electric bus under full power ${\omega }^b$ was set to 160 kWh. At present, the suppliers of the centralized charging station module mainly include Niolai, Titan, Tonghe, Huawei and other manufacturers. The charging power is between 10 kW and 60 kW, and the charging voltage is between 200 V and 500 V. Therefore, the constant charging power $P_{ev}^b$ of the electric bus battery is 40 kW, so it takes four hours to charge from 0 to 100%. According to the power consumption per unit mileage of the electric bus and the mileage of a cycle, it can be seen that the bus needed 20 kWh power for a round trip. Therefore, switching was required when the battery charge state $SO{C}_{e,i}^b$ of the first electric bus reached the station after a cycle of operation was less than 15%. The relevant parameters of the operation of the bus-to-bus power station under the battery swapping mode are shown in

Table 1. Relevant parameters of the operation of the bus power-changing station in the power-changing mode.

Parameter Name	Parameter Notation	Parameter Value	Parameter Unit
First bus operating time	$T_s^b$	6:00	time
Last bus operating hours	$T_e^b$	22:00	time
Bus runs one cycle time	$T_r^b$	60	min
Departure time between every two buses	$T_g^b$	10	min
The time it takes for a bus to replace a battery	$T_c^b$	10	min
The mileage of the bus running a cycle	$M^b$	20	km
Electricity consumption per bus mileage	${\phi }^b$	100	kWh/100 km
Rated capacity when the bus is fully charged	${\omega }^b$	160	kWh
Rated charging power of the bus battery	$P_{ev}^b$	40	kW
The bus needs to change the state of charge critical value	$SO{C}_{e,i}^b$	15	%

.

In the operation of a public power station, this paper mainly analyzes and studies electric taxis with high operating efficiency requirements. According to the statistical data of electric taxi travel in a certain area, the number of electric taxis in the area $M^T$ was 1000 and the average daily mileage $M_d^T$ was about 350 km. The performance parameters of electric taxi vehicles are mainly referred to the current mainstream new energy EU260 pure electric taxi of Beiqi. Under the condition of full charge and considering the actual road condition, the endurance mileage $M_{em}^T$ is set to 200 km. The rated capacity ${\omega }^T$ of the power battery was 40 kWh. When the state of charge $SO{C}_e^T$ of the electric taxi was less than 10%, it needed to be replaced at the public power station. The replaced electric taxi battery uses the slow charging method to supplement the electric energy with a constant charging power $P_{ev}^T$ of 10 kW and a constant power. Therefore, the charging time of each power battery is about 4 h. The relevant parameters of the operation of the public power station under the battery swapping mode are shown in

Table 2. Relevant parameters of operation of public power-changing station in power-changing mode.

Parameter Name	Parameter Notation	Parameter Value	Parameter Unit
Number of electric taxis	$M^T$	1000	unit
Average daily mileage of electric taxis	$M_d^T$	350	km
Electric taxis have a cruising range	$M_{em}^T$	200	km
Rated capacity of electric taxis	${\omega }^T$	40	kWh
The time it takes for an electric taxi to replace the battery	$T_c^T$	5	min
Electric taxis need to change the state of charge threshold	$SO{C}_e^T$	10	%
Rated charging power of electric taxi batteries	$P_{ev}^T$	10	kW

.

