Power distribution network two-stage optimization regulation and control method considering uncertain charging of electric vehicle

Abstract

The invention discloses a power distribution network two-stage optimization regulation and control method considering uncertain charging of an electric vehicle, and belongs to the technical field of power distribution network optimization operation. The method comprises the following steps: establishing an uncertainty model of an electric vehicle charging load based on a multi-factor composite probability model and dynamic time sequence parking demand prediction; constructing a two-stage optimization regulation and control model of the power distribution network containing the large-scale electric vehicle charging load by taking the minimum system operation loss as a target, wherein the model comprises a first-stage decision variable and a second-stage decision variable; and solving the model by adopting a column and constraint generation algorithm, and generating and executing a power distribution network optimization regulation and control strategy. According to the method, the uncertainty of the charging load of the electric vehicle is effectively dealt with, the operation loss of the system is remarkably reduced through two-stage optimization, and the economical efficiency, the safety and the new energy consumption capability of operation of the power distribution network are improved.

Description

Technical Field

[0001] This invention belongs to the field of distribution network optimization operation and dispatching technology, and relates to a two-stage optimization control method for distribution networks that considers the uncertain charging of electric vehicles. Background Technology

[0002] As the penetration rate of new energy sources such as wind power and photovoltaics in distribution networks continues to increase, distribution networks are evolving from traditional unidirectional power supply networks to receiving-end networks with active support capabilities. In this process, the large-scale integration of electric vehicles has brought new challenges: their charging load has significant spatiotemporal uncertainty, is affected by multiple factors such as user behavior, regional functions, and traffic conditions, and is prone to overlap with the inherent peak load of the power grid, leading to problems such as localized overload of distribution areas, uneven power flow distribution, and increased network losses.

[0003] Currently, the analysis of the coupling relationship between the uncertainty of electric vehicle charging and distribution network dispatching strategies is insufficient. Most dispatching methods fail to effectively account for the randomness of charging behavior, resulting in limited distribution network operating efficiency and safety margin, high network loss costs, and even power supply risks. Therefore, there is an urgent need to develop an economical dispatching method for distribution networks that can adapt to the uncertain access of electric vehicles.

[0004] Against this backdrop, achieving power sharing across multi-regional distribution networks through DC interconnection technology has become an effective way to improve system flexibility and resilience. DC interconnection structures can integrate power generation resources from different regions, enabling cross-regional energy support, thereby enhancing the distribution network's adaptability to random charging loads and its capacity for renewable energy absorption. However, how to construct an optimized model that can collaboratively address charging uncertainties and operational economics under this new network structure remains a critical issue that urgently needs to be addressed. Summary of the Invention

[0005] To address the problems existing in the background technology, this invention proposes a two-stage optimization control method for power distribution networks that considers the uncertain charging of electric vehicles.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a two-stage optimization and control method for power distribution networks considering uncertain charging of electric vehicles, comprising the following steps: An uncertainty model of electric vehicle charging load is established based on a multi-factor composite probability model and dynamic time-series parking demand forecasting. Based on the uncertainty model, a two-stage optimization control model for the distribution network is constructed with the goal of minimizing system operating losses. The two-stage optimization control model for the distribution network includes decision variables for the first stage and decision variables for the second stage. The decision variables in the first stage include line switch state variables, energy storage charging and discharging state variables, and capacitor bank switching state variables. The decision variables for the second stage include the power of the distribution transformer, the power of the converter, the charging and discharging power of the energy storage, the reactive power compensation power of the photovoltaic inverter, and the load shedding power. The column and constraint generation algorithm is used to solve the two-stage optimization control model of the distribution network, generate the distribution network optimization control strategy and execute it.

[0007] Specifically, the uncertainty model for electric vehicle charging load established based on a multi-factor composite probability model includes: Electric vehicle users are divided into three categories: private car users, ride-hailing users, and official vehicle users; Establish an independent log-normal probability density function for each user type; The composite probability density function of the total daily mileage of electric vehicles is obtained by weighted summation of the log-normal probability density functions of the three types of users. The actual daily mileage is obtained by introducing seasonal and regional correction factors to adjust the baseline mileage in real time.

[0008] Specifically, the uncertainty model for establishing electric vehicle charging load based on dynamic time-series parking demand forecasting includes: The functional areas are divided into residential areas, industrial and commercial areas, and public facilities areas; The parking demand in residential areas is modeled using a normal distribution function centered at dusk. The parking demand in industrial and commercial areas is modeled using a bi-peak or wide-peak model centered on midday. Different parameters are used to model parking demand in public facility areas, distinguishing between weekdays and weekends; The total parking demand curve is obtained by superimposing the parking demand of the three functional areas.

[0009] Specifically, the uncertainty model for electric vehicle charging load also includes: The Monte Carlo method is used to simulate the charging load of electric vehicles, including parking simulation and charging simulation. In the parking simulation cycle, the vehicle entry and exit status is determined based on the difference between parking space demand and the number of vehicles, and the parking time of each vehicle is calculated. In the charging simulation cycle, charging behavior is arranged and charging load power is calculated based on the availability of charging piles and the state of charge of electric vehicles. The charging load prediction error is described by constructing a charging load uncertainty set based on the charging load prediction values ​​obtained through a multi-factor composite probability model and dynamic time-series parking demand prediction.

[0010] Specifically, the objective function for constructing the two-stage optimization and control model of the distribution network is as follows: System operating losses include network loss costs, distribution transformer loss costs, converter loss costs, energy storage charging and discharging loss costs, and load shedding costs. All cost items take into account electricity price factors and time intervals. Network loss cost is calculated based on the product of the square of the branch current amplitude and the resistance. The cost of distribution transformer losses includes iron losses and copper losses; Converter loss cost is calculated based on converter loss coefficient; Energy storage charging and discharging losses and costs take into account charging and discharging efficiency. The load shedding cost is calculated based on the load shedding penalty coefficient.

[0011] Specifically, the two-stage optimization control model for the distribution network also includes the following operational constraints: AC power flow balance constraints include AC node active and reactive power injection balance constraints, AC branch voltage drop constraints, AC branch Ohm's law constraints, and AC branch capacity constraints. DC power flow balance constraints include DC node active power injection balance constraints, DC branch voltage drop constraints, and DC branch Ohm's law. Distribution network reconfiguration constraints include radial operation constraints guaranteed by virtual power flow constraints, branch switch status constraints, and branch switch maximum daily operation constraints.

[0012] Specifically, the two-stage optimization and control model for the power distribution network also includes the following equipment operation constraints: Capacitor bank operation constraints include reactive power compensation constraints based on the number of switching banks and the switching capacity of a single bank, upper limit constraints on the number of switching banks, switching action constraints, and maximum daily switching frequency constraints. Operating constraints for distribution transformers include operating power factor constraints, loss calculation constraints based on iron and copper losses, load rate calculation constraints, and load rate upper limit constraints. Converter operating constraints include power coupling constraints with distribution transformers, capacity constraints, loss calculation constraints, and AC / DC side power balance constraints. Energy storage operation constraints include charging and discharging power balance constraints, simultaneous charging and discharging not allowed constraints, energy balance constraints, upper and lower limits of energy, charging and discharging state switching constraints, and maximum number of daily charging and discharging cycles constraints. Distributed power source operation constraints include upper and lower limits of active and reactive power output constraints for distributed power sources connected to AC nodes and upper and lower limits of active power output constraints for distributed power sources connected to DC systems. Load shedding constraints include AC node load shedding constraints and DC node load shedding constraints, wherein the load shedding amount does not exceed the set upper limit of the load shedding ratio.

[0013] Specifically, the algorithm for solving the two-stage optimization control model of the distribution network using column and constraint generation includes: The two-stage optimization control model of the distribution network is decomposed into a main problem and sub-problems; The main problem involves finding the optimal scheduling decision in the first stage under finite adverse scenarios to provide a lower bound solution. The subproblems are substituted into the solution of the current main problem to obtain the first-stage scheduling decision and solve the optimal second-stage scheduling decision under the worst scenario, so as to identify the worst scenario and provide an upper bound solution; Based on the strong duality theorem, the bi-level optimization problem of the subproblem is transformed into a single-level optimization problem, and the nonlinear term is processed by the Big-M method after discretizing the uncertain set of electric vehicle charging load. In solving the two-stage optimization control model, non-convex nonlinear terms are handled.

[0014] Specifically, the processing of nonconvex nonlinear terms includes: Transform non-convex nonlinear constraints into convex or linear constraints. The absolute value constraints are directly expanded into linear constraints, and the quadratic equality constraints are transformed into second-order cone constraints using second-order cone relaxation techniques. The problem is eventually transformed into an optimization problem containing only linear and cone constraints, which is then solved iteratively until the convergence condition is met.

[0015] Specifically, the distribution network optimization and control strategy is obtained and the following operations are performed: Adjusting the switch status of distribution network lines to achieve network reconfiguration; Control the charging and discharging power and status of energy storage devices; Adjust the number of capacitor banks switched on / off; Adjust the power of the distribution transformer, the power of the converter, and the reactive power compensation power of the photovoltaic inverter, and perform load shedding operations based on the upper limit of the load shedding ratio set in the load shedding constraints.

[0016] Compared with the prior art, the present invention has the following beneficial effects: Effectively addressing charging load uncertainty. Through a multi-factor composite probability model and dynamic time-series parking demand forecasting, the travel and parking patterns of different types of electric vehicle users are accurately described. Furthermore, the Monte Carlo method is used to simulate charging behavior, constructing a charging load uncertainty set, which significantly improves load forecasting accuracy and provides reliable input for subsequent optimization.

[0017] Achieving synergistic optimization of system operation economy and safety. The constructed two-stage optimization and control model for the distribution network aims to minimize system operating losses, comprehensively considering network losses, equipment losses, and load shedding costs, and encompassing various constraints such as power flow balance, network reconfiguration, and equipment operation, ensuring the safe and stable operation of the distribution network while reducing total operating costs.

[0018] A robust optimization and control strategy is generated. A column and constraint generation algorithm is used for solving the problem. Through iteration of the main problem and subproblems, the non-convex and nonlinear terms in the model are effectively handled, ultimately resulting in a robust scheduling scheme that can adapt to the most severe charging scenarios, significantly improving the distribution network's ability to cope with load fluctuations.

