Consider the electric vehicle automatic driving of battery swap optimization configuration and guide method and system

By constructing a battery swapping optimization configuration and guidance model for a power-transportation coupled network, and utilizing autonomous electric vehicles to swap batteries themselves, the problems of high configuration costs and long charging times for electric vehicle battery swapping facilities are solved, thereby reducing battery swapping time and hardware costs.

CN119413164BActive Publication Date: 2026-05-29ECONOMIC & TECH RES INST OF HUBEI ELECTRIC POWER COMPANY SGCC

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
ECONOMIC & TECH RES INST OF HUBEI ELECTRIC POWER COMPANY SGCC
Filing Date
2024-09-03
Publication Date
2026-05-29

AI Technical Summary

Technical Problem

In the existing technology, the configuration cost of electric vehicle battery swapping facilities is high, the limited battery swapping facilities are difficult to meet the battery swapping needs of a high proportion of electric vehicles, and traditional charging methods are time-consuming. The application of autonomous driving technology in the field of battery swapping has not been fully utilized.

Method used

A battery swapping optimization configuration and guidance model is constructed for the power-transportation coupled network. Autonomous electric vehicles can travel to battery swapping stations on their own during off-peak hours to swap batteries, thereby optimizing battery flow conversion, reducing battery swapping time and hardware configuration costs, and meeting the constraints of power distribution network and traffic.

Benefits of technology

By optimizing and guiding the battery swapping configuration of autonomous electric vehicles, the time and hardware configuration costs of battery swapping are reduced, the utilization rate and load flexibility of battery swapping stations are improved, and the time consumption of electric vehicle users is reduced.

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Abstract

A battery replacement planning and optimization configuration and guidance method and system based on automatic driving of electric vehicles, the method first constructs a battery replacement optimization configuration and guidance model with the minimum comprehensive battery replacement cost of the automatic driving electric vehicle as the target, considering the operation constraints of the battery replacement station and the battery replacement constraints of the electric vehicle, then solves the battery replacement optimization configuration and guidance model to obtain the optimal configuration scheme of the electric vehicle battery replacement station and the vehicle battery replacement guidance scheme. The present application not only effectively reduces the user battery replacement time cost under the premise of meeting the traffic constraints, but also reduces the hardware configuration cost and the power purchase cost of the battery replacement service provider while meeting the power distribution network access requirements.
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Description

Technical Field

[0001] This invention relates to a battery swapping planning and optimization guidance method, and more particularly to a battery swapping optimization configuration and guidance method and system considering autonomous driving of electric vehicles. Background Technology

[0002] Electric vehicle battery swapping and autonomous driving technologies have made significant progress in recent years, becoming important technological directions driving future transportation transformation. Battery swapping technology solves the problem of long charging times associated with traditional charging methods by quickly replacing battery packs at dedicated swapping stations. This technology has significant advantages for frequently used vehicles, greatly reducing the time required for recharging and improving vehicle utilization. Furthermore, battery swapping technology can reduce the pressure on the power grid to some extent by concentrating battery charging during off-peak hours. However, the deployment cost of battery swapping facilities is high, and the limited existing facilities still cannot meet the future battery swapping needs of a high proportion of electric vehicles during peak hours.

[0003] The progress of autonomous driving technology is equally remarkable. Its core lies in enabling vehicles to autonomously complete driving tasks in different scenarios through sensors, artificial intelligence algorithms, and high-precision maps. With continuous technological iteration, the safety and stability of autonomous driving have been significantly improved. Beyond daily commutes, effectively utilizing the advantages of autonomous electric vehicles in the field of battery swapping is also a direction worth exploring. Summary of the Invention

[0004] The purpose of this invention is to overcome the aforementioned problems in the prior art and to provide a battery swapping optimization configuration and guidance method and system that considers autonomous driving of electric vehicles.

[0005] To achieve the above objectives, the technical solution of the present invention is:

[0006] In a first aspect, the present invention proposes a battery swapping optimization configuration and guidance method considering autonomous driving of electric vehicles, comprising:

[0007] S1. Construct a battery swapping optimization configuration and guidance model for the power-transportation coupled network. The battery swapping optimization configuration and guidance model aims to minimize the overall battery swapping cost of autonomous electric vehicles and takes into account the operation constraints of battery swapping stations and the battery swapping constraints of electric vehicles.

[0008] S2. Solve the battery swapping optimization configuration and guidance model to obtain the electric vehicle battery swapping station optimization configuration scheme and vehicle battery swapping guidance scheme.

[0009] The objective function of the battery swapping optimization configuration and guidance model includes:

[0010] min C H[(1+α) γ -1] / αγ 2 +C E +C T ;

[0011]

[0012] In the above formula, C H The cost of configuring the battery swapping station facilities; α is the discount rate; γ is the investment period; C E C is the cost of purchasing electricity for the battery swapping station. T For battery swapping time cost; PR represents the number of battery swapping facilities in the battery swapping station at node n. S The configuration cost of a single battery swapping facility; PR represents the number of battery charging facilities in the battery swapping station at node n. C The configuration cost for a single battery charging facility; d is the number of typical days in a year, and t is the time period within a typical day; The active power output from the distribution network to the battery swapping station connected at node e during time period t; The electricity purchase price for time period t; PR represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; T Cost per unit of time.

