The scheduling of EHDT-BSS fundamentally relies on the coordinated charging and discharging of on-site battery resources. However, distinct from standard passenger vehicle stations, EHDT-BSS facilities operate with a limited battery inventory and exhibit a tight coupling between swapping and charging processes. Consequently, battery availability fluctuates dynamically, driven by variations in charging protocols and swapping demand. To address these constraints, we propose a classification strategy based on SOC grading. In contrast to the static grading [14] or the highly discretized multi-energy-level division of batteries [11], the complex battery states are specifically classified into the following three SOC categories in this study. By categorizing and scheduling battery packs according to distinct grades, a robust mapping relationship is established between battery status and charging/discharging protocols. To facilitate the analysis of the scheduling optimization, the following assumptions are made:

All battery packs deployed in the battery swapping station are assumed to have uniform specifications and to operate under constant-power charging and discharging.

Let SOCi,t denote the state of charge of the i-th battery pack within the station at a discrete time step t. In line with the operational characteristics of BSS, the following SOC thresholds are defined: SOCmin represents the minimum safety limit for battery operation; SOClow denotes the lower bound at which a battery retains flexible regulation capability; and SOChigh indicates the minimum SOC required for deployment in EHDT swapping. Based on these thresholds, the station’s battery inventory is classified into three distinct SOC grades, denoted as S1, S2, and S3, in descending order of charge level: (a)

Category 1: Fully Charged Reserve Batteries. This category represents the highest SOC range. Batteries in this classification satisfy the requisite criteria for swapping operations and are immediately deployable without the need for supplementary charging. Functioning as the core service resource of the BSS, this inventory is dedicated strictly to guaranteeing baseline swapping demands across all operational intervals. Consequently, under nominal conditions, these batteries are withheld from participating in grid discharge. The quantity of batteries in this category is denoted by Nf, and the corresponding set is defined as follows:

(1)Ωf,t={i|SOCi,t≥SOChigh}

where: Ωf,t represents the set of Category 1 batteries at time t; SOCi,t represents the SOC value of the i-th battery at time t. (b)

Category 2: Flexible Regulation Batteries. This category comprises batteries whose SOC falls within the medium range. These batteries are capable of not only addressing extreme swapping demands in the next time period but also serving as the core flexible resource for the BSS to participate in grid frequency regulation services, possessing bidirectional charging and discharging capabilities. When current swapping demands are sufficiently covered by the quantity of Category 1 batteries, frequency regulation services can be provided by this category of batteries in response to under-frequency and over-frequency events in the power grid by following AGC commands. The quantity of batteries in this category is denoted by Nd, and the corresponding set is defined as:

(2)Ωd,t={i|SOClow≤SOCi,t<SOChigh}

where: Ωd,t represents the set of Category 2 batteries at time t.

The charging power of the BSS at each time period is expressed as:

(4){PBSS,t=Prigid,t+Pflex,tPrigid,t=∑i∈Ωc,tPch,i,tPflex,t=∑i∈Ωd,t(Pch,i,t−Pdis,i,t)

where: PBSS,t represents the charging power of the battery swapping station during time period t; Prigid,t denotes the rigid charging power, generated by the depleted battery set; Pflex,t represents the flexible charging/discharging power, contributed by the flexible regulation batteries; Pch,i,t and Pdis,i,t denote the charging and discharging power of the i-th battery during time period t, respectively.

Compared with normal battery-swapping electric vehicles (EVs), the load of EHDTs exhibits distinct characteristics, specifically concentrated temporal distribution and high-power demand. On the one hand, constrained by the strict timeliness requirements of logistics tasks, battery-swapping demand often surges during specific shift handover periods, resulting in significant peak loads. On the other hand, although the operation schedules of EHDTs are relatively fixed, their transportation tasks are subject to the coupled influence of complex factors such as order dynamics, traffic conditions, and weather. Consequently, their battery-swapping behavior exhibits significant non-linearity and time-varying uncertainty, making it difficult for traditional linear prediction methods to capture the underlying deep dynamic patterns. Therefore, this paper proposes a stacked Long Short-Term Memory (LSTM) prediction model integrated with an attention mechanism [24]. This model utilizes historical operation data to accurately predict battery-swapping demand for future time intervals.