[0019] Improving the operational efficiency of the distribution network and the level of renewable energy integration. Based on the optimization strategy, operations such as network reconfiguration, energy storage control, reactive power compensation, and power mutual assistance effectively reduce network losses, improve voltage quality, smooth load fluctuations, and enhance power support between different regions through DC interconnection structures, thereby improving the distribution network's adaptability to large-scale electric vehicles and renewable energy integration. Attached Figure Description

[0020] Figure 1 This is a diagram of the multi-node AC / DC hybrid distribution network topology of the present invention; Figure 2 This is a comparison chart of the scheduling costs in different scenarios of the present invention; Figure 3 This is a time-series comparison of network loss in different scenarios according to the present invention; Figure 4 This is a diagram of the dynamic reconfiguration strategy for DC interconnected distribution networks according to the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] like Figures 1-4 As shown, the technical solution adopted in this invention is as follows: a two-stage optimization and control method for power distribution networks considering uncertain charging of electric vehicles, comprising the following steps: An uncertainty model of electric vehicle charging load is established based on a multi-factor composite probability model and dynamic time-series parking demand forecasting. Based on the uncertainty model, a two-stage optimization control model for the distribution network is constructed with the goal of minimizing system operating losses. The two-stage optimization control model for the distribution network includes decision variables for the first stage and decision variables for the second stage.

[0023] The decision variables in the first stage include line switch state variables, energy storage charging and discharging state variables, and capacitor bank switching state variables.

[0024] The decision variables for the second stage include the power of the distribution transformer, the power of the converter, the charging and discharging power of the energy storage, the reactive power compensation power of the photovoltaic inverter, and the load shedding power.

[0025] The column and constraint generation algorithm is used to solve the two-stage optimization control model of the distribution network, generate the distribution network optimization control strategy and execute it.

[0026] Specifically, the uncertainty model for electric vehicle charging load established based on a multi-factor composite probability model includes: Electric vehicle users are divided into three categories: private car users, ride-hailing users, and official vehicle users.

[0027] Establish an independent log-normal probability density function for each user type.

[0028] The composite probability density function of the total daily mileage of electric vehicles is obtained by weighted summation of the log-normal probability density functions of the three types of users.

[0029] The actual daily mileage is obtained by introducing seasonal and regional correction factors to adjust the baseline mileage in real time.

[0030] Because the travel patterns of private car users, ride-hailing users, and official vehicle users differ significantly, it is necessary to establish an independent log-normal distribution probability density function for each user type to accurately reflect the daily mileage distribution patterns of each type of user: Private car user model: Private car users have strong travel patterns, with short and concentrated daily mileage. Therefore, their daily mileage follows a log-normal distribution, with the probability density function being... .

[0031] in, Represents daily mileage; This corresponds to an average daily mileage of approximately 40km, and is a statistical result based on short-distance travel scenarios such as daily commuting and shopping for private car users; This reflects the dispersion of daily mileage driven by private car users. A smaller value indicates that the mileage distribution is more concentrated, which is consistent with the stable travel patterns of private cars.

[0032] Ride-hailing / taxi user model: Due to the nature of their operations, ride-hailing / taxi users need to drive for long periods of time and at high frequency, resulting in long daily mileages and a wide distribution. Their daily mileage also follows a log-normal distribution, with the probability density function being... .

[0033] in, This corresponds to an average daily mileage of approximately 200km, meeting the long-mileage requirements of ride-hailing / taxi operations throughout the day; Although the average daily mileage is long, the mileage dispersion is slightly lower than that of private cars because the operating routes are relatively fixed (such as taking orders within the city). Value less than .

[0034] Official vehicle user model: Official vehicle users travel for official business trips, meetings, etc., with a mode of travel between private cars and ride-hailing services. The average daily mileage is moderate, and the daily mileage follows a log-normal distribution with the following probability density function: .in, This corresponds to an average daily mileage of approximately 100km, which aligns with the characteristics of official travel that is neither short-distance nor excessively long-distance. The mileage dispersion is between that of private cars and ride-hailing services, reflecting both the planned nature of official travel and the mileage differences in different official scenarios, such as meetings in the city and business trips to the suburbs.

[0035] Furthermore, to comprehensively reflect the random patterns of daily mileage for all electric vehicle users within the region, it is necessary to perform a weighted summation of the sub-distributions of the three user groups to obtain the composite probability density function of the total daily mileage. .

[0036] in, For the proportion of private car users, For the proportion of ride-hailing users, The weight for the proportion of official vehicle users is derived from a survey and statistical analysis of the electric vehicle user structure in the actual region. This ensures that the composite function can accurately match the user composition of the region and avoids the idealistic flaw that a single user type model cannot cover the entire user group.

[0037] To further improve model accuracy and compensate for the shortcomings of the baseline mileage, a seasonal correction factor is introduced to address the limitation of daily mileage calculated using the composite probability density function, which does not take into account environmental and geographical factors. and regional correction factor The baseline mileage is adjusted in real time to obtain the actual daily mileage. ,in This is the baseline mileage.

[0038] Seasonal correction factor This takes into account the dual impact of temperature on vehicle range and user travel intentions. In summer, increased battery consumption due to air conditioning use leads to shorter range, and high temperatures may also reduce users' willingness to travel long distances. Multiplying the baseline mileage by this factor reduces the actual mileage, matching summer travel characteristics. In winter, the driving range is further shortened due to vehicle heating, and low temperatures may also suppress user travel demand. The actual mileage decreased further compared to summer. Spring and autumn temperatures are suitable, vehicle range is normal, and users have a high willingness to travel, therefore... The actual mileage was slightly higher than the benchmark, which is consistent with the characteristics of active travel in spring and autumn.

[0039] Regional correction factor This considers the impact of urban functional layout on user travel distances. Urban core areas are densely populated and have well-developed public transportation; shorter commutes and reduced traffic congestion may decrease unnecessary travel. The actual mileage is reduced. Users in suburban or satellite cities need to travel to the city center for work or shopping, resulting in longer commutes. Actual mileage increases. Users in mixed-use areas (combining residential, commercial, and office functions) have moderate travel distances, therefore... The actual mileage is consistent with the benchmark, which fits the characteristics of nearby travel in mixed areas.

[0040] On the one hand, by establishing independent log-normal distributions according to user type, the study accurately captures the travel differences among private cars (short mileage, high concentration), ride-hailing vehicles (long mileage, low dispersion), and official vehicles (medium mileage, medium dispersion), avoiding the limitations of single distribution models that cannot distinguish user types. On the other hand, a multi-factor composite probability model is constructed based on the weights of actual surveys to ensure that the model covers all user groups within the region and conforms to the real user structure. Furthermore, by using seasonal and regional dynamic correction factors to adapt to changes in temperature and geographical environment in real time, the daily mileage data reflects both user type differences and environmental scenario differences, ultimately more closely resembling the random mileage characteristics of electric vehicles in actual operation.

[0041] Daily mileage is fundamental for assessing the energy consumption and charging demand of electric vehicles. Mileage directly determines vehicle energy consumption (the longer the mileage, the higher the energy consumption), and energy consumption directly determines charging demand (the higher the energy consumption, the higher the charging power and charging time requirements). Accurate actual daily mileage output by a multi-factor composite probability model provides precise basic data for subsequent charging load modeling based on dynamic time-series parking demand and Monte Carlo simulation of charging load. For example, knowing the actual daily mileage allows calculation of the vehicle's remaining battery power (State of Charge), thus determining whether the vehicle needs charging and the charging power requirement. Combined with the parking demand model, charging periods can be determined, ultimately leading to accurate calculation of the charging load power. By reducing the prediction error of daily mileage, the uncertainty of charging load is reduced from the source, providing reliable input data for subsequent two-stage optimization and control models of the distribution network, and avoiding deviations in distribution network scheduling decisions due to charging load errors.

[0042] Specifically, the uncertainty model for establishing electric vehicle charging load based on dynamic time-series parking demand forecasting includes: The functional areas are divided into residential areas, industrial and commercial areas, and public facilities areas.

[0043] The parking demand in residential areas is modeled using a normal distribution function centered at dusk.

[0044] The parking demand in industrial and commercial areas is modeled using a bi-peak or wide-peak model centered on midday.

[0045] Different parameters are used to model parking demand in public facility areas, distinguishing between weekdays and weekends.

[0046] The total parking demand curve is obtained by superimposing the parking demand of the three functional areas.

[0047] The parking demand model for residential areas is designed to match the evening peak and daytime trough characteristics of residents' daily routines. Given the high correlation between electric vehicle parking demand in residential areas and residents' commuting and home-based schedules, a model is constructed using a normal distribution function centered on evening, with the formula as follows: .

[0048] The meanings of each parameter and the design logic are as follows: The total number of electric vehicles in the residential area is a fundamental scale parameter of the model, which directly determines the upper limit of the total parking demand in the area. Its value is obtained by statistically analyzing the actual number of electric vehicles registered in the residential area, ensuring that the model closely matches the actual number of vehicles in the area.

[0049] The peak parking demand time corresponds to the scenario where residents return home to park in the evening after get off work. It is based on the time sequence parameters of urban residents' common commuting time, such as 9 to 5 or 10 to 6, to accurately pinpoint the peak time of parking demand in residential areas.

[0050] The hourly interval is a parameter for controlling the peak period width, reflecting the concentration of residents' off-get off work time. A 2-hour width means that the peak period covers 17:00-19:00, which includes normal off-get off work time, as well as taking into account the slight time shift caused by overtime work and commuting congestion, avoiding excessive narrowing or widening of the peak period.

[0051] The peak load factor represents peak hours. Around 6:00 PM, approximately 60% of electric vehicles in residential areas are parked. This figure is based on actual surveys. Residents park their vehicles in the community after get off work, with only a small number needing to travel again (such as shopping or picking up / dropping off), hence the higher but not 100% parking rate.

