Modeling method of multi-time-sequence EV equivalent power supply model considering vehicle travel rule

Abstract

A multi-time-sequence EV equivalent power supply model modeling method considering a vehicle travel rule comprises the following steps: according to dynamic evolution characteristics of the travel rule of an electric vehicle user, combining travel sample data, dividing into a summer scene and a winter scene according to seasons, and dividing into a workday scene and a holiday scene according to a time sequence to complete data fitting; then, a vehicle travel state transition matrix is established through a semi-Markov chain SMC, and a Monte Carlo method MCM is utilized to perform random simulation on vehicle behaviors to obtain available discharge capacities of the electric vehicles at all moments, so that an electric vehicle cluster in a region is equivalent to a time-varying power supply model, and a multi-time-sequence EV equivalent power supply model is established; according to the method, by introducing a semi-Markov chain and a Monte Carlo random simulation method, available energy storage capacity distribution characteristics of an electric vehicle group in different scenes are described. The model can reflect energy storage laws of residential areas, working areas and shopping areas in different seasons and days, and dynamic quantitative evaluation of the EV available power potential is realized.

Description

Modeling Method of Multi-Time-Sequence EV Equivalent Power Supply Considering Vehicle Travel Patterns Technical Field

[0001] This invention relates to the field of power system and electric vehicle V2G cooperative scheduling technology, specifically to a multi-time-series EV equivalent power source modeling method that considers vehicle travel patterns. Background Technology

[0002] With the rapid expansion of electric vehicle (EV) fleets and the maturity of V2G technology, EVs are gradually evolving from transportation tools into distributed energy storage and flexible regulation resources within the power system. Leveraging their bidirectional energy flow capabilities, EVs can charge during off-peak hours and discharge during peak hours, participating in peak shaving and supply-demand balancing. In sudden power outages or disaster scenarios, they can also support critical loads through group collaboration, enhancing system resilience. However, existing research primarily focuses on energy optimization and scheduling under normal operating conditions, paying insufficient attention to emergency recovery after power outages. Furthermore, it lacks system modeling for multi-temporal characteristics, seasonal differences, and vehicle dynamic availability, limiting the efficient utilization of EV resources in emergency scenarios.

[0003] Existing emergency power supply models typically employ static or single-moment equivalent power descriptions, which fail to capture the dynamic characteristics of vehicle travel and charging / discharging behavior. This leads to biases in available power assessments and impacts dispatch efficiency. Load-side assessments are also largely based on static or averaging methods, failing to adequately reflect load importance, continuous demand, and temporal variations. Consequently, limited power sources are difficult to allocate accurately, making it challenging to balance reliability and economy. Summary of the Invention

[0004] To overcome the problems of static emergency power supply models for electric vehicles (EVs), incomplete load loss assessment, and lack of multi-time-series adaptability in existing technologies, this invention proposes an EV-EPSV collaborative grid power restoration strategy. This strategy establishes a multi-time-series EV equivalent power source model and constructs a load loss assessment system to propose a method for the collaborative optimization scheduling of EVs and emergency power supply vehicles, thereby achieving efficient allocation of limited power resources and improving power restoration efficiency. It can effectively enhance the scheduling flexibility of EV resources and the resilience of the power grid in the event of a sudden power outage.

[0005] The technical solution adopted in this invention is as follows: a power grid power restoration strategy for electric vehicles (EVs) cooperating with EPSVs in multiple time domains, including the following steps: Step 1: In the event of a power grid outage, establish a multi-time-series EV equivalent power supply model based on the travel patterns of EV users in typical travel scenarios; Step 2: Construct a load importance index system and, in conjunction with load capacity and outage duration, establish a load outage loss model to quantitatively calculate the economic and social losses of different types of loads during multi-time-series outages; Step 3: Construct an optimized power supply model for the collaboration between EVs and EPSVs to achieve static power allocation for EVs and dynamic path and power optimization scheduling for EPSVs.

[0006] Step 1, which considers the multi-temporal EV equivalent power model modeling method based on vehicle travel patterns, includes the following steps: S1: Based on the dynamic evolution characteristics of electric vehicle user travel patterns and combined with NHTS2017 travel sample data, the data is divided into summer and winter scenarios by season and weekday and holiday scenarios by time series to complete data fitting; S2: Then, a vehicle travel state transition matrix is ​​established through a semi-Markov chain (SMC), and the vehicle behavior is stochastically simulated using the Monte Carlo method (MCM) to obtain the available discharge capacity of electric vehicles at each time point, thereby equating the electric vehicle cluster in the region to a time-varying power model; and then establishing a multi-temporal EV equivalent power model.

[0007] In step 1, in order to characterize the travel patterns of electric vehicle users under different seasons and time periods, the travel sample data of NHTS2017 is first divided into summer and winter scenarios according to season, and into weekday and holiday scenarios according to time period, thus forming four typical travel scenarios.

[0008] For each typical travel scenario, samples of departure and arrival times of electric vehicle users are extracted, and a weighted model is performed using a Mixture of Wrapped Gaussians (MWG) model. The probability density function is shown in Equation (1): (1); In formula (1): Let be the probability density function of scene s, region k, and behavior type q at time t; This indicates the number of Gaussian components used in scene s, region k, and behavior type q; The weights of each component satisfy the following conditions: , ; and These represent the center (hours) and standard deviation of the component, respectively. To wrap around the Gaussian kernel, it is used to achieve 24-hour periodization and ensure the continuity and uniformity of the distribution in the interval [0,24); t represents the corresponding intraday time, with a value range of 0–24 hours in the periodic interval; s represents four typical operating scenarios: summer, winter, weekday, and holiday; k represents three typical areas: residential area, work area, and shopping area; q represents the behavior type, used to distinguish the two types of vehicle usage behavior of electric vehicles: departure and arrival. This represents the index of the c-th Gaussian component in the Gaussian mixture.

[0009] To further avoid the distortion of the distribution of electric vehicle departure / arrival times at the 24-hour boundary and to maintain periodic consistency, the wrap-around Gaussian kernel function is defined as shown in equation (2): (2); In formula (2): The wrapping Gaussian kernel function has a period of 24 hours; t is the time variable (unit: h); μ and σ are the mean and standard deviation, respectively; m is the 24-hour shift index used for periodic extension of the time axis; Let Z represent the set of integers, i.e., Z = {…, −2, −1, 0, 1, 2, …}.

[0010] When the sample size is small or there is morphological skew, the Periodic Kernel Density Estimation (PKDE) method is used for smooth estimation, and its expression is shown in Equation (3): (3); In formula (3): Let be the periodic kernel density function under scene s, region k, and behavior type q; This represents the total number of samples used for periodic kernel density estimation; h is the bandwidth parameter. Let m represent the i-th sample time; m∈{−1,0,1} is the periodic translation term, used to smoothly connect at the [0,24] boundary; This represents an exponential function with base e, i.e., 𝑒 (⋅) .

[0011] By combining equations (1) to (3) with the Gaussian mixture model and the periodic kernel density estimation, a time distribution function that is both smooth and consistent with the 24-hour cycle can be obtained under different sample sizes and morphological conditions, providing a unified input for subsequent statistical modeling of travel chains and dwell time.

[0012] In step 1, after completing the data fitting, a mathematical model of multi-time series electric vehicle travel behavior is established based on the vehicle transition kernel matrix of the semi-Markov chain (SMC) and the Monte Carlo method (MCM). To avoid symbol redundancy, the scenario subscript s is omitted in the derivation of the semi-Markov chain transition matrix and the Monte Carlo region state matrix below, but the actual calculations are constructed under four typical scenarios (summer, winter, weekday, and holiday). First, the time-related transition probability of the vehicle between three areas: residential area, work area, and shopping area is described by the semi-Markov chain. Then, the definition of the vehicle semi-Markov kernel matrix can be shown in equation (4): (4); In formula (4): Let be the semi-Markov transition kernel matrix at time t; This represents the probability that an electric vehicle will move to region n when it is in region m and its dwell time does not exceed t. It also describes the probability of moving from m to n and the distribution of dwell time in that state. Here, m, n∈{1,2,3}, and regions 1 / 2 / 3 correspond to residential area / work area / shopping area, respectively.