[0013] The operational constraints of the battery swapping station include:

[0014]

[0015]

[0016] In the above formula, WB t,n WB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t. M The maximum number of fully charged batteries that can be stored within a battery swapping station; VB t,n VB represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t; M This refers to the maximum number of batteries waiting to be charged that can be stored in a charging station; WB t-1,n CB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t-1; t,n SB represents the number of batteries that have completed charging at the battery swapping station at node n in time period t; t,n WT represents the number of batteries performing battery swapping operations at the battery swapping station at node n in time period t; t,n,m VB represents the number of fully charged batteries transported from the battery swapping station at node m to the battery swapping station at node n during time period t; t-1,n VT represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t-1;t,n,m δ represents the number of batteries to be charged transported from the battery swapping station at node m to the battery swapping station at node n during time period t; M For large M constants; σ W and σ V These are the decision variables for the flow of batteries that have been charged and batteries that are to be charged, respectively. When the value is 1, the battery is transported from battery swapping station n to battery swapping station m. When the value is 0, the battery is transported from battery swapping station m to battery swapping station n. Let n be the number of battery charging facilities in the battery swapping station at node n. Let n be the number of battery swapping facilities in the battery swapping station at node n. Let be the binary programming decision variables for the battery swapping station, when At that time, a battery swapping station was built at node n. At that time, no battery swapping station will be built at node n; BS M This represents the maximum number of battery swapping stations; BS M This represents the maximum number of battery swapping stations. T represents the number of battery swapping facilities in the battery swapping station at node n; U T is a unit of time; US The baseline time for battery swapping services; T represents the number of battery charging facilities in the battery swapping station at node n; C The time it takes to charge a single battery charge.

[0017] The constraints on electric vehicle battery swapping behavior include:

[0018]

[0019]

[0020] In the above formula, and These represent the travel time and battery swapping time for a battery swapping trip that starts at time t during the idle period; dm is the battery swapping demand number; kv and kj are the outbound route numbers for the battery swapping trip during the idle period and the vehicle usage period, respectively; L t,kv Let kv be the total length of path kv at time t; v is the congestion coefficient for time period t; A The average driving speed of an autonomous electric vehicle; For time period The congestion coefficient; The return trip for the battery swapping journey during the off-peak hours; T US The baseline time for battery swapping services; FV dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; τ is the return route number for battery swapping trips during off-peak hours. V For binary auxiliary variables; δ M For large M constants; TS dm,t For the battery swapping demand dm, the travel type determination constant in time period t, when TS dm,t When TS = 1, time period t is the vehicle usage time corresponding to the battery swapping demand dm. dm,t When = 0, time period t is the idle time period of the vehicle corresponding to the battery swapping demand dm; tx is an auxiliary time period variable; FJ represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; dm,t,kj For the battery swapping demand dm, during time period t, the traffic flow generated by the battery swapping scheme based on the vehicle usage time period of route kj; SB t,n This represents the number of batteries that perform battery swapping operations at the battery swapping station at node n in time period t. Let be the correlation coefficient between path kv and node n; Let be the correlation coefficient between path kj and node n; FD dm,t Let dm be the number of vehicles corresponding to the battery swapping demand within time period t.

[0021] The battery swapping optimization configuration and guidance model also considers distribution network operation constraints and traffic demand constraints, including:

[0022]

[0023] In the above formula, FT t,l For time period t, FV represents the total traffic flow on road l. dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; Let kv be the correlation coefficient between path kv and road l; FC is the correlation coefficient between path kj and road l; l The maximum traffic capacity of road l;

[0024] The power distribution network operation constraints include:

[0025]

[0026] In the above formula, CB represents the active power output from the distribution network to the battery swapping station connected at node e during time period t. t,nE represents the number of batteries that have completed charging at the battery swapping station at node n in time period t. D The average charging energy requirement for a single battery; T is the correlation coefficient between traffic network node n and distribution network node e; U Unit of time; and These represent the active and reactive power on line w at time t, respectively; w represents all lines connected to node e in the distribution network. and These represent the basic active and reactive loads connected at node e of the distribution network during time period t; LC w The capacity of the distribution network line w; ΔU t,w The voltage drop on the distribution network line w during time period t; and These represent the resistance and reactance of the distribution network line w, respectively; U N U is the rated voltage of the distribution network busbar; t,a and U t,b U represents the bus voltages of distribution network nodes a and b during time period t, where nodes a and b are the two endpoints of distribution network line w; m and U M These are the upper and lower limits of the distribution network bus voltage, respectively; U t,e Let be the bus voltage at node e during time period t.

[0027] Secondly, this invention proposes a battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles, including a model building module and a model solving module;

[0028] The model building module is used to build a battery swapping optimization configuration and guidance model. The battery swapping optimization configuration and guidance model aims to minimize the overall battery swapping cost of autonomous electric vehicles, and takes into account the operation constraints of battery swapping stations and the battery swapping constraints of electric vehicles.

[0029] The model solving module is used to solve the battery swapping optimization configuration and guidance model to obtain the electric vehicle battery swapping station optimization configuration scheme and vehicle battery swapping guidance scheme.

[0030] The objective function of the battery swapping optimization configuration and guidance model includes:

[0031] min C H [(1+α) γ -1] / αγ 2 +C E +C T ;

[0032]

[0033] In the above formula, C HThe cost of configuring the battery swapping station facilities; α is the discount rate; γ is the investment period; C E C is the cost of purchasing electricity for the battery swapping station. T For battery swapping time cost; PR represents the number of battery swapping facilities in the battery swapping station at node n. S The configuration cost of a single battery swapping facility; PR represents the number of battery charging facilities in the battery swapping station at node n. C The configuration cost for a single battery charging facility; d is the number of typical days in a year, and t is the time period within a typical day; The active power output from the distribution network to the battery swapping station connected at node e during time period t; The electricity purchase price for time period t; PR represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; T Cost per unit of time.