[0052] The base parking coefficient represents the fact that even during off-peak hours (such as 9:00-17:00), 30% of electric vehicles are still parked, corresponding to scenarios such as working from home, resting at night, and vehicles being idle, to avoid the model ignoring the actual situation that there is still parking demand during off-peak hours.

[0053] Modeling Parking Demand in Industrial and Commercial Areas: Matching the "Daytime Peak and Evening Off-Peak" Characteristics to Work Rhythms. Considering the synchronization of electric vehicle parking demand in industrial and commercial areas with work and business activities, a bi-peak or broad-peak model centered on midday is adopted to construct the model. The formula is as follows: .

[0054] The meanings of each parameter and the design logic are as follows: The total number of electric vehicles in the industrial and commercial area represents the total number of vehicles used for company commuting, business purposes, and employee private cars. The figure is obtained by statistically analyzing the number of electric vehicles around industrial and commercial parks and office buildings, and matches the scale of vehicles used for business activities in the area.

[0055] The parking demand may exhibit a dual-peak pattern, with peak times in the morning (10:00 AM) and afternoon (2:00 PM). The midday peak corresponds to the period when employees take lunch breaks and business activities are suspended. The dual-peak pattern corresponds to the concentrated parking demand at 10:00 AM, the stable period for business activities, and 2:00 PM, the stable period after the start of afternoon work, which aligns with the rhythm of vehicles staying in industrial and commercial areas during working hours.

[0056] The hour is a parameter for controlling the peak width. When using midday... When using the single-peak model centered on the vehicle, peak hours can cover 9:00-15:00, accurately matching the concentrated parking characteristics of vehicles during the midday work period. When using the bi-peak model with 10:00 AM and 2:00 PM, the two peaks, each 3 hours wide, overlap (11:00-13:00 is the overlap area), covering the entire period from 8:00 AM to 5:00 PM. The peak coverage range of both models aligns with the typical working hours of businesses from 8:30 AM to 5:30 PM, effectively reflecting the continuous parking demand for electric vehicles during working hours in industrial and commercial areas.

[0057] The peak coefficient represents the percentage of electric vehicles parked in industrial and commercial areas during peak working hours. Since these vehicles are mainly used for commuting during working hours, they are mostly parked in park or office building parking lots after arrival, with only a small number used for business trips. Therefore, the parking rate is higher than that in residential areas during peak hours.

[0058] The basic parking coefficient represents non-working hours. For example, if only 10% of electric vehicles are parked at 18:00 the next day at 8:00, this corresponds to vehicles on night duty or temporarily parked vehicles, which is consistent with the actual situation of sparse people and vehicles in industrial and commercial areas during non-working hours.

[0059] Modeling of parking demand in public facilities areas, distinguishing intraday fluctuation characteristics by date.

[0060] Considering the significant impact of weekday or weekend differences on electric vehicle parking demand in public facilities areas, a model is constructed using date type differentiation and sinusoidal fluctuations. The formula is as follows: .

[0061] The meanings of each parameter and the design logic are as follows: This represents the total number of electric vehicles in the public facility area, covering user vehicles going to the facility for consumption, medical treatment, and entertainment. The value is obtained by counting the average number of vehicles in parking spaces around the public facility per day, matching the service coverage scale of the facility.

[0062] Time represents working days. The time period represents the weekend and is used to switch the base parking ratio for different dates to address the difference between fewer people on weekdays and more people on weekends.

[0063] , The figures show the average parking percentages for weekdays and weekends, respectively. On weekdays, users are mostly at work and visit public facilities less frequently, resulting in an average parking percentage of 40%. On weekends, users have more leisure time and visit public facilities more frequently, resulting in an average parking percentage of 80%, reflecting the busy weekday and leisurely weekend lifestyle of urban residents.

[0064] The daily fluctuation range represents the intensity of fluctuations in parking demand compared to the daily average. A range of 0.2 implies that demand can reach as high as 1.2 times the daily average and as low as 0.8 times, avoiding the model outputting an idealized demand curve with no fluctuations, and matching users' travel habits of less in the morning and more in the afternoon.

[0065] As a phase adjustment parameter, by adjusting the phase of the sine function, the peak parking demand occurs in the afternoon (e.g., 15:00-17:00), which conforms to the actual travel patterns of users going to shopping malls, hospitals for follow-up visits, and cultural and sports centers in the afternoon, further improving the accuracy of the timing.

[0066] The total parking demand reflects the overall parking patterns in the area.

[0067] Since real-world urban areas often include residential areas, industrial and commercial areas, and public facility areas (such as mixed-use areas combining residential, commercial, and hospital facilities), a single-function area model cannot cover the overall demand. Therefore, the parking demand of the three functional areas is superimposed to obtain the total parking demand curve. This overlay logic can comprehensively reflect the coupling relationship of parking demand in different scenarios within the area, and ultimately output parking demand data that matches the actual operating rhythm of the area.

[0068] Dynamic time-series parking demand models accurately depict parking time-series characteristics, improving the accuracy of charging load forecasting. Electric vehicle charging behavior primarily occurs during parking periods, and the temporal and spatial distribution of parking demand directly determines the spatiotemporal characteristics of charging load. The dynamic time-series parking demand model designs differentiated time-series schemes for three functional areas: residential areas focus on evening peaks, industrial and commercial areas on daytime peaks, and public facility areas on weekend high demand and afternoon peaks. Parameters such as date, fluctuation amplitude, and peak width are introduced to optimize details, and finally, total demand is superimposed to reflect the overall coupling pattern of the region. Based on this, the charging time periods, areas, and number of vehicles can be clearly identified, improving the accuracy of charging load spatiotemporal distribution forecasting.

[0069] A dynamic time-series parking demand model supports Monte Carlo simulation. Monte Carlo simulation is a method for modeling charging load uncertainty, and the total parking demand curve output by the dynamic time-series parking demand model is its key input. In parking simulation, the difference between parking space demand and the current number of parked vehicles is used to determine vehicle entry and exit status and calculate parking duration. In charging simulation, charging behavior is arranged by combining charging pile availability and vehicle SOC, and charging load power is calculated, thereby supporting the construction of the charging load uncertainty set. This parking demand curve is the source input for Monte Carlo simulation and supports the modeling of charging load uncertainty.

[0070] Specifically, the uncertainty model for electric vehicle charging load also includes: The Monte Carlo method is used to simulate the charging load of electric vehicles, including parking simulation and charging simulation. In the parking simulation cycle, the vehicle entry and exit status is determined based on the difference between parking space demand and the number of vehicles, and the parking time of each vehicle is calculated. In the charging simulation cycle, charging behavior is arranged and charging load power is calculated based on the availability of charging piles and the state of charge of electric vehicles. The charging load prediction error is described by constructing a charging load uncertainty set based on the charging load prediction values ​​obtained through a multi-factor composite probability model and dynamic time-series parking demand prediction.

[0071] Parking simulation is a prerequisite for charging simulation. Based on dynamic time-series parking demand, it reconstructs the dynamic process of vehicles entering and exiting parking spaces through random sampling, and finally outputs the charging time window for each vehicle. Before starting the simulation, the total parking demand curve obtained based on the prediction of dynamic time-series parking demand needs to be imported. This curve provides a quantitative basis for parking space demand at various times; simultaneously, it initializes all electric vehicles in the area to a parked state. Enter parking simulation: At the current time, if the difference between parking space demand and the number of parked vehicles... If the parking simulation fails, a new vehicle is selected to enter the parking state; otherwise, a vehicle is selected to leave. After the parking simulation ends, the parking duration for each vehicle can be obtained. .

[0072] Then, the time is reset, and the charging simulation begins. Charging behavior is scheduled based on the availability of charging stations and the electric vehicle's SOC (State of Charge) status. After calculating the charging load power at the current moment, the simulation proceeds to the next moment. Finally, the 24-hour electric vehicle charging load curve is output.

[0073] There are two conditions that trigger the charging behavior. On the vehicle side, the current SOC must be lower than a preset threshold (usually 20% to avoid over-discharging the battery). The initial SOC value is calculated from the actual daily mileage (the longer the mileage, the greater the SOC drop). On the device side, there must be an available charging station. If the charging station is fully loaded, it will be queued in order of SOC from low to high, and charging will start sequentially after the charging station becomes available.

[0074] The degree of battery drain after driving is calculated by multiplying the electric vehicle's energy consumption coefficient per 100 kilometers by the actual daily mileage, and then dividing by the product of the battery capacity and 100. The energy consumption coefficient per 100 kilometers is a fixed parameter of the vehicle, the actual daily mileage is determined by a multi-factor probability model, and the battery capacity is the total energy stored in the vehicle's battery. This calculation provides a basis for determining whether charging is necessary.

[0075] The required charging amount for a single vehicle is determined. The difference between the target charging state (typically set to 80%) and the vehicle's current battery level is multiplied by the battery capacity to obtain the total amount of charging required. Charging demand is triggered only when the current battery level is below 20%. This calculation determines the total electrical energy required to charge the vehicle from its current level to the target level.

[0076] The charging power for a single vehicle is determined by dividing the required charging amount by the vehicle's parking time. This value should not exceed the charging station's rated power. The parking time is derived from a parking simulation cycle, and the charging station's rated power is the equipment's safe upper limit. This step determines the power required for the vehicle during actual charging.

[0077] At any given moment, the individual charging power of all vehicles currently charging is summed to obtain the total charging load power at that moment. This aggregated data provides load input for the optimized control of the power distribution network.

[0078] The simulation is carried out in 15-minute time steps. Each step repeatedly updates the parking queue, judges the charging trigger conditions, allocates charging piles, and calculates the power flow. The process is iterated for 96 consecutive steps (24 hours) to finally output a complete 24-hour electric vehicle charging load curve.

[0079] Furthermore, due to unpredictable user travel behaviors such as temporary overtime work and sudden travel, the charging load curve (predicted value) output by Monte Carlo simulation deviates from the actual load. It is necessary to clarify the error range through uncertainty set, and the specific logic is as follows: Based on the predicted power obtained from Monte Carlo simulation and combined with the prediction error coefficients statistically analyzed from historical data, an interval-type uncertainty set is constructed: ; in, for Time of the first The actual load power of an electric vehicle charging station; for Time of the first Predicted load power of each charging station; for The real-time prediction error coefficient is obtained by statistically analyzing the deviation rate of actual power predicted power over the past month. The total number of electric vehicle charging stations; The total number of scheduling periods (e.g., 24 hours) is used to ensure that the collection covers all charging stations and all time periods.