[0013] After obtaining the transition kernel matrix, in order to obtain the group-level time-series trajectory samples, the Monte Carlo Method (MCM) is used to randomly sample and evolve the vehicles' states. The vehicle state matrix for 24 hours in a day is defined as shown in Equation (5): (5); In formula (5): For the vehicle state matrix; Let represent the region i where the j-th electric vehicle is located at time t, where i = 1, 2, 3: represents the region number, 1 represents a residential area, 2 represents a work area, 3 represents a shopping area; t = 1, 2, ..., 24: represents the 24 hours of the day; j represents the j-th electric vehicle, j = 1, 2, ..., , This indicates the total number of electric vehicles included in the statistical sample.

[0014] The semi-Markov kernel matrix of the vehicle given in equation (4) provides a probability-driven approach, while the vehicle state matrix given in equation (5) carries the temporal distribution of the group obtained through Monte Carlo sampling. Together, they constitute the core input and output of the multi-temporal electric vehicle travel chain model and provide a complete spatiotemporal statistical basis for the equivalent power source model.

[0015] In step 1, for the sake of simplicity, the scenario subscript 's' will not be explicitly labeled below, but all calculations are performed separately for the four scenarios. Based on this vehicle state matrix... It is possible to count the number of vehicles and their proportion in each region at any given time, and then construct the available power model of the electric vehicle group, as shown in equation (6): (6); In formula (6): Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. Let k ∈ {1,2,3} represent the regional state of the vehicle at time t; k ∈ {1,2,3} correspond to the residential area, the work area, and the shopping area, respectively; t ∈ {1,2,…,24} is the time index.

[0016] According to the definition in equation (6), the number and proportion of vehicles in the area can be calculated, as shown in equations (7) and (8) respectively: (7); (8); In the above formula: Let be the number of vehicles in region k at time t; This represents the percentage of vehicles in the area. Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This represents the total number of electric vehicles included in the statistical sample.

[0017] The above results characterize the spatial distribution pattern of vehicles over 24 hours, laying the foundation for calculating the available power of the electric vehicle group. In power aggregation calculation, not all vehicles in the stationary area can immediately participate in V2G discharge. Discharge availability is constrained by the battery state of charge (SOC). Let the upper and lower limits of SOC be Y1 and Y2, respectively, then the discharge state function of the j-th vehicle at time t is defined as shown in equation (9): (9); In equation (9): It is the discharge state function; Let j be the state of charge of the j-th vehicle; and These are the lower discharge threshold and the upper charge threshold, respectively, satisfying... .when At that time, the vehicle is allowed to discharge; when At this time, charging is only allowed; when When the value is between the two thresholds, the vehicle is in standby mode and is not included in the discharge set.

[0018] Combining equations (6) and (9), the number of vehicles that can participate in the discharge in region k at time t can be calculated, as shown in equation (10): (10); In formula (10): Let k be the number of vehicles that can discharge at time t. This is a region indicator function, indicating whether the j-th vehicle is stationary and located in region k at time t; Let {1} be the discharge state function; let {1} be the indicator function, if and only if the vehicle satisfies the discharge availability condition of equation (9). The value is 1.

[0019] To further consider the randomness of vehicle participation in V2G behavior, a Bernoulli random variable is introduced. This indicates whether the vehicle participates in the actual discharge. It follows the parameter... The Bernoulli distribution is shown in equation (11): (11); In formula (11): This indicates whether the j-th vehicle participates in the discharge at time t, with 1 indicating participation and 0 indicating non-participation; The average participation rate of the group reflects the probability that a vehicle will participate in V2G when it is in a state where it can be discharged. This represents a Bernoulli distribution, and the output is a random variable of 0–1.

[0020] Based on equation (11), the expected number of vehicles that can be discharged at a given time in the region can be calculated, as shown in equation (12): (12); In formula (12): For expectation operators; Indicates the proportion of group discharge participation; This represents the number of vehicles in region k at time t; Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This indicates whether the j-th vehicle participates in the discharge at time t, with 1 indicating participation and 0 indicating non-participation.

[0021] Equation (12) shows that under large sample conditions ( The average effect of random participation in a group is equivalent to that of proportional participation. Scaling the number of vehicles occupying a region provides a resolvable input for subsequent power aggregation.

[0022] Once the number of vehicles capable of discharging is determined, power layer aggregation can be further performed. Let the rated discharge power of a single vehicle be... Then the instantaneous equivalent output power of region k at time t is shown in equation (13): (13); In formula (13): Let be the equivalent discharge power of region k; This refers to the rated discharge power of a single vehicle. The total number of electric vehicles included in the statistics; approximation symbol " "This means that, in the sense of the population average, the expected value is used to replace the fluctuations caused by sample randomness.

[0023] At the population average level, taking the mathematical expectation of equation (13), we can obtain the expected form of regional power as shown in equation (14): (14); In formula (14): Let k be the average equivalent power in region k at time t; The mathematical expectation of the total number of vehicles in region k at time t; This represents the percentage of vehicles in the area.

[0024] Finally, by superimposing the power of the three types of areas—residential area, work area, and shopping area—the total equivalent output power of the system can be obtained, as shown in equation (15): (15); In formula (15): Let be the total equivalent output power of the system at time t.

[0025] By combining vehicle travel chains, SOC constraints, participation probabilities, and power aggregation using formulas (1) to (15), a multi-time-series electric vehicle (EV) equivalent power source model was established to describe the temporal behavior characteristics of the group. This model can dynamically characterize the available discharge capacity of electric vehicle groups in different regions, providing a reliable quantitative basis for load regulation and energy storage optimization on the grid side.

[0026] This invention presents a collaborative power grid power restoration strategy for electric vehicles considering multi-time-domain EV-EPSV, with the following technical effects: 1) This invention establishes a multi-time-series EV equivalent power source model considering vehicle travel patterns. By introducing a semi-Markov chain and Monte Carlo stochastic simulation method, the distribution characteristics of available energy storage capacity of electric vehicle groups under different scenarios are characterized. This model can reflect the energy storage patterns of residential areas, work areas, and shopping areas under different seasons (summer, winter) and day types (weekdays, holidays), realizing a dynamic quantitative assessment of the potential of available power sources for EVs. The advantages of this modeling method are: ① It overcomes the shortcomings of traditional static capacity models that cannot reflect the spatiotemporal travel characteristics of vehicles; ② Through multi-time-series probabilistic modeling, the energy storage dispatchability assessment is closer to real operation; ③ It provides a quantifiable spatiotemporal energy supply boundary for subsequent emergency power dispatch.

[0027] 2) This invention constructs a multi-dimensional load power outage loss assessment system, realizing the comprehensive quantification of load importance and time dimension. By introducing a load importance index system, a quantitative calculation model for load power outage loss is established. The model is based on load type, outage duration, and regional characteristics, comprehensively considering three dimensions: life safety, economic loss, and social impact, and realizes the priority division of loads in multiple regions.

[0028] 3) This invention proposes a multi-time-sequence electric vehicle collaborative emergency power supply optimization strategy to achieve multi-stage and multi-regional dynamic power supply restoration. This strategy comprehensively considers the complementary characteristics of electric vehicles (EVs) and emergency power supply vehicles (EPSVs), constructing a two-stage collaborative optimization model based on a genetic algorithm (GA) and an adaptive large neighborhood search algorithm (ALNS): In the first stage, GA optimizes the static power allocation and node scheduling of EVs to improve local power supply coverage and energy utilization; in the second stage, ALNS optimizes the dynamic path and power allocation of EPSVs to achieve precise power supply replenishment to key areas. This collaborative model balances the timeliness and economy of system power supply, enabling a multi-stage recovery mechanism of "rapid response followed by flexible replenishment" after a grid failure.

[0029] 4) This invention achieves efficient and economical power restoration in multiple scenarios. Simulation analysis results across multiple scenarios (summer, winter, holidays, weekdays) and regions (residential areas, work areas, commercial areas) show that the collaborative restoration strategy improves the overall energy saving rate by 34%–70% compared to relying solely on the EV solution. Residential areas show the highest average energy saving rate (approximately 65%), work areas perform best on weekdays (approximately 50%), and shopping areas show a significant advantage on holidays (approximately 60%). This technology achieves continuity and smoothness in the power restoration process through rapid EV activation and subsequent EPSV support, effectively reducing energy lag and voltage fluctuations, thereby improving system resilience and operational stability.

