EVTOL cluster task planning method for lithium battery life optimization

Abstract

The invention relates to an eVTOL cluster task planning method for lithium battery life optimization. The eVTOL cluster task planning method comprises the following three steps: (1) establishing a single task lithium battery SOH degradation amount estimation model; (2) establishing a mixed integer nonlinear programming model of an eVTOL cluster task programming problem; and (3) solving an optimal task planning scheme. Based on the method, the service life of the eVTOL cluster lithium battery can be prolonged, the operation and maintenance cost of the cluster can be reduced, and a new thought and a new solution are provided for improving the economy and the reliability of eVTOL cluster operation.

Description

[0001] Specification (1) Technical Field

[0002] The present invention belongs to the technical field of UAV logistics, and particularly relates to an eVTOL swarm mission planning method for optimizing the lifespan of lithium batteries. (2) Background Art

[0003] The state of health (SOH) of lithium batteries has a direct and crucial impact on the operation reliability and economy of eVTOL swarms. If the decline problem of lithium battery SOH is ignored, it will lead to uneven distribution of battery resources within the swarm, ultimately shortening the service life of the entire swarm, increasing maintenance costs, and existing research on planning eVTOL swarm missions mostly focuses on the goal of distance minimization, without considering the SOH of lithium batteries and its degradation trajectory.

[0004] Therefore, this paper proposes an eVTOL swarm mission planning method for optimizing the lifespan of lithium batteries, with the minimum total SOH degradation of the eVTOL swarm as the optimization goal, constructs a differential mission planning model considering the SOH of lithium batteries, and uses the genetic algorithm to solve the optimal mission planning scheme. This method is committed to delaying the degradation process of lithium batteries, extending the service life of lithium batteries, and reducing the operation and maintenance costs of the swarm, providing new ideas and solutions for improving the economy and reliability of eVTOL swarm operation. (3) Summary of the Invention

[0005] The purpose of the present invention is to provide an eVTOL swarm mission planning method for optimizing the lifespan of lithium batteries, mainly including the following steps:

[0006] Step 1: Establish an estimation model for the SOH degradation of lithium batteries in a single mission;

[0007] According to the mission characteristics of eVTOL, taking the key factors affecting the SOH degradation of lithium batteries as inputs, establish an SOH degradation model for a single delivery mission, and the expression is as follows:

[0008] DSOH k = F(SOH k , DOD k , C k ) (1)

[0009] In the formula, DSOH k represents the SOH degradation of the k-th eVTOL during the delivery mission; F(·) represents the constructed model; SOH k represents the current SOH of the k-th eVTOL; DOD k represents the depth of discharge of the single delivery mission performed by the k-th UAV; C kRepresents the maximum discharge rate of a single delivery task performed by the k-th eVTOL.

[0010] Step 2: Establish a mixed-integer non-linear programming model for the eVTOL cluster task planning problem;

[0011] Taking the minimum total SOH degradation of the eVTOL cluster as the optimization objective, a task planning model considering the SOH of lithium batteries is constructed. This step includes 3 sub-steps:

[0012] Step 1: Construct the task scenario

[0013] Construct a single-warehouse scenario, design multiple eVTOLs to carry pre-planned goods, each visit different user points to achieve material distribution, and finally all return to the warehouse;

[0014] Step 2: Determine the objective function

[0015] The objective of the model is to minimize the total SOH degradation of the cluster. The expression of the objective function is as follows:

[0016]

[0017] In the formula, Total_DSOH represents the total SOH degradation of the cluster;

[0018] Step 3: Determine the constraint conditions

[0019] The constraint conditions include path topology constraints, service uniqueness constraints, flow balance constraints, delivery integrity constraints, load capacity constraints, energy consumption constraints, remaining energy constraints, depth of discharge constraints, and maximum discharge rate constraints;

[0020] (1) Path topology constraints

[0021] The path topology constraints force the flight path of each eVTOL to form a closed Euler circuit, requiring each eVTOL to start from the warehouse node and finally return to the warehouse, as shown in the following formula:

[0022]

[0023] In the formula, x k0j represents the path of the k-th eVTOL flying from the warehouse to node j; E ki0 represents the path of flying back to the warehouse from node i;

[0024] (2) Service uniqueness constraints

[0025] The service uniqueness constraints limit the solution space to a set of non-intersecting paths, ensuring an exact coverage of the user vertex set through double equalities, as shown in the following formula:

[0026]

[0027] where x kij is a binary variable. If the planned path of the k-th eVTOL contains the arc (N i , N j ), it is 1; otherwise, it is 0;

[0028] (3) Flow balance constraint

[0029] The flow balance constraint eliminates isolated nodes and path fragments, ensuring the connectivity of the solution. Based on the principle of network flow balance, it is required that the in-degree of non-warehouse nodes is equal to the out-degree, as shown in the following equation:

[0030]

[0031] (4) Delivery integrity constraint

[0032] The delivery integrity constraint transforms the discrete delivery logic into linear constraints through the big M method to ensure that the material requirements of user points are accurately met. When x ki0 = 1, the eVTOL returns to the warehouse empty; when x kij = 1, the difference between the load variables W ki and W kj is strictly limited to c i to simulate the process of material unloading; when x kij = 0 and x ki0 = 0, the big M value makes the constraint relaxation ineffective, as shown in the following equation:

[0033]

[0034] where W ki represents the total material load of the k-th eVTOL flying to node i; c i represents the material requirement of node i; M represents a very large number;

[0035] (5) Payload capacity constraint

[0036] The payload capacity constraint transforms the maximum takeoff weight in the airworthiness certification of the aircraft into a mathematical boundary condition to ensure the engineering feasibility of the solution, as shown in the following equation:

[0037]

[0038] where L k represents the maximum payload capacity of the k-th eVTOL;

[0039] (6) Energy consumption constraint

[0040] The energy consumption constraint associates the path selection variable with the energy consumption model through the big M method. Equations (9) to (11) model the energy consumption from the warehouse to the user point, from the user point to the user point, and from the user point to the warehouse respectively, as shown below:

[0041]

[0042] In the formula, ME k represents the rated energy of the k-th eVTOL battery; RE kj represents the remaining battery energy of the k-th eVTOL when it arrives at node i; E k0j represents the energy consumed by the k-th eVTOL flying from the warehouse to node j; E ki0 represents the energy consumed when flying back from node i to the warehouse;

[0043] (7) Remaining energy constraint

[0044] The remaining energy constraint ensures the remaining energy of each eVTOL for the return flight through the dynamic threshold ε·SOH k ·NE k to ensure the safety of flight operations and prevent battery damage due to overuse, as shown below:

[0045]

[0046] In the formula, ε represents the remaining energy safety threshold;

[0047] (8) Depth of discharge constraint

[0048] The depth of discharge constraint establishes the quantitative relationship between the DOD of each eVTOL and the flight energy consumption, providing input variables for the SOH degradation model, as shown below:

[0049]

[0050] (9) Maximum discharge rate constraint

[0051] The maximum discharge rate constraint establishes the maximum discharge rate during the flight of each eVTOL, providing input variables for the SOH degradation model, as shown below:

[0052]

[0053] In the formula, P takeoff represents the takeoff power;

[0054] Step 3: Solve the optimal task planning scheme;

[0055] Use the heuristic algorithm to solve Step 2 to obtain the optimal task planning scheme. (IV) Description of the drawings

[0056] Figure 1 Method flow chart

[0057] Figure 2 Schematic diagram of eVTOL cluster mission planning

[0058] Figure 3 Flow chart of solving adaptive genetic algorithm

[0059] Figure 4 Task planning result diagram (V) Specific implementation manners

[0060] The method flow of the present invention is as Figure 1 shown. In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Step 1: Establish an estimation model for the SOH degradation amount of a single mission lithium battery;

[0062] In this case, a regression LSTM network is used to estimate the SOH degradation amount of a single eVTOL delivery mission, and the expression of the SOH degradation model for a single delivery mission is constructed as follows:

[0063] DSOH k = LSTM(SOH k , DOD k , C k ) (15)

[0064] Step 2: Establish a mixed-integer non-linear programming model for the eVTOL cluster mission planning problem;

[0065] The schematic diagram of the constructed mission scenario is as Figure 2 shown. Specifically: 10 non-overlapping user point coordinates are randomly generated within a 20km×20km area. The cargo demand c i of each user point is randomly generated within the range of [15Kg, 25Kg]. The warehouse location is set at the center of the area to ensure the maximization of delivery efficiency. 4 eVTOL aircraft are used for delivery. The initial SOH value of each eVTOL is randomly generated within the range of [88%, 96%] to reflect the differences in the health status of heterogeneous eVTOLs in the actual scenario.

[0066] The expression of the objective function is as follows:

[0067]

[0068] The constraints include path topology constraints, service uniqueness constraints, flow balance constraints, delivery integrity constraints, load capacity constraints, energy consumption constraints, remaining energy constraints, depth of discharge constraints, and maximum discharge rate constraints.