[0080] The uncertainty set clarifies the worst-case scenario for charging load fluctuations by defining the interval boundaries. Upper limit. The lower limit corresponds to the load exceeding the forecast (distribution network overload risk). The corresponding load is lower than the forecast (risk of insufficient absorption of new energy), which transforms the abstract uncertainty into a quantifiable mathematical boundary.

[0081] Uncertainty ensembles address the discrepancy between simulated forecasts and actual load, quantifying error boundaries and transforming load fluctuations caused by the randomness of user travel into defined ranges. This allows dispatchers to understand the upper and lower limits of load fluctuations, preventing dispatch failures due to unknown errors. It supports the worst-case scenario handling in the second stage of a two-stage model by screening high-cost, high-risk loads within the ensemble and optimizing variables such as converter power and load shedding to ensure the effectiveness of control strategies across all fluctuation scenarios. By clearly defining the error range, it avoids model reliance on ideal predictions, ensuring voltage stability and controllable network losses when the distribution network responds to sudden increases in charging load, thus enhancing its resilience to disturbances.

[0082] Specifically, the objective function for constructing the two-stage optimization and control model of the distribution network is as follows: System operating losses include network loss costs, distribution transformer loss costs, converter loss costs, energy storage charging and discharging loss costs, and load shedding costs. All cost items take into account electricity price factors and time intervals.

[0083] Network loss cost is calculated based on the product of the square of the branch current amplitude and the resistance.

[0084] The cost of distribution transformer losses includes iron losses and copper losses.

[0085] The converter loss cost is calculated based on the converter loss coefficient.

[0086] Energy storage charging and discharging loss costs are calculated based on charging and discharging power and efficiency.

[0087] The load shedding cost is calculated based on the load shedding penalty coefficient.

[0088] Furthermore, in the DC interconnection scenario, the objective function of the two-stage optimization and control model for the distribution network focuses on minimizing the total operating cost under the worst-case scenario, as expressed below: ; in, The first-stage decision variable vector includes line switch state variables, energy storage charging and discharging state variables, and capacitor bank switching state variables. These variables need to be decided in advance and should not be adjusted with fluctuations in charging load. The second-stage decision variable vector includes the power of the distribution transformer, the power of the converter, the charging and discharging power of the energy storage, the reactive power compensation power of the photovoltaic inverter, and the load shedding power. These variables are used to cope with the uncertainty of the charging load and are dynamically adjusted based on the first-stage decision. For electric vehicle charging load power, For the uncertain set of electric vehicle charging load, The measures must cover the worst-case load scenarios to ensure the robustness of the control strategies.

[0089] Total operating costs The specific composition is as follows: .

[0090] Network loss cost Based on Joule's law of resistive heating in AC / DC branches of the distribution network, the set of distribution network branches needs to be considered. Losses in all branches, multiplied by the electricity price. and time interval The calculation formula is: ; in, This represents the total number of scheduling periods, typically 24 hours, divided into hourly or 15-minute increments. for Time Branch The square of the current amplitude; branch road The resistance; It is a collection of distribution network branches, including AC branches and DC interconnection branches, covering the current path of the entire network.

[0091] First, multiply the square of the current in all branches within each time period by the resistance and sum them to obtain the total network loss power for that time period. Then, sum up all time periods to obtain the total network loss cost, ensuring the energy consumption economic cost of covering the entire network and all time periods.

[0092] Distribution transformer loss cost Including iron losses (no-load losses) and copper losses (load losses), the total number of distribution transformers in the DC interconnection area needs to be considered. and multiplied by the electricity price and time interval The calculation formula is: ; in, for Time distribution transformer The operating power loss is calculated by combining iron loss and copper loss. First, the real-time power loss of a single transformer is calculated based on fixed iron loss and copper loss that varies with load rate. Then, the results are summed for all transformers and all time periods to ensure an accurate reflection of the energy consumption cost of the transformer throughout its entire operating cycle.

[0093] VSC (Voltage Switchgear) Loss Cost Power loss calculations based on loss factors show that DC interconnects rely on voltage source converters (VSCs) to achieve AC-DC power conversion, and their losses need to take into account the total number of VSCs in the interconnected region. and multiplied by the electricity price and time interval The calculation formula is: ; in, for Time of the first Power loss of each VSC.

[0094] Energy storage charging and discharging loss cost Considering the energy loss due to charging and discharging efficiency, energy storage devices experience energy loss during the charging and discharging process. This actual loss needs to be corrected using the charging and discharging efficiency and multiplied by the electricity price. and time interval The calculation formula is: ; in, This refers to the number of energy storage devices, covering all energy storage units in the DC interconnected distribution network; and They are respectively Energy storage at all times The charging and discharging efficiency; and Energy storage devices The charging efficiency and discharging efficiency range from 0 to 1.

[0095] Shedding Costs Based on the penalty coefficient for power supply reliability, load shedding is a last resort for dealing with extreme scenarios. The emphasis on power supply reliability needs to be reflected through a penalty coefficient multiplied by the electricity price. and time interval The calculation formula is: ; in, This represents the total number of distribution network nodes, covering both AC and DC nodes, and reflects all possible locations where load shedding may occur. for Time Node The load shedding power is generated only when the load exceeds the limit and is an adjustment variable for the two-stage decision-making process. The load shedding penalty factor is much greater than 1, such as... High penalties are imposed to encourage users to avoid cutting off load as much as possible, thus ensuring power supply to users.

[0096] Total operating costs By comprehensively considering the above five costs, a comprehensive model of the economic efficiency of distribution network operation is achieved. Network loss costs directly reflect line transmission efficiency; transformer and converter loss costs quantify the operating energy efficiency of key equipment; energy storage loss costs reflect the economic costs of energy conversion; and load shedding costs serve as a guarantee mechanism for the safe operation of the system. This integrated modeling approach for multiple cost factors ensures that the optimization results reduce the total operating cost of the system while taking into account equipment operating efficiency and power supply reliability.

[0097] Specifically, the two-stage optimization control model for the distribution network also includes the following operational constraints: AC power flow balance constraints include active and reactive power injection balance constraints at AC nodes, voltage drop constraints in AC branches, Ohm's law constraints in AC branches, and capacity constraints in AC branches.

[0098] DC power flow balance constraints include DC node active power injection balance constraints, DC branch voltage drop constraints, and DC branch Ohm's law.

[0099] Distribution network reconfiguration constraints include radial operation constraints guaranteed by virtual power flow constraints, branch switch status constraints, and branch switch maximum daily operation constraints.

[0100] The active and reactive power injection balance constraint at AC nodes is based on Kirchhoff's current law. The active / reactive power injection at any AC node is equal to the sum of the active / reactive power of all incoming and outgoing branches of that node, as shown in the formula:

[0101] in, The set of AC nodes covers all AC distribution network nodes; / for Time Node Active / reactive power injection; For nodes The set of branch end nodes with the first node; For nodes The set of the first nodes of the branch with the last node; / for Time Branch Active / reactive power; for Time Branch The square of the current amplitude; branch road The resistance; branch road The resistance.

[0102] The active and reactive power injection power balance constraint at AC nodes ensures the power supply and demand balance at each node, providing a basis for subsequent voltage and current calculations; it also indirectly relates to electric vehicle charging load and new energy output, ensuring that node power still meets the conservation requirement when the load fluctuates, and avoiding local power accumulation.

[0103] AC branch voltage drop constraints are based on the AC circuit voltage drop formula, combined with branch switch states. The formula for determining whether a branch road should be used is: ; in, / for Time Node / The square of the voltage amplitude; branch road Switch state variables (1 = closed, 0 = open); For sufficiently large positive numbers, when When (branch disconnected), This makes the inequality automatically true and does not constrain the voltage of the disconnected branch. / branch road Resistance / reactance.

[0104] Closed branch The voltage drop must conform to the law of resistance voltage drop + reactance voltage drop; disconnect the branch. No current is required, and voltage relationships do not need to be constrained. This ensures that the voltage drop in closed branches remains within a reasonable range, preventing excessive voltage drops from causing the terminal node voltage to fall below the limit, thus guaranteeing voltage quality. The first-stage switching state of the associated distribution network reconfiguration decision enables voltage constraints to be dynamically adjusted with topology changes to adapt to the reconfigured power grid structure.

[0105] The Ohm's law constraint for AC branches is based on Ohm's law, where the apparent power of an AC branch equals the node voltage multiplied by the branch current, as shown in the formula: ; in, for Time Branch The current amplitude; branch road The apparent power squared. In AC circuits, current, apparent power, and voltage satisfy a linear relationship. This constraint is needed to link power and current, providing current data for subsequent branch capacity constraints. Establishing a quantitative relationship between power, voltage, and current avoids contradictions such as excessive power but abnormal current calculations, ensuring accurate calculation of subsequent network losses. It provides a current basis for branch capacity constraints, indirectly ensuring that branch currents do not exceed rated values.

[0106] AC branch capacity constraints are based on the branch's rated capacity limit; the apparent power of the branch must not exceed the rated capacity, as shown in the formula: ; in, branch road Rated capacity; This represents the upper limit of the apparent power when a branch is closed. Exceeding the rated power of a branch can lead to overheating of the conductors and damage to the insulation; therefore, a square-form constraint on the apparent power limit is necessary. This prevents AC branch power overload from damaging equipment and ensures the safe operation of the distribution network. It also indirectly limits the centralized access of electric vehicle charging loads and guides the load to be rationally distributed within the network.

[0107] The active power injection balance constraint at DC nodes is based on Kirchhoff's current law. The active power injected into any DC node is equal to the sum of the active power of all incoming and outgoing branches of that node, as shown in the formula: ; in, For DC node set; For DC path collection; for DC node at any time The active power injected; DC branch at time t The active power. DC nodes only transmit active power; injected power must be fully transferred through DC branches to ensure power conservation. Functional constraints on the power balance of the DC interconnect network ensure that cross-regional power exchange conforms to physical laws. Simultaneously, the power of the VSC converter is correlated, providing constraint boundaries for the second-stage decision-making.