[0030] 5) This invention forms a closed-loop system of model-evaluation-strategy, significantly improving the dispatchability and grid resilience of electric vehicles in emergency power supply. The strategy theoretically improves the research system for the coordinated recovery of distributed energy storage and mobile power sources, and has good scalability in engineering. This method ensures the reliability of emergency power supply while taking into account economy, flexibility, and universality, providing theoretical support and technical implementation path for the construction of new resilient distribution networks. Attached Figure Description

[0031] The invention will be further described below with reference to the accompanying drawings and examples; Figure 1 is a heat map of the entry and exit behavior and dwell time of electric vehicles in residential areas, work areas and shopping areas in summer.

[0032] Figure 2 shows a heat map of electric vehicle entry and exit behavior and dwell time in residential, work and shopping areas during winter.

[0033] Figure 3 shows the heat map of electric vehicle entry and exit behavior and dwell time in residential areas, work areas and shopping areas on weekdays.

[0034] Figure 4 shows the heat map of electric vehicle entry and exit behavior and dwell time in residential areas, work areas and shopping areas during holidays.

[0035] Figure 5 shows the equivalent power output curves of electric vehicles in residential, work, and shopping areas during the summer.

[0036] Figure 6 shows the equivalent power output curves of electric vehicles in residential, work, and shopping areas during winter.

[0037] Figure 7 shows the equivalent power output curves of electric vehicles in residential, work, and shopping areas during weekday scenarios.

[0038] Figure 8 shows the equivalent power output curves of electric vehicles in residential, work, and shopping areas during holidays.

[0039] Figure 9 is a schematic diagram of the network topology of the improved IEEE 33-node distribution network system.

[0040] Figure 10 shows the curves of load loss as a function of power outage duration for three types of areas: residential area, work area, and shopping area.

[0041] Figure 11 is a comparison of power loss losses between the residential area collaborative power supply restoration strategy and the traditional EV-only power supply solution in a summer scenario.

[0042] Figure 12 is a comparison of power loss between the collaborative power supply recovery strategy for the work area and the traditional EV-only power supply solution in a summer scenario.

[0043] Figure 13 is a comparison of power loss losses between the collaborative power supply restoration strategy for shopping areas and the traditional EV-only power supply solution in a summer scenario.

[0044] Figure 14 is a comparison of power loss losses between the residential area collaborative power supply restoration strategy and the traditional EV-only power supply solution in a weekday scenario.

[0045] Figure 15 is a comparison of power loss losses between the collaborative power supply recovery strategy for the work area and the traditional EV-only power supply solution in a weekday scenario.

[0046] Figure 16 is a comparison of power loss losses between the collaborative power supply restoration strategy for shopping areas and the traditional EV-only power supply solution in a weekday scenario.

[0047] Figure 17 is a flowchart of the GA-ALNS two-stage optimization algorithm for the multi-time-domain EV-EPSV collaborative power supply recovery strategy of the present invention. Detailed Implementation

[0048] This paper considers a multi-time-domain EV-EPSV collaborative power grid restoration strategy. First, based on the typical travel patterns of EVs in different seasons (summer and winter) and different day types (weekdays and holidays), a multi-time-series EV equivalent power source model is constructed, and the power supply capacity of the vehicles is modeled through vehicle parking characteristics. Second, for three typical areas—residential areas, work areas, and shopping areas—a multi-time-series load loss assessment system is established based on load capacity, importance, and outage duration, providing a quantitative basis for the subsequent zonal allocation of limited power supply resources. Finally, based on the multi-time-series EV equivalent power source model and the load loss assessment system, a multi-objective optimization model involving EVs and EPSVs is constructed. A genetic algorithm (GA) is used to complete the initial allocation of EVs, and then an adaptive large neighborhood search algorithm (ALNS) is used to optimize the path and scheduling tasks of EPSVs, aiming to minimize system load loss and improve power restoration efficiency. Multi-scenario simulations are conducted on the IEEE-33 node system to verify that the collaborative strategy of this invention has significant advantages in terms of restoration speed, power supply continuity, and economy.

[0049] (I) Multi-time series EV equivalent power supply model: The multi-time series EV equivalent power supply model is used to characterize the spatiotemporal distribution characteristics and power supply capabilities of electric vehicles under different seasons, different day types and different functional areas. This embodiment first divides the travel sample data of NHTS2017 into summer and winter scenarios according to season, and into weekday and holiday scenarios according to day type, thus forming four typical travel scenarios. For each scenario, the user departure and arrival time samples are extracted, and the Mixture of Wrapped Gaussians (MWG) model is first used for weighted modeling, and its probability density function is shown in Equation (1): (1); In formula (1): Let be the probability density function of scene s, region k, and behavior type q (departure / arrival) at time t; Number of mixed components; The weights of each component satisfy the following conditions: , ; and These represent the center (hours) and standard deviation of the component, respectively. To wrap around the Gaussian kernel, it is used to achieve 24-hour periodization and ensure the continuity and normalization of the distribution in the interval [0,24); t represents the corresponding intraday time, with a value range of 0–24 hours in the periodic interval; s represents four typical operating scenarios: summer, winter, weekdays and holidays; k represents three typical areas: residential area, work area and shopping area; q represents the behavior type, used to distinguish the two types of vehicle use behavior of electric vehicles: departure and arrival.

[0050] To further avoid distribution distortion at the 24-hour boundary and maintain periodic consistency, the wrap-around Gaussian kernel function is defined as shown in equation (2): (2); In formula (2): is a wrapping Gaussian kernel function with a period of 24h; t is the time variable (unit: h); μ and σ are the mean and standard deviation, respectively; m is the 24h shift index, used for periodic extension of the time axis.

[0051] When the sample size is small or there is morphological skew, the Periodic Kernel Density Estimation (PKDE) method is used for smooth estimation, and its expression is shown in Equation (3): (3); In formula (3): Let be the periodic kernel density function for scene s, region k, and behavior type q; N be the total number of samples; h be the bandwidth parameter; t be the periodic kernel density function for scene s, region k, and behavior type q ... j Let m be the j-th sample time; m∈{−1,0,1} is the periodic translation term used to smoothly connect at the boundary [0,24].

[0052] By using equations (1) to (3), and through joint modeling with the Gaussian mixture model and periodic kernel density estimation, a time distribution function that is both smooth and consistent with the 24-hour period can be obtained under different sample sizes and morphological conditions, providing input for subsequent vehicle travel chain probability transfer modeling.

[0053] After completing the data fitting, it is assumed that there are 10,000 electric vehicles participating in the operation scheduling in the study area, and the scheduling period is 24 hours a day. A mathematical model of multi-time series electric vehicle travel behavior is established based on the vehicle transition kernel matrix of the semi-Markov chain (SMC) and the Monte Carlo method (MCM). To avoid symbol redundancy, the scenario subscript s is omitted in the derivation of the semi-Markov chain transition matrix and the Monte Carlo region state matrix below, but the actual calculations are constructed under four typical scenarios (summer, winter, weekday, and holiday). First, the time-related transition probability of vehicles between three regions (residential area, work area, and shopping area) is described by the semi-Markov chain, and its vehicle state kernel matrix is ​​defined as shown in Equation (4): (4); In formula (4): Let be the semi-Markov transition kernel matrix at time t; (m,n∈{1,2,3}) represents the probability that an electric vehicle, when in region m, will move to region n with a dwell time not exceeding t. It simultaneously characterizes the probability of moving from m to n and the dwell time distribution in that state; regions 1 / 2 / 3 correspond to residential area / work area / shopping area, respectively.

[0054] After obtaining the transition kernel matrix, the Monte Carlo Method (MCM) is used to randomly sample and evolve the vehicles' states. For ease of statistical analysis and subsequent power aggregation, a vehicle state matrix is ​​defined for each of the 24 hours of the day, as shown in equation (5): (5); In formula (5): For the vehicle state matrix; Let represent the region i where the j-th electric vehicle is located at time t, where: i = 1, 2, 3: represent the region number (1 represents a residential area, 2 represents a work area, 3 represents a shopping area); t = 1, 2, ..., 24: represent the 24 hours of the day; j = 1, 2, ..., : indicates the j-th electric vehicle.

