Non-iterative coordination method and system for power distribution network and power conversion system based on projection

Abstract

The invention discloses a projection-based non-iterative coordination method and system for a power distribution network and a power conversion system, and belongs to the technical field of traffic electrification. The method comprises the following steps: firstly, respectively constructing a continuous time battery logistics model of the cross-regional battery replacement system and an economic operation model of each power distribution network; unifying the time scales of the two through an improved discrete time scheme; compressing each power distribution network model into a privacy protection projection space only containing charging power and price signals based on a projection theory; and finally, integrating the space as a constraint into a power conversion system model for one-time solution to obtain an optimal coordination scheme, and issuing the optimal coordination scheme to each power distribution network to complete local scheduling. According to the method, collaborative optimization without iterative data exchange among multiple systems is realized, and the global operation economy and the calculation efficiency are remarkably improved while the sensitive data of each operator is hidden.

Description

Technical Field

[0001] This invention belongs to the field of transportation electrification technology, specifically relating to a non-iterative coordination method and system for a projection-based power distribution network and battery swapping system. Background Technology

[0002] With the advancement of the global zero-carbon transition, transportation electrification has become a key path to reduce greenhouse gas emissions, and the adoption rate of electric vehicles continues to increase. Battery swapping and charging systems (BSCS) are gradually becoming an important energy replenishment solution for electric vehicles because they can avoid the problems of long waiting times for plug-in charging, accelerated battery degradation from fast charging, and high construction costs of supercharging facilities.

[0003] Currently, most BSCSs operate within a single distribution network, achieving centralized battery management by integrating charging facilities into the Battery Swapping Station (BSS). While this model can meet small-scale energy replenishment needs, with the increase in electric vehicle range and cross-regional travel, BSCSs need to break through the boundaries of a single power grid and operate collaboratively with multiple distribution networks, presenting several limitations to the existing technological system.

[0004] In terms of architecture and logistics modeling, BSCS are mainly divided into two categories: centralized and decentralized. The centralized approach co-locates battery swapping and charging facilities at the BSS, simplifying battery health management. However, each BSS needs to be equipped with charging equipment, resulting in high construction costs. Furthermore, in areas with high load density, sudden increases in local power can easily lead to grid risks. The decentralized approach geographically separates the BSS from the centralized charging station (CCS) and relies on battery transport vehicles (BDVs) to build a closed-loop logistics system of "empty battery recycling - charging - full battery delivery".

[0005] However, existing logistics scheduling modeling suffers from limitations. Traditional methods either use binary variables to describe the arrival, service, and departure states of BDVs, leading to a dramatic increase in variable size and computational complexity; or they rely on discrete spatiotemporal networks, requiring an exhaustive search of all path combinations and generating a large number of redundant candidate paths, making it difficult to adapt to dynamic road conditions. Although some studies have attempted to use continuous-time logistics modeling, they cannot accurately characterize the combined behavior of BDVs simultaneously completing fully charged battery delivery and depleted battery recovery at the same station. Furthermore, BSCS logistics scheduling has time flexibility, while distribution network scheduling is based on a fixed time scale, making it difficult to unify the two and restricting collaborative efficiency.

[0006] Regarding BSCS and multi-distribution network coordination mechanisms, existing technologies face the dual challenges of privacy protection and computational efficiency. Centralized coordination requires sharing sensitive information such as load, topology, and distributed energy resources across various power grids, posing a risk of privacy leakage. Furthermore, the model size grows exponentially with the number of distribution networks, increasing the computational burden. While decentralized coordination methods (such as ADMM and Benders decomposition) protect privacy through iterative interaction, they incur significant communication overhead. In multi-power grid and multi-CCS scenarios, the number of iterations increases, making them susceptible to communication interruptions and difficult to converge. In addition, existing coordination mechanisms lack refined charging pricing strategies, often using power demand as a single coordination signal without coordinating the nodal marginal electricity price of the distribution network with the charging scheduling of the BSCS. This results in the BSCS charging cost failing to reflect the real-time operating status of the distribution network (such as line congestion and DRE output fluctuations), making it difficult to maximize the overall economic benefits of the system. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and to provide a non-iterative coordination method and system for distribution networks and battery swapping systems based on projection.

[0008] The specific technical solution adopted in this invention is as follows:

[0009] In a first aspect, the present invention provides a non-iterative coordination method for distribution networks and battery swapping systems based on projection, the specific steps of which are as follows:

[0010] S1: Construct a battery logistics model for a battery swapping system that supports cross-regional operations and has multiple battery swapping stations and charging stations. Plan the routes and capacity of battery transport vehicles in a continuous time frame to jointly manage the collection and distribution of empty and full batteries between multiple sites.

[0011] S2: For the independent operation needs of each distribution network, considering distributed photovoltaic, wind power and distributed power generation equipment, construct an economic operation model for each distribution network; the economic operation model takes minimizing the total operating cost of the distribution network as the objective function, including power balance constraints, grid physical security constraints, transmission capacity constraints, distributed power generation output boundary constraints, distributed renewable energy operation constraints and power purchase constraints; based on the optimization results of the economic operation model, use the nodal marginal price to formulate a charging pricing strategy for charging stations;

[0012] S3: An improved discrete-time scheme is adopted to unify the variable time interval battery logistics model and the fixed time interval economic operation model in the same time scheme, ensuring that the path behavior of battery transport vehicles is consistent with the operation behavior of multiple distribution networks.

[0013] S4: Construct a non-iterative coordination framework, compress the economic operation model of the distribution network based on projection theory, hide the internal variables, and obtain a projection space containing only coordination variables and cost auxiliary variables through dimensionality reduction.

[0014] S5: Substitute the projection space as a constraint into the battery logistics model of the battery swapping system constructed in step S1, and solve for the charging power and charging price in the coordination variables; each distribution network solves its economic operation model based on the received charging power and charging price to obtain internal variables for coordination.

[0015] Preferably, the battery logistics model described in step S1 takes minimizing the total operating cost of the cross-regional swapping system as its objective function, including constraints on battery transport vehicle allocation, service boundary constraints of battery swapping stations, path continuity constraints, service continuity constraints, time connection constraints, time window constraints, total working time constraints, battery flow balance constraints, station battery exchange volume constraints, and vehicle carrying capacity constraints.

[0016] Furthermore, the total operating cost in the battery logistics model includes the driving cost of the battery transport vehicle and the charging fee paid to the power grid. The specific objective function is as follows:

[0017] ;

[0018] In the formula: This indicates that battery transport vehicle k travels from station m to station n; and Representing regions The electricity price and charging power of charging station node d in the power distribution network at the current moment; and They represent from the site Travel time and cost to reach the station; , , These represent the set of battery transport vehicles, the set of power distribution networks, and the set of time, respectively.