To ensure that the temporal resolution of the prediction model aligns with the physical operational characteristics of the BSS, this paper first defines the prediction time step. The model discretizes the 24-h day into T equal-length intervals. To achieve temporal consistency in the operation scheduling of the BSS, the time intervals are segmented based on battery charging characteristics. The interval step size, denoted as tp (in minutes), is calculated according to Eq. (5):

(5)tp=WBPce×60

where: WB denotes the rated capacity of the battery; Pce represents the rated charging power of the battery swapping station. The day is discretized into multiple equal-length time intervals starting from 00:00. If the final interval of the current day is shorter than a complete time step tp, it is completed using time from the subsequent day.

On this basis, a multi-dimensional feature matrix is constructed as the model input. Given the significant periodicity and regularity exhibited by the battery-swapping demand of electric heavy-duty trucks, the input features are primarily composed of historical battery-swapping order sequences and multi-dimensional temporal features. Specific time-step information is included in the temporal features, and workdays and non-workdays are also explicitly distinguished. After being standardized, the operational and scheduling patterns of electric heavy-duty trucks across different day types and time periods can be effectively reflected by these multi-dimensional features, whereby rich contextual information is provided for the model to capture deep dynamic time-series patterns.

The backbone of the prediction model adopts a stacked LSTM structure to hierarchically extract the temporal features of battery-swapping demand. The lower-layer LSTM captures short-term intraday fluctuation characteristics, while the upper-layer LSTM focuses on learning long-term inter-day patterns. Furthermore, considering the peak load characteristics of EHDT battery-swapping demand, this paper incorporates an attention mechanism at the LSTM output layer. This mechanism performs adaptive weighting on the hidden state sequence H={h1,h2,…,hL} output by the LSTM, enabling the model to focus on the historical time steps that are most relevant to the current prediction time t. At time t, for the i-th historical hidden state hi, its normalized weight coefficient αt,i is calculated via the Softmax function:

(6)αt,i=exp⁡(score(ht,hi))∑j=1Lexp⁡(score(ht,hj))

where: L denotes the length of the input time window; score(⋅) represents a correlation scoring function used to evaluate the significance of the hidden state hi at historical time step i regarding the prediction result at the current time step t; ht represents the LSTM hidden state at the current prediction time t; hi and hj represent the i-th and j-th historical hidden states within the sequence H, respectively.

Based on the calculated weights, the context vector ct, which encodes key historical information, is obtained via a weighted summation:

(7)ct=∑i=1Lαt,ihi

where: ct denotes the context vector at prediction time t.

Finally, the context vector is fed into a fully connected layer for decoding, which outputs the predicted value of basic battery-swapping demand for the current time interval, denoted as Np. To fully account for the uncertainty in BSS operations, a statistical analysis method is simultaneously employed to extract historical extreme scenarios. The maximum historical battery-swapping frequency for each time interval is defined as the predicted extreme demand value, denoted as Nm. This realizes a dual-demand prediction framework that balances both baseline battery-swapping demand and extreme scenarios. The structure of the LSTM-Attention model is illustrated in Fig. 2.

To ensure uninterrupted battery swap service, the following battery dispatch strategy is formulated for the current period. This strategy dynamically adjusts the battery status and types based on the actual battery swap demand, building upon the day-ahead forecasting output. Relevant parameter values are set as follows: SOChigh=90% and SOCemerg=85% as the minimum SOC threshold for emergency battery swaps. Pch,max is the maximum charging power, WB is the battery rated capacity, and twait is the maximum driver waiting time, which is set to 15 min.