In terms of the spot distribution and battery swapping operation of mobile battery swapping vehicles, the private vehicle users who had high requirements on the time and place of battery swapping and approved the battery swapping mode were mainly analyzed and studied. The number of electric private cars simulated in the area $M^p$ was 2000. Through the simulation sampling of the probability density function of electric private cars fitted by the survey data, the possible switching time and daily mileage were obtained. The critical value $SO{C}_{e,i}^p$ of the state of charge when the electric private car changed electricity according to the needs of travel was set to 10%, the start running time $t_s^p$ of the spot distribution and change electricity mode of the mobile electric energy car was set to 8:00, and the end running time $t_e^p$ was set to 17:00. The time $T_c^p$ required for a single mobile power-change vehicle to complete a battery replacement for an electric vehicle was 5 min, the average time $T_{ca}^p$ required to reach the scheduled power-change location was 20 min, and the time $T_{rca}^p$ for the mobile power-change vehicle to return to the centralized charging station from the agreed power-change location was 20 min. The number of schedulable mobile battery-changing energy vehicles in the region $N^p$ was 10. The battery of the replaced electric private car was charged using the slow charging method with a constant charging power $P_{ev}^p$ of 10 kW and a constant power. The rated capacity ${\omega }^p$ of the power battery of the private car was 40 kWh, so the charging time of each power battery was about 4 h. The relevant parameters of the battery swapping operation of the mobile battery swapping vehicle are shown in

Table 3. Relevant parameters of the operation of mobile charge and changing energy vehicles in the power-changing mode.

Parameter Name	Parameter Notation	Parameter Value	Parameter Unit
Number of electric private cars in the area	$M^p$	2000	unit
The start time of the mobile battery-swappable energy vehicle	$t_s^p$	8:00	time
The end of running time of the mobile battery-swappable energy vehicle	$t_e^p$	17:00	time
Time required to replace the battery	$T_c^p$	5	min
Time required to arrive at the reserved location	$T_{ca}^p$	20	min
Time to return to centralized charging station	$T_{rca}^p$	20	min
Number of mobile battery-swappable energy vehicles	$N^p$	10	vehicle
Electric private cars need to change the state of charge threshold	$SO{C}_{e,i}^p$	10	%
Rated capacity of private car power battery	${\omega }^p$	40	kWh
Electricity consumption of electric private car per mileage	${\phi }^b$	15	kWh/100 km
Rated charging power of electric private car batteries	$P_{ev}^p$	10	kW

.

In terms of the construction and configuration of the photovoltaic storage centralized charging station, in order to meet the needs of users in a timely manner and better participate in the demand response of the power grid, 10,000 square meters of centralized charging stations are planned according to the current construction level, and the basic parameters of Weilai’s second generation power station are estimated. About 2000 power batteries can be charged at the same time. In the planning of the photovoltaic power generation system in the centralized charging station, the photovoltaic power generation system adopts the configuration mode combined with buildings. Assuming that the area of the photovoltaic panel available for the centralized charging station is 50% of the total area, the photovoltaic material takes the single crystal silicon with high conversion efficiency and mature technology as an example. The single crystal high efficiency photovoltaic module is calculated according to the output power of 540 W, and the installation size of the single photovoltaic panel is 2279 × 1134 × 35 mm. By calculating the power and area ratio of the single crystal, the high efficiency photovoltaic panel is about 180 W/m². Therefore, the total capacity of photovoltaic power generation in the centralized charging station is 900 kW.

6.2. Discussion of Charging Load in Switching Mode

According to the time series analysis model of the bus switching state in Section 4.1 and the relevant scheduling plan data, the operation of a single bus line within a day was simulated. At the same time, considering the time required by the bus to replace the battery, seven buses were needed to meet the most basic operation state of the single line, and 14 switching demands were generated every day. Therefore, charging immediately after the replacement of the battery and the load generated by the bus power battery without the optimized charging plan is shown in Figure 7.

According to the charging load of the power battery of the electric taxi in the public switching power station, and the time series analysis model of the switching state of the public switching power station in Section 4.2 above, the computer used the Monte Carlo method to simulate the sampling according to the Poisson distribution probability density function fitted according to the statistical data. The charging load of the electric taxi is shown in Figure 8 when the replaced battery is not optimally managed.