[0019] Furthermore, the constraints in step S1 are as follows:

[0020] The battery transport vehicle allocation constraints are as follows: Before a battery transport vehicle begins operation, each vehicle must be allocated to a corresponding charging station, and each vehicle can only be allocated once. The specific constraint formula is as follows:

[0021] ;

[0022] In the formula: This indicates the situation where battery transport vehicle k is assigned to charging station d; This indicates that battery transport vehicle k travels from charging station d to station n;

[0023] Service boundary constraints for battery swapping stations: Each battery swapping station is ensured to be accessed by at least one battery transport vehicle, while not exceeding the set maximum number of accessing vehicles, thus establishing the service boundary for each battery swapping station. The specific constraint formula is as follows:

[0024] ;

[0025] In the formula: This indicates the maximum number of vehicles that can be accessed.

[0026] Path continuity constraint: Ensure the path continuity of each battery transport vehicle between the starting station, intermediate stations, and the destination station during its journey. The specific constraint formula is as follows:

[0027] ;

[0028] Service continuity constraint: Ensure that each battery transport vehicle eventually returns to the originating charging station. Specific constraints are as follows:

[0029] ;

[0030] Time coherence constraint: Ensure the arrival times of battery transport vehicles between stations are logical and consistent. The expression after McCormick envelope relaxation is:

[0031] ;

[0032] ;

[0033] In the formula: This indicates whether the battery transport vehicle k stops at station m; 1 indicates a stop, and 0 indicates continued driving. and These represent the times when battery transport vehicle k arrives at stations m and n, respectively. This indicates the required dwell time at station m; This represents a large constant used to relax constraints;

[0034] Time window constraint: Ensure that the arrival time of the battery transport vehicle falls within the time window specified for that station. This constraint, relaxed using the McCormick envelope, is expressed as follows:

[0035] ;

[0036] In the formula: and These represent the lower and upper bounds of the time window for station m, respectively.

[0037] Total working time constraint: Ensure that each battery transport vehicle returns to its corresponding starting charging station before its maximum driving time is exceeded. The corresponding constraint is:

[0038] ;

[0039] In the formula: This indicates the maximum operating time of battery transport vehicle k; This indicates that battery transport vehicle k travels from station m to charging station d; This represents the travel time from station m to charging station d;

[0040] Battery flow balance constraint: Ensure that the change in the number of batteries carried by a vehicle while traveling between stations is logical. If battery transport vehicle k travels from station m to station n, then the number of batteries it carries upon arrival at station n must be equal to the number of batteries it carries upon leaving station m minus / plus the number of batteries exchanged at station m. The relationship between the number of fully loaded batteries carried by the battery transport vehicle before arriving at stations m and n, expressed by McCormick envelope relaxation, is as follows:

[0041] ;

[0042] ;

[0043] In the formula: and These represent the number of fully charged batteries carried by battery transport vehicle k before it arrives at stations m and n, respectively. This indicates the number of full batteries exchanged by battery transport vehicle k at station m;

[0044] The relationship between the number of empty batteries loaded on the battery transport vehicle and the number of empty batteries during transportation is similar to that of full batteries. The relationship between the number of empty batteries loaded before arriving at stations m and n is shown below:

[0045] ;

[0046] ;

[0047] In the formula: and These represent the number of empty batteries carried by battery transport vehicle k before it arrives at stations m and n, respectively. This indicates the number of empty batteries exchanged by battery transport vehicle k at station m;

[0048] Site battery exchange constraints: Limit the number of batteries a vehicle can load and unload at a single site, and ensure that battery exchange only occurs when the vehicle actually stops at that site; the number of full batteries exchanged by the battery transport vehicle at site m is subject to the stop indication variable. Similar to the upper and lower limits on the number of exchanges, the constraint logic for empty batteries is the same as that for full batteries, and the specific constraint formula is as follows:

[0049] ;

[0050] ;

[0051] In the formula: and These represent the lower and upper limits for battery transport vehicle k to exchange for a full battery at station m, respectively. and These represent the lower and upper limits, respectively, for battery transport vehicle k to exchange empty batteries at station m;

[0052] Vehicle carrying capacity constraint: The total number of fully loaded and empty batteries on a battery transport vehicle must not exceed its maximum carrying capacity at any time, as specified in the following formula:

[0053] ;

[0054] In the formula: This indicates the maximum number of batteries that battery transport vehicle k can carry.

[0055] Preferably, the total operating cost of the distribution network in the economic operation model described in step S2 is the sum of the fuel cost of distributed power sources, the penalty for abandoning renewable energy, the cost of purchasing electricity from the transmission network, and the revenue from selling electricity to charging stations. The specific objective function is as follows:

[0056] ;

[0057] In the formula: The function representing the generation cost of distributed power sources; and These represent the unit costs of abandoning distributed renewable energy and purchasing electricity from the upstream transmission network, respectively. , , and These represent the active power output of distributed power source g, the abandoned power of distributed renewable energy source e, the purchased power of substation s, and the charging power of charging station d in the distribution network area r at the current moment, respectively. and These represent the set of distributed power sources and the set of distributed renewable energy sources, respectively.

[0058] Preferably, the constraints in step S2 are as follows:

[0059] The power balance constraints are as follows:

[0060] ;

[0061] ;

[0062] in: and These represent the active power and reactive power purchased by substation s, which is connected to the upstream power grid, at the current moment, respectively. and These represent the active and reactive power outputs of the distributed power source g at the current moment, respectively. and These represent the active power output and power factor angle of the distributed renewable energy source e at the current moment, respectively. This represents the charging power consumed by charging station d at the current moment; and These represent the active power flow and reactive power flow from node i to node j at the current moment, respectively. and These represent the active and reactive loads of node j at the current moment, respectively. Represents a set of nodes; and These are the dual variables of the active power balance constraint and the reactive power balance constraint at node j, respectively. and These represent the active power flow and reactive power flow from node j to node k' at the current moment, respectively. and They represent the lines respectively. The starting set and the ending set;

[0063] The specific physical security constraints of the power grid are as follows:

[0064] The voltage drop across the branch is constrained by the current flowing through it, as detailed below:

[0065] ;

[0066] In the formula: and These represent the voltage magnitudes of node i and node j at the current moment, respectively. and Representing branch roads Resistance and reactance; Indicates the amplitude of the system reference voltage; Represents the set of branches; Represents the dual variable of the branch voltage drop constraint;

[0067] The voltage of each node is constrained to remain within a safe operating range, as follows:

[0068] ;

[0069] In the formula: and These represent the lower and upper limits of the voltage amplitude at node j, respectively; and These represent the dual variables of the lower and upper limits of the node voltage amplitude constraints, respectively.