[0108] DC branch voltage drop constraint is based on the DC circuit voltage drop formula, which is: ; in, A collection of DC branches; / for DC node at any time / The voltage; DC branch The DC branch voltage drop is determined solely by active power and resistance, conforming to Ohm's law. DC branch voltage drop constraints ensure reasonable voltage drops, preventing DC node voltage deviations from rated values ​​and guaranteeing stable operation of the VSC converter. Limiting DC power transmission distance guides power exchange within a reasonable range.

[0109] The Ohm's law constraint for DC branches is based on the DC Ohm's law, which states that the active power of a DC branch equals the node voltage multiplied by the branch current, as shown in the formula: ; in, for DC branch The current; DC branch The square of the active power. In DC circuits, current, active power, and voltage satisfy a linear relationship, eliminating the need to consider reactive components, making the constraint form simpler than in AC circuits. Establishing a quantitative relationship between DC power, voltage, and current ensures accurate calculation of DC branch currents, providing a basis for calculating losses in DC equipment. Indirectly constraining DC current to keep it within rated values ​​prevents equipment overload.

[0110] AC distribution network reconfiguration must avoid the formation of ring networks, as ring networks can easily lead to excessive short-circuit currents. Virtual power flow constraints are needed to ensure a radial topology, while also constraining the switching frequency.

[0111] Radial operating constraints simulate radial topology characteristics through virtual power flow, ensuring that the reconfigured AC distribution network is a single-source radial network without loops. The key formulas and logic are as follows: Connectivity constraints: ;in, for The virtual power flowing into the distribution network from the upstream power grid at any given time; The total number of AC nodes; the virtual power of the upstream grid node is equal to the sum of the virtual power of its outflow branches, ensuring that the grid is connected to all nodes from the upstream power source.

[0112] Virtual load constraints: ;in, for Constant communication of branch lines Virtual power on; The set of nodes connected to the upper-level power grid; For nodes The set of branch end nodes with the first node; For nodes The set of the first nodes of the branch with the last node; This is a set of communication nodes.

[0113] Except for the upstream node, all AC nodes have a "virtual power net outflow of 1, simulating a unit virtual load, ensuring that there are no isolated nodes."

[0114] Topological constraints: .in, branch road exist The on / off state at any given time. This is the set of communication branches. The number of closed branches is equal to the total number of communication nodes minus 1. Based on the topological nature of radial networks, n nodes require n-1 branches to connect, resulting in a network without loops.

[0115] Cut off branch constraints: The virtual power of a disconnected branch is 0, thus preventing virtual power from flowing in the disconnected branch.

[0116] Branch switch state constraints constrain the switching logic of branch switches to prevent frequent fluctuations in switch states. The formula is as follows: ;in, branch road Maximum daily number of branch circuit breaker operations. Real-time operation status of the breaker can be recorded, providing data support for subsequent operation count constraints. This prevents unexplained fluctuations in breaker status between adjacent time periods, ensuring the stability of reconfiguration decisions.

[0117] The daily maximum number of operations constraint for branch switches is used to limit the daily operating frequency of branch switches and avoid damage to the equipment due to frequent operation. The formula is: ;in branch road Maximum daily number of branch circuit breaker operations. Limiting the maximum daily number of branch circuit breaker operations can protect switchgear, extend its service life, and reduce maintenance costs; it also prevents reconfiguration decisions from relying excessively on switch operations, balancing economic efficiency and equipment safety.

[0118] Specifically, the two-stage optimization and control model for the power distribution network also includes the following equipment operation constraints: Capacitor bank operation constraints include reactive power compensation constraints based on the number of switching groups and the switching capacity of a single group, upper limit constraints on the number of switching groups, switching action constraints, and maximum daily switching frequency constraints.

[0119] Operating constraints for distribution transformers include operating power factor constraints, loss calculation constraints based on iron and copper losses, load rate calculation constraints, and load rate upper limit constraints.

[0120] Converter operating constraints include power coupling constraints with distribution transformers, capacity constraints, loss calculation constraints, and AC / DC side power balance constraints.

[0121] Energy storage operation constraints include charging and discharging power balance constraints, simultaneous charging and discharging not allowed constraints, energy balance constraints, upper and lower limits of energy, charging and discharging state switching constraints, and maximum number of daily charging and discharging cycles constraints.

[0122] Distributed power source operation constraints include upper and lower limits of active and reactive power output constraints for distributed power sources connected to AC nodes, and upper and lower limits of active power output constraints for distributed power sources connected to DC systems.

[0123] Load shedding constraints include AC node load shedding constraints and DC node load shedding constraints, wherein the load shedding amount does not exceed the set upper limit of the load shedding ratio.

[0124] Furthermore, based on the reactive power compensation constraints of the number of switching capacitor banks and the single-bank switching capacity, the total reactive power compensation of the capacitor bank is determined by the product of the number of switching capacitor banks and the single-bank capacity, and must be matched with the reactive power demand of the distribution network. The formula is as follows: ;in, for Capacitor bank at time The number of throw groups; For capacitor bank Single-group switching capacity; This refers to a collection of capacitor bank equipment. Reactive power compensation is adjusted by switching capacitor banks in groups. Since the capacity of a single group is fixed, the total compensation is linearly positively correlated with the number of groups switched, avoiding equipment impact caused by continuous adjustment of the compensation.

[0125] The principle behind the upper limit constraint on the number of switching groups is that the number of switching groups must not exceed the maximum allowable number of groups in the equipment design. The formula is: ;in, For capacitor bank The maximum number of capacitor banks that can be switched. Each capacitor bank has a rated withstand voltage and current limit. Exceeding the maximum number of switching banks will cause the total capacity to exceed the limit, leading to insulation breakdown or overheating failure.

[0126] The principle of switching action constraint is that the change in the number of switching groups in adjacent time periods should not exceed one group, to avoid voltage fluctuations caused by sudden changes in reactive power compensation. The formula is: ; When capacitor banks are switched on or off, reactive inrush current is generated. If the number of banks changes by ≥2 in adjacent time periods, the inrush current will increase sharply, which can easily lead to violent fluctuations in bus voltage and affect the operation of sensitive loads.

[0127] The principle behind the daily maximum switching frequency constraint is that the total number of switching operations in a single day shall not exceed the equipment's allowable upper limit. The formula is: ;in, The maximum number of times the capacitor bank can be switched on and off per day is c. The mechanical life of the capacitor bank switching switch is limited. Frequent switching will accelerate contact wear, leading to poor contact or fault tripping.

[0128] Furthermore, the constraint formula for the number of capacitor banks to be switched, based on the binary combination number representation, is as follows: ;in, for The highest bit when using a combined binary representation; For the corresponding combination of binary numbers 0 / 1 variables.

[0129] The principle of power factor constraint is that the power factor of the distribution transformer must be within a reasonable range to avoid excessive reactive power leading to increased losses. The formula is: ; where, in the formula A collection of distribution transformers; and They are respectively Time distribution transformer The active and reactive power; This is the power factor angle corresponding to the lowest power factor of a distribution transformer. A low power factor (high reactive power ratio) will lead to increased transformer winding current and increased copper losses. When the power factor is too high (close to 1.0), the reactive power regulation margin is insufficient, making it susceptible to load fluctuations.

[0130] The principle of loss calculation constraints based on iron loss and copper loss is that the total transformer loss is the sum of iron loss and copper loss, and must conform to the equipment loss characteristics. The formula is: ; in, and These are the rated iron loss and copper loss of the distribution transformer, respectively. for Time distribution transformer Load rate; For distribution transformers No-load reactive power loss; For distribution transformers Short-circuit reactive power loss. Iron loss is determined by the core material and voltage; copper loss is proportional to the square of the load rate, conforming to Joule's law. As the current increases linearly with the load rate, the loss increases with the square of the current.

[0131] The principle behind load factor calculation constraints is that the load factor is the ratio of the actual load on the transformer to its rated capacity. It requires quantitative calculation of the associated power and capacity, using the following formula: ;in, For distribution transformers The rated capacity. The load factor directly reflects the load on the transformer and is an indicator for judging whether the equipment is overloaded. It needs to be quantitatively characterized by actual power or rated capacity.

[0132] The principle behind the load rate limit constraint is that the load rate must not exceed the maximum allowable limit of the equipment to avoid long-term overload leading to insulation aging. The formula is: ;in This refers to the maximum load rate of the distribution transformer. When the load rate exceeds the upper limit, the winding current becomes excessive, leading to increased heat generation, which accelerates the aging of insulation materials, shortens the transformer's lifespan, and in severe cases, causes short-circuit faults.

[0133] The principle of power coupling constraint with distribution transformers is that converters are usually connected to the low-voltage side of distribution transformers, and their AC side power must not exceed the remaining capacity of the corresponding transformer. The formula is: ; In the formula: For the set of VSC devices in the system; In order to be with the first A collection of distribution transformers connected to VSC; and The first Active and reactive power of each VSC; and This refers to the active and reactive load power connected to the distribution transformer. The AC power of the converter is obtained from the transformer, and the remaining capacity must be used after deducting the local load to avoid overloading the transformer due to the power superposition of the converter.

[0134] The principle of converter capacity constraint is that the apparent power of the converter must not exceed the rated capacity to avoid damage from overcurrent or overvoltage. The formula is: In the formula: For the first The rated capacity of each VSC; Let be the loss factor for the k-th VSC. The semiconductor devices in the converter have rated current and voltage limits. Exceeding the rated apparent power will cause the device current or voltage to exceed the limit, leading to overheating or breakdown.

[0135] The principle of loss calculation constraints is that converter losses are proportional to apparent power and must conform to equipment loss characteristics. The formula is: In the formula, For converter The loss factor. Since the converter loss mainly comes from the conduction loss and switching loss of semiconductor devices, both of which increase linearly with the apparent power, the loss is linearly related to the apparent power.

[0136] The principle of AC / DC power balance constraint is that the DC output power of the converter equals the AC input power minus its own losses, ensuring power conservation. The formula is: In the formula, where For the first Active power injected into the DC-side nodes by each VSC.