[0055] Based on equations (4) and (5), multiple rounds of Monte Carlo simulations were conducted to statistically analyze the number of entries and exits and the dwell time in different areas under each scenario. This yielded the following: Figures 1-4 show heatmaps of electric vehicle entry / exit behavior and dwell time in residential, work, and shopping areas under four typical time-series scenarios (summer, winter, holidays, and weekdays). Figures 1-4 show that: residential areas have the highest dwell probability in the early morning and evening, exhibiting a clear bimodal structure of early departure and late return; work areas have a high concentration of vehicles during the day on weekdays but are almost empty at night, with dwell characteristics highly consistent with the office cycle; shopping areas have a relatively dispersed vehicle dwell distribution, with a significantly increased dwell probability from afternoon to evening on holidays, reflecting the high activity level of commercial activities during holidays. These spatiotemporal distribution characteristics provide a statistical basis for subsequently equating vehicle behavior to time-varying power sources.

[0056] Based on the aforementioned multi-scenario travel time modeling and travel chain simulation, and using the time distribution of NHTS sample data, a time series simulation was performed combining a semi-Markov chain (SMC) and the Monte Carlo method (MCM) to obtain the regional state matrix of electric vehicles in a 24-hour discrete time series. Therefore, the state Z of the j-th vehicle in the region t∈{1,2,…,24} can be obtained. j (t)∈{1,2,3}, where 1, 2, and 3 represent the residential area, the work area, and the shopping area, respectively. This state matrix is ​​generated by SMC transition probabilities and MCM random sampling, providing basic data for constructing a multi-time-series electric vehicle equivalent power source model.

[0057] To statistically analyze the number of vehicles and their proportion in each region at any given time, a vehicle location indication function is defined, as shown in equation (6): (6); In formula (6): Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. Let k ∈ {1,2,3} represent the regional state of the vehicle at time t; k ∈ {1,2,3} correspond to the residential area, the work area, and the shopping area, respectively; t ∈ {1,2,…,24} is the time index.

[0058] According to the definition in equation (6), the number and proportion of vehicles in the area can be calculated, as shown in equations (7) and (8) respectively: (7); (8); Upper Middle: Let be the number of vehicles in region k at time t; This represents the percentage of vehicles in the area. Let $t$ be an indicator variable indicating whether the j-th electric vehicle is located in region $k$ at time $t$. $t$ is set to $1$ if and only if the j-th electric vehicle belongs to region $k$ in the hour $t$, otherwise $t$ is set to $0$. $k$ ∈ {1, 2, 3} corresponds to residential area, work area, and shopping area respectively. $t$ ∈ {1, 2, ..., 24} is the time index. This represents the total number of electric vehicles included in the statistical sample.

[0059] The above results characterize the spatial distribution pattern of vehicles over 24 hours, laying the foundation for calculating the available power of the electric vehicle group. In power aggregation calculation, not all vehicles in the stationary area can immediately participate in V2G discharge. Discharge availability is constrained by the battery state of charge (SOC). Let the upper and lower limits of SOC be Y1 and Y2, respectively, then the discharge state function of the j-th vehicle at time t is defined as shown in equation (9): (9); In equation (9): It is the discharge state function; Let j be the state of charge of the j-th vehicle; and These are the lower discharge threshold and the upper charge threshold, respectively, satisfying... .when At that time, the vehicle is allowed to discharge; when At this time, charging is only allowed; when When the value is between the two thresholds, the vehicle is in standby mode and is not included in the discharge set.

[0060] Combining equations (6) and (9), the number of vehicles that can participate in the discharge in region k at time t can be calculated, as shown in equation (10): (10); In formula (10): Let k be the number of vehicles that can discharge at time t. This is a region indicator function, indicating whether the j-th vehicle is stationary and located in region k at time t; Let {1} be the discharge state function; let {1} be the indicator function, if and only if the vehicle satisfies the discharge availability condition of equation (9). The value is 1 when ) This represents the total number of vehicles included in the statistics.

[0061] To further consider the randomness of vehicle participation in V2G behavior, a Bernoulli random variable is introduced. This indicates whether the vehicle participates in the actual discharge. It follows the parameter... The Bernoulli distribution is shown in equation (11): (11); In formula (11): This indicates whether the j-th vehicle participates in the discharge at time t (1 for participation, 0 for non-participation). The average participation rate of the group reflects the probability that a vehicle will participate in V2G when it is in a state where it can be discharged.

[0062] Based on equation (11), the expected number of vehicles that can be discharged at a given time in the region can be calculated, as shown in equation (12): (12); In formula (12): For expectation operators; Indicates the proportion of group discharge participation; This represents the number of vehicles in region k at time t; Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This indicates whether the j-th vehicle participates in the discharge at time t (1 for participation, 0 for non-participation). This represents the number of vehicles that can participate in the discharge; k∈{1,2,3} corresponds to the residential area, the work area, and the shopping area, respectively; t∈{1,2,…,24} is the time index; This represents the total number of electric vehicles included in the statistical sample.

[0063] This formula shows that under large sample conditions ( The average effect of random participation in a group is equivalent to that of proportional participation. Scaling the number of vehicles occupying a region provides a resolvable input for subsequent power aggregation.

[0064] Once the number of vehicles capable of discharging is determined, power layer aggregation can be further performed. Let the rated discharge power of a single vehicle be... Then the instantaneous equivalent output power of region k at time t is shown in equation (13): (13); In formula (13): Let be the equivalent discharge power of region k; This refers to the rated discharge power of a single vehicle. This represents the total number of electric vehicles included in the statistical sample. Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This indicates whether the j-th vehicle participates in the discharge at time t (1 for participation, 0 for non-participation). Indicates the proportion of group discharge participation; This represents the number of vehicles in region k at time t; the approximation symbol "". "This means that, in the sense of the population average, the expected value is used to replace the fluctuations caused by sample randomness.

[0065] At the population average level, taking the mathematical expectation of equation (13), we can obtain the expected form of regional power as shown in equation (14): (14); In formula (14): Let k be the average equivalent power in region k at time t; The mathematical expectation of the total number of vehicles in region k at time t; Indicates the proportion of group discharge participation; This refers to the rated discharge power of a single vehicle. This represents the total number of electric vehicles included in the statistical sample. This represents the percentage of vehicles in the area.

[0066] Finally, by superimposing the power of the three types of areas (residential area, work area, and shopping area), the total equivalent output power of the system can be obtained, as shown in equation (15): (15); In formula (15): This represents the total equivalent output power of the system at time t. Let t represent the equivalent discharge power of region k; k∈{1,2,3} corresponds to the residential area, work area, and shopping area, respectively; t∈{1,2,…,24} is the time index.

[0067] Based on the power aggregation model constructed by equations (7) to (15), the vehicle distribution and discharge capacity of residential areas, work areas, and shopping areas under four typical time-series scenarios—summer, winter, holidays, and weekdays—are calculated, resulting in the equivalent power output curves of electric vehicles in residential areas, work areas, and shopping areas shown in Figures 5 to 8. Figures 5 to 8 show that: the output of residential areas is most stable at night, with continuous power supply capacity from 22:00 to 6:00 the next day; the output of work areas exhibits a bi-peak structure, corresponding to morning and evening commuting peaks; the power of shopping areas is concentrated between 16:00 and 20:00, reflecting the short-term response characteristics of commercial activities. Seasonal comparisons show that the overall power output is higher in summer than in winter, indicating a more relaxed travel rhythm; in winter, vehicles stay in residential areas for longer periods, with charging and discharging activities concentrated at night. Regarding daytime differences, the activity level of shopping areas increases significantly during holidays, and the output curves of residential areas and shopping areas tend to be synchronized; while on weekdays, the power curves of residential areas and work areas show a significant complementary relationship, forming temporal energy coordination and balance.

[0068] This section establishes an EV equivalent power supply model with multiple scenarios, regions, and time sequences, providing time-varying energy boundary conditions for the construction of the load power loss assessment system in the subsequent section 2, and also laying the foundation for the optimization of the power supply restoration strategy of multi-time sequence electric vehicle collaborative emergency power supply vehicle in the third section.

[0069] (II) Multi-regional Load Importance Assessment and Power Outage Loss Modeling: Load power outage loss refers to the various economic and social losses caused by the inability of loads to operate normally during the period from the occurrence of a power outage to the restoration of power supply. To quantitatively characterize the differences in the impact of loads in different regions during the power outage process, this section first constructs a multi-dimensional load importance index system from three aspects: life safety, economic benefits, and social operation. For typical load scenarios, this invention takes the improved IEEE 33-node distribution network system as the research object. The example area is divided into three functional areas: residential area, work area, and shopping area. Power outage load points are set at nodes 21, 14, and 5. The network topology is shown in Figure 9. Assuming a sudden power outage event occurs at a specific time (12:00), the set of load importance factors is set as ε. i Furthermore, taking into account the differences in importance weights of different types of loads (residential area, work area, and shopping area loads), a calculation model for the load importance index is established, and its specific expression is shown in equation (16).