[0070] Transmission capacity constraints: Ensure that the active and reactive power flowing through each branch does not exceed its transmission capacity limit, as detailed below:

[0071] ;

[0072] ;

[0073] In the formula: and Representing branch roads There are upper limits to both active and reactive current flows; and Let represent the dual variables of the lower and upper limits of the active power flow constraints, respectively. and These represent the dual variables of the lower and upper limits of reactive power flow constraints, respectively.

[0074] The output boundary constraints of distributed power sources are as follows:

[0075] ;

[0076] ;

[0077] In the formula: and These represent the lower and upper limits of the active power output of the distributed power source g, respectively. and These represent the lower and upper limits of the reactive power output of the distributed power source g, respectively. Represents a collection of distributed power sources; and The dual variable representing the lower and upper limits of the active power output of the distributed power source g; and The dual variable representing the lower and upper limits of the reactive power output of the distributed generation g;

[0078] Operational constraints for distributed renewable energy sources are as follows:

[0079] ;

[0080] ;

[0081] In the formula: and These represent the active power output and power curtailment of distributed renewable energy source e at the current moment, respectively. This represents the available power of distributed renewable energy source e at the current moment; Represents a collection of distributed renewable energy sources; Dual variables constraining the relationship between active power output and curtailment of distributed renewable energy sources; The dual variable representing the lower bound constraint on the active power output of distributed renewable energy; The dual variable representing the lower bound constraint on the curtailment power of distributed renewable energy;

[0082] Electricity purchase restrictions are as follows:

[0083] ;

[0084] in: and These represent the lower and upper limits of the active power that substation s can purchase, respectively. and These represent the lower and upper limits of reactive power that substation s can purchase, respectively. and These are the dual variables for the lower and upper limits of active power purchased from the substation, respectively. and These are the dual variables for the lower and upper limits of reactive power purchased from the substation, respectively.

[0085] As a preferred approach, the charging pricing strategy for charging stations is formulated using nodal marginal prices as follows: A corresponding dual variable is introduced into the power balance constraint of the economic operation model described in step S2; the dual variable of the active power balance constraint consists of generation cost, power transmission cost, and voltage support cost; the dual variable of the active power balance constraint is solved to obtain the nodal marginal price, as shown in the following formula:

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] ;

[0095] ;

[0096] In the formula: and Let represent the dual variables of the active power balance constraint and the reactive power balance constraint of the distributed power source g, respectively. This represents the active power output of node j at the current moment; and The dual variable representing the active power balance constraint and reactive power balance constraint of distributed renewable energy e; This represents the unit cost of discarding distributed renewable energy source e; and These represent the dual variables of the lower and upper limits of the node voltage amplitude constraints, respectively. and Let i and j represent the dual variables of the active power balance constraint at node i and node j, respectively. and Let i and j represent the dual variables of the reactive power balance constraint at node i and node j, respectively. and These represent the dual variables of the lower and upper limits of the active power flow constraint, respectively. The dual variable representing the lower bound constraint on the active power output of distributed renewable energy; These represent the dual variables of the lower limit constraint on the curtailment power of distributed renewable energy.

[0097] Preferably, the improved discrete-time scheme is as follows:

[0098] S31: Introducing Discrete Indicator Variables This indicates whether the battery transport vehicle arrived at the station within the time interval, with 1 indicating arrival and 0 indicating non-arrival. Using McCormick's envelope technique, the actual continuous arrival time of the battery transport vehicle is compared with the discrete indicator variable. Perform logical associations;

[0099] S32: By indicator variables By connecting the battery logistics model and the economic operation model, the requirements for battery swapping stations to load full batteries and transport empty batteries within a time window must be met by battery transport vehicles that arrive within the discrete time period corresponding to that time window; the requirements for battery transport vehicles to perform battery swapping or charging services only after arriving at the station; and the requirements for battery transport vehicles departing from the charging station to have already completed the loading of full batteries and the unloading of empty batteries.

[0100] As a preferred option, step S4 is as follows: reconstruct the economic operation model of each distribution network to include internal variables. Coordination variables and cost auxiliary variables The equivalent form is obtained to get the original feasible space; the original feasible space is reduced in dimension using projection theory to obtain a form consisting only of coordination variables. and cost auxiliary variables The projection space is constructed; for any boundary condition in this projection space, at least one feasible internal variable can be found in the original feasible space. And the corresponding operating cost is no greater than This approach hides internal variables while preserving the external coordination characteristics of the economic operation model; the model is shown below:

[0101] ;

[0102] in: and These represent the regional distribution network. Internal variables and coordinating variables; This represents the cost auxiliary variable introduced into the objective function; for The corresponding upper bound; and These represent the regional distribution network. The constraints and objective function of the distribution network operation within the region;

[0103] Original feasible space ;in express The real space of dimensional numbers; express A real space of dimensionless numbers; a projective space that hides internal variables. .

[0104] Furthermore, the construction of the projection space is as follows:

[0105] S41: Solve the extremum problem along the positive and negative directions of each coordinate axis in the coordinate variable space to obtain the initial set of extreme points; the extremum problem is as follows:

[0106] ;

[0107] In the formula: , and Representing internal variables respectively Coordination variables The coupling matrix and the constraint right-hand side terms; That is, constraints and The expansion expression;

[0108] S42: Calculate the corresponding hyperplane based on the initial set of extreme points. To describe the current projection space; calculate the geometric center of the initial extreme point set as the new origin, and perform coordinate transformation to obtain the new extreme point set;

[0109] S43: Calculate the unit external normal vector of each hyperplane in the current projection space. And along each normal vector, solve the optimization problem under the internal constraints, searching for candidate extrema points outside the current projection space; the optimization problem is as follows:

[0110] ;

[0111] ;

[0112] In the formula: To obtain the objective function value;

[0113] S44: Calculate the improvement rate of the projected space boundary brought about by the search step. If the change in the maximum improvement rate between two consecutive iterations is less than the preset error threshold, the algorithm is determined to have converged and the current projection space is completed; otherwise, steps S42 and S43 are repeated for iteration until the algorithm converges.

[0114] The formula for calculating the improvement rate is as follows:

[0115] ;

[0116] In the formula: This indicates that the optimal value of the objective function is obtained in step S43.

[0117] Secondly, the present invention provides a non-iterative coordination system for multiple distribution networks and cross-regional battery swapping systems based on spatial projection, comprising:

[0118] The battery swapping system modeling module is configured to: build a battery logistics model for a battery swapping system that supports cross-regional operations and has multiple battery swapping stations and charging stations; plan the routes and capacity of battery transport vehicles in a continuous time frame; and jointly manage the collection and distribution of empty and full batteries between multiple stations.