[0137] The principle of charge / discharge power balance constraint is that the charging or discharging power of energy storage must not exceed the rated power to avoid excessive charging and discharging current. The formula is: ; In the formula: and These are the state variables for energy storage charging and discharging, respectively; A collection of energy storage devices; and These are the upper limits for charging and discharging power of energy storage batteries. Energy storage batteries have limits on the charging and discharging current; exceeding the rated power will lead to excessive current, causing battery overheating, lifespan reduction, and even thermal runaway.

[0138] The principle behind the restriction against simultaneous charging and discharging is that energy storage can only be in either a charging or discharging state at any given time, and these two states are mutually exclusive. The formula is as follows: The charging and discharging process of energy storage batteries involves the directional movement of electrolyte ions. At the same time, charging and discharging can cause disordered ion movement, damage the battery structure, significantly shorten its lifespan, and even cause internal short circuits.

[0139] The principle of energy balance constraint is that the current energy storage capacity equals the energy storage capacity at the previous moment plus the charging capacity and minus the discharging capacity. Charging and discharging efficiency must be considered. The formula is: In the formula, for Energy storage at all times The amount of electricity; The time interval between adjacent scheduling periods; This refers to a collection of energy storage devices. During charging, the actual amount of electricity stored in the battery is the charging power × time × efficiency; during discharging, the battery needs to release the discharge power × time / efficiency to meet the output demand, which conforms to the law of conservation of energy.

[0140] The principle behind the upper and lower limits of battery capacity is that the remaining energy storage capacity must be between the minimum protection capacity and the rated capacity to avoid battery damage. The formula is: In the formula, and These are the upper and lower limits for energy storage capacity, respectively. Over-discharging will cause sulfation of the battery's negative electrode, irreversibly damaging its capacity. Overcharging will cause electrolyte decomposition, leading to battery bulging and leakage.

[0141] The principle of charge / discharge state switching constraints is that energy storage state switching between adjacent time periods needs to be recorded through switching variables to avoid frequent switching without reason. The formula is: .in, For energy storage exist The constant switching between charging and discharging states is a variable. When the energy storage state switches, the direction of ion movement inside the battery changes. Frequent switching can cause ion movement disorder, increasing losses. At the same time, frequent operation of switching devices will accelerate wear.

[0142] The principle behind the daily maximum charge / discharge cycle constraint is that the total number of energy storage state switching cycles per day should not exceed the equipment's allowable upper limit. The formula is: In the formula, This is the maximum daily charge / discharge switching limit. Each state switch causes an impact on the battery and switch. Exceeding the limit will significantly shorten the equipment's lifespan and increase the probability of failure.

[0143] The principle of distributed power source operation constraints is based on the output boundary constraints of the equipment's rated characteristics. Distributed power sources connected to AC nodes need to transmit both active and reactive power simultaneously, both of which are limited by the equipment's rated capacity and reactive power regulation capability. The formula is: ; In the formula, A collection of AC distributed power sources; and They are respectively Distributed power supply p The meritorious and the ineffective contributions; This is the power factor angle corresponding to the lowest power factor of a distributed power source. The main component of an AC distributed power source is the inverter, whose apparent power must not exceed its rated capacity. Therefore, the upper limits for active and reactive power output must be constrained separately. Exceeding the rated active power output will cause overcurrent and overheating in the inverter's semiconductor devices, and exceeding the reactive power regulation capacity will cause overload in the inverter's reactive power module, both of which may lead to equipment failure. The lower limit for active power output is 0, because the power source cannot output active power when natural resources are insufficient.

[0144] Distributed power sources connected to a DC system only have upper and lower limits for their active power output. Since distributed power sources connected to a DC system only transmit active power, only active power output needs to be constrained. The formula is as follows: In the formula: It is a collection of DC distributed power sources. This represents the upper limit of active power output for distributed power sources. DC systems interconnect power through converters, transmitting only active power; therefore, reactive power regulation is not required for distributed DC power sources. The upper limit of active power output is determined by the rated current and voltage of the DC-side equipment. Exceeding the rated voltage will cause overcurrent on the DC side, triggering converter protection tripping and interrupting power transmission in the DC network.

[0145] Load shedding constraints are used to control the scale of load reduction in extreme scenarios. The principle is based on the load reduction boundary constraints of power supply reliability. Load shedding is divided into AC node load shedding and DC node load shedding according to node type. Both types of constraints must ensure that the load shedding amount does not exceed a set upper limit for the load shedding ratio. The formula for AC node load shedding constraints is: In the formula: and For nodes The active and reactive power of the load; This is the upper limit of the load shedding ratio; For nodes The amount of reactive load shedding on the device; For nodes The active load shedding capacity.

[0146] The DC node load shedding constraint formula is: .

[0147] Distributed power generation operation constraints and load shedding constraints provide boundaries for the first-stage power pre-scheduling and the second-stage load emergency adjustment, respectively, ensuring that optimization decisions are both compliant and feasible, and supporting the safe and economical operation of the distribution network under the large-scale access of electric vehicles.

[0148] Specifically, the algorithm for solving the two-stage optimization control model of the distribution network using column and constraint generation includes: The two-stage optimization and control model of the distribution network is decomposed into a main problem and sub-problems.

[0149] The main problem involves finding the optimal scheduling decision in the first stage under finite adverse scenarios to provide a lower bound solution.

[0150] The subproblems are substituted into the solution of the current main problem to obtain the first-stage scheduling decision, and the optimal second-stage scheduling decision under the worst scenario is solved to identify the worst scenario and provide an upper bound solution.

[0151] Based on the strong duality theorem, the bi-level optimization problem of the subproblem is transformed into a single-level optimization problem, and the nonlinear term is processed by discretizing the uncertain set of electric vehicle charging load and then using the Big-M method.

[0152] In solving the two-stage optimization control model of the distribution network, non-convex nonlinear terms are handled.

[0153] Specifically, the processing of nonconvex nonlinear terms includes: Transform non-convex nonlinear constraints into convex or linear constraints.

[0154] The absolute value constraints are directly expanded into linear constraints, and the quadratic equality constraints are transformed into second-order cone constraints using second-order cone relaxation techniques.

[0155] The problem is eventually transformed into an optimization problem containing only linear and cone constraints, which is then solved iteratively until the convergence condition is met.

[0156] Furthermore, the original form of the two-stage optimization control model for the distribution network is a three-level optimization problem: ,in These are the decision variables for the first stage, namely, the state variables of the line switch, the state variables of the energy storage charging and discharging, and the state variables of the capacitor bank switching. For the second stage decision variables, For the uncertain set of electric vehicle charging loads.

[0157] Since the three-level optimization is extremely difficult to solve directly, the Column and Constraint Generation (CCG) algorithm breaks it down into a main problem (MP) and a sub-problem (SP) for iterative solution. The logic is to gradually identify adverse scenarios and iteratively narrow the optimal solution range.

[0158] The main problem (MP) involves finding the first-stage decision and lower bound solution. The main problem fixes a finite number of identified adverse scenarios and solves for the first-stage decision variables. The optimal value, formula: ; In the formula, This serves as an intermediate auxiliary variable, used to characterize the minimum total operating cost under the current finite scenario; This represents the current iteration number, corresponding to the number of identified [items / items]. A severe electric vehicle charging load scenario; The s-th worst-case scenario for electric vehicle charging load is identified for the sub-problem; For the first Second-stage decision variable vector under adverse scenarios; , , , , , , , , , For coefficient matrices or vectors, such as For the first Scalar values ​​in a cone constraint. Linear constraints on decision variables in the first stage (such as the upper limit of the number of capacitor banks to be switched on and off, and the constraint on the number of line switch operations). It is a second-order cone constraint, obtained by relaxation of the second-order constraint.

[0159] In the limited number of identified adverse scenarios, find the first-stage decision. The optimal solution involves determining the on / off state of the line switches, the charging / discharging mode of the energy storage devices, and the number of capacitor banks to be switched on or off, ensuring that these pre-determined variables are suitable for the known risk scenarios. Since the main problem only covers some severe scenarios, the calculated total operating cost is the most optimistic minimum cost, constituting the lower bound of the entire optimization problem. In subsequent iterations, the lower bound will gradually increase, approaching the true optimal value.

[0160] Subproblems (SPs) identify worst-case scenarios and find upper bound solutions. The first-stage decision-making process fixes the output of the main problem for each subproblem. Solve for the worst-case charging load scenario and the corresponding second-stage decision. The original form is a two-layer optimization: ; This form involves maximizing the outer layer (finding the worst-case scenario) to minimizing the inner layer (finding the corresponding two-stage decision). It is difficult to solve directly and requires transformation through strong duality theorem and discretization of uncertain sets.

[0161] Step 1: Transform the strong duality theorem into a two-level optimization

[0162] Based on the strong duality theorem, the dual problem of the inner minimization problem and the outer maximization problem are merged and transformed into a single-layer optimization: ; , , The dual variables are the dual factors of the linear constraint and the second-order cone constraint, respectively. The strong duality theorem states that when both the primal and dual problems are feasible, their optimal values ​​are equal. Therefore, the dual variables can be used to transform the bi-level optimization into a single-level maximization problem, eliminating the inner minimization stage. This simplifies the bi-level logic of finding the scenario and then finding the decision from the subproblem into a single-level logic of simultaneously solving the worst-case scenario and the dual variables, significantly reducing the difficulty of the solution.

[0163] Step 2: Discretization of the uncertain set of electric vehicle charging load

[0164] Since the worst-case scenario typically occurs within the uncertain set of electric vehicle charging loads, where the charging load exceeds the upper limit of the prediction or falls below the lower limit of the prediction, the following approach is based on discretizing the uncertain set of electric vehicle charging loads: ; In the formula, Forecast values ​​for electric vehicle charging load demand; This is a vector consisting of state variables representing the state variables of the electric vehicle charging load demand reaching the upper boundary. This is a vector consisting of state variables representing the lower boundary state of electric vehicle charging load demand. This is a coefficient vector composed of the prediction error coefficients of electric vehicles; The robustness coefficient is the upper limit of the number of times the electric vehicle charging load demand reaches the boundary. It transforms the continuous uncertain set into a finite number of discrete scenarios (boundary scenarios), avoiding traversing infinite scenarios while ensuring coverage of the critical scenarios with the most severe load fluctuations and highest operating costs.