Each time a battery swap demand occurs, it checks whether the current number of available fully charged Category 1 batteries Nf is greater than 0, i.e.,

(8)Nf>0

If condition (8) is not satisfied, the emergency adjustment strategy is triggered. First, it determines whether the number of Category 2 batteries in the station satisfies:

(9)Nd≥1

If condition (9) is satisfied, Emergency Battery Adjustment Strategy 1 is adopted; if condition (9) is not satisfied, Emergency Battery Adjustment Strategy 2 is implemented. (a)

Battery Emergency Adjustment Strategy 1: When a battery swap demand occurs at the station but the number of Category 1 batteries is zero—meaning there are no batteries with SOCi≥SOChigh available for swapping—the battery with the highest SOC among Category 2 batteries is selected and denoted as battery j, with its SOC denoted as SOCj:

(10)j=arg max SOCi(t)i∈Ωd

Its target SOC is set to SOChigh, and it is charged immediately at the maximum power Pch,max. The required charging time is:

(11)tch,II=(SOChigh−SOCj)×WBPch,max×100

The quantities of each battery category are updated as follows:

(12)Nd(t)′=Nd(t)−1

(13)Nf(t)′=Nf(t)+1

If this condition is not satisfied, the newly depleted battery is removed from the vehicle, put into charging, its SOC target is set to SOChigh=90%, and it is classified as a Category 1 battery.

(a)

Battery Update Strategy 1: To ensure that the basic battery swap demand for the next period Np,next is met, the number of fully charged batteries remaining in the current period, combined with those being charged and converted to Category 1, must satisfy the requirement. Before the end of the current period t, ensure:

(19)Nf+N1,ch≥Np,next

where: N1,ch denotes the number of batteries already designated as Category 1 and currently under charging during this period.

If condition (19) is not satisfied, calculate the battery shortfall:

(20)ΔNf=Np,next−(Nf+N1,ch)

Then select the ΔNf batteries with the highest SOC from Category 3, charge them to convert to Category 1, and set their target SOC to SOChigh. (b)

Battery Update Strategy 2: To address potential extreme battery swap demand Nm,next in the next period, ensure that the sum of the remaining fully charged batteries, Category 2 batteries, and the number of batteries undergoing charging to be converted to Category 2 in the current period satisfies the following condition before the end of period t:

(21)Nf+Nd+Nch≥Nm,next

(22)Nch=N1,ch+N2,ch

where: N2,ch represents the number of batteries already designated as Category 2 and currently under charging in this period; Where Nch represents the total number of batteries transitioning from the charging state to Category 1 and Category 2.

If condition (21) is not satisfied, calculate the battery shortfall:

(23)ΔNd=Nm,next−(Nf+Nd+Nch)

Then select the ΔNd batteries with the highest SOC from Category 3 and charge them to convert to Category 2 batteries. Their target SOC should fall within the range SOClow≤SOCtarget<SOChigh.

The overall battery scheduling strategy is illustrated in Fig. 3 below:

Heavy-duty truck battery swapping stations need to optimize the scheduling of the battery charging and discharging process to maximize their responsiveness to grid frequency regulation demands while ensuring user battery swap services. This aims to achieve the maximization of the station’s revenue.

The objective function is to maximize the net revenue of the swap station:

(24)maxF1=f1+f2−f3−f4

f1 is defined as the total charges paid by EV users per swapping event, consisting of two components: the swapping service fee and the electricity consumption fee, i.e.,

(25)f1=∑t=1T(αswapR(t)+∑i=1R(t)λs[1−SOCi,t]WB)

where: αswap is the fee per swap service, R(t) is the actual number of battery swaps; λs is the retail electricity price for battery charging; SOCi,t is the battery state of charge of vehicle i during the battery swap in time period t; WB is the rated capacity of the battery. Constant power charging is assumed.

f2 represents the revenue from the battery swapping station’s participation in auxiliary frequency regulation services. Frequency regulation revenue includes capacity revenue and mileage revenue. Capacity revenue refers to the income earned by reserving adjustable capacity for frequency regulation services, while mileage revenue refers to the income earned based on the sum of the absolute values of upward or downward power adjustments in response to frequency regulation signals:

(26)f2=∑t=1T(Rcap,t+Rperf,t)