[0119] The distribution network modeling and pricing module is configured to: construct an economic operation model for each distribution network based on the independent operation needs of each distribution network, taking into account distributed photovoltaic, wind power and distributed power equipment; and formulate a charging pricing strategy for the charging station based on the optimization results of the economic operation model and using the node marginal price.

[0120] The time scheme coordination module is configured to: adopt an improved discrete time scheme to unify the battery logistics model with variable time intervals and the economic operation model with fixed time intervals in the same time scheme, so as to ensure that the path behavior of battery transport vehicles is consistent with the operation behavior of multiple distribution networks.

[0121] The projection space construction module is configured to: construct a non-iterative coordination framework, compress the economic operation model of the power distribution network based on projection theory, hide the internal variables, and obtain a projection space containing only coordination variables and cost auxiliary variables through dimensionality reduction.

[0122] The non-iterative coordination solution module is configured to: substitute the projection space as a constraint into the battery logistics model of the battery swapping system, solve for the charging power and charging price in the coordination variables, and send the charging power and charging price to each distribution network; each distribution network solves its own economic operation model based on the received charging power and charging price to obtain internal variables to achieve coordination.

[0123] Compared with the prior art, the present invention has the following advantages:

[0124] This invention proposes a flexible coordination model for cross-regional battery swapping systems and multiple distribution networks. This model integrates sophisticated pricing strategies, improving operational efficiency while addressing privacy issues among multiple operators. A battery logistics model supporting multiple sites is adopted to jointly manage battery collection and distribution. Based on this, an improved continuous-time scheme is proposed to coordinate two different time schemes: variable-time interval operation of the cross-regional battery swapping system and fixed-time interval multi-distribution network scheduling. Finally, a non-iterative privacy protection framework is proposed to avoid privacy leaks and iterative computations during the coordination process between the two systems. Attached Figure Description

[0125] Figure 1 The flowchart of the non-iterative coordination method provided by the present invention is shown. Detailed Implementation

[0126] The present invention will be further described and illustrated below with reference to the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly, provided that there is no mutual conflict.

[0127] The non-iterative coordination method provided by this invention is as follows: Figure 1 As shown.

[0128] Step 1: Construct a battery logistics model for a battery swapping system that supports cross-regional operations and includes multiple battery swapping stations and charging stations. Plan the routes and capacity of battery transport vehicles within a continuous time frame to jointly manage the collection and distribution of empty and full batteries across multiple stations.

[0129] In step one, the battery logistics model takes minimizing the total operating cost of the cross-regional swapping system as its objective function. This includes constraints on battery transport vehicle allocation, service boundary constraints of battery swapping stations, path continuity constraints, service continuity constraints, time connection constraints, time window constraints, total working time constraints, battery flow balance constraints, station battery exchange volume constraints, and vehicle carrying capacity constraints. The total operating cost includes the driving cost of battery transport vehicles and the charging fees paid to the distribution network.

[0130] The battery logistics model of the battery swapping system schedules battery transport vehicles to depart from charging stations within a specific time window, arrive at designated battery swapping stations, deliver fully loaded batteries and collect empty batteries, and then return to their originating charging station to charge the collected empty batteries. Indicates a collection of charging stations; This represents a collection of battery swapping stations. This represents the set of charging stations the battery-charging truck passes through during its route. Since each charging station serves as both the starting and ending point of the battery transport vehicle's journey, they are represented by [missing information - likely a typo]. and These represent the starting point set of charging stations and the ending point set of charging stations, respectively. This represents a node in the battery transport vehicle's path. Represents all potential starting points, This represents all potential endpoints.

[0131] The objective function of the battery logistics model for the battery swapping system is as follows:

[0132] ;

[0133] In the formula: This indicates that battery transport vehicle k travels from station m to station n; and Representing regions The electricity price and charging power of charging station node d in the power distribution network at the current moment; and They represent from the site Travel time and cost to reach the station; , , These represent the set of battery transport vehicles, the set of power distribution networks, and the set of time, respectively.

[0134] The routing of battery transport vehicles between multiple stations is determined by a series of events, such as arrival and departure between stations, and is defined by departure and arrival time boundaries. These factors collectively form the battery logistics model of the battery swapping system. The constraints of the battery logistics model for the battery swapping system are as follows:

[0135] (1) Battery transport vehicle allocation constraints: Before the battery transport vehicles start driving, each battery transport vehicle needs to be allocated to the corresponding charging station, and each battery transport vehicle can only be allocated once. The specific constraint formula is as follows:

[0136] ;

[0137] In the formula: This indicates the situation where battery transport vehicle k is assigned to charging station d; This indicates that battery transport vehicle k travels from charging station d to station n.

[0138] (2) Service boundary constraints for battery swapping stations: Ensure that each battery swapping station is accessed by at least one battery transport vehicle, while not exceeding the set maximum number of accessing vehicles, to establish the service boundary of each battery swapping station. The specific constraint formula is as follows:

[0139] ;

[0140] In the formula: This indicates the maximum number of vehicles that can be accessed.

[0141] (3) Path continuity constraint: Ensure the path continuity between the starting station, intermediate stations and the ending station for each battery transport vehicle during its journey. The specific constraint formula is as follows:

[0142] ;

[0143] (4) Service continuity constraint: It is necessary to ensure that each battery transport vehicle eventually returns to the starting charging station. The specific constraints are as follows:

[0144] ;

[0145] (5) Time Coherence Constraints: To ensure the logical and coherent arrival times of battery transport vehicles between stations, McCormick envelope relaxation technique is used to transform the constraint formulas into a set of linear inequality constraints, enabling the model to be solved efficiently, as follows:

[0146] ;

[0147] ;

[0148] In the formula: This indicates whether the battery transport vehicle k stops at station m; 1 indicates a stop, and 0 indicates continued driving. and These represent the times when battery transport vehicle k arrives at stations m and n, respectively. This represents the required dwell time at station m. M represents a large constant used to relax the constraints.

[0149] (6) Time window constraint: The arrival time of the battery transport vehicle at the station must fall within the time window specified by the station. The expression for this constraint after McCormick envelope relaxation is as follows:

[0150] ;

[0151] In the formula: and These represent the lower and upper bounds of the time window for station m, respectively.

[0152] (7) Total working time constraint: Ensure that each battery transport vehicle returns to its corresponding starting charging station before its maximum driving time is exceeded. The corresponding constraint is:

[0153] ;

[0154] In the formula: This indicates the maximum operating time of battery transport vehicle k; This indicates that battery transport vehicle k travels from station m to charging station d; This represents the travel time from station m to charging station d.