[0165] Step 3: Big-M method for handling nonlinear terms

[0166] Subproblems exist These nonlinear terms are linearized using the Big-M formula: ; In the formula, , , Auxiliary variables introduced; Coefficient matrix The List; Electric vehicle charging load vector dimensionality; For the prediction error vector The One component; State variables The One component; State variables The One component; The nonlinear term is a sufficiently large positive number. The problem is transformed into a linear constraint and combined with the discretized 0-1 variables to form a mixed integer second-order cone optimization problem. The mixed integers are derived from the 0-1 variables, and the second-order cones are derived from the previous quadratic constraint relaxation, ensuring that the subproblems can be solved by commercial solvers.

[0167] The two-stage optimization control model of the distribution network contains absolute value constraints and quadratic equality constraints, both of which are non-convex and nonlinear constraints. They cannot be directly incorporated into the linear or cone optimization framework and need to be transformed through the following methods.

[0168] First, perform a linearization transformation for the absolute value constraint.

[0169] Both the switching state transition constraints and the energy storage state transition constraints in the model contain absolute value terms, and the transformation logic is as follows:

[0170] After directly expanding the absolute value constraint, it can be transformed into the following linear constraint: These are the state variables to be constrained. As auxiliary variables, they represent the values ​​of the absolute value term; the absolute value constraint is completely replaced by two linear constraints. This transforms the nonlinear absolute value constraint into a linear constraint, avoiding non-convex discontinuities during optimization and ensuring the model can be solved linearly.

[0171] Then, a second-order cone relaxation transformation with quadratic equality constraints is performed.

[0172] In the model, Ohm's law for the AC branch, Ohm's law for the DC branch, the load rate of the distribution transformer, and VSC losses are all quadratic equality constraints. These need to be transformed into convex constraints through second-order cone relaxation, as detailed below: The second-order cone-relaxed AC branch of Ohm's law is: ; The DC branch is: .

[0173] Since the objective function is positively correlated with network loss (the lower the loss, the lower the cost), the optimization process will automatically select the solution that makes the relaxation equation true, so there is no need to worry about relaxation error.

[0174] The second-order cone relaxation of the equipment constraints results in the following distribution transformer load factor: .

[0175] VSC loss is: .

[0176] By using the convexity of a second-order cone to replace the non-convexity of the quadratic equation, and because the objective function is positively correlated with equipment loss, the relaxation solution is completely consistent with the solution of the original problem.

[0177] After all constraints are transformed, the model contains only linear constraints and second-order cone constraints, and its compact form is shown in the formula: ; ; ; ; In the formula, A vector consisting of the charging load of electric vehicles; It is a vector consisting of the coefficients of the variables in the objective function; , , , This is the coefficient matrix corresponding to the linear constraint coefficients; , This is the coefficient vector corresponding to the linear constraint coefficients; For the first The coefficient matrix corresponding to each cone constraint coefficient; For the first The coefficient vector corresponding to each cone constraint coefficient; For the first The scalar value in the cone constraint; the number of cone constraints.

[0178] The original non-convex model is transformed into a linear and second-order cone convex optimization model, ensuring that both the main problem and subproblems can be solved by efficient algorithms, laying the foundation for subsequent iterative convergence.

[0179] Finally, the complete process of iterative convergence is performed to approximate the optimal solution.

[0180] Initialization settings: First, determine the initial parameters related to the iteration, set the number of iterations to 0, the initial lower bound to negative infinity, and the initial upper bound to positive infinity. At the same time, set the convergence threshold to 10 to the power of negative 4. This threshold is used to determine whether subsequent iterations have reached the convergence state.

[0181] Solving the main problem involves two cases. When the iteration count is 0, an initial severe electric vehicle charging load scenario is randomly generated. When the iteration count is greater than or equal to 1, the new severe electric vehicle charging load scenario identified in the previous subproblem is added to the main problem. The main problem is then solved to obtain the first-stage decision for the current iteration round and a new lower bound, which is not less than the lower bound of the previous round.

[0182] Solve the subproblem: Fix the first-stage decision of the current round obtained from solving the main problem in the previous step, solve the transformed mixed integer second-order cone problem, identify the new round of severe electric vehicle charging load scenarios through this subproblem, and obtain a new upper bound, which is no greater than the upper bound of the previous round.

[0183] Convergence judgment: Calculate the difference between the new upper bound and the new lower bound. If the difference is less than or equal to the preset convergence threshold, the iteration terminates and the final optimal first-stage decision and optimal second-stage decision are output. If the difference is greater than the convergence threshold, the iteration count is increased by 1, and the process returns to step 2 to continue the next round of iteration.

[0184] Specifically, the distribution network optimization and control strategy is obtained and the following operations are performed: Adjust the status of power distribution line switches to achieve network reconfiguration.

[0185] Control the charging and discharging power and status of energy storage devices.

[0186] Adjust the number of capacitor banks switched on and off.

[0187] Adjust the power of the distribution transformer, the power of the converter, and the reactive power compensation power of the photovoltaic inverter, and perform load shedding operations based on the upper limit of the load shedding ratio set in the load shedding constraints.

[0188] Furthermore, network reconfiguration optimizes the distribution network topology by controlling the state variables of line switches. While ensuring the distribution network maintains a radial operation, system operating losses are reduced by optimizing power flow distribution paths. Radial operation is a fundamental requirement for distribution networks; virtual power flow constraints ensure network connectivity without forming loops.

[0189] During execution, based on optimization results, the system adjusts the branch switch state variables at specific times, closing some branches while disconnecting others. Specifically, during periods of high photovoltaic output and strong sunlight, branches connecting photovoltaic-rich areas are closed to promote local consumption of new energy; during peak load periods, reconfiguration operations transfer some of the load from heavily loaded lines to relatively lightly loaded lines to achieve balanced load distribution.

[0190] By selecting the optimal power transmission path, network loss costs are significantly reduced. Load levels across all lines are balanced to prevent localized equipment overload and ensure safe equipment operation. In the event of a fault, the faulty area can be quickly isolated, and power can be restored to non-faulty areas, improving power supply reliability.

[0191] The control of an energy storage system includes adjusting the state variables of energy storage charging and discharging, as well as the charging and discharging power. Its working principle is based on the concept of energy time shift, charging during periods of abundant electricity and low electricity prices, and discharging during periods of energy shortage or high electricity prices.

[0192] Energy storage operations must meet strict operational constraints: Simultaneous charging and discharging are not permitted, ensuring that the device can only be in either charging or discharging state at any given time. Charging and discharging power must be within the upper and lower limits allowed by the equipment. The stored energy capacity must be maintained within the safe range specified by the upper and lower limits of each capacity constraint. Simultaneously, the maximum daily charge and discharge cycles must be met to prevent excessive switching from affecting equipment lifespan.

[0193] Energy storage systems play multiple roles in power distribution networks: effectively mitigating power fluctuations caused by electric vehicle charging load fluctuations; reducing the peak-to-valley difference in system operation and optimizing the load curve through off-peak charging and peak discharging; providing active power support through discharge when the voltage is low, helping to maintain voltage stability; and simultaneously improving the absorption capacity of intermittent renewable energy sources such as wind power and photovoltaics.

[0194] The principle of capacitor bank regulation is to change the reactive power compensation by adjusting the number of capacitor banks switched on and off. The system determines how many capacitor banks to switch on or off during specific time periods based on the optimization results, thus achieving step-by-step reactive power compensation regulation.

[0195] The number of switching groups cannot exceed the maximum number of switching groups specified by the upper limit constraint. Changes in the number of switching groups between adjacent time periods must meet the switching action constraints to avoid voltage fluctuations caused by sudden changes in reactive power compensation. Furthermore, the total number of switching operations per day must meet the daily maximum switching operation constraint to protect the mechanical life of the equipment.

[0196] The main functions of capacitor banks include: providing local reactive power compensation, reducing long-distance reactive power transmission, and lowering network losses; improving system voltage quality through reactive power support and preventing voltage exceedance; and forming a hierarchical compensation architecture with photovoltaic inverter reactive power compensation to achieve more refined reactive power regulation.

[0197] The converter power and photovoltaic inverter reactive power compensation power are used to perform load shedding operations based on the upper limit of the load shedding ratio set in the load shedding constraint.

[0198] This step involves the coordinated control of the power of various devices and, when necessary, the execution of load shedding operations.

[0199] The key to power regulation of distribution transformers is to ensure they operate within a reasonable power factor constraint range, while avoiding overload operation through load factor calculation constraints and load factor upper limit constraints. This ensures the safe operation of the transformer and reduces distribution transformer loss costs by optimizing load distribution.

[0200] Converter power control enables power mutual assistance in AC / DC hybrid distribution networks. By adjusting the converter power, power can be flexibly transferred between distribution networks in different regions, transmitting electrical energy from areas with surplus power to areas with shortage power, thereby enhancing the distribution network's ability to support the uncertain charging load of electric vehicles.

[0201] The reactive power compensation of the photovoltaic inverter is adjusted within its capacity constraints, providing dynamic reactive power support. This reactive power compensation complements the fixed compensation of the capacitor bank, enabling more refined reactive power regulation and further optimizing the system voltage distribution.

[0202] Load shedding is the last resort for ensuring system safety. When the system faces severe overload or voltage exceedance risks, and all other control measures have been exhausted, the system will execute load shedding based on the upper limit of the load shedding ratio set in the load shedding constraints. This operation ensures that it is only activated in extreme situations by setting a high load shedding penalty cost, thereby maximizing power supply reliability.

[0203] All these control operations are based on the solution results of the two-stage optimization control model of the distribution network, forming a complete operation strategy system. The various operations cooperate and work together to enable the distribution network with large-scale electric vehicle charging loads to effectively cope with the uncertainty of charging loads, minimize system operating losses and maximize energy utilization efficiency while ensuring safe and reliable power supply, and improve voltage quality and disturbance rejection capability.