[0069] (1) Path topology constraints

[0070] The path topology constraints force the flight path of each eVTOL to form a closed Eulerian circuit, requiring each eVTOL to start from the warehouse node and finally return to the warehouse, as shown in the following formula:

[0071]

[0072] In the formula, x k0j represents the path of the kth eVTOL flying from the warehouse to node j; E ki0 represents the path of flying back to the warehouse from node i;

[0073] (2) Service uniqueness constraints

[0074] The service uniqueness constraints limit the solution space to a set of non-intersecting paths, ensuring an exact coverage of the user vertex set through a double equality, as shown in the following formula:

[0075]

[0076] In the formula, x kij is a binary variable. If the planned path of the kth eVTOL contains the arc (N i , N j ), it is 1; otherwise, it is 0;

[0077] (3) Flow balance constraints

[0078] The flow balance constraints eliminate isolated nodes and path fragments, ensuring the connectivity of the solution. Based on the principle of network flow balance, it is required that the in-degree of non-warehouse nodes is equal to the out-degree, as shown in the following formula:

[0079]

[0080] (4) Delivery integrity constraints

[0081] The delivery integrity constraints transform the discrete delivery logic into linear constraints through the big M method to ensure that the material requirements of user points are exactly met. When x ki0 = 1, the eVTOL returns to the warehouse with an empty load; when x kij = 1, the difference between the load variables W ki and W kj is strictly limited to c i , thus simulating the process of material unloading; when x kij = 0 and x ki0When = 0, the large M value causes the constraint relaxation to fail, as shown in the following equation:

[0082]

[0083] In the formula, W ki represents the total load of supplies when the k-th eVTOL flies to node i; c i represents the supply demand at node i; M represents a very large number;

[0084] (5) Payload capacity constraint

[0085] The payload capacity constraint converts the maximum takeoff weight in the aircraft airworthiness certification into a mathematical boundary condition to ensure the engineering feasibility of the solution, as shown in the following equation:

[0086]

[0087] In the formula, L k represents the maximum payload capacity of the k-th eVTOL;

[0088] (6) Energy consumption constraint

[0089] The energy consumption constraint associates the path selection variable with the energy consumption model through the large M method. Formulas (9) to (11) respectively model the energy consumption from the warehouse to the user point, from the user point to the user point, and from the user point to the warehouse, as shown in the following equation:

[0090]

[0091] In the formula, NE k represents the rated energy of the battery of the k-th eVTOL; RE kj represents the remaining battery energy of the k-th eVTOL when it arrives at node i; E k0j represents the energy consumed by the k-th eVTOL flying from the warehouse to node j; E ki0 represents the energy consumed when flying back to the warehouse from node i;

[0092] (7) Remaining energy constraint

[0093] The remaining energy constraint ensures the remaining energy for each eVTOL to return by means of the dynamic threshold ε·SOH k ·NE k to ensure the safety of flight operations and prevent the battery from being damaged due to overuse, as shown in the following equation:

[0094]

[0095] In the formula, ε represents the remaining energy safety threshold;

[0096] (8) Depth of discharge constraint

[0097] The depth of discharge constraint establishes the quantitative relationship between the DOD of each eVTOL and the flight energy consumption, providing an input variable for the SOH degradation model, as shown in the following formula:

[0098]

[0099] (9) Maximum discharge rate constraint

[0100] The maximum discharge rate constraint establishes the maximum discharge rate during the flight of each eVTOL, providing an input variable for the SOH degradation model, as shown in the following formula:

[0101]

[0102] In the formula, P takeoff represents the takeoff power;

[0103] Step 3: Solve the optimal mission planning scheme;

[0104] In this case, the adaptive genetic algorithm is used to solve the optimal mission planning scheme in Step 2. The flowchart of the adaptive genetic algorithm solution is as shown in Figure 3 Figure. First, a random initialization strategy is adopted to generate the initial population. Then, a weighted penalty fitness function is designed to achieve the efficient search for the optimal solution within the feasible domain of the genetic algorithm. The expression of the fitness function is as follows:

[0105]

[0106] In the formula, object represents the objective function value, which reflects the total SOH degradation of the cluster and comes from formula (2); penalty payload represents the load penalty term, which represents the part where the cumulative cargo demand of users in the mission planning solution exceeds the maximum load capacity of the eVTOL; penalty energy represents the energy consumption penalty term, which represents the part where the remaining energy of the eVTOL is lower than the safety power ε·SOH k ·NE k when the eVTOL returns to the warehouse; ω1, ω2, and ω3 are used to adjust the contribution degrees of the objective function and the penalty terms respectively.

[0107] The optimal solution results are as shown in Figure 4 Figure. Through result analysis, it can be seen that the proposed model sacrifices the optimality of the flight path during the mission planning process in exchange for minimizing the total SOH degradation of the cluster.