[0155] (8) Battery Flow Balance Constraint: Ensure that the number of batteries carried by a vehicle changes logically when it travels between stations. If a battery transport vehicle k travels from station m to station n, then the number of batteries it carries when it arrives at station n must be equal to the number of batteries it carries when it leaves station m minus / plus the number of batteries exchanged at station m. The relationship between the number of fully loaded batteries carried by the battery transport vehicle before arriving at stations m and n is shown below, and using McCormick envelope relaxation, the specific constraint formula is as follows:

[0156] ;

[0157] ;

[0158] In the formula: and These represent the number of fully charged batteries carried by battery transport vehicle k before it arrives at stations m and n, respectively. This indicates the number of full batteries exchanged by battery transport vehicle k at station m.

[0159] The relationship between the number of empty batteries loaded on the battery transport vehicle and the number of empty batteries during transportation is similar to that of full batteries. The relationship between the number of empty batteries loaded before arriving at stations m and n is shown below:

[0160] ;

[0161] ;

[0162] In the formula: and These represent the number of empty batteries carried by battery transport vehicle k before it arrives at stations m and n, respectively. This indicates the number of empty batteries exchanged by battery transport vehicle k at station m.

[0163] (9) Battery Exchange Constraints at Each Station: These constraints limit the number of batteries a vehicle can load and unload at a single station, ensuring that battery exchange only occurs when the vehicle actually stops at that station. This includes two sets of constraints: one for full batteries and one for empty batteries. The number of full batteries exchanged by the battery transport vehicle at station m is determined by the stop indicator variable. Similar to the upper and lower limits on the number of exchanges, the constraint logic for empty batteries is the same as that for full batteries, and the specific constraint formula is as follows:

[0164] ;

[0165] ;

[0166] In the formula: and These represent the lower and upper limits for battery transport vehicle k to exchange for a full battery at station m, respectively. and These represent the lower and upper limits, respectively, for battery transport vehicle k to exchange empty batteries at station m.

[0167] (10) Vehicle carrying capacity constraint: The total number of fully loaded and empty batteries on a battery transport vehicle shall not exceed its maximum carrying capacity at any time. The specific formula is as follows:

[0168] ;

[0169] In the formula: This indicates the maximum number of batteries that battery transport vehicle k can carry.

[0170] Step 2: To address the independent operation needs of multiple distribution networks, this step covers various equipment such as distributed photovoltaic, wind power, and distributed power sources, and utilizes nodal marginal prices to formulate charging pricing strategies for charging stations, thereby constructing an economic operation model for each distribution network.

[0171] Specifically, because the cross-regional battery swapping system covers multiple distribution network operating areas, each distribution network is fully controlled and operated by its own independent operator, and all operate in accordance with unified regulations and procedures. The independent operators of the distribution networks coordinate distributed power sources, distributed renewable energy sources, and electricity purchases from the upper-level transmission network, while calculating the marginal electricity price at each node to determine the charging price at the charging station, in order to ensure the economical and efficient operation of the distribution network.

[0172] The corresponding economic operation model takes minimizing the total operating cost of the distribution network as its objective function, including power balance constraints, grid physical security constraints, transmission capacity constraints, distributed generation output boundary constraints, distributed renewable energy operation constraints, and electricity purchase constraints. The total operating cost is the sum of distributed generation fuel costs, renewable energy curtailment penalties, electricity purchase costs from the transmission network, and revenue from selling electricity to charging stations.

[0173] The objective function is as follows:

[0174] ;

[0175] In the formula: The function representing the generation cost of distributed power sources; and These represent the unit costs of abandoning distributed renewable energy and purchasing electricity from the upstream transmission network, respectively. , , and These represent the active power output of distributed power source g, the abandoned power of distributed renewable energy source e, the purchased power of substation s, and the charging power of charging station d in the distribution network area r at the current moment, respectively. and These represent the set of distributed power sources and the set of distributed renewable energy sources, respectively.

[0176] (1) Power balance constraint:

[0177] The distribution network in each region operates using a radial topology. Power flow constraints are represented using a linearized Dist-flow model, decoupled into independent active and reactive power flows, and designed to maintain stable voltage amplitudes at each node. The active and reactive power balance constraints at each node are shown below:

[0178] ;

[0179] ;

[0180] in: and These represent the active power and reactive power purchased by substation s, which is connected to the upstream power grid, at the current moment, respectively. and These represent the active and reactive power outputs of the distributed power source g at the current moment, respectively. and These represent the active power output and power factor angle of the distributed renewable energy source e at the current moment, respectively. This represents the charging power consumed by charging station d at the current moment; and These represent the active power flow and reactive power flow from node i to node j at the current moment, respectively. and These represent the active and reactive loads of node j at the current moment, respectively. Represents a set of nodes; and These are the dual variables of the active power balance constraint and the reactive power balance constraint at node j, respectively. and These represent the active power flow and reactive power flow from node j to node k' at the current moment, respectively. and They represent the lines respectively. The starting set and the ending set.

[0181] (2) Power grid physical safety constraints: Constraining the voltage drop of the current flowing through the branch, specifically as follows:

[0182] ;

[0183] In the formula: and These represent the voltage magnitudes of node i and node j at the current moment, respectively. and Representing branch roads Resistance and reactance; Indicates the amplitude of the system reference voltage; Represents the set of branches; This represents the dual variable of the branch voltage drop constraint.

[0184] The voltage of each node is constrained to remain within a safe operating range, as follows:

[0185] ;

[0186] In the formula: and These represent the lower and upper limits of the voltage amplitude at node j, respectively; and These represent the dual variables of the lower and upper limits of the node voltage amplitude constraints, respectively.

[0187] (3) Transmission capacity constraint: Ensure that the active and reactive power flowing through each branch does not exceed its transmission capacity limit to prevent line overload, as follows:

[0188] ;

[0189] ;

[0190] In the formula: and Representing branch roads There are upper limits to both active and reactive current flows; and Let represent the dual variables of the lower and upper limits of the active power flow constraints, respectively. and These represent the dual variables of the lower and upper limits of reactive power flow constraints, respectively.

[0191] (4) Boundary constraints on the output of distributed power sources, as follows:

[0192] ;

[0193] ;

[0194] In the formula: and These represent the lower and upper limits of the active power output of the distributed power source g, respectively. and These represent the lower and upper limits of the reactive power output of the distributed power source g, respectively. Represents a collection of distributed power sources; and The dual variable representing the lower and upper limits of the active power output of the distributed power source g; and The dual variable represents the lower and upper limits of the reactive power output of the distributed power source g.