(27)Rcap,t=Pcap,t×λcap,t×T

(28)Rperf,t=Dmile,t×λmile,t×Kperf,t

where: Rcap,t is the frequency regulation capacity revenue in time period t; Rperf,t is the frequency regulation mileage revenue in time period t; Pcap,t is the awarded frequency regulation capacity bid submitted by the battery swapping station to the grid in time period t; λcap,t and λmile,t are the compensation prices for frequency regulation capacity and mileage in the frequency regulation market for time period t, respectively; Kperf,t is the frequency regulation performance coefficient; Dmile,t is the actual frequency regulation mileage completed in time period t; T is the service duration (in hours).

f3 represents the electricity purchasing cost of the battery swapping station, i.e.,

(29)f3=∑t=1TPBSS,tλbuy(t)

where: PBSS,t is the total charging power in time period t; λbuy(t) is the electricity purchasing price.

f4 represents the cost associated with the risk of load curtailment. To prioritize user battery swap services, this term economically quantifies the positive deviation between the forecasted demand and the actual number of available fully charged batteries using a relatively large penalty factor. This effectively mitigates the risk of battery swap failures resulting from excessive pursuit of frequency regulation revenue:

(30)f4=β∑t=1Tmax(0,NP,t−N1,t)

where: β is the penalty coefficient; NP,t represents the forecasted basic battery swapping demand at time t; and N1,t represents the number of Category 1 batteries at time t.

Overall, the priority order of the aforementioned four key factors is clearly defined by the proposed model through the objective function and various constraints. First, guaranteeing the heavy-duty truck swapping demand is set as the highest priority of the system; this bottom line is not only restricted by strict physical constraints but also reflected in the penalty term formulated in Eq. (30). Second, owing to the high economic compensation provided by the auxiliary service market (Eqs. (26)–(28)), flexible batteries will be prioritized and dispatched by the optimization model to respond to grid frequency regulation, thereby maximizing the overall net revenue. Finally, the response to TOU prices is adopted as the fundamental cost-reduction measure of the system, whereby operational costs are further controlled under the premise that the preceding two high-priority tasks are satisfied.

(a)

Battery Quantity Constraint:

(31)N=Nf(t)+Nd(t)+Nc(t)

where: N represents the total number of batteries in the swap station.

where: Pch,i,t is the charging power of battery 1 in time period t; Pdis,i,t is the discharging power of battery i in time period t; Pch(t) and Pdis(t) are the total charging and total discharging power in time period t, respectively; Pdis,max denotes the maximum discharge power. (c)

SOC Constraint:

(37)SOCi,t+1=SOCi,t+Pch,i,tηchΔt−(Pdis,i,t/ηdis)ΔtWB

(38)SOCmin≤SOCi≤SOCmax,∀i∈N,∀t

where: SOCi,t denotes the state of charge of the i-th battery at time step t; ηch and ηdis represent the constant charging and discharging efficiencies, respectively. (d)

Declared Frequency Regulation Capacity Constraints:

(39)0≤Pcap,tup≤∑i∈Ωd(t)Pdis,i,t

(40)0≤Pcap,tdown≤∑i∈Ωd(t)Pch,i,t+∑i∈Ωc(t)Pch,i,t

where: Pcap,tup represents the declared upward frequency regulation capacity at time t; and Pcap,tdown represents the declared downward frequency regulation capacity at time t. (e)

Transformer Capacity Constraint:

(41)Pcz(t)≤PT,max

where: Pcz(t) is the total input power of the battery swapping station at time t, and PT,max is the capacity limit of the transformer equipped at the station.

The objective of the real-time phase is to mitigate power fluctuations caused by day-ahead prediction errors, ensuring that the actual operation closely tracks the day-ahead plan to reduce economic losses due to uncertainty, while also responding to the real-time AGC instructions issued by the distribution grid. The optimization model aims to minimize the deviation between the real-time output and the day-ahead plan, as well as the deviation in responding to actual frequency regulation instructions. The model is formulated as follows:

(42)minF2=∑t=1T[λ1(PBSS,t−P∗BSS,t)2+λ2Cfe,t]

where: PBSS,t is the actual power of the battery swapping station during the intraday time period t; P∗BSS,t is the power scheduled for time period t obtained from day-ahead optimization; λ1 and λ2 are deviation coefficients; Cfe,t is the penalty term for deviations in responding to frequency regulation instructions, expressed as:

(43)Cfe.t=|∑i=1N(Pi,tup−rtfu+Pi,tdown−rtfd)|

where: Pi,tup and Pi,tdown are the actual upward and downward frequency regulation outputs provided by batteries; rtfu and rtfd are the real-time upward and downward frequency regulation instruction values issued by the grid.

