A multi-electric aircraft energy scheduling method based on distribution robust optimization

Abstract

The application discloses a kind of multi-electric aircraft energy scheduling methods based on distribution robust optimization, comprising the following steps: S1, constructing multi-stage distribution robust model;S2, based on PLDR method and Wasserstein distance, multi-stage distribution robust model is reconfigured as PLDRO model;S3, obtain the load historical data set of multi-electric aircraft and real-time monitoring equipment available state;S4, according to load historical data set, equipment available state and preset energy management parameter, PLDRO model is solved using solver, and in the scheduling period of multi-electric aircraft, based on rolling scheduling method, after observing uncertain load, energy management decision is calculated according to the solving result of PLDRO model and is executed, realize the energy scheduling of multi-electric aircraft.Can realize adaptive scheduling under uncertain load, with good economy and robustness.

Description

Technical Field

[0001] This invention belongs to the field of energy scheduling technology for multi-electric aircraft, specifically relating to a multi-electric aircraft energy scheduling method based on distributed bar optimization. Background Technology

[0002] To achieve lower fuel consumption and environmental pollution, bulky and inefficient hydraulic, pneumatic, and mechanical actuators are gradually being replaced by electric systems. More-electric aircraft, based on the principles of green, environmentally friendly, and energy-efficient aircraft, represent the future direction of advanced aircraft technology. They not only significantly reduce fossil fuel consumption and carbon emissions but also offer lower maintenance costs. The stable operation of the electric system provides crucial assurance for aircraft safety and airworthiness. However, the significant increase in the electrical load of more-electric aircraft makes developing a reliable and resilient power system energy dispatch strategy a challenge.

[0003] Existing technologies treat the power output of airborne generators and the connections between different airborne electrical devices (such as various busbars, loads, energy storage devices, etc.) as decision variables, thus formulating the energy scheduling problem of more-electric aircraft as a mixed-integer programming problem, and using commercial solvers to solve it. However, load uncertainty will lead to the unexecutability of deterministic scheduling decisions, thereby affecting the economy and stability of the more-electric aircraft's power system. Common methods for handling load uncertainty include stochastic programming, robust optimization, and partial Brouwers optimization. Stochastic optimization tends to produce overly aggressive decisions, resulting in poor out-of-sample performance, while robust optimization decisions are too conservative, leading to poor economic efficiency. Therefore, partial Brouwers optimization was proposed. It seeks the worst-case distribution within a fuzzy set composed of a series of distribution clusters with similar statistical properties and further optimizes the decision using decision rules to appropriately balance the economy and conservatism of scheduling. The conventional approach in existing technologies is to construct a two-stage partial Brouwers optimization problem. However, two-stage optimization does not follow the unpredictability of load scheduling, and its decisions are based on information about globally uncertain parameters. This usually does not reflect real-world scheduling scenarios because decision-makers can only observe the uncertain parameters at the current moment. Furthermore, decision rules can be divided into two categories: linear decision rules (LDR) and nonlinear decision rules (NLDR). Neither can adequately balance the scaling and optimal characteristics under the sub-Bruker bar approximation. Given the harsh operating environment and unique topology of multi-electric aircraft, establishing a safe, reliable, and efficient energy scheduling system is a meaningful and challenging problem. This invention proposes a multi-electric aircraft energy scheduling method based on sub-Bruker bar optimization to overcome the pain points of existing technologies, such as unpredictable adaptive scheduling under uncertain loads and low-cost fuel consumption decisions. Summary of the Invention

[0004] The purpose of this invention is to address the above-mentioned problems by proposing a multi-electric aircraft energy scheduling method based on distributed bar optimization, which can achieve adaptive scheduling under uncertain loads and has good economy and robustness.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention proposes a multi-electric aircraft energy scheduling method based on decomposed bar optimization. The multi-electric aircraft includes at least one generator, a main busbar, a secondary busbar, and an energy storage system. The multi-electric aircraft energy scheduling method based on decomposed bar optimization includes the following steps:

[0007] S1. Construct a multi-stage sub-Bruker model, the process is as follows:

[0008] 1) Determine the constraints

[0009] 1.1) Power balance constraints

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] In the formula, This represents the output power of generator k during time period t. This represents the transmission power between generator k and main bus m during time period t. This represents the power supplied by the primary bus m to the secondary bus during time period t. This represents the transmission power between generator k and main bus m during time period t. This represents the power from the primary busbar m to the secondary busbar j during time period t. This represents the power supplied to the energy storage system by the secondary busbar j during time period t. This represents the power supplied from secondary busbar j to the charging module of the energy storage system during time period t. This represents the power from the secondary busbar j to the discharge module of the energy storage system during time period t. This represents the uncertain load connected to secondary bus j during time period t. This represents the energy transfer efficiency between generator k and main busbar m. α represents the energy transfer efficiency between the primary bus m and the secondary bus j. j,t The binary variable representing the secondary bus bar j in time period t. Represents a time set, Indicates generator set, Let S represent the primary bus set, S represent the secondary bus set, S1 represent the secondary bus set connected to the energy storage system, and S2 represent the secondary bus set not connected to the energy storage system. S = S1 ∪ S2.