[0195] (5) Operational constraints of distributed renewable energy sources are as follows:

[0196] ;

[0197] ;

[0198] In the formula: and These represent the active power output and power curtailment of distributed renewable energy source e at the current moment, respectively. This represents the available power of distributed renewable energy source e at the current moment; Represents a collection of distributed renewable energy sources; Dual variables constraining the relationship between active power output and curtailment of distributed renewable energy sources; The dual variable representing the lower bound constraint on the active power output of distributed renewable energy; The dual variable represents the constraint on the lower limit of the curtailment power of distributed renewable energy.

[0199] (6) Power purchase constraints: Constraints on the active and reactive power output purchased from substations, as detailed below:

[0200] ;

[0201] in: and These represent the lower and upper limits of the active power that substation s can purchase, respectively. and These represent the lower and upper limits of reactive power that substation s can purchase, respectively. and These are the dual variables for the lower and upper limits of active power purchased from the substation, respectively. and These are the dual variables for the lower and upper limits of reactive power purchased from the substation, respectively.

[0202] Based on the strong duality theorem, a set of constraints consisting of dual variables is introduced to couple charging power and charging price. Charging power is affected by the demand for battery swapping at battery swapping stations, the routing path of battery transport vehicles, and routing time; while charging price is constrained by the dual variables of the active power balance constraints at the nodes in the distribution network. The marginal node price, which consists of generation costs, line congestion prices, and voltage support prices, together constitutes the cost of energy consumed by each charging station in the electricity market, and is therefore used to provide pricing strategies for charging stations.

[0203] This invention employs a method that does not require a hierarchical model to solve for the dual variables, incorporating the complete dual problem into the optimization problem to solve for the dual variables of the active power balance constraint. The specific formula is as follows:

[0204] ;

[0205] ;

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] ;

[0211] ;

[0212] ;

[0213] ;

[0214] In the formula: and Let represent the dual variables of the active power balance constraint and the reactive power balance constraint of the distributed power source g, respectively. This represents the active power output of node j at the current moment; and The dual variable representing the active power balance constraint and reactive power balance constraint of distributed renewable energy e; This represents the unit cost of discarding distributed renewable energy source e; and These represent the dual variables of the lower and upper limits of the node voltage amplitude constraints, respectively. and Let i and j represent the dual variables of the active power balance constraint at node i and node j, respectively. and Let i and j represent the dual variables of the reactive power balance constraint at node i and node j, respectively. and These represent the dual variables of the lower and upper limits of the active power flow constraint, respectively. The dual variable representing the lower bound constraint on the active power output of distributed renewable energy; These represent the dual variables of the lower limit constraint on the curtailment power of distributed renewable energy.

[0215] The above constraints are embedded into the independent economic operation models of multiple distribution networks established in step two, so as to simultaneously solve for the optimal charging power and the corresponding price.

[0216] Step 3: Construct a unified time frame for the variable time interval battery logistics model of the battery swapping system built in Step 1 and the fixed time interval distribution network economic operation model built in Step 2; integrate the event-driven scheduling in the battery logistics model of the battery swapping system and the periodic-driven scheduling in the distribution network economic operation model into the same time coordinate.

[0217] The economic operation model of the power distribution network system adopts a fixed time interval scheme, while the routing of battery transport vehicles in the cross-regional battery swapping system depends on the route selection, service decisions within the station, travel time along the route, and service time within the station, which are continuously represented by variable time intervals. Therefore, this invention introduces indicator variables. To achieve system coordination between two different time schemes, ensuring that the routing behavior of battery transport vehicles in the variable time interval scheme is consistent with the operation behavior of multiple distribution networks in the fixed time interval scheme.

[0218] (1) Service constraints of battery swapping stations

[0219] For a battery swapping station, the battery transport vehicle providing swapping services at time t needs to arrive at the corresponding station within the time interval (t-1, t]. The McCormick envelope relaxation technique is used to determine the arrival time of battery transport vehicle k at station m within the time interval (t-1, t]. Whether to remain within this interval is constrained as follows:

[0220] ;

[0221] ;

[0222] In the formula: This is an indicator variable representing the arrival time of battery transport vehicle k at station m. A value of 1 indicates arrival, and a value of 0 indicates not yet arrived.

[0223] The battery swapping demand at battery swapping stations is limited within the time window. The specific constraint formulas for the possible values ​​are as follows:

[0224] ;

[0225] ;

[0226] In the formula: and These represent the time window of battery swapping station m. The internal demand for full battery loading and empty battery transportation; and These represent the lower and upper bounds of the time window for station m, respectively.

[0227] For a battery swapping station, a battery swapping operation can only be performed if and only if the battery transport vehicle arrives at station m at the current time. The specific constraint formula is as follows:

[0228] ;

[0229] In the formula: This indicates whether the battery transport vehicle k stops at station m; 1 indicates a stop, and 0 indicates continued driving. This indicates that battery transport vehicle k travels from station n to station m; This indicates the arrival time of battery transport vehicle k at station m.

[0230] (2) Charging station service constraints

[0231] For charging stations, battery transport vehicles departing within the time period [t, t+1) must complete the unloading of empty batteries and the loading of full batteries at time t. This is also achieved through McCormick envelope relaxation, with the specific constraint formula as follows:

[0232] ;

[0233] ;

[0234] In the formula: The indicator variable represents the arrival time of battery transport vehicle k at station d at the current time; 1 indicates arrival, and 0 indicates no arrival. This indicates whether the battery transport vehicle k stops at the charging station d; 1 indicates stopping, and 0 indicates continuing to travel. This indicates the time when battery transport vehicle k arrives at station d; This indicates the service time spent at charging station d.

[0235] The dynamic balance between the number of fully charged batteries and the number of empty batteries in charging station d is managed using the following constraint formula:

[0236] ;

[0237] ;

[0238] In the formula: and These represent the number of fully charged batteries and the number of empty batteries at charging station d at the current moment, respectively. and These represent the number of fully charged batteries and the number of empty batteries at charging station d at the previous moment, respectively. This indicates the number of empty batteries converted to full batteries at charging station d at the current moment; The indicator variable represents the arrival time of battery transport vehicle k at station d at the current moment; and These represent the number of full batteries and empty batteries exchanged by battery transport vehicle k at station d, respectively.

[0239] The number of empty-to-full battery conversions is determined based on the charging power. The specific constraint formula for the influence is as follows:

[0240] ;

[0241] In the formula: Ca represents the unit battery capacity.

[0242] For charging stations, battery swapping can only be performed after the battery transport vehicle arrives at the charging station at time t, with the following specific constraints:

[0243] .