(a)

Response to Frequency Regulation Signal Constraints:

When responding to AGC instructions, the battery swapping station must not exceed its maximum frequency regulation capacity while tracking the frequency regulation commands.

(44){0≤Pi,tup≤Pi,tup,max, 0≤Pi,tdown≤Pi,tdown,max∑i=1NPi,tup≤rtfu, ∑i=1NPi,tdown≤rtfdPi,tup⋅Pi,tdown=0

where: Pi,tdown,max and Pi,tup,max denote the maximum upward and downward frequency regulation of the i-th battery at time t.

The remaining constraints remain consistent with the day-ahead constraints.

The frequency regulation capacity declared by the BSS is shown in Fig. 6. The figure shows the declared upward and downward regulation capacities in each time period and their relationship with the battery swapping demand. As can be observed from Fig. 6, the declared upward and downward regulation capacities of the BSS exhibit a clear negative correlation with battery swapping demand. The overall trend indicates that higher battery swapping demand corresponds to lower declared frequency regulation capacity. Conversely, when battery swapping demand is low, a higher regulation capacity is declared to increase revenue from frequency regulation services. For example, during time periods 3 and 4, the swapping demand reaches the daily peak, and the corresponding declared regulation capacities in these two periods are extremely low. During time periods 6 to 11, the swapping demand remains at a relatively low level, and thus the declared regulation capacity stays at a high level. These results verify the flexibility of the proposed day-ahead optimization strategy, which ensures swapping service reliability while increasing economic benefits by allocating more regulation capacity during low-demand periods.

Fig. 7 shows the baseline charging schedule of the BSS under multiple constraints, which exhibits a clear stepwise pattern. The system responds to TOU electricity prices by charging at high power during off-peak periods. For instance, the charging power increases significantly during periods 2–5 and reaches its daily peak at 05:00, effectively utilizing low-cost electricity and preparing sufficient energy for the morning swapping demand peak. In contrast, charging power is reduced during high-price periods, such as 9–10 and 21–22, to lower electricity costs. However, the charging strategy is not solely driven by price signals, as it is also constrained by swapping demand and frequency regulation requirements. During high-demand periods, the system performs advanced charging even at higher prices to avoid service interruption penalties, highlighting the trade-off between reliability and economic efficiency. Moreover, the baseline power reserves adequate flexibility for real-time AGC response, enabling coordinated optimization of electricity price arbitrage and ancillary service provision.

Fig. 8 illustrates the overall operational profiles of the battery swapping station. Fig. 8a presents the total equivalent charging and discharging power of the station, while Fig. 8b shows the average SOC of the station at the initial time step. In Fig. 8a, the green bars represent the maximum charging power that can be provided by the station in each period. It should be noted that the red bars do not indicate continuous net discharging power; instead, they represent the maximum equivalent discharging power reserved by the station. This capacity comprises the actual power injected into the grid and the reduction in scheduled charging power. In practice, the regulation is primarily achieved by reducing the baseline charging power, and only when the required regulation exceeds the total scheduled charging power in a given period is short-term reverse discharging of batteries additionally employed. Overall, the charging load is shifted forward to low electricity price periods or delayed to flat-price periods along the time dimension, thereby avoiding operation during peak price periods and reducing cost pressure. Meanwhile, this flexibility enables valuable downward frequency regulation capacity to be provided to the grid. For example, during peak price periods (11:00–14:00 and 18:00–20:00), charging behaviors are shifted forward or delayed, which effectively contributes to system stability by providing downward regulation capacity.