[0034] The operational constraints of the battery swapping station include:

[0035]

[0036]

[0037] In the above formula, WB t,n WB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t. M The maximum number of fully charged batteries that can be stored within a battery swapping station; VB t,n VB represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t; M This refers to the maximum number of batteries waiting to be charged that can be stored in a charging station; WB t-1,n CB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t-1; t,n SB represents the number of batteries that have completed charging at the battery swapping station at node n in time period t; t,n WT represents the number of batteries performing battery swapping operations at the battery swapping station at node n in time period t; t,n,m VB represents the number of fully charged batteries transported from the battery swapping station at node m to the battery swapping station at node n during time period t; t-1,n VT represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t-1; t,n,m δ represents the number of batteries to be charged transported from the battery swapping station at node m to the battery swapping station at node n during time period t; M For large M constants; σ W and σ VThese are the decision variables for the flow of batteries that have been charged and batteries that are to be charged, respectively. When the value is 1, the battery is transported from battery swapping station n to battery swapping station m. When the value is 0, the battery is transported from battery swapping station m to battery swapping station n. Let n be the number of battery charging facilities in the battery swapping station at node n. Let n be the number of battery swapping facilities in the battery swapping station at node n. Let be the binary programming decision variables for the battery swapping station, when At that time, a battery swapping station was built at node n. At that time, no battery swapping station will be built at node n; BS M This represents the maximum number of battery swapping stations; BS M This represents the maximum number of battery swapping stations. T represents the number of battery swapping facilities in the battery swapping station at node n; U T is a unit of time; US The baseline time for battery swapping services; T represents the number of battery charging facilities in the battery swapping station at node n; C The time it takes to charge a single battery charge.

[0038] The constraints on electric vehicle battery swapping behavior include:

[0039]

[0040] In the above formula, and These represent the travel time and battery swapping time for a battery swapping trip that starts at time t during the idle period; dm is the battery swapping demand number; kv and kj are the outbound route numbers for the battery swapping trip during the idle period and the vehicle usage period, respectively; L t,kv Let kv be the total length of path kv at time t; v is the congestion coefficient for time period t; A The average driving speed of an autonomous electric vehicle; For time period The congestion coefficient; The return trip for battery swapping during off-peak hours; T US The baseline time for battery swapping services; FV dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the specified time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; τ is the return route number for battery swapping trips during off-peak hours. V For binary auxiliary variables; δ M For large M constants; TS dm,tFor the battery swapping demand dm, the travel type determination constant in time period t, when TS dm,t When TS = 1, time period t is the vehicle usage time corresponding to the battery swapping demand dm. dm,t When = 0, time period t is the idle time period of the vehicle corresponding to the battery swapping demand dm; tx is an auxiliary time period variable; FJ represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; dm,t,kj For the battery swapping demand dm, during time period t, the traffic flow generated by the battery swapping scheme based on the vehicle usage time period of route kj; SB t,n This represents the number of batteries that perform battery swapping operations at the battery swapping station at node n in time period t. Let be the correlation coefficient between path kv and node n; Let be the correlation coefficient between path kj and node n; FD dm,t Let dm be the number of vehicles corresponding to the battery swapping demand within time period t.

[0041] The battery swapping optimization configuration and guidance model also considers distribution network operation constraints and traffic demand constraints, including:

[0042]

[0043] In the above formula, FT t,l For time period t, FV represents the total traffic flow on road l. dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the specified time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; Let kv be the correlation coefficient between path kv and road l; FC is the correlation coefficient between path kj and road l; l The maximum traffic capacity of road l;

[0044] The power distribution network operation constraints include:

[0045]

[0046] In the above formula, CB represents the active power output from the distribution network to the battery swapping station connected at node e during time period t. t,n E represents the number of batteries that have completed charging at the battery swapping station at node n in time period t. D The average charging energy requirement for a single battery; T is the correlation coefficient between traffic network node n and distribution network node e; U Unit of time; and These represent the active and reactive power on line w at time t, respectively; w represents all lines connected to node e in the distribution network. and These represent the basic active and reactive loads connected at node e of the distribution network during time period t; LC w The capacity of the distribution network line w; ΔU t,w The voltage drop on the distribution network line w during time period t; and These represent the resistance and reactance of the distribution network line w, respectively; U N U is the rated voltage of the distribution network busbar; t,a and U t,b U represents the bus voltages of distribution network nodes a and b during time period t, where nodes a and b are the two endpoints of distribution network line w; m and U M These are the upper and lower limits of the distribution network bus voltage, respectively; U t,e Let be the bus voltage at node e during time period t.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] The proposed battery swapping optimization configuration and guidance model for autonomous electric vehicles fully leverages the advantages of autonomous electric vehicles, allowing them to automatically travel to battery swapping stations during users' off-peak hours, significantly reducing the time cost of battery swapping operations while meeting traffic constraints. Furthermore, it utilizes the flexibility of autonomous electric vehicles to optimize battery flow, rationally planning the entry, exit, and conversion of charged and uncharged batteries at various times, further improving the load flexibility of battery swapping stations. This not only meets the requirements of power grid access but also reduces the hardware configuration and electricity purchase costs for battery swapping service providers. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of the power-transportation coupled network structure in Embodiment 1 of the present invention.

[0050] Figure 2 This is the congestion coefficient time-series characteristic curve in Embodiment 1 of the present invention.

[0051] Figure 3 This refers to the time-of-use electricity price in Embodiment 1 of the present invention.

[0052] Figure 4 This is a flowchart of the method described in this invention.

[0053] Figure 5 This is a schematic diagram of the architecture and operation mode of the battery swapping system in Embodiment 1 of the present invention.

[0054] Figure 6This is a schematic diagram of the battery swapping station configuration in Embodiment 1 of the present invention.

[0055] Figure 7 This is a structural diagram of the system described in this invention. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0057] This invention proposes an optimized configuration and guidance method for battery swapping considering autonomous driving of electric vehicles. This method leverages the fact that autonomous electric vehicles can autonomously travel to battery swapping stations during off-peak hours without user intervention. This saves users time costs associated with battery swapping, and improves the utilization rate of equipment during off-peak hours for battery swapping stations. It also reduces queuing time and enhances the operational flexibility of battery swapping stations. By optimizing the configuration of battery swapping and charging facilities, and rationally arranging the location and time for battery swapping of autonomous electric vehicles (i.e., a vehicle battery swapping guidance scheme), this method effectively reduces the hardware configuration costs and electricity purchase costs for battery swapping service providers, and the time costs for electric vehicle users due to battery swapping operations, while meeting the requirements of power grid access and traffic constraints.