[0017] 1.2) Capacity Constraints

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] In the formula, A binary variable representing the state of generator k during time period t. This represents the minimum power output limit of generator k. This represents the maximum power output limit of generator k. A binary variable representing the connection state between generator k and main busbar m during time period t. This indicates the power transfer limit between generator k and main bus m. This indicates the power limit of the main bus bar m. The binary variable representing the connection state between the primary bus m and the secondary bus j during time period t. This indicates the power transfer limit between the primary bus m and the secondary bus j. U represents the power supplied to the energy storage system by the secondary busbar j. jESS,t A binary variable representing the connection status between secondary busbar j and the energy storage system during time period t. This indicates the power transfer limit between the secondary bus bar j and the energy storage system;

[0026] 1.3) Energy storage constraints

[0027]

[0028]

[0029] In the formula, Δt is the time interval, and SoC EsS,t This indicates the state of the energy storage system during time period t. This indicates the charging efficiency of the energy storage system. This indicates the discharge efficiency of the energy storage system. Indicates the maximum capacity of the energy storage system. SoC ESS Indicates the boundary of the charged state, Indicates the upper bound of the charged state;

[0030] 1.4) Equipment connection constraints

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] In the formula, This indicates the availability of generator k during time period t. This indicates the availability of main bus line m during time period t. This indicates the availability of secondary bus bar j during time period t;

[0037] 1.5) Uncertain load constraints

[0038]

[0039] In the formula, ξ j,t The random variable representing the load forecast error on secondary busbar j during time period t is... This represents the uncertain load connected to secondary bus j during time period t. This represents the expected value of the uncertain load connected to secondary busbar j during time period t;

[0040] 2) Determine the objective function:

[0041] 2.1) Equipment Priority

[0042]

[0043] In the formula, ζ km ζ represents the connection weight between generator k and main busbar m. mj This indicates the connection weight between the primary bus m and the secondary bus j;

[0044] 2.2) Fuel consumption cost

[0045]

[0046] In the formula, c k This represents the fuel consumption cost coefficient of generator k. This represents the cost factor for charging the energy storage system connected to the secondary busbar j. This represents the cost factor for discharging energy from the energy storage system connected to secondary busbar j;

[0047] 3) Obtain the initial energy scheduling model for the more-electric aircraft, as shown in the following formula:

[0048]

[0049] 4) The initial multi-electric aircraft energy scheduling model is reconstructed into a multi-stage sub-Bruker model, as shown in the following formula:

[0050]

[0051]

[0052] C t y t (ξ [t]^ )+D t y t-1 (ξ [t-1]^ )=d t (74)

[0053] W t x t +H t y t (ξ [τ]^ )≤B t ξ [t]^ (75)

[0054] In the formula, X represents x t The feasible region, Y represents y t The feasible region, formula (26) contains formulas (16)-(20); vector y t The uncertain loads constitute all the decision variables in formulas (1)-(15) and (21), corresponding to formulas (27) and (28); c t For the corresponding x in the objective function t The coefficient vector, q t For the corresponding y in the objective function t The coefficient vector, T is the transpose, A and b are the coefficient matrix and vector of formula (26) respectively, C t and D t Let d be the coefficient matrix of formula (27).t W is the coefficient vector of formula (27). t H t and B t For the coefficient matrix of formula (28), define Let t be the vector of uncertain parameters, and let its uncertainty set be Ξ. t N t Let represent the vector dimension of time period t. Then, all revealed uncertainties collected from the beginning to time period t are represented as: in Specifically, ξ = ξ [t＝T]^ Parameter ξ0=ξ 0,0 Set to 1, utilizing its non-degenerate property to set (ξ1,...,ξ) t ) is represented as ξ [t]^ A linear function, For Wasserstein fuzzy sets, Let be the probability distribution function. Let T be the expectation of the worst probability distribution function in the Wasserstein fuzzy set, and T be the scheduling period.

[0055] S2. Based on the PLDR method and Wasserstein distance, the multi-stage sub-BLRO model is reconstructed into a PLDRO model;

[0056] S3. Acquire historical load data of multi-electric aircraft and monitor equipment availability status in real time;

[0057] S4. Based on the load history dataset, equipment availability status, and preset energy management parameters, the PLDRO model is solved using a solver. In the scheduling cycle of the multi-electric aircraft, based on the rolling scheduling method, after observing uncertain loads, energy management decisions are calculated and executed according to the solution results of the PLDRO model, thereby realizing the energy scheduling of the multi-electric aircraft.