[0070] (16); In formula (16): This is the overall importance coefficient of the load; the larger the value, the higher the priority of this type of load in resource security and recovery. This is a safety amplification factor that only applies to the life / safety dimension; These are parameters for this type in terms of life / safety, economics, and special / social impact.

[0071] Equation (16) can be used to comprehensively measure the multidimensional sensitivity of load to safety, economy and society, and provide a priority quantitative basis for subsequent loss assessment.

[0072] To characterize the cumulative characteristics of economic losses during power outages over time, a load loss loss modeling system based on the time-rate-of-loss method is established. Let the rate of change of economic losses from load loss between adjacent time points be the "load loss rate of increase," and its calculation method is shown in equation (17): (17); In formula (17): For load type k in the interval Internal loss growth rate (unit: yuan / kW·min); The cumulative cost curve for nodes of load type k (yuan / kW); t s t s+1 These represent adjacent calculation times; s is the index of the s-th time interval.

[0073] Equation (17) provides the rate of increase of load loss over time, laying the foundation for subsequent cumulative loss calculations. To further reflect the role of different types of load capacity in the loss, a weighted model is introduced for comprehensive calculation, as shown in Equation (18): (18); In formula (18): The cumulative loss of load type k during the power outage duration d (unit: yuan). For the load capacity of type k; This is the overall importance coefficient of the load; the larger the value, the higher the priority of this type of load in resource security and recovery. For load type k in the interval Internal loss growth rate (unit: yuan / kW·min); Representing the interval [0,d] and the segment The effective overlap duration; s is the index of the s-th time interval.

[0074]

[0075]

[0076]

[0077] Based on the multi-area load importance and power outage loss model established by equations (16) to (18), and combined with the improved load composition structure of three typical areas (residential area, work area, and shopping area) in the IEEE 33-node system, according to the cumulative cost of various load nodes given in Table 1, the importance parameters for various loads given in Table 2, and the typical load capacity values ​​of the three types of areas given in Table 3, the power outage loss of the residential area, work area, and shopping area under different power outage durations is calculated piecewise. Thus, the curve of the power outage loss of the three typical areas (residential area, work area, and shopping area) as a function of power outage duration can be plotted as shown in Figure 10.

[0078] As shown in Figure 10, the power loss curve of the residential area load increases relatively slowly during the short-term power outage phase, indicating that residential loads have a certain tolerance to short-term power interruptions. The loss curve of the work area load increases approximately linearly with the power outage time, reflecting the continuous accumulation of losses after the interruption of production and business activities. The loss curve of the shopping area load rises sharply in the initial stage of the power outage, indicating that even a short-term power outage can lead to high economic losses. When the power outage duration exceeds about 500 minutes, the curve increase gradually slows down, but the absolute loss level is significantly higher than that of the other two types of areas, indicating that commercial activities are most dependent on the continuity of power.

[0079] In summary, the load importance index system and time-rate loss model established in this section can dynamically reflect the differences in power outage duration, capacity, and importance of different loads, providing a scientific and quantifiable basis for subsequent power optimization allocation and rapid recovery strategies.

[0080] (III) Multi-time-series power restoration strategy for electric vehicles (EVs only): The multi-time-series power restoration strategy for EVs only first constructs an optimized power restoration model based on the aforementioned multi-time-series EV equivalent power source model and load power loss assessment system, and then uses a genetic algorithm (GA) to optimize the power allocation of EVs in the time domain and between nodes. On this basis, for typical load scenarios, the improved IEEE 33-node distribution network system is selected as the case study. The study area is divided into three functional areas: residential area, work area, and shopping area. Power loss load points are set at nodes 21, 14, and 5. The network topology is shown in Figure 9. It is assumed that a sudden power outage event occurs at a specific time (12:00). In the initial stage of the power outage, local rapid power restoration is achieved solely by electric vehicles already connected to the distribution network.

[0081] In the above scenario, the economic cost of the system recovery process mainly comes from three parts: switching operation cost, mobile power supply usage cost, and load power loss loss. The switching operation cost S is used to describe the operational cost of the system during network reconstruction; the mobile power supply usage cost is used to quantify the comprehensive cost incurred during the discharge of electric vehicles (EVs) and the replenishment and maintenance of emergency power supply vehicles (EPSVs), and is treated as a unified cost item in the model; the load power loss loss reflects the economic and social impact of the load during the period from power outage to restoration.

[0082] Since different nodes are located at different distances from the power source, the cost is positively correlated with the distance, as shown in equation (19): (19); In equation (19): α is the operating cost coefficient corresponding to a unit electrical distance, used to characterize the increased operating cost for each additional unit electrical distance; The electrical distance between the power source of the j-th switch and the powered load can be the impedance distance, line length, or distance converted based on the equivalent voltage level. Let $C$ be the cost of a single operation of the $j$-th switch, used to quantify the economic cost of the switch during fault isolation and power restoration.

[0083] After obtaining the operating cost of a single switch, assume there are a total of [costs] during the recovery period. If there are multiple operating switches, the total cost of switch operation can be expressed as shown in equation (20): (20); In equation (20): S is the total cost of switching operation; n s Number of operating switches; Let $\frac{j}{j}$ be the cost of a single operation of the $j$-th switch.

[0084] In addition to considering the switching operation costs, it is also necessary to characterize the comprehensive costs incurred during the discharge of electric vehicles (EVs) and the replenishment and maintenance of emergency power supply vehicles (EPSVs). The cost of using a mobile power source consists of the costs of conventional use. With compensation costs It consists of two parts, and the conventional usage cost is shown in equation (21) below: (21); In formula (21): C1 is the regular usage cost of the mobile power collection (EV and EPSV) in a single power supply cycle; W is the cost of unit equivalent electrical energy (yuan / kWh), which takes into account the EV discharge settlement price and the EPSV fuel consumption conversion value; D1 represents the EV discharge price or EPSV fuel conversion cost; D2 represents the energy loss and life depreciation equivalent cost; M is the unified operation and maintenance cost of EV and EPSV.

[0085] If some mobile power sources need to be replenished with energy during the later stages of recovery (grid power replenishment for EVs and fuel supply for EPSVs), the compensation cost is shown in equation (22): (22); In formula (22): C2 is the compensation cost incurred by the mobile power collection (EV and EPSV) to restore available capacity after the power outage event; W is the cost of unit equivalent electrical energy (yuan / kWh), which takes into account the settlement price of EV discharge and the converted value of EPSV fuel consumption; D1 represents the EV discharge price or the converted cost of EPSV fuel.

[0086] Given the regular usage cost C1 and the compensation cost C2, the total usage cost of the mobile power supply set (EV and EPSV) in a single power supply cycle can be expressed as the sum of the two, as shown in equation (23): (23); In equation (23): The total cost of using a collection of mobile power supplies (EVs and EPSVs) over a single power cycle; The typical operating cost of a mobile power bank collection (EV and EPSV) over a single power supply cycle; The cost of restoring usable capacity for the mobile power collection (EV and EPSV) after a power outage is denoted as W; the cost of equivalent electrical energy per unit (RMB / kWh) is calculated by considering the EV discharge settlement price and the EPSV fuel consumption conversion value; D1 represents the EV discharge price or EPSV fuel conversion cost; D2 represents the energy loss and life depreciation equivalent cost; and M is the unified operation and maintenance cost of EV and EPSV.

[0087] Besides the switching operation costs and the cost of using a mobile power supply, the economic losses caused by the load's inability to obtain normal power supply during a power outage are also significant. The power deficit of the system at any given time can be represented by the difference between the demand power and the actual power supplied, as shown in equation (24): (24); In equation (24): The power deficit of the system at time t represents the unmet load demand at that time. Let be the load demand power of region k at time t; The available power provided by the EV vehicle.