[0058] Example 1:

[0059] This embodiment uses a topological structure such as Figure 1 The 11-node distribution network-17-node transportation network shown is the object (parameters: investment period is 10 years; discount rate is 0.05; unit time is 1 hour; investment period is 10 years; typical number of days in a year is 365 days; rated voltage of the distribution network is 10 kV; upper and lower limits of the distribution network bus voltage are 10.5 kV and 9.5 kV respectively; maximum power of a single battery charging facility is 40 kW; average charging energy demand of a single battery is 40 kWh; configuration cost of a single battery charging facility is 20,000 yuan; cost of a single electric vehicle battery swapping facility is 600,000 yuan; unit time cost is 20 yuan / hour; average driving speed of electric vehicles is 40 km / h when the congestion coefficient is 1; maximum number of battery swapping stations is 2; base time for battery swapping service is 0.3 hours; time consumed for a single battery charge is 0.5 hours; congestion coefficient time-series characteristic curve and time-of-use electricity price are as follows). Figure 2 and Figure 3 As shown), implement a battery swapping optimization configuration and guidance method that considers autonomous driving of electric vehicles, such as... Figure 4 As shown, it includes the following steps:

[0060] 1. Construct a battery swapping optimization configuration and guidance model

[0061] The battery swapping optimization configuration and guidance model treats the power-transportation coupled network as a whole, and its optimization objective is to minimize the overall battery swapping cost of autonomous electric vehicles. This overall battery swapping cost includes the configuration cost C of battery swapping station facilities. H Electricity purchase cost of battery swapping station C E and battery swapping time cost C T The schematic diagram of the battery swapping system's architecture and operation mode is shown below. Figure 5 As shown, autonomous electric vehicles can either travel to a battery swapping station on their own during off-peak hours or during the user's trip. Since only the latter scenario incurs time costs for the user, the calculation of battery swapping time cost only considers the time cost incurred during the trip. The objective function of the model is shown in equations (1)-(4):

[0062] min C H [(1+α) γ -1] / αγ 2 +C E +C T Equation (1)

[0063]

[0064]

[0065] In the above formula, C H Cost of configuring battery swapping station facilities; C E C is the cost of purchasing electricity for the battery swapping station. T α represents the battery swapping time cost; α represents the discount rate; γ represents the investment period. Let n be the number of battery charging facilities in the battery swapping station at node n. d represents the number of battery swapping facilities in the battery swapping station at node n; d represents the number of typical days in a year; and t represents the various time periods within a typical day. PR represents the active power output from the distribution network to the battery swapping station connected at node e during time period t. S The configuration cost of a single battery swapping facility; PR C The configuration cost for a single battery charging facility; The electricity purchase price for time period t; PR T Cost per unit of time; This represents the total time consumed during battery swapping during vehicle usage within time period t.

[0066] The constraints of the model include:

[0067] (1) Operational constraints of battery swapping stations

[0068] like Figure 5As shown, a battery swapping station is equipped with battery swapping facilities, battery charging facilities, and batteries. The battery swapping facilities are responsible for providing battery swapping services for electric vehicles; the swapping process consumes a fully charged battery, creating a battery to be charged. The battery charging facilities are responsible for charging the battery to be charged, thus obtaining a fully charged battery. To ensure the flexibility of the battery swapping service in a system comprising multiple swapping stations, battery transfer between different swapping stations is permitted. Therefore, the specific operational constraints for the swapping stations are set as follows:

[0069]

[0070]

[0071] In the above formula, WB t,n VB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t; t,n WB represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t. t-1,n VB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t-1; t-1,n WB represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t-1. M The maximum number of fully charged batteries that can be stored within a battery swapping station; VB M This is the maximum number of batteries waiting to be charged that can be stored in a charging station; CB t,n SB represents the number of batteries that have completed charging at the battery swapping station at node n in time period t; t,n WT represents the number of batteries performing battery swapping operations at the battery swapping station at node n in time period t; t,n,m VT represents the number of fully charged batteries transported from the battery swapping station at node m to the battery swapping station at node n during time period t; t,n,m δ represents the number of batteries to be charged transported from the battery swapping station at node m to the battery swapping station at node n during time period t; M For large M constants; σ W and σ V These are the decision variables for the flow of batteries that have been charged and batteries that are to be charged, respectively. When the value is 1, the battery is transported from battery swapping station n to battery swapping station m. When the value is 0, the battery is transported from battery swapping station m to battery swapping station n. Let n be the number of battery charging facilities in the battery swapping station at node n. Let n be the number of battery swapping facilities in the battery swapping station at node n. Let n be the number of battery charging facilities in the battery swapping station at node n. T represents the number of battery swapping facilities in the battery swapping station at node n; US The baseline time for battery swapping services; T C The time required to charge a single battery charge; T U Unit of time; Let be the binary programming decision variables for the battery swapping station, when At that time, a battery swapping station was built at node n. At that time, no battery swapping station will be built at node n; BS M This represents the maximum number of battery swapping stations.

[0072] In this constraint, Equations (5)-(6) are the upper limit constraints on the number of batteries in various states stored in the battery swapping station; Equations (7)-(8) are the electric vehicle battery flow constraints; in order to avoid duplicate transportation, only one-way transportation of batteries in the same state (completed charging or waiting to be charged) is allowed between two battery swapping stations in the same time period, Equations (9)-(10) are the battery flow direction constraints for the two states; Equations (13)-(14) are the configuration constraints of battery swapping facilities and battery charging facilities; Equation (15) is the maximum number constraint of battery swapping stations; Equations (16)-(17) are the battery swapping service capacity constraints and battery charging capacity constraints of the battery swapping station.