[0244] Step 4: Design a non-iterative coordination framework based on projection theory to achieve privacy protection during the coordination optimization process. The core of this framework is that each participant does not need to disclose internal private information (internal variables) such as generator parameters, network topology, and battery transport vehicle parameters; optimal system operation can be achieved simply by exchanging two coordination variables: charging power and charging price.

[0245] During the projection calculation phase, the detailed economic operation model of each distribution network is compressed into an equivalent model that retains only the input-output relationships, thereby omitting the internal variables. The relevant models are shown below:

[0246] ;

[0247] in: and These represent the internal variables and coordination variables of the regional distribution network r, respectively; This represents the cost auxiliary variable introduced into the objective function; for The corresponding upper bound; and Let represent the constraints and objective function of the distribution network operation within the regional distribution network r, respectively.

[0248] The model is formulated as a minimization procedure, where the optimal solution will force... It is exactly equal to when solving. This ensures strict equivalence with the original problem. The feasible space of the distribution network economic operation model is denoted as the original feasible space. ;in express The real space of dimensional numbers; express The real space of dimension .

[0249] In order to start from the original feasible space The projection space of the hidden internal variables is obtained. A progressive extreme point generation algorithm is proposed, which is executed locally within each distribution network without the need to exchange coordination variables. The specific steps are as follows:

[0250] (1) Initialize the extreme point set of the distribution network.

[0251] Define an empty set, and obtain initial extreme points by solving a series of maximum and minimum value problems along the positive and negative directions of each coordinate axis in the coordinate variable space, and add them to the set. To achieve at least to Add at least Several points are used to ensure that their projection space is within [a certain range]. A non-degenerate polyhedron is formed in the middle. The extremum problem is as follows:

[0252] ;

[0253] In the formula: , and Representing internal variables respectively Coordination variables The coupling matrix and the constraint right-hand side terms; That is, constraints and The expanded expression.

[0254] (2) Construct the projection space and calibrate the origin.

[0255] Based on the current set of extreme points Calculate its corresponding hyperplane This describes the current projected space. To optimize numerical computation, the set of extreme points is... The new origin is obtained by summing all the extreme points and dividing by the number of extreme points. Subtract the new origin from the coordinates of all original extrema points in the projection space. The coordinates are used to obtain the new extreme point. This forms a new set of extreme points.

[0256] (3) Search for new extreme points.

[0257] Based on the set of extreme points The midpoint defines the current projection space, and the unit outward normal vector of each hyperplane in the current projection space is calculated. Then along each The objective function is solved in a directional manner to search for candidate extrema outside the current projection space. The specific objective function is as follows:

[0258] ;

[0259] ;

[0260] In the formula: To solve for the above objective function value.

[0261] (4) Verification and convergence judgment.

[0262] Calculate the improvement rate in each direction This is used to quantify the contribution of each hyperplane to the shape of the projected space during subsequent searches. It also defines the total change in a single search. ;

[0263] ;

[0264] In the formula: This indicates that the optimal value of the objective function is obtained in step (3).

[0265] If the two main loops The difference is less than or equal to the preset error threshold. If the algorithm converges, it means that the projection space remains unchanged after two consecutive searches. Construction complete; otherwise, repeat steps (2) and (3) to continue iterating until convergence.

[0266] Step 5: Substitute the projection space obtained in Step 4 as a constraint into the battery logistics model of the battery swapping system constructed in Step 1, and solve for the coordination variables. The charging power and charging price are considered; each distribution network solves its economic operation model based on the received charging power and charging price to obtain internal variables. This enables coordination. Throughout the process, coordination between multiple distribution network systems and cross-regional battery swapping systems does not require iterative computation, achieving privacy protection within a non-iterative framework.

[0267] Example

[0268] In a multi-distribution network system consisting of IEEE 14 nodes, IEEE 12 nodes, and IEEE 10 nodes, and a cross-regional power swapping system with 12 nodes, this embodiment compares and analyzes a coordination scheme that does not consider privacy protection, an ADMM privacy protection scheme based on two-layer iteration, and the method provided by this invention to illustrate the effectiveness of the proposed scheme in load restoration.

[0269] Option 1: A centralized computing solution that does not consider privacy protection;

[0270] Option 2: A privacy protection scheme based on two-layer iteration of ADMM;

[0271] Solution 3: The non-iterative privacy protection scheme based on spatial projection proposed in this invention.

[0272] Table 1 compares the cost of solving the three schemes.

[0273] Table 1 Comparison of operating costs for Schemes 1-3

[0274]

[0275] The results of the centralized framework in Scheme 1 are used as a benchmark for comparison. Due to the influence of accumulated errors, the method based on two-layer iterative ADMM in Scheme 2 has some deviation in the optimal solution. In contrast, the non-iterative privacy-preserving scheme based on spatial projection provided by this invention can accurately extract the coordination boundary information without sacrificing accuracy. Therefore, the cost results obtained in its coordination process are completely consistent with the centralized framework in Scheme 1.

[0276] Table 2 compares the problem size and solution time of the three schemes.

[0277] Table 2 Comparison of optimization problem size and computation time for schemes 1-3

[0278]

[0279] Table 2 compares the number of variables, constraints, and solution information in Schemes 1-3, verifying the advantages of the proposed framework in achieving privacy protection and efficient information exchange. In the centralized model of Scheme 1, all information of the distribution network, including load status, network topology, and generation parameters, needs to be shared with the cross-regional battery swapping system. This not only leads to a huge optimization problem (a total of 13,772 variables and 15,885 constraints) but also poses a risk of sensitive operational data leakage. In contrast, in the two-layer iterative ADMM method of Scheme 2 and the non-iterative method proposed in Example III, coordination variables are exchanged only between the battery swapping system and each distribution network, effectively hiding the internal details of the system and significantly reducing communication overhead. However, the ADMM-based method in Scheme 2 requires the introduction of additional constraints during the coordination process to maintain cross-system variable consistency, thus expanding the problem size and requiring multiple iterations to converge. In the test system, its convergence process requires 34 iterations, with a total computation time exceeding 7000 seconds and an average computation time of 223.42 seconds per iteration, resulting in a large amount of redundant computation and information transmission. In contrast, the method provided by this invention requires only one boundary information exchange between the cross-regional battery swapping system and multiple distribution networks. For each distribution network, only coordination variables × time intervals need to be considered and encapsulated in the projection space, while internal variables remain hidden. Therefore, the proposed method effectively reduces the problem size and significantly improves computational efficiency. As shown in Table 2, the projection space computation time of the proposed method is 25.91 seconds, the coordination computation time is 45.57 seconds, and the total computation time is 71.48 seconds. Compared with the centralized framework, the computation time is reduced by 76.9%, fully demonstrating the significant advantages of this invention in terms of computational performance and efficiency.