[0088] To convert the power deficit into an economic loss rate, a loss growth rate function is introduced. This reflects the economic loss caused by a unit power deficit per unit time. The economic loss rate of the system at time t can be defined as shown in equation (25): (25); In equation (25): The economic loss rate of the system at time t (unit: yuan / min); The power deficit of the system at time t represents the unmet load demand at that time. It is the loss growth rate function of the system at time t (unit: yuan / (min·kW)), used to quantify the sensitivity of the power outage duration to economic losses, such as the impact of peak hours on critical loads. The load will be significantly higher than during normal or off-peak periods, and its value can be determined by the segmented increment rate for each load type. The weighted average is obtained.

[0089] Integrating the instantaneous loss rate over the entire power outage period yields the cumulative economic loss of the system during the power outage event, as shown in equation (26): (26); In equation (26): The total cumulative economic loss of the system during the power outage duration [0, T]; T is the upper limit of the duration of this power outage event; Let be the economic loss rate of the system at time t.

[0090] After comprehensively considering the economic losses from the outage, the switching operation costs, and the V2G usage costs of electric vehicles, the overall power loss loss of this power outage event can be uniformly expressed as shown in equation (27): (27); In equation (27): The total power loss of the system during a single power outage-recovery process; S represents the total cumulative economic loss of the system during the power outage duration [0, T]; S represents the total cost of the switching operation. The total cost of using a collection of mobile power supplies (EVs and EPSVs) over a single power cycle.

[0091] Based on the optimal time-space scheduling strategy obtained through GA convergence, a comprehensive node importance weight is introduced to reflect the differences in reliability and economy among different nodes. and node economic loss growth rate Weighting the power deficit, the overall power loss of the system is expressed as shown in equation (28): (28); In equation (28): This refers to the total power loss of the system when only electric vehicles participate in power restoration; Assuming a comprehensive importance weight for each node, Increased rate of economic loss at nodes; and Let be the power demand and recovery power of the node at time t, respectively; S is the total cost of the switching operation. The total cost of using a collection of mobile power supplies (EVs and EPSVs) over a single power cycle.

[0092] Based on this, a comprehensive optimization objective function for the EV scenario only is constructed, as shown in equation (29): (29); In equation (29): This is the comprehensive objective function value in the EV scenario only, and it is also the evaluation index of individual fitness in GA (the smaller the value, the better the solution). Let be the shortest electrical distance (km) from the j-th power source to load node a; The power supply (kW) for node j; This refers to the total power loss of the system when only electric vehicles participate in power restoration; , These are the weighting coefficients for distance cost and power outage loss, respectively.

[0093] To ensure that the solution results satisfy the physical and operational constraints, the power allocation of EV also needs to be constrained during the GA iteration process. The typical constraint can be expressed as shown in equation (30): (30); In formula (30): The power allocation ratio coefficient for supplying power from vehicle j to region k; The available power provided by the EV vehicle; Let be the load demand power of region k. The first constraint states that the sum of the vehicle power allocation ratio coefficients does not exceed 1 to ensure the vehicle power supply capacity constraint; the second constraint states that the node recovery power cannot be negative, nor can it exceed 1.1 times the demand power, to ensure system voltage stability.

[0094]

[0095] Based on the above-mentioned EV power supply recovery model and GA optimization process, combined with the load power loss assessment results and equations (28) to (30), simulation calculations were carried out on four typical time-series scenarios (summer, winter, weekday, and holiday) and three types of areas (residential area, work area, and shopping area). The node power allocation results of EVs in each scenario can be obtained, and the EV allocation details are summarized in Table 1. Table 1 shows the statistical results of EV power supply allocation and utilization rate in different scenarios, different areas, and key nodes. As can be seen from Table 1: in the night and winter scenarios, the residential area node receives the highest proportion of EV power support, indicating that EVs mainly form stable energy storage support in the residential area; during the daytime hours of weekdays, some EV power is tilted towards the work area node, reflecting the priority recovery demand of the daytime office load; in the holiday scenario, the proportion of EV power supply in the shopping area node is significantly increased, which is consistent with the characteristics of active shopping travel during holidays in the multi-time-series travel model described in Section 1.

[0096] (iv) Modeling of EV-EPSV Coordinated Power Supply Restoration Strategy: This step further introduces emergency power supply vehicles (EPSVs) to participate in power supply scheduling, forming a coordinated optimization strategy of "EV static allocation + EPSV dynamic compensation". In the first stage, the Genetic Algorithm (GA) completes the initial power and node allocation of EVs; in the second stage, the Adaptive Large Neighborhood Search (ALNS) algorithm is introduced to dynamically optimize the driving path and stopping order of EPSVs.

[0097] Based on this, an improved IEEE 33-node distribution network was selected as the case study system. The network was divided into three areas: residential, work, and shopping. Power outage load points were set at nodes 21, 14, and 5, and EPSV sites were deployed at nodes 20, 15, and 8, with 30 emergency power supply vehicles configured. Assuming a sudden power outage occurs at 12:00, the EV (Electric Power Vehicle) first achieves rapid local restoration according to the GA (General Aspect Ratio) optimization results. Subsequently, the EPSVs are sequentially connected for compensation according to the GA-ALNS two-stage optimization results. The network topology is shown in Figure 9, and the two-stage optimization process of the multi-time-domain EV-EPSV collaborative power restoration strategy is shown in Figure 17.

[0098] Based on this, the EV group provides initial support, while EPSV provides mobile support to key nodes. Together, they form a regional coordinated power supply capability, as shown in equation (31): (31); In formula (31): Let the equivalent combined power supply of region k at time t be denoted as ; Power allocation factor; Let be the equivalent power of node j; The power supplied by the emergency vehicle v to the load k.

[0099] To simplify the subsequent derivation, the power provided by EV and EPSV to region k is denoted as follows: and The equivalent representation of the combined power supply is obtained, as shown in equation (32): (32); In formula (32): The combined EV-EPSV power supply for region k at time t; Let k be the power supplied by the EV group to region k at time t. Let $t$ be the power supplied by EPSV to region $k$ at time $t$.

[0100] Since the importance and load scale of nodes vary in different regions, a regional weighting coefficient is introduced to reflect this unevenness in the system evaluation. The region weight is defined as shown in equation (33): (33); In formula (33): This is the weighted importance coefficient for region k, which comprehensively reflects the load scale and key node weights within that region; Let k be the set of nodes within region k. Let i be the importance weight of node i; Let be the power required by node i.

[0101] To maintain notation consistency, the total power demand in region k is denoted as... Its definition is shown in equation (34): (34); In equation (34): Let K be the power demand of region k at time t; Let be the load demand power of region k at time t.

[0102] Based on the above definitions, and considering the differences in load scale and critical node distribution across different regions, a regional weighting coefficient is introduced. Weighting the power deficit, the overall power loss of the system under the EV-EPSV collaborative recovery scheme is shown in equation (35): (35); In formula (35): The overall power loss loss under the EV and EPSV collaborative power supply scheme; is the weighted importance coefficient for region k; Let K be the power demand of region k at time t; The combined power supply for the EV and EPSV; S is the total cost of switching operations; Let $\frac{EV}{EPSV}$ be the total cost of using the mobile power supply set (EV and EPSV) in a single power supply cycle. Considering the balance between power supply resource fairness and economic efficiency, a corresponding comprehensive optimization objective function is constructed. The comprehensive optimization objective in the EV-EPSV collaborative scenario can then be expressed as shown in equation (36): (36); In formula (36): The comprehensive objective function value under the EV–EPSV collaborative power supply scheme is the fitness evaluation index in the ALNS search process; is the weighted importance coefficient for region k; Let K be the power demand of region k at time t; The combined power supply of the EV and EPSV; λ is the weighting coefficient; The proportion of power supplied to the target node; The total nominal power supply capacity (maximum power supply capacity) available for the EV-EPSV vehicle group during the cooperative power supply phase. The first item represents the residual load loss item; the second item represents the fairness penalty item.