[0073] (2) Constraints on electric vehicle battery swapping behavior

[0074] To determine the appropriate usage patterns for electric vehicles, a typical day can be divided into usage periods and idle periods. During usage periods, the user drives the vehicle to the battery swapping station along their designated route, incurring time costs. During idle periods, the vehicle autonomously travels to the swapping station, eliminating the need for additional time costs for the user. The specific constraints on electric vehicle battery swapping behavior are set as follows:

[0075]

[0076] In the above formula, dm is the number of the battery swapping demand; kv and kj are the outbound path numbers of the battery swapping trip during idle periods and vehicle usage periods. The return trip for battery swapping during off-peak hours; The return route number for battery swapping trips during off-peak hours; and These represent the travel time and battery swapping time for the idle period during which the trip begins at time t; L t,kv FV is the total length of path kv at time t. dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the specified time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; Let be the congestion coefficient for time period t; For time period The congestion coefficient; v A T represents the average driving speed of an autonomous electric vehicle. US The baseline time for battery swapping services; TS dm,t For the battery swapping demand dm, the travel type determination constant in time period t, when TS dm,t When TS = 1, time period t is the vehicle usage time corresponding to the battery swapping demand dm. dm,t When τ = 0, time period t is the idle time period of the vehicle corresponding to the battery swapping demand dm; tx is the auxiliary time period variable; τ V For binary auxiliary variables; δ M It is a large M constant; Let be the correlation coefficient between path kv and node n; Let be the correlation coefficient between path kj and node n; FJ represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; dm,t,kj For the battery swapping demand dm, during time period t, the traffic flow generated by the battery swapping scheme based on the vehicle usage time of route kj; FD dm,t Let dm be the number of vehicles corresponding to the battery swapping demand within time period t.

[0077] In this constraint, Equations (18)-(19) represent the driving time and battery swapping operation time during vehicle usage periods, respectively. Since traffic demand and battery swapping demand are concentrated during vehicle usage periods, traffic congestion and battery swapping queues may occur, leading to increased time consumption. Equations (20)-(23) represent battery swapping constraints during idle periods. Equation (20) represents the traffic constraint for the round trip of autonomous driving battery swapping during idle periods; Equation (21) represents the time window constraint for autonomous driving battery swapping during idle periods, i.e., the vehicle must return before the end of the idle period; Equations (22) and (23) represent the traffic flow constraints generated by battery swapping during idle periods, i.e., this type of traffic flow can only occur during idle periods. Equations (24)-(25) represent battery swapping constraints during vehicle usage periods. Equation (24) represents the traffic flow constraint generated by battery swapping during vehicle usage periods, i.e., this type of traffic flow can only occur during vehicle usage periods; Equation (25) represents the constraint on the relationship between traffic flow and battery flow for battery swapping during idle periods. Equation (26) represents the constraint on the relationship between traffic flow and battery flow for battery swapping in different time periods. Equation (27) represents the constraint on the balance of battery swapping demand.

[0078] (3) Traffic demand constraints

[0079]

[0080] In the above formula, FT t,l For time period t, the total traffic flow on road l; FC l The maximum traffic capacity of road l; Let kv be the correlation coefficient between path kv and road l; Let be the correlation coefficient between path kj and road l.

[0081] (4) Distribution network operation constraints

[0082]

[0083]

[0084] In the above formula, CB represents the active power output from the distribution network to the battery swapping station connected at node e during time period t. t,n E represents the number of batteries that have completed charging at the battery swapping station at node n in time period t. D The average charging energy requirement for a single battery; T is the correlation coefficient between traffic network node n and distribution network node e; U Unit of time; and These represent the active and reactive power on line w at time t, respectively; w represents all lines connected to node e in the distribution network. and These represent the basic active and reactive loads connected at node e of the distribution network during time period t; LC w The capacity of the distribution network line w; ΔU t,w The voltage drop on the distribution network line w during time period t; and These represent the resistance and reactance of the distribution network line w, respectively; U N U is the rated voltage of the distribution network busbar; t,a and U t,b U represents the bus voltages of distribution network nodes a and b during time period t, where nodes a and b are the two endpoints of distribution network line w; m and U M These are the upper and lower limits of the distribution network bus voltage, respectively; U t,e Let be the bus voltage at node e during time period t.

[0085] In this constraint, Equation (30) is the battery charging power demand constraint for electric vehicle swapping stations, Equations (31) and (32) are the active and reactive power balance constraints of distribution network nodes, Equation (33) is the distribution network line capacity constraint, and Equations (34)-(36) are the distribution network node voltage constraints.

[0086] 2. Solve the battery swapping optimization configuration and guidance model to obtain the optimal configuration scheme for electric vehicle battery swapping stations and the vehicle battery swapping guidance scheme. The optimal configuration scheme for electric vehicle battery swapping stations is as follows: Figure 5 As shown, the two battery swapping stations are located at P2(T2) and P6(T8) respectively, with 5 and 8 battery swapping facilities respectively, and 13 and 20 battery charging facilities respectively.

[0087] To verify the effectiveness of the proposed method, the electric vehicle battery swapping optimization configuration and guidance method without considering autonomous driving mode was applied as Strategy 2 (battery swapping is not performed using autonomous driving mode, and all battery swapping needs are completed by the vehicle owner at the battery swapping station during the trip) to the 11-node distribution network-17-node transportation network. The economic efficiency was compared with that of the proposed method (Strategy 1). The results are shown in Table 1:

[0088] Table 1 Economic Comparison

[0089]

[0090] The comparison shows that the annualized comprehensive charging cost is lower when using Strategy 1. Regarding the annualized configuration cost of battery swapping station facilities, Strategy 1 reduces it by 22.38% compared to Strategy 2; the annual electricity purchase cost of battery swapping stations reduces it by 2.01%; the annual battery swapping time cost reduces it by 41.53%; and the annual comprehensive charging cost is reduced by 16.00% compared to Strategy 2. Therefore, the method proposed in this invention achieves the effect of reducing the hardware configuration cost and electricity purchase cost for battery swapping service providers, and the time cost for electric vehicle users due to battery swapping operations, while meeting the requirements of power grid access and traffic constraints.