[0058] Preferably, the multi-stage sub-Bruker model is reconstructed into a PLDRO model based on the PLDR method and Wasserstein distance, as follows:

[0059] S21. Use lifting operations to obtain a lifted uncertain set;

[0060] S22. Constructing the equivalent convex hull of lifting uncertain sets.

[0061] S23. Obtaining Wasserstein fuzzy sets based on Wasserstein distance.

[0062] S24. Based on the lifting uncertainty set and Wasserstein fuzzy set, the multi-stage sub-Bruker model is reconstructed into a PLDRO model.

[0063] Preferably, the lifting operation is used to obtain the lifted uncertainty set, including:

[0064] S211. Based on the M load data samples collected from the secondary busbar j during time period t, the load uncertainty set Ξ is obtained. j,t The formula is as follows:

[0065]

[0066] In the formula, ξ is the lower bound of the load data sample of secondary bus j in time period t. j,t Let be the load uncertainty parameter for secondary bus bar j during time period t. This is the upper bound of the load data sample for secondary bus bar j in time period t;

[0067] S212, Definition and And in each uncertain parameter ξ j,t Insert r within the interval j,t A breakpoint of -1 maps uncertain parameters to a high-dimensional space, as shown below:

[0068]

[0069] In the formula, Represents the r-th time interval within time interval t. j,t -1 breakpoints, r j,t Let r be the number of segments in time period t. For ξ0, take r. 0,0 =1;

[0070] S213, Define nonlinear operations Mapping ξ j,t to in Operation It is expressed as follows:

[0071]

[0072] In the formula, q = 1, 2, ..., r j,t ;

[0073] S214. Obtain the improved ξ according to step S213. t Right now Uncertain set Ξ t Represented as a lifting uncertainty set:

[0074]

[0075] In the formula, Let be the lower bound vector of the load during time period t. Let be the upper bound vector of the load during time period t. For the boosted random variable.

[0076] Preferably, constructing a convex hull equivalent to lifting an uncertain set. Specifically as follows:

[0077] S221. For any j = 1, ..., N t ,make Define the set of poles in the lift space for:

[0078]

[0079] in,

[0080]

[0081] S222, the convex hull of the secondary bus bar j in time period t. The structure is as follows:

[0082]

[0083] In the formula, Indicates the pole The corresponding coefficients, and

[0084] S223, Based on the convex hull The separability of the property yields: and At the same time, and

[0085] Preferably, the multi-stage sub-Bruker model is reconstructed into a PLDRO model based on the lifting uncertainty set and the Wasserstein fuzzy set, as follows:

[0086] S241, y t Mapping to all realized uncertain parameters, the formula is as follows:

[0087]

[0088] In the formula, The vector corresponding to time period t The coefficient matrix, take

[0089] S242, Reconstruct formula (28), as follows:

[0090] S2421. Substitute formula (31) into formula (28) to restate formula (28) as follows:

[0091]

[0092] S2422, Combine formula (32) and Rewritten in matrix form:

[0093]

[0094]

[0095] In the formula, Z t for The corresponding first matrix, for The corresponding second matrix, for The corresponding third matrix, For λ [t]^ The corresponding first matrix, For λ [t]^ The corresponding second matrix, λ [t]^ The coefficient vector corresponding to the pole vector. This is the first coefficient vector. This is the second coefficient vector;

[0096] S2423. Based on strong duality theory, formula (33) is expressed as formula (35), thus completing the reconstruction of formula (28):

[0097]

[0098] In the formula, With π t Let T be the dual variable, and T be the transpose.

[0099] S243, Reconstruct formula (27), as follows:

[0100] S2431. Substituting formula (31) into formula (27), formula (27) is reconstructed as follows:

[0101]

[0102] In the formula, Q t for The corresponding matrix;

[0103] S2432. According to formula (36), let Q t The g-th action d t The g-th action get:

[0104]

[0105] S2433, For any convex hull Construct r j,t ∑_(i=1)^n linearly independent vectors as the convex hull The linear representation of the convex hull, and utilizing the separability of the convex hull, the convex hull is... structure linearly independent vectors To express, for For a vector of all 1s within a given space, formula (37) is expressed as:

[0106]

[0107] In the formula, and e and A vector, e, is a completely one vector, satisfying... and Then formula (36) is equivalent to:

[0108]

[0109] S244, Reconstruct formula (25), as follows:

[0110] S2441. Under formula (31), the function Represented as Therefore, the part of the blue rod in formula (25) It can be represented as a finite convex programming approach, with the following formula:

[0111]