[0103] To ensure that the optimization results are physically and operationally feasible, it is also necessary to introduce constraints on the EPSV output and service relationship, as shown in equation (37): (37); In equation (37): The combined power supply for EV and EPSV; Let K be the power demand of region k at time t; The power supplied by the emergency vehicle v to the load k; This represents the vehicle's maximum output capacity. This is a binary variable indicating whether the vehicle is enabled (1 indicates enabled, 0 indicates disabled); Constraint variables are assigned to the power supply task. The first constraint states that the combined power supply power of the region cannot be negative and cannot exceed the power demand of the region, so as to ensure that the power supply level of each region is physically feasible and meets the basic supply and demand balance constraint. The second constraint states that the power provided by the emergency power supply vehicle to the region shall not exceed the vehicle's maximum output capacity and shall be consistent with the start-stop state variable, so as to ensure that the output of a single vehicle does not exceed the limit and conforms to the vehicle's activation state. The third constraint states that the sum of the service allocation variables of each region at the same time does not exceed 1, so as to ensure that each region is served by at most one emergency power supply vehicle, thereby ensuring that task allocation and route scheduling are feasible in actual operation.

[0104]

[0105] Based on the EV-EPSV collaborative optimization model constructed using equations (31) to (37), and the static allocation results of EVs provided by GA, the paths and power of EPSVs are dynamically reconstructed by ALNS. By jointly solving multiple scenarios (summer, winter, weekdays, holidays) and multiple regions (residential areas, work areas, shopping areas), the departure time, service order, and node power supply of each emergency power supply vehicle can be obtained as scheduling schemes. By statistically summarizing the EPSV scheduling results under each scenario, the EPSV allocation summary table shown in Table 2 can be obtained.

[0106] As shown in Table 2, under the collaborative power supply scheme, the residential area receives a higher proportion of EPSV supplementary power in all four typical time-series scenarios, reflecting the priority of this area in terms of life safety and basic living security; the working area sees a significant increase in the proportion of EPSV input on weekdays, consistent with its characteristics of high daytime load and high sensitivity to production activities; the shopping area receives more EPSV support during holidays, reflecting the high economic loss risk corresponding to commercial load during holidays. Overall, the collaborative optimization model constructed by equations (31) to (37), solved by the GA–ALNS two-stage algorithm, enables EV and EPSV to achieve a relatively balanced and coordinated resource allocation in the time and space dimensions, laying a quantitative foundation for the comparative analysis of power loss and saving rate between the EV-only scheme and the collaborative scheme in the next section.

[0107] (V) Comparative analysis of EV-only scheme and EV-EPSV collaborative scheme: In order to quantitatively evaluate the economic differences and recovery effects of EV-only power supply scheme and EV-EPSV collaborative power supply scheme under different time and space scenarios, this section compares and analyzes four typical time-series scenarios (summer, winter, weekday, and holiday) and three typical areas (residential area, work area, and shopping area) based on the power loss model (28) of EV-only scheme in Section 3 and the power loss model (35) of collaborative scheme in Section 4.

[0108] In scenarios where only EVs participate in power supply, a comprehensive node importance weight is introduced to reflect the differences in node importance and loss sensitivity. and node economic loss growth rate Weighting the power deficit, the overall power loss of the system is expressed as shown in equation (28): (28); In equation (28): This refers to the total power loss of the system when only electric vehicles participate in power restoration; Assuming a comprehensive importance weight for each node, Increased rate of economic loss at nodes; and Let be the power demand and recovery power of the node at time t, respectively; S is the total cost of the switching operation. The total cost of using an electric vehicle over a complete V2G cycle.

[0109] Based on the above definitions, and considering the differences in load scale and critical node distribution across different regions, a regional weighting coefficient is introduced. Weighting the power deficit, the overall power loss of the system under the EV-EPSV collaborative recovery scheme is shown in equation (35): (35); In formula (35): The overall power loss loss under the EV and EPSV collaborative power supply scheme; is the weighted importance coefficient for region k; Let K be the power demand of region k at time t; The combined power supply for the EV and EPSV; S is the total cost of switching operations; The total cost of using an electric vehicle over a complete V2G cycle.

[0110] Based on equations (28) and (35), a comparison of power outage losses between the collaborative power supply restoration strategy of this invention and the traditional EV-only power supply scheme can be obtained in four typical time-series scenarios (summer, winter, weekday, and holiday) and three types of areas (residential area, work area, and shopping area). Taking the summer and weekday scenarios as examples, Figures 11 to 16 are obtained. As can be seen from Figures 11 to 16, in the initial stage of the power outage, the starting points of the loss curves of the two schemes are close, indicating that the rapid grid-connected discharge of the EV group can provide initial support for the load in a short period of time; however, as time goes on, the curve of the EV-only scheme rises significantly in the middle and late stages due to the limited energy storage capacity and spatial distribution, resulting in power attenuation and recovery lag. The curve of the collaborative scheme is significantly lower than that of the EV-only scheme and is smoother, indicating that the EPSV effectively makes up for the power supply gap after the EV energy release through cross-regional mobile energy replenishment in the middle and late stages, making the power supply restoration process more continuous and stable, and significantly improving the system's dynamic response capability and overall power supply reliability.

[0111] In addition to comparing cumulative losses, a relative savings rate index is introduced to quantify the economic differences between the two strategies across multiple scenarios (summer, winter, holidays, weekdays) and multiple regions (residential areas, work areas, commercial areas). As shown in equation (38): (38); In formula (38): This represents the relative savings rate of the EV-EPSV collaborative power supply scheme compared to the EV-only scheme in scenario s region a. The larger the value, the more obvious the economic advantage of the collaborative solution in this spatiotemporal scenario; This represents the total power loss of the EV solution only in region a of scenario s; This represents the total power loss of the EV-EPSV collaborative solution in area a of scenario s; s represents the scenario type (summer, winter, weekday, holiday); a represents the area category (residential area, work area, shopping area).

[0112]

[0113] Based on Equation (38), the cumulative power loss in each scenario and region in Figures 11-16 is normalized and calculated, resulting in Table 3, which shows the power loss saving rate for each scenario and region. The results show that the collaborative strategy achieves positive savings in all cases, with the overall saving rate ranging from 34% to 70%. From the perspective of regions, the residential area has the most significant saving effect, with an average saving rate of about 60% to 70%, indicating that under the condition that the travel in the residential area has obvious characteristics of "concentration at night and dispersal during the day", the stable nighttime residence of EVs and the cross-time replenishment of EPSVs form a good synergy. The work area has a lower saving rate during holidays (about 34%), while it rises to about 50% on weekdays, reflecting that the characteristics of concentrated vehicles and rigid load in the work area on weekdays are more conducive to the role of collaborative scheduling. The shopping area performs best under holiday conditions, with a saving rate of about 60%, indicating that when the commercial load increases significantly during holidays, the joint scheduling of EVs and EPSVs can effectively reduce the high losses caused by the interruption of high-value commercial activities.

[0114] From a scenario perspective, the savings rate in summer and winter is generally similar, with summer slightly better than winter. This is mainly because the load base and adjustable energy storage are both higher in summer, allowing for greater flexibility in peak load reduction and continuous energy supply through coordinated scheduling. Holidays are generally better than weekdays, which is related to increased activity in shopping areas and more dispersed EV spatial distribution, making the mobility advantage of EPSVs more prominent at these times.

[0115] In summary, the comparative evaluation results based on equations (28), (35) and (38) show that, compared with the EV-only power supply scheme, the EV-EPSV collaborative power supply recovery strategy proposed in this invention can significantly reduce system power loss, improve recovery speed and power supply continuity under different time scenarios and regional types, and take into account both economy and reliability. This verifies the effectiveness and practical value of the aforementioned multi-time-sequence EV equivalent power supply model, load power loss assessment system and EV-EPSV two-stage collaborative optimization framework.

Claims

1. A modeling method for multi-time-series EV equivalent power supply models considering vehicle travel patterns, characterized in that... Includes the following steps: S1: Based on the dynamic evolution characteristics of electric vehicle user travel patterns and combined with travel sample data, the data is divided into summer and winter scenarios by season and weekday and holiday scenarios by time series to complete the data fitting; S2: A vehicle travel state transition matrix is ​​established through a semi-Markov chain, and the Monte Carlo method is used to stochastically simulate vehicle behavior to obtain the available discharge capacity of electric vehicles at each time; the electric vehicle cluster in the region is equivalent to a time-varying power source model; and then a multi-time series EV equivalent power source model is established.

2. The multi-temporal EV equivalent power supply modeling method considering vehicle travel patterns according to claim 1, characterized in that: In S1, in order to characterize the travel patterns of electric vehicle users under different seasons and time periods, the travel sample data of NHTS2017 is first divided into summer and winter scenarios according to season, and into weekday and holiday scenarios according to time period, thus forming four typical travel scenarios.