[0091] Example 2:

[0092] A battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles includes a model building module and a model solving module;

[0093] The model building module is used to build a battery swapping optimization configuration and guidance model, and the objective function of the battery swapping optimization configuration and guidance model is:

[0094] min C H [(1+α) γ -1] / αγ 2 +C E +C T ;

[0095]

[0096] In the above formula, C H The cost of configuring the battery swapping station facilities; α is the discount rate; γ is the investment period; C E C is the cost of purchasing electricity for the battery swapping station. T For battery swapping time cost; PR represents the number of battery swapping facilities in the battery swapping station at node n. S The configuration cost of a single battery swapping facility; PR represents the number of battery charging facilities in the battery swapping station at node n. C The configuration cost for a single battery charging facility; d is the number of typical days in a year, and t is the time period within a typical day; The active power output from the distribution network to the battery swapping station connected at node e during time period t; The electricity purchase price for time period t; PR represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; T Cost per unit of time;

[0097] The constraints include:

[0098] The operational constraints of the battery swapping station include:

[0099]

[0100] In the above formula, WB t,n WB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t. M The maximum number of fully charged batteries that can be stored within a battery swapping station; VB t,n VB represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t; M This refers to the maximum number of batteries waiting to be charged that can be stored in a charging station; WB t-1,n CB represents the number of fully charged batteries stored in the battery swapping station at node n in time period t-1; t,n SB represents the number of batteries that have completed charging at the battery swapping station at node n in time period t; t,n WT represents the number of batteries performing battery swapping operations at the battery swapping station at node n in time period t; t,n,m VB represents the number of fully charged batteries transported from the battery swapping station at node m to the battery swapping station at node n during time period t; t-1,n VT represents the number of batteries waiting to be charged stored in the battery swapping station at node n in time period t-1; t,n,m δ represents the number of batteries to be charged transported from the battery swapping station at node m to the battery swapping station at node n during time period t; M For large M constants; σ W and σ V These are the decision variables for the flow of batteries that have been charged and batteries that are to be charged, respectively. When the value is 1, the battery is transported from battery swapping station n to battery swapping station m. When the value is 0, the battery is transported from battery swapping station m to battery swapping station n. Let n be the number of battery charging facilities in the battery swapping station at node n. Let n be the number of battery swapping facilities in the battery swapping station at node n. Let be the binary programming decision variables for the battery swapping station, when At that time, a battery swapping station was built at node n. At that time, no battery swapping station will be built at node n; BS M This represents the maximum number of battery swapping stations; BS M This represents the maximum number of battery swapping stations. T represents the number of battery swapping facilities in the battery swapping station at node n; U T is a unit of time; US The baseline time for battery swapping services; T represents the number of battery charging facilities in the battery swapping station at node n; C The time it takes to charge a single battery charge.

[0101] The constraints on electric vehicle battery swapping behavior include:

[0102]

[0103] In the above formula, and These represent the travel time and battery swapping time for a battery swapping trip that starts at time t during the idle period; dm is the battery swapping demand number; kv and kj are the outbound route numbers for the battery swapping trip during the idle period and the vehicle usage period, respectively; L t,kv Let kv be the total length of path kv at time t; v is the congestion coefficient for time period t; A The average driving speed of an autonomous electric vehicle; For time period The congestion coefficient; The return trip for battery swapping during off-peak hours; T US The baseline time for battery swapping services; FV dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; τ is the return route number for battery swapping trips during off-peak hours. V For binary auxiliary variables; δ M For large M constants; TS dm,t For the battery swapping demand dm, the travel type determination constant in time period t, when TS dm,t When TS = 1, time period t is the vehicle usage time corresponding to the battery swapping demand dm. dm,t When = 0, time period t is the idle time period of the vehicle corresponding to the battery swapping demand dm; tx is an auxiliary time period variable; FJ represents the total time consumed by the battery swapping station during the vehicle usage period within time period t; dm,t,kj For the battery swapping demand dm, during time period t, the traffic flow generated by the battery swapping scheme based on the vehicle usage time period of route kj; SB t,nThis represents the number of batteries that perform battery swapping operations at the battery swapping station at node n in time period t. Let be the correlation coefficient between path kv and node n; Let be the correlation coefficient between path kj and node n; FD dm,t Let dm be the number of vehicles corresponding to the battery swapping demand within time period t.

[0104] The battery swapping optimization configuration and guidance model also considers distribution network operation constraints and traffic demand constraints, including:

[0105]

[0106] In the above formula, FT t,l For time period t, FV represents the total traffic flow on road l. dm,t,kv To meet the battery swapping demand dm, during time period t, the traffic flow generated on the outbound journey is calculated using the idle time battery swapping scheme of path kv. To meet the battery swapping demand, during the time period Use path The off-peak battery swapping scheme generates traffic flow during the return trip; Let kv be the correlation coefficient between path kv and road l; FC is the correlation coefficient between path kj and road l; l The maximum traffic capacity of road l;

[0107] The power distribution network operation constraints include:

[0108]

[0109]

[0110] In the above formula, CB represents the active power output from the distribution network to the battery swapping station connected at node e during time period t. t,n E represents the number of batteries that have completed charging at the battery swapping station at node n in time period t. D The average charging energy requirement for a single battery; T is the correlation coefficient between traffic network node n and distribution network node e; U Unit of time; and These represent the active and reactive power on line w at time t, respectively; w represents all lines connected to node e in the distribution network. and These represent the basic active and reactive loads connected at node e of the distribution network during time period t; LC w The capacity of the distribution network line w; ΔU t,w The voltage drop on the distribution network line w during time period t; and These represent the resistance and reactance of the distribution network line w, respectively; U N U is the rated voltage of the distribution network busbar; t,a and U t,b U represents the bus voltages of distribution network nodes a and b during time period t, where nodes a and b are the two endpoints of distribution network line w; m and U M These are the upper and lower limits of the distribution network bus voltage, respectively; U t,e Let be the bus voltage at node e during time period t.