[0204] An analysis of the effectiveness of the two-stage optimization control method.

[0205] To verify the effectiveness of the proposed two-stage optimization and control method for distribution networks considering the uncertain charging of electric vehicles, a deterministic model is used to analyze a DC interconnection scenario in the distribution network. In the deterministic model, the uncertainty of electric vehicle charging load is ignored, and its predicted value is used as input. The optimization model is constructed with the goal of minimizing system operating losses.

[0206] Set up the following two comparison scenarios: Scenario 1: The distribution network has no DC interconnection. The electric vehicle charging load and photovoltaic power supply of node 39 are connected to node 31, and the electric vehicle charging load and energy storage device of node 44 are connected to node 3.

[0207] Scenario 2: The distribution network adopts a DC interconnection structure, and its topology is as follows: Figure 1 As shown.

[0208] Table 1 shows a comparison of scheduling costs for each scenario. Analysis reveals that in Scenario 1, due to the lack of DC interconnection, the mutual support between different feeders is insufficient. To ensure that line power and node voltage do not exceed limits, node 30 experienced load shedding during the peak load periods of 21:00 and 23:00. In contrast, Scenario 2 significantly improved power adjustment flexibility through DC interconnection, resulting in a significant reduction in network losses and no load shedding. Specifically, the total operating cost of Scenario 2 is 1592.5 yuan, a decrease of 8.35% compared to Scenario 1's 1737.6 yuan.

[0209]

[0210] Table 1. Comparison of scheduling costs in different scenarios

[0211] Network loss at different times in different scenarios, for example Figure 2 As shown in the figure. After DC interconnection, the power flow of the distribution network is flexibly adjusted through VSC. During peak load periods, the network loss in Scenario 2 is significantly reduced compared to Scenario 1. The total network loss in Scenario 2 is 1590.8kW, which is 10.1% lower than the 1770.2kW in Scenario 1.

[0212] For example, the voltage ratios of each node in the system Figure 3 As shown, DC interconnection effectively achieves power sharing between different feeders, reduces power transmission distance, and lowers node voltage offset. After DC interconnection, the voltage offset at the end nodes of the AC distribution network feeders is significantly reduced, and the system node voltage distribution is significantly improved. Specifically, the total voltage offset in Scenario 2 is 14.51 pu, which is 15.1% lower than the 17.09 pu in Scenario 1.

[0213] Analysis of DC interconnection scheduling strategies.

[0214] The results of distribution network reconfiguration under DC interconnection are as follows Figure 4 As shown. The optimal control strategy obtained based on the optimization solution: The switchable branch 18-33 is located at the end of the feeder, and the node voltage is low. Closing the switch will result in a large loss. Therefore, the switch status variable of its line remains in the open state throughout the 24-hour period.

[0215] Branches 23-24 are located at the beginning of the feeder. To reduce power loss at the end of the feeder, the state variables of their line switches are kept closed throughout the 24-hour period.

[0216] Photovoltaic output is higher during periods of strong sunlight. In order to fully realize local photovoltaic consumption and reduce the distance of power transmission, the state variables of the line switches of branches 8-21 and 25-29 can be kept closed during this period.

[0217] The photovoltaic output is low during periods of low light and no light. In order to reduce the power supply distance of the feeder end node where node 18 is located and reduce network losses, the line switch state variable of branch 8-21 can be turned off to open, while branch 12-22 can be closed.

[0218] The above-described operations based on the optimal control strategy effectively reduced network losses in the distribution network, verifying the effectiveness of the method described in this invention in improving system operation economy and voltage quality.

[0219] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles, characterized in that, Includes the following steps: An uncertainty model of electric vehicle charging load is established based on a multi-factor composite probability model and dynamic time-series parking demand forecasting. Based on the uncertainty model, a two-stage optimization control model for the distribution network is constructed with the goal of minimizing system operating losses. The two-stage optimization control model for the distribution network includes decision variables for the first stage and decision variables for the second stage. The decision variables in the first stage include line switch state variables, energy storage charging and discharging state variables, and capacitor bank switching state variables. The decision variables for the second stage include the power of the distribution transformer, the power of the converter, the charging and discharging power of the energy storage, the reactive power compensation power of the photovoltaic inverter, and the load shedding power. The column and constraint generation algorithm is used to solve the two-stage optimization control model of the distribution network, generate the distribution network optimization control strategy and execute it.

2. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 1, characterized in that, The uncertainty model for electric vehicle charging load established based on a multi-factor composite probability model includes: Electric vehicle users are divided into three categories: private car users, ride-hailing users, and official vehicle users; Establish an independent log-normal probability density function for each user type; The composite probability density function of the total daily mileage of electric vehicles is obtained by weighted summation of the log-normal probability density functions of the three types of users. The actual daily mileage is obtained by introducing seasonal and regional correction factors to adjust the baseline mileage in real time.

3. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 2, characterized in that, The uncertainty model for electric vehicle charging load based on dynamic time-series parking demand forecasting specifically includes: The functional areas are divided into residential areas, industrial and commercial areas, and public facilities areas; The parking demand in residential areas is modeled using a normal distribution function centered at dusk. The parking demand in industrial and commercial areas is modeled using a bi-peak or wide-peak model centered on midday. Different parameters are used to model parking demand in public facility areas, distinguishing between weekdays and weekends; The total parking demand curve is obtained by superimposing the parking demand of the three functional areas.

4. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 3, characterized in that, The uncertainty model for establishing the electric vehicle charging load also includes: The Monte Carlo method is used to simulate the charging load of electric vehicles, including parking simulation and charging simulation. In the parking simulation cycle, the vehicle entry and exit status is determined based on the difference between parking space demand and the number of vehicles, and the parking time of each vehicle is calculated. In the charging simulation cycle, charging behavior is arranged and charging load power is calculated based on the availability of charging piles and the state of charge of electric vehicles. The charging load prediction error is described by constructing a charging load uncertainty set based on the charging load prediction values ​​obtained through a multi-factor composite probability model and dynamic time-series parking demand prediction.

5. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 1, characterized in that, The objective function for constructing the two-stage optimization and control model of the power distribution network is specifically: System operating losses include network loss costs, distribution transformer loss costs, converter loss costs, energy storage charging and discharging loss costs, and load shedding costs. All cost items take into account electricity price factors and time intervals. Network loss cost is calculated based on the product of the square of the branch current amplitude and the resistance. The cost of distribution transformer losses includes iron losses and copper losses; Converter loss cost is calculated based on converter loss coefficient; Energy storage charging and discharging loss costs are calculated based on charging and discharging power and efficiency. The load shedding cost is calculated based on the load shedding penalty coefficient.

6. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 1, characterized in that, The two-stage optimization control model for the power distribution network also includes the following operational constraints: AC power flow balance constraints include AC node active and reactive power injection balance constraints, AC branch voltage drop constraints, AC branch Ohm's law constraints, and AC branch capacity constraints. DC power flow balance constraints include DC node active power injection balance constraints, DC branch voltage drop constraints, and DC branch Ohm's law constraints. Distribution network reconfiguration constraints include radial operation constraints guaranteed by virtual power flow constraints, branch switch status constraints, and branch switch maximum daily operation constraints.

7. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 6, characterized in that, The two-stage optimization and control model for the power distribution network also includes the following equipment operation constraints: Capacitor bank operation constraints include reactive power compensation constraints based on the number of switching banks and the switching capacity of a single bank, upper limit constraints on the number of switching banks, switching action constraints, and maximum daily switching frequency constraints. Operating constraints for distribution transformers include operating power factor constraints, loss calculation constraints based on iron and copper losses, load rate calculation constraints, and load rate upper limit constraints. Converter operating constraints include power coupling constraints with distribution transformers, capacity constraints, loss calculation constraints, and AC / DC side power balance constraints. Energy storage operation constraints include charging and discharging power balance constraints, simultaneous charging and discharging not allowed constraints, energy balance constraints, upper and lower limits of energy, charging and discharging state switching constraints, and maximum number of daily charging and discharging cycles constraints. Distributed power source operation constraints include upper and lower limits of active and reactive power output constraints for distributed power sources connected to AC nodes and upper and lower limits of active power output constraints for distributed power sources connected to DC systems. Load shedding constraints include AC node load shedding constraints and DC node load shedding constraints, wherein the load shedding amount does not exceed the set upper limit of the load shedding ratio.

8. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 1, characterized in that, The algorithm for solving the two-stage optimal control model of the distribution network using column and constraint generation includes: The two-stage optimization control model of the distribution network is decomposed into a main problem and sub-problems; The main problem involves finding the optimal scheduling decision in the first stage under finite adverse scenarios to provide a lower bound solution. The subproblems are substituted into the solution of the current main problem to obtain the first-stage scheduling decision and solve the optimal second-stage scheduling decision under the worst scenario, so as to identify the worst scenario and provide an upper bound solution; Based on the strong duality theorem, the bi-level optimization problem of the subproblem is transformed into a single-level optimization problem, and the nonlinear term is processed by the Big-M method after discretizing the uncertain set of electric vehicle charging load. In solving the two-stage optimization control model of the distribution network, non-convex nonlinear terms are handled.

9. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 8, characterized in that, The processing of nonconvex nonlinear terms includes: Transform non-convex nonlinear constraints into convex or linear constraints. The absolute value constraints are directly expanded into linear constraints, and the quadratic equality constraints are transformed into second-order cone constraints using second-order cone relaxation techniques. The problem is eventually transformed into an optimization problem containing only linear and cone constraints, which is then solved iteratively until the convergence condition is met.

10. The two-stage optimization control method for power distribution networks considering uncertain charging of electric vehicles according to claim 1, characterized in that, Obtain the distribution network optimization and control strategy and perform the following operations: Adjusting the switch status of distribution network lines to achieve network reconfiguration; Control the charging and discharging power and status of energy storage devices; Adjust the number of capacitor banks switched on / off; Adjust the power of the distribution transformer, the power of the converter, and the reactive power compensation power of the photovoltaic inverter, and perform the load shedding operation based on the upper limit of the load shedding ratio set in the load shedding constraint.

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