[0280] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A non-iterative coordination method for distribution networks and battery swapping systems based on projection, characterized in that, The specific steps are as follows: S1: Construct a battery logistics model for a battery swapping system that supports cross-regional operations and has multiple battery swapping stations and charging stations. Plan the routes and capacity of battery transport vehicles in a continuous time frame to jointly manage the collection and distribution of empty and full batteries between multiple sites. S2: For the independent operation needs of each distribution network, considering distributed photovoltaic, wind power and distributed power generation equipment, construct an economic operation model for each distribution network; the economic operation model takes minimizing the total operating cost of the distribution network as the objective function, including power balance constraints, grid physical security constraints, transmission capacity constraints, distributed power generation output boundary constraints, distributed renewable energy operation constraints and power purchase constraints; based on the optimization results of the economic operation model, use the nodal marginal price to formulate a charging pricing strategy for charging stations; S3: An improved discrete-time scheme is adopted to unify the variable time interval battery logistics model and the fixed time interval economic operation model in the same time scheme, ensuring that the path behavior of battery transport vehicles is consistent with the operation behavior of multiple distribution networks. S4: Construct a non-iterative coordination framework, compress the economic operation model of the distribution network based on projection theory, hide the internal variables, and obtain a projection space containing only coordination variables and cost auxiliary variables through dimensionality reduction. S5: Substitute the projection space as a constraint into the battery logistics model of the battery swapping system constructed in step S1, and solve for the charging power and charging price in the coordination variables; each distribution network solves its economic operation model based on the received charging power and charging price to obtain internal variables for coordination.

2. The non-iterative coordination method according to claim 1, characterized in that, The battery logistics model described in step S1 takes minimizing the total operating cost of the cross-regional swapping system as its objective function, including constraints on battery transport vehicle allocation, service boundary constraints of battery swapping stations, path continuity constraints, service continuity constraints, time connection constraints, time window constraints, total working time constraints, battery flow balance constraints, station battery exchange volume constraints, and vehicle carrying capacity constraints.

3. The non-iterative coordination method according to claim 1, characterized in that, The total operating cost in the battery logistics model described in step S1 includes the driving cost of the battery transport vehicle and the charging fee paid to the power distribution network.

4. The non-iterative coordination method according to claim 1, characterized in that, The total operating cost of the distribution network in the economic operation model described in step S2 is the sum of the fuel cost of distributed power sources, the penalty for abandoning renewable energy, the cost of purchasing electricity from the transmission network, and the revenue from selling electricity to charging stations.

5. The non-iterative coordination method according to claim 1, characterized in that, The specific steps for formulating charging pricing strategies for charging stations using nodal marginal prices are as follows: Introduce corresponding dual variables into the power balance constraints in the economic operation model described in step S2; the dual variables of the active power balance constraints are composed of generation costs, power transmission costs, and voltage support costs; solve for the dual variables of the active power balance constraints to obtain the nodal marginal prices.

6. The non-iterative coordination method according to claim 1, characterized in that, The improved discrete-time scheme is as follows: S31: Introducing Discrete Indicator Variables This indicates whether the battery transport vehicle arrived at the station within the time interval; 1 indicates arrival, and 0 indicates no arrival. Using McCormick envelope technology, the actual continuous arrival time of battery transport vehicles is compared with discrete indicator variables. Perform logical associations; S32: By indicator variables By connecting the battery logistics model and the economic operation model, the requirements for battery swapping stations to load full batteries and transport empty batteries within a time window must be met by battery transport vehicles that arrive within the discrete time period corresponding to that time window; the requirements for battery transport vehicles to perform battery swapping or charging services only after arriving at the station; and the requirements for battery transport vehicles departing from the charging station to have already completed the loading of full batteries and the unloading of empty batteries.

7. The non-iterative coordination method according to claim 1, characterized in that, Step S4 is as follows: Reconstruct the economic operation model of each distribution network to include internal variables. Coordination variables and cost auxiliary variables The equivalent form is obtained to get the original feasible space; the original feasible space is reduced in dimension using projection theory to obtain a form consisting only of coordination variables. and cost auxiliary variables The projection space is constructed; for any boundary condition in this projection space, at least one feasible internal variable can be found in the original feasible space. And the corresponding operating cost is no greater than This allows the economic operation model to retain its external coordination characteristics while hiding internal variables.

8. The non-iterative coordination method according to claim 7, characterized in that, The projection space is constructed as follows: S41: Solve the extremum problem along the positive and negative directions of each coordinate axis in the coordinate variable space to obtain the initial set of extreme points; S42: Calculate the corresponding hyperplane based on the initial set of extreme points to describe the current projection space; Calculate the geometric center of the initial extreme point set as the new origin, and perform coordinate transformation to obtain a new extreme point set; S43: Calculate the unit external normal vector of each hyperplane in the current projection space, and solve the optimization problem under internal constraints along each normal vector, searching for candidate extreme points outside the current projection space; S44: Calculate the improvement rate of the projection space boundary brought about by the search step. If the maximum improvement rate change between two consecutive iterations is less than the preset error threshold, the algorithm is determined to have converged and the current projection space is completed. Otherwise, repeat steps S42 and S43 iteratively until the algorithm converges.

9. A non-iterative coordination system for multi-distribution networks and cross-regional battery swapping systems based on spatial projection, characterized in that, include: The battery swapping system modeling module is configured to: build a battery logistics model for a battery swapping system that supports cross-regional operations and has multiple battery swapping stations and charging stations; plan the routes and capacity of battery transport vehicles in a continuous time frame; and jointly manage the collection and distribution of empty and full batteries between multiple stations. The distribution network modeling and pricing module is configured to: construct an economic operation model for each distribution network based on the independent operation needs of each distribution network, taking into account distributed photovoltaic, wind power and distributed power equipment; and formulate a charging pricing strategy for the charging station based on the optimization results of the economic operation model and using the node marginal price. The time scheme coordination module is configured to: adopt an improved discrete time scheme to unify the battery logistics model with variable time intervals and the economic operation model with fixed time intervals in the same time scheme, so as to ensure that the path behavior of battery transport vehicles is consistent with the operation behavior of multiple distribution networks. The projection space construction module is configured to: construct a non-iterative coordination framework, compress the economic operation model of the power distribution network based on projection theory, hide the internal variables, and obtain a projection space containing only coordination variables and cost auxiliary variables through dimensionality reduction. The non-iterative coordination solution module is configured to: substitute the projection space as a constraint into the battery logistics model of the battery swapping system, solve for the charging power and charging price in the coordination variables, and send the charging power and charging price to each distribution network; each distribution network solves its own economic operation model based on the received charging power and charging price to obtain internal variables to achieve coordination.

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