[0111] The model solving module is used to solve the battery swapping optimization configuration and guidance model to obtain the electric vehicle battery swapping station optimization configuration scheme and vehicle battery swapping guidance scheme.

Claims

1. A battery swapping optimization configuration and guidance method considering autonomous driving of electric vehicles, characterized in that: The method includes: S1. Construct a battery swapping optimization configuration and guidance model for a power-transportation coupled network. The battery swapping optimization configuration and guidance model aims to minimize the overall battery swapping cost of autonomous electric vehicles and considers the operation constraints of battery swapping stations, electric vehicle battery swapping constraints, distribution network operation constraints, and traffic demand constraints. S2. Solve the battery swapping optimization configuration and guidance model to obtain the electric vehicle battery swapping station optimization configuration scheme and vehicle battery swapping guidance scheme; The objective function of the battery swapping optimization configuration and guidance model includes: ; ; ; ; In the above formula, Cost of configuring battery swapping station facilities; The discount rate; For the investment cycle; The cost of purchasing electricity for the battery swapping station; For battery swapping time cost; For nodes The number of battery swapping facilities in the battery swapping stations at the location; The configuration cost of a single battery swapping facility; For nodes The number of battery charging facilities in the battery swapping stations; The configuration cost for a single battery charging facility; The number of typical days in a year. For each time period of a typical day; For time period Distribution network to nodes The active power output of the battery swapping station connected at the location; For time period The electricity purchase price; For time period The total time consumed by the battery swapping station during internal vehicle use; Cost per unit of time.

2. The battery swapping optimization configuration and guidance method considering autonomous driving of electric vehicles according to claim 1, characterized in that: The operational constraints of the battery swapping station include: ; ; ; ; ; ; ; ; ; ; ; ; ; In the above formula, For time period node The number of fully charged batteries stored in the battery swapping station at the location; This is the maximum number of fully charged batteries that can be stored within a battery swapping station. For time period node The number of batteries waiting to be charged stored in the battery swapping station at the location; This is the maximum number of batteries that can be stored in a charging station and are ready to be charged. For time period node The number of fully charged batteries stored in the battery swapping station at the location; For time period node The number of batteries that have been charged at the battery swapping station. For time period node The number of batteries performing battery swapping operations at the battery swapping station; For time period From node The battery swapping station at the node The number of fully charged batteries transported by the battery swapping station at the location; For time period node The number of batteries waiting to be charged stored in the battery swapping station at the location; For time period From node The battery swapping station at the node The number of batteries awaiting charging transported by the battery swapping station at the location; It is a large M constant; and These are the decision variables for the flow of batteries that have completed charging and batteries that are yet to be charged, respectively. When the value is 1, the batteries are transferred from the battery swapping station. Transported to the battery swapping station When its value is 0, the battery is supplied by the battery swapping station. Transported to the battery swapping station ; For nodes The number of battery charging facilities in the battery swapping stations; For nodes The number of battery swapping facilities in the battery swapping stations at the location; Let be the binary programming decision variables for the battery swapping station, when At the node A battery swapping station has been built there. At the node No battery swapping stations will be built in this area; This represents the maximum number of battery swapping stations. For nodes The number of battery swapping facilities in the battery swapping stations at the location; Unit of time; The baseline time for battery swapping services; For nodes The number of battery charging facilities in the battery swapping stations; The time it takes to charge a single battery charge.

3. The battery swapping optimization configuration and guidance method considering autonomous driving of electric vehicles according to claim 2, characterized in that: The constraints on electric vehicle battery swapping behavior include: ; ; ; ; ; ; ; ; ; ; In the above formula, and Time periods The driving time and battery swapping time of the battery swapping trip during the idle period of the trip starting at the designated time; This is a number representing the battery swapping request; and Number the outbound route for battery swapping trips during idle and vehicle usage periods; For time period At that time, path The total length; For time period The congestion coefficient; The average driving speed of an autonomous electric vehicle; For time period The congestion coefficient; The return trip for battery swapping during off-peak hours; The baseline time for battery swapping services; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow on the outbound journey; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow during the return trip; The return route number for battery swapping trips during off-peak hours; A binary auxiliary variable; It is a large M constant; For battery swapping needs During the period The trip type determination constant, when Time, period For battery swapping needs The corresponding vehicle usage time period, when Time, period For battery swapping needs The corresponding idle time period of the vehicle; As an auxiliary time period variable; For time period The total time consumed by the battery swapping station during internal vehicle use; For battery swapping needs During the period , using path Traffic flow generated by the battery swapping scheme during vehicle usage periods; For time period node The number of batteries performing battery swapping operations at the battery swapping station; For path With nodes The correlation coefficient; For path With nodes The correlation coefficient; For time period Internal battery swapping demand The corresponding number of vehicles.

4. The battery swapping optimization configuration and guidance method considering autonomous driving of electric vehicles according to claim 1, characterized in that: The traffic demand constraints include: ; ; In the above formula, For time period ,the way Total traffic flow on the road; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow on the outbound journey; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow during the return trip; For path With roads The correlation coefficient; For path With roads The correlation coefficient; For roads The maximum traffic capacity; The power distribution network operation constraints include: ; ; ; ; ; ; ; In the above formula, For time period At that time, the distribution network sends to the node The active power output of the battery swapping station connected at the location; For time period node The number of batteries that have been charged at the battery swapping station. The average charging energy requirement for a single battery; For transportation network nodes With distribution network nodes The correlation coefficient; Unit of time; and Time periods Time Line Active and reactive power; To connect with distribution network nodes All connected lines; and Time periods At that time, distribution network nodes The basic active and reactive loads connected at the point; For distribution network lines The capacity; For time period Internal power distribution network lines Voltage drop on; and Distribution network lines Resistance and reactance; This refers to the rated voltage of the distribution network busbar. and Time periods Internal distribution network nodes and Bus voltage, node and Distribution network lines The two endpoints; and These are the upper and lower limits of the distribution network bus voltage, respectively. For time period node The bus voltage.