Fig. 8b presents the overall SOC profile of the station along with the number of batteries reserved for participation in discharging. To prioritize the battery swapping demand of heavy-duty trucks, only a limited number of batteries are scheduled to participate in V2G discharging. Throughout the day, the station’s overall SOC is maintained within the range of 40%–90%. During peak swapping periods (e.g., Periods 3 and 4), a high SOC is maintained, and no frequency regulation discharging service is provided. In contrast, during low swapping demand periods when upward regulation is required by the grid (e.g., Periods 18 and 19), support is provided through reduced charging power and limited short-term battery discharging, during which the overall SOC decreases but remains above 50%. In general, the optimized strategy effectively shifts the charging load to non-peak electricity price periods, thereby reducing operational costs while simultaneously ensuring both the battery swapping demand for heavy-duty trucks and reliable frequency regulation support for the grid.

As shown in Table 4, the revenues of the battery swapping station before and after optimization are compared. In the day-ahead optimized scenario, the station obtains 4278.35 CNY from frequency regulation services. Although electricity purchasing costs increase, the ancillary service revenue offsets the additional cost, resulting in a net profit of 8960.75 CNY. In contrast, the non-optimized scenario has lower charging costs (3971.45 CNY) but no regulation revenue, leading to lower overall profit. These results indicate that the proposed frequency regulation participation strategy can significantly improve the economic performance of the battery swapping station.

To verify the economic adaptability of the proposed framework, a sensitivity analysis on regulation prices is conducted in this section. With other parameters kept constant, the baseline prices (0.035 CNY/kW for regulation capacity and 0.05 CNY/kW for mileage) are scaled by ±40%, respectively. The results are summarized in Table 5.

The data indicate that price signals are effectively responded to by the proposed model. As regulation compensation increases, the scheduling priority is tilted toward ancillary services. In the scenario with higher regulation prices, although the procurement cost slightly rises to 5827.74 CNY due to the enhancement of regulation capacity, the total profit increases by approximately 25.5%. Conversely, when the regulation prices decrease, the declared capacity is reduced by the model to focus on minimizing procurement costs via peak-valley price differentials. Throughout all scenarios, the swapping service revenue remains constant, validating the strategy’s capability in prioritizing swapping demand while flexibly allocating resources and synergistically optimizing multi-objective revenues.

Due to the uncertainty of user swapping demand, although day-ahead forecasting is performed, there are inevitable deviations between the actual number of battery swaps and the predicted results. In addition, the real-time AGC signals issued by the grid may also differ from the day-ahead AGC signals. Therefore, intraday real-time adjustments are required. Through the battery scheduling strategy and intraday optimization, the charging and discharging power of the station’s battery system is adjusted to rapidly respond to AGC signals while ensuring user swapping demand, thereby ensuring close consistency between the regulation market response and the actual AGC commands.

As shown in Fig. 9, the battery swapping station is able to effectively track the AGC signal during most periods, with the actual regulation power closely following the command curve, demonstrating good dynamic response and tracking performance. However, during the period of 18:00–19:00, the regulation output decreases to a certain extent, leading to deviations in responding to upward regulation commands. This is mainly due to the significantly increased swapping demand during 16:00–17:00, which reduces the available battery resources for frequency regulation as the system prioritizes the reliability of swapping services, thereby limiting the regulation capability in subsequent periods. This phenomenon indicates a trade-off between battery swapping service provision and frequency regulation performance, while also demonstrating the adaptability of the proposed strategy in dynamically allocating battery resources under different operating conditions.

Table 6 presents a comparison of the revenue results of the battery swapping station after day-ahead and intraday optimization. It can be observed that the net profit in the intraday stage is 8223.46 CNY, which is only reduced by 8.23% compared with the day-ahead plan but increased by 28.56% compared with the unoptimized system. This verifies the economic stability of the proposed model in real-time operation. Due to the uncertainty of user swapping behavior, the intraday adjustment strategy prioritizes swapping service reliability by reducing real-time frequency regulation capacity, resulting in a decrease in total regulation revenue to 3796.98 CNY and the introduction of certain penalty costs. However, this strategy successfully avoids the risk of energy replenishment shortages caused by a sudden increase in vehicle arrivals, and the overall revenue of the battery swapping station remains considerable.