The charging load of the electric private car battery was carried by the mobile battery swapping energy vehicle after returning to the centralized charging station. According to the analysis model of the battery swapping state of the mobile battery swapping energy vehicle in Section 4.3 above, it can be seen that the generation of the battery swapping demand was mainly based on the driving mileage of the electric private car user and the convenience of the time and the place of the replacement of the electric energy. Therefore, the time was mainly concentrated in the daytime and had strong randomness. Through the simulation analysis, it can be obtained that the specific charging load is shown in Figure 9 under the mode of the mobile battery swapping energy vehicle returning to the centralized charging station.

Through the above calculation, we obtained the different types of electric vehicles in the power battery after the battery immediately began to charge the load situation. In order to better explore the scale of electric vehicles connected to the regional power grid and the influence of the load on the regional power grid, this paper demonstrates how the electric bus, electric taxi and electric private car battery charging loads were superimposed and summarizes the specific load situation as shown in Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9.

It can be seen from Figure 10 that if the standby battery has no response coordination margin in the switching mode, most electric vehicles will choose to recharge the electric energy by charging at night when the valley price is relatively favorable. Therefore, there were fewer vehicles that generated electricity demand in the second half of the night and in the morning. In addition, it took a certain period of time to return from the power station and the mobile energy vehicle to the centralized charging station at the reservation place, which affected the load delay of the centralized charging station. Therefore, the charging load of the power battery replaced by the electric vehicle mainly started after 12:00 and formed a peak around 16:00–17:00. Then, as the power battery completed charging successively, the load began to decrease continuously. The conventional load of the regional power grid and the charging load of the power battery replaced by the electric vehicle were superimposed. It can be seen that the second peak load of the regional power grid was further pulled up between 17:00 and 19:00. At this time, the maximum load of the regional power grid was 315.92 MW, and the peak-valley difference rate was 42.38%. Due to the limited number of electric vehicles, if the scale of the power battery needing to be charged continued to increase, the peak-valley difference in the regional power grid load would be further widened.

6.3. Discussion of Charging Load Optimization Results in Battery Swapping Mode

In the battery swapping mode, we considered the actual load situation of the regional power grid and took the minimum impact on the peak-valley difference in the regional power grid load as the optimization management objective. The computer was used for iterative optimization through the solution method in Section 5.3. The acceleration constant $c_1=c_2=2$, the initial inertia weight value $w_s$ and the inertia weight value $w_e$ of the maximum number of iterations were set to 0.9 and 0.4, respectively. The charging schemes of power batteries with different vehicle types were optimized, and the charging load of the replaced batteries was optimized to better complete the demand response to the regional power grid.

6.3.1. Discussion of Optimization Results

In the switching mode, only when the configuration size of the standby battery exceeds the minimum demand $Q_{min}$, then the charging time of the battery replaced will have a certain adjustment margin. According to the calculation, the maximum number of single-line electric buses charging at the same time was 7, and the minimum number of spare batteries $Q_{min}^b$ was 7. The maximum number of electric taxis charging at the same time was 799, and the minimum number of spare batteries $Q_{min}^T$ was 702. The maximum number of electric private cars charging at the same time was 135, and the minimum number of standby batteries $Q_{min}^p$ was 96. Therefore, this section first adds 60% $Q_{min}$ to the number of batteries configured on the basis of $Q_{min}$ for optimization, and at the same time gives priority to the output of the photovoltaic power generation system of centralized charging stations. The specific conditions of the optimized power battery charging load and regional power grid load are shown in Figure 11.

It can be seen from Figure 11 that the optimized charging load can respond to the regional power grid load more accurately. Before optimization, the charging load of the power battery of the electric vehicle was mainly concentrated on about 15–18 in the afternoon. After increasing the number of 60% $Q_{min}$ standby batteries, the charging load of some power batteries was transferred to the valley section at night for energy supplement due to the increase in the adjustment margin, which had played a good response effect on the valley filling demand. On the other hand, due to the output of the photovoltaic power generation system of the centralized charging station, the first peak load of the regional power grid in the morning was also alleviated, and the local consumption of photovoltaic new energy power was promoted. At that time, the maximum load value of the regional power grid was 308.53 MW, the minimum load value was 186.93 MW and the peak-valley difference was reduced by 12.27 MW compared with that before optimization. The peak-valley difference rate of the regional power grid load was reduced from 42.38% before optimization to 39.41% after optimization. This shows that in the battery swapping mode, through the unified management of the charging load of the electric vehicle battery and the optimization of the charging load plan, the effect of transferring the charging load of the electric vehicle battery can be achieved, and the purpose of participating in the power grid demand response can be better realized.