3. The multi-time-series EV equivalent power supply modeling method considering vehicle travel patterns according to claim 2, characterized in that: For each typical travel scenario, samples of departure and arrival times of electric vehicle users are extracted, and a weighted model is performed using a wrapped Gaussian mixture model. The probability density function is shown in equation (1): (1); In formula (1): Let be the probability density function of scene s, region k, and behavior type q at time t; This indicates the number of Gaussian components used in scene s, region k, and behavior type q; The weights of each component satisfy the following conditions: 、 ； and These represent the center and standard deviation of the component, respectively. To wrap around the Gaussian kernel, it is used to achieve 24-hour periodization and ensure the continuity and uniformity of the distribution in the interval [0,24); t represents the corresponding intraday time, with a value range of 0–24 hours in the periodic interval; s represents four typical operating scenarios: summer, winter, weekday, and holiday; k represents three typical areas: residential area, work area, and shopping area; q represents the behavior type, used to distinguish the two types of vehicle usage behavior of electric vehicles: departure and arrival. This represents the index of the c-th Gaussian component in the Gaussian mixture.

4. The multi-temporal EV equivalent power supply modeling method considering vehicle travel patterns according to claim 3, characterized in that: To further avoid the distortion of the distribution of electric vehicle departure / arrival times at the 24-hour boundary and to maintain periodic consistency, the wrap-around Gaussian kernel function is defined as shown in equation (2): (2); In formula (2): This is a wrapping Gaussian kernel function with a period of 24 hours; t is the time variable; μ and σ are the mean and standard deviation, respectively; m is the 24-hour shift index, used for periodic extension of the time axis; Represents a set of integers.

5. The multi-temporal EV equivalent power supply modeling method considering vehicle travel patterns according to claim 4, characterized in that: When the sample size is small or there is morphological skew, the periodic kernel density estimation method is used for smooth estimation, and its expression is shown in equation (3): (3); In formula (3): Let be the periodic kernel density function under scene s, region k, and behavior type q; This represents the total number of samples used for periodic kernel density estimation; h is the bandwidth parameter. Let m represent the i-th sample time; m∈{−1,0,1} is the periodic translation term, used to smoothly connect at the [0,24] boundary; This represents an exponential function with base e.

6. The multi-time-series EV equivalent power supply modeling method considering vehicle travel patterns according to claim 5, characterized in that: In S2, after data fitting is completed, a mathematical model of multi-time series electric vehicle travel behavior is established based on the vehicle transition kernel matrix of the semi-Markov chain and the Monte Carlo method; the semi-Markov chain describes the time-related transition probability of the vehicle between three areas: residential area, work area and shopping area, and the definition of the vehicle semi-Markov kernel matrix is ​​as shown in Equation (4): (4); In formula (4): Let be the semi-Markov transition kernel matrix at time t; This represents the probability that an electric vehicle will move to region n when it is in region m and its dwell time does not exceed t. It also describes the probability of moving from m to n and the distribution of dwell time in that state. Here, m, n∈{1,2,3}, and regions 1 / 2 / 3 correspond to residential area / work area / shopping area, respectively.

7. The multi-time-series EV equivalent power supply modeling method considering vehicle travel patterns according to claim 6, characterized in that: To obtain group-level time-series trajectory samples, the Monte Carlo method is used to randomly sample and evolve the state of vehicles. The vehicle state matrix for 24 hours in a day is defined as shown in Equation (5): (5); In formula (5): For the vehicle state matrix; Let represent the region i where the j-th electric vehicle is located at time t, where i = 1, 2, 3: represents the region number, 1 represents a residential area, 2 represents a work area, 3 represents a shopping area; t = 1, 2, ..., 24: represents the 24 hours of the day; j represents the j-th electric vehicle, j = 1, 2, ..., ， The number of electric vehicle samples participating in the statistics is represented by the vehicle semi-Markov kernel matrix given by equation (4) above, which provides probability driving, while the vehicle state matrix given by equation (5) carries the group temporal distribution obtained by Monte Carlo sampling. Together, they constitute the core input and output of the multi-temporal electric vehicle travel chain model and provide a complete spatiotemporal statistical basis for the equivalent power source model.

8. The multi-time-series EV equivalent power supply modeling method considering vehicle travel patterns according to claim 7, characterized in that: Based on this vehicle state matrix The number of vehicles and their proportion in each region at any given time are statistically analyzed, and then the available power model of the electric vehicle group is constructed, as shown in equation (6): (6); In formula (6): Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. Let k ∈ {1,2,3} be the regional state of the vehicle at time t; k ∈ {1,2,3} correspond to the residential area, the work area, and the shopping area, respectively; t ∈ {1,2,…,24} is the time index; according to the definition of equation (6), the number and proportion of vehicles in the region are calculated, as shown in equations (7) and (8), respectively: （7）； (8); In the above formula: Let be the number of vehicles in region k at time t; This represents the percentage of vehicles in the area. Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This represents the total number of electric vehicles included in the statistical sample.

9. The multi-time-series EV equivalent power supply modeling method considering vehicle travel patterns according to claim 8, characterized in that: Discharge availability is constrained by the battery's state of charge (SOC); let the upper and lower SOC thresholds be Y1 and Y2, respectively, then the discharge state function of the j-th vehicle at time t is defined as shown in equation (9): (9); In equation (9): It is the discharge state function; Let j be the state of charge of the j-th vehicle; and These are the lower discharge threshold and the upper charge threshold, respectively, satisfying... ;when At that time, the vehicle is allowed to discharge; when At this time, charging is only allowed; when When the value is between the two thresholds, the vehicle is in standby mode and is not included in the discharge set; combining equations (6) and (9), the number of vehicles that can participate in the discharge in region k at time t is calculated, as shown in equation (10): (10); In formula (10): Let k be the number of vehicles that can discharge at time t. This is a region indicator function, indicating whether the j-th vehicle is stationary and located in region k at time t; Let {1} be the discharge state function; let {1} be the indicator function, if and only if the vehicle satisfies the discharge availability condition of equation (9). The value is 1; to further consider the randomness of vehicle participation in V2G behavior, a Bernoulli random variable is introduced. This indicates whether the vehicle participated in actual discharge; Its obeys the parameter is The Bernoulli distribution is shown in equation (11): (11); In formula (11): This indicates whether the j-th vehicle participates in the discharge at time t, with 1 indicating participation and 0 indicating non-participation; The average participation rate of the group reflects the probability that a vehicle will participate in V2G when it is in a state where it can be discharged. Let represent a Bernoulli distribution, with the output being a random variable of 0–1; based on equation (11), the expected number of dischargeable vehicles at the region-time level is calculated, as shown in equation (12): (12); In formula (12): For expectation operators; Indicates the proportion of group discharge participation; This represents the number of vehicles in region k at time t; Let be an indicator variable for whether the j-th electric vehicle is located in region k at time t. It takes the value 1 if and only if the j-th electric vehicle belongs to region k at hour t, and 0 otherwise. This indicates whether the j-th vehicle participates in discharging at time t, with 1 indicating participation and 0 indicating non-participation. After obtaining the number of vehicles capable of discharging, further power layer aggregation is performed. Let the rated discharge power of a single vehicle be... Then the instantaneous equivalent output power of region k at time t is shown in equation (13): (13); In formula (13): Let be the equivalent discharge power of region k; This refers to the rated discharge power of a single vehicle. The total number of electric vehicles included in the statistical sample; approximation symbol " "This means that, under the meaning of the population average, the expected value is used to replace the fluctuation caused by the randomness of the sample; at the level of the population average, taking the mathematical expectation of equation (13), we can obtain the expected form of the regional power as shown in equation (14): (14); In formula (14): Let k be the average equivalent power in region k at time t; The mathematical expectation of the total number of vehicles in region k at time t; This represents the percentage of vehicles in the area.

10. The multi-temporal EV equivalent power supply modeling method considering vehicle travel patterns according to claim 9, characterized in that: By superimposing the power of the three types of areas—residential area, work area, and shopping area—the total equivalent output power of the system can be obtained, as shown in equation (15): (15); In formula (15): The total equivalent output power of the system at time t is given by formulas (1) to (15). By combining the vehicle's travel chain, SOC constraint, participation probability and power aggregation, a multi-time series electric vehicle EV equivalent power model that can describe the temporal behavior characteristics of the group is established.

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