Claims

1. An eVTOL swarm mission planning method for lithium battery life optimization, characterized in that: It includes the following steps: Step 1: Establish an estimation model for the degradation amount of the SOH of the lithium battery for a single mission; According to the mission characteristics of eVTOL, taking the key factors affecting the degradation of the SOH of the lithium battery as inputs, establish an SOH degradation model for a single delivery mission. The expression is as follows: DSOH k = F(SOH k , DOD k , C k ) Where DSOH k represents the SOH degradation amount of the k-th eVTOL performing the delivery task; F(·) represents the constructed model; SOH k represents the current SOH of the k-th eVTOL; DOD k represents the depth of discharge of a single delivery task performed by the k-th drone; C k represents the maximum discharge rate of a single delivery task performed by the k-th eVTOL; Step 2: Establish a mixed-integer non-linear programming model for the eVTOL cluster mission planning problem; Taking the minimum total SOH degradation of the eVTOL cluster as the optimization objective, construct a mission planning model considering the SOH of the lithium battery. This step includes 3 sub-steps: Step 1: Construct the mission scenario Construct a single-warehouse scenario. Design multiple eVTOLs to carry pre-planned goods and each access different user points to achieve material distribution, and finally all return to the warehouse. During this process, each eVTOL not only has to strictly comply with the maximum load limit and safety energy constraints, but also needs to ensure that the goods requirements at each user point are uniquely and completely met; Step 2: Determine the objective function The objective of the model is to perform mission planning under the premise of meeting the energy consumption and maximum load constraints to minimize the total SOH degradation of the cluster. The expression of the objective function is as follows: In the formula, Total_DSOH represents the total SOH degradation of the cluster; Step 3: Determine the constraint conditions The constraint conditions include path topology constraints, service uniqueness constraints, flow balance constraints, delivery integrity constraints, load capacity constraints, energy consumption constraints, remaining energy constraints, depth of discharge constraints, and maximum discharge rate constraints; (1) Path topology constraints The path topology constraints force the flight path of each eVTOL to form a closed Euler circuit, requiring each eVTOL to start from the warehouse node and finally return to the warehouse, as shown in the following formula: where x k0j represents the path of the k-th eVTOL flying from the warehouse to node j; E ki0 represents the path of flying back to the warehouse from node i; (2) Service uniqueness constraints The service uniqueness constraints limit the solution space to a set of non-intersecting paths, ensuring the exact coverage of the user vertex set through double equalities, as shown in the following formula: where x kij is a binary variable. If the planned path of the k-th eVTOL contains the arc (N i , N j ), it is 1; otherwise, it is 0. (3) Flow balance constraints The flow balance constraints eliminate isolated nodes and path fragments, ensuring the connectivity of the solution. Based on the principle of network flow balance, it is required that the in-degree of non-warehouse nodes is equal to the out-degree, as shown in the following formula: (4) Delivery integrity constraints The delivery integrity constraint transforms the discrete delivery logic into linear constraints through the big M method to ensure that the material requirements at the user points are precisely met. When x ki0 = 1, the eVTOL returns to the warehouse empty; when x kij = 1, the difference between the load variables W ki and W kj is strictly limited to c i to simulate the process of unloading materials; when x kij = 0 and x ki0 = 0, the big M value makes the constraint relaxation ineffective, as shown in the following formula: Where W ki represents the total load of supplies when the k-th eVTOL flies to node i; c i represents the supply demand of node i; M represents a very large number; (5) Load capacity constraints The load capacity constraints convert the maximum takeoff weight in the airworthiness certification of the aircraft into a mathematical boundary condition to ensure the engineering feasibility of the solution, as shown in the following formula: where L k represents the maximum payload capacity of the k-th eVTOL; (6) Energy consumption constraints The energy consumption constraints associate the path selection variables with the energy consumption model through the big M method. Formulas (9) to (11) respectively model the energy consumption from the warehouse to the user point, from the user point to the user point, and from the user point to the warehouse, as shown in the following formula: where, NE k represents the rated energy of the k-th eVTOL battery; RE kj represents the remaining battery energy of the k-th eVTOL when it arrives at node i; E k0j represents the energy consumed by the k-th eVTOL flying from the warehouse to node j; E ki0 represents the energy consumed for flying back from node i to the warehouse; (7) Remaining energy constraints The remaining energy constraint is through the dynamic threshold ε·SOH k ·NE k which ensures the remaining energy for each eVTOL to return, guaranteeing the safety of flight operations and preventing the battery from being damaged due to overuse, as shown in the following formula: In the formula, ε represents the remaining energy safety threshold; (8) Depth of discharge constraints The depth of discharge constraints establish a quantitative relationship between the DOD of each eVTOL and the flight energy consumption, providing input variables for the SOH degradation model, as shown in the following formula: (9) Maximum discharge rate constraints The maximum discharge rate constraints establish the maximum discharge rate during the flight of each eVTOL, providing input variables for the SOH degradation model, as shown in the following formula: where P takeoff represents the takeoff power; Step 3: Solve the optimal mission planning scheme; Use a heuristic algorithm to solve Step 2 to obtain the optimal mission planning scheme.

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