6.3.2. Sensitivity Analysis of Battery Configuration to Demand Response Capability

The number of power batteries allocated by centralized charging stations in the battery swapping mode will directly affect the response degree of participating in the demand response of the power grid. In this section, the sensitivity analysis method commonly used in management is used to analyze the influence of the number of power batteries on the optimization effect of charging load and the response degree of participating in the demand response of the power grid. The sensitivity analysis method is an uncertainty factor analysis method. In this section, the sensitivity analysis is carried out according to the above 60% $Q_{min}$ reserve battery number and only 80% $Q_{min}$ increase in the step size of 10%. The analysis results are shown in Figure 12.

It can be seen from Figure 12 that with the increasing number of standby batteries in centralized charging stations, the valley filling effect of its response to grid demand will become better and better. According to the current configuration of electric vehicles, when the number of standby batteries increases by 80% $Q_{min}$, the maximum transfer load can reach 6580 kW. Therefore, through the optimization management of charging load of electric vehicle battery under the mode of electric vehicle battery swapping, it can better use the night load trough period to charge it and can play the effect of peak shifting and valley filling and improve the load curve of the regional power grid. In the future, with the rapid development of the electric vehicle industry in the regional power grid, it will be more coordinated and interactive with the power grid. The detailed parameter descriptions can be found in Appendix A.

7. Conclusions

This paper developed a demand response management framework for electric vehicle participation under the battery swapping mode and constructs time series analysis models to evaluate the state of swapping mode operations. Furthermore, an optimal scheduling management model for charging plans was designed, with the objective of reducing the peak-valley load difference in the regional power grids. Through the case analysis, several key findings are highlighted as follows:

(1)

Grid demand response: The battery swapping mode, facilitated by centralized charging stations, offers enhanced control over charging times, allowing more responsive and flexible integration with the grid. Optimized management decisions can significantly improve grid response rates and alleviate urban electricity consumption pressures. The coordination between supply and demand during peak and valley periods is greatly enhanced, promoting the efficient absorption of renewable energy and improving overall energy utilization.

(2)

User experience: From the perspective of electric vehicle users, the battery swapping mode provides a fast and efficient energy replenishment experience. The time required for battery swapping is comparable to the refueling time for traditional internal combustion engine vehicles, effectively addressing issues such as range anxiety and low battery concerns. This enhances user satisfaction and fosters broader adoption of electric vehicles.

(3)

Power battery management: Centralized battery management at swapping stations enables the uniform handling of large quantities of batteries, which contributes to maintaining battery performance. This not only improves the operational efficiency of power batteries but also extends their service life, maximizing resource utilization. Proper battery management is critical for sustaining long-term battery health and reducing the frequency of battery replacements.

In conclusion, the findings of this study provide significant insights into the role of battery swapping in the demand response and optimal scheduling of electric vehicles in the regional power grids. The research contributes to the development of more efficient energy management strategies and supports the integration of electric vehicles with renewable energy systems. Future work should explore the impact of various battery types and standardization on the scalability of the battery swapping model and further enhance the interaction between electric vehicles and the power grid.

Finally, the shortcoming of this model is that the current research only takes the number of standby batteries as a constraint and does not consider the differences in different battery types and power conversion standards of the same type of vehicle. Therefore, in further research, the battery swapping standards of different technical routes will be refined and optimized in order to better promote the coordinated interaction between electric vehicles and power grids in the future.