5. A battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles, characterized in that: The system includes a model building module and a model solving module; The model building module is used to build a battery swapping optimization configuration and guidance model. The battery swapping optimization configuration and guidance model aims to minimize the overall battery swapping cost of autonomous electric vehicles and takes into account the operation constraints of battery swapping stations, electric vehicle battery swapping constraints, power distribution network operation constraints, and traffic demand constraints. The model solving module is used to solve the battery swapping optimization configuration and guidance model to obtain the electric vehicle battery swapping station optimization configuration scheme and vehicle battery swapping guidance scheme. The objective function of the battery swapping optimization configuration and guidance model includes: ; ; ; ; In the above formula, Cost of configuring battery swapping station facilities; The discount rate; For the investment cycle; The cost of purchasing electricity for the battery swapping station; For battery swapping time cost; For nodes The number of battery swapping facilities in the battery swapping stations at the location; The configuration cost of a single battery swapping facility; For nodes The number of battery charging facilities in the battery swapping stations; The configuration cost for a single battery charging facility; The number of typical days in a year. For each time period of a typical day; For time period Distribution network to nodes The active power output of the battery swapping station connected at the location; For time period The electricity purchase price; For time period The total time consumed by the battery swapping station during internal vehicle use; Cost per unit of time.

6. A battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles according to claim 5, characterized in that: The operational constraints of the battery swapping station include: ; ; ; ; ; ; ; ; ; ; ; ; ; In the above formula, For time period node The number of fully charged batteries stored in the battery swapping station at the location; This is the maximum number of fully charged batteries that can be stored within a battery swapping station. For time period node The number of batteries waiting to be charged stored in the battery swapping station at the location; This is the maximum number of batteries that can be stored in a charging station and are ready to be charged. For time period node The number of fully charged batteries stored in the battery swapping station at the location; For time period node The number of batteries that have been charged at the battery swapping station. For time period node The number of batteries performing battery swapping operations at the battery swapping station; For time period From node The battery swapping station at the node The number of fully charged batteries transported by the battery swapping station at the location; For time period node The number of batteries waiting to be charged stored in the battery swapping station at the location; For time period From node The battery swapping station at the node The number of batteries awaiting charging transported by the battery swapping station at the location; It is a large M constant; and These are the decision variables for the flow of batteries that have completed charging and batteries that are yet to be charged, respectively. When the value is 1, the batteries are transferred from the battery swapping station. Transported to the battery swapping station When its value is 0, the battery is supplied by the battery swapping station. Transported to the battery swapping station ; For nodes The number of battery charging facilities in the battery swapping stations; For nodes The number of battery swapping facilities in the battery swapping stations at the location; Let be the binary programming decision variables for the battery swapping station, when At the node A battery swapping station has been built there. At the node No battery swapping stations will be built in this area; This represents the maximum number of battery swapping stations. For nodes The number of battery swapping facilities in the battery swapping stations at the location; Unit of time; The baseline time for battery swapping services; For nodes The number of battery charging facilities in the battery swapping stations; The time it takes to charge a single battery charge.

7. A battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles according to claim 6, characterized in that: The constraints on electric vehicle battery swapping behavior include: ; ; ; ; ; ; ; ; ; ; In the above formula, and Time periods The driving time and battery swapping time of the battery swapping trip during the idle period of the trip starting at the designated time; This is a number representing the battery swapping request; and Number the outbound route for battery swapping trips during idle and vehicle usage periods; For time period At that time, path The total length; For time period The congestion coefficient; The average driving speed of an autonomous electric vehicle; For time period The congestion coefficient; The return trip for battery swapping during off-peak hours; The baseline time for battery swapping services; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow on the outbound journey; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow during the return trip; The return route number for battery swapping trips during off-peak hours; A binary auxiliary variable; It is a large M constant; For battery swapping needs During the period The trip type determination constant, when Time, period For battery swapping needs The corresponding vehicle usage time period, when Time, period For battery swapping needs The corresponding idle time period of the vehicle; As an auxiliary time period variable; For time period The total time consumed by the battery swapping station during internal vehicle use; For battery swapping needs During the period , using path Traffic flow generated by the battery swapping scheme during vehicle usage periods; For time period node The number of batteries performing battery swapping operations at the battery swapping station; For path With nodes The correlation coefficient; For path With nodes The correlation coefficient; For time period Internal battery swapping demand The corresponding number of vehicles.

8. A battery swapping optimization configuration and guidance system considering autonomous driving of electric vehicles according to claim 5, characterized in that: The traffic demand constraints include: ; ; In the above formula, For time period ,the way Total traffic flow on the road; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow on the outbound journey; For battery swapping needs During the period , using path The off-peak battery swapping scheme generates traffic flow during the return trip; For path With roads The correlation coefficient; For path With roads The correlation coefficient; For roads The maximum traffic capacity; The power distribution network operation constraints include: ; ; ; ; ; ; ; In the above formula, For time period At that time, the distribution network sends to the node The active power output of the battery swapping station connected at the location; For time period node The number of batteries that have been charged at the battery swapping station. The average charging energy requirement for a single battery; For transportation network nodes With distribution network nodes The correlation coefficient; Unit of time; and Time periods Time Line Active and reactive power; To connect with distribution network nodes All connected lines; and Time periods At that time, distribution network nodes The basic active and reactive loads connected at the point; For distribution network lines The capacity; For time period Internal power distribution network lines Voltage drop on; and Distribution network lines Resistance and reactance; This refers to the rated voltage of the distribution network busbar. and Time periods Internal distribution network nodes and Bus voltage, node and Distribution network lines The two endpoints; and These are the upper and lower limits of the distribution network bus voltage, respectively. For time period node The bus voltage.