[0112] In the formula, λ and s p z p All are introduced variables, where ∈ is the radius of the Wasserstein sphere and M is the number of collected load data samples. For the observed sample of the random variable, ||·|| * Denotes the dual norm;

[0113] S2442. Substituting formula (31) into formula (40), the only constraint in formula (40) containing an uncertain variable is expressed as:

[0114]

[0115] S2443. Based on the strong duality theorem and combined with the convex hull... Representing formula (41) as follows:

[0116]

[0117] In the formula, and π T,p Let be the dual vector of sample p in time period T. For time period T The corresponding first matrix, For time period T The corresponding first matrix, For time period T The corresponding coefficient vector, for The coefficient vector corresponding to time period T, For time period T The corresponding second matrix, For time period T The corresponding second matrix;

[0118] Combining this with formula (40), we get:

[0119]

[0120] S245. Combining formulas (35), (39) and (43), the PLDRO model is obtained. The PLDRO model is as follows:

[0121]

[0122]

[0123] Preferably, Wasserstein fuzzy sets The formula is as follows:

[0124]

[0125] Among them, Wasserstein distance satisfy:

[0126]

[0127] In the formula, for The marginal distribution represents the true distribution. for The marginal distribution of Π is and The joint distribution of , where ‖·‖ is the norm, For a given boosting support space, Let be the space of the probability distribution function. For random variables under the true distribution, for The differential, for The differential;

[0128] The radius of the Wasserstein sphere is estimated using the following formula:

[0129]

[0130] The Wasserstein sphere radius ∈ and the constant R are calculated as follows:

[0131]

[0132]

[0133]

[0134] In the formula, η is the confidence level. ρ is the mean of the collected load data samples, and ρ is a variable. M represents the number of load data samples collected. For Dirac measurement, To improve the load data sample p in the space, P{·} is the probability.

[0135] Preferably, the solver is a GUROBI solver or a CPLEX solver.

[0136] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0137] This method establishes an energy dispatch model for multi-electric aircraft (MEA) while considering equipment availability and priority. This model not only improves the reliability and safety of MEA energy dispatch systems but also reduces fuel consumption during MEA operation, achieving lower carbon emissions. It also considers the unpredictability of MEA fault decision-making and dispatch processes in real-world applications. Utilizing a Wasserstein distance-based bibliometric optimization method and piecewise linear decision rules, it adapts to the load uncertainty in the MEA power system, exhibiting good economic efficiency and robustness. While maximizing power supply, it allows decision-makers to flexibly adjust the bibliometric optimization dispatch scheme based on dispatch requirements by changing the Wasserstein sphere radius. Furthermore, this method fully follows the actual dispatch process; as uncertain loads are revealed sequentially, the MEA power system energy dispatch scheme is executed in a rolling manner, respecting the unpredictability of the real dispatch process. Attached Figure Description

[0138] Figure 1 This is a flowchart of the multi-electric aircraft energy scheduling method based on split-blob bar optimization according to the present invention;

[0139] Figure 2This is a structural block diagram of the multi-electric aircraft of the present invention;

[0140] Figure 3 This diagram shows a cost comparison between the PLDRO model used in this invention and the SAA and RO models used in the prior art for different Wasserstein sphere radii.

[0141] Figure 4 This is a cost comparison chart of the TDRO model and PLDRO model under different RSDs according to the present invention;

[0142] Figure 5 This figure shows the cost comparison results of the TDRO model and PLDRO model under different Wasserstein sphere radii in this invention;

[0143] Figure 6 The diagram shows the scheduling results of this invention in four typical scenarios. Detailed Implementation

[0144] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0145] It should be noted that, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application.

[0146] To overcome the problems of existing technologies, such as unpredictable adaptive scheduling under uncertain loads and low-cost fuel consumption decisions, this invention provides a multi-electric aircraft energy scheduling method based on split-Brow bar optimization. Specifically, this invention constructs a multi-stage split-Brow bar model based on Wasserstein distance, considering equipment failures and equipment connection priorities. This model respects the unpredictability of fault state decisions and scheduling processes. Compared with existing multi-stage methods based on LDR, PLDR is introduced to achieve a tighter approximation without sacrificing scalability. Furthermore, for computational tractability, the proposed model is reformulated as a mixed integer linear programming (MILP) model, which performs scheduling in a rolling manner based on continuously interpretable uncertainties in real-world scenarios, thereby realizing a multi-electric aircraft energy scheduling scheme that combines handling uncertain loads with low carbon emissions.

[0147] like Figure 1-6 As shown, a multi-electric aircraft energy scheduling method based on sub-Bruker optimization is presented. The multi-electric aircraft includes at least one generator, a main busbar, a secondary busbar, and an energy storage system. The multi-electric aircraft energy scheduling method based on sub-Bruker optimization includes the following steps:

[0148] S1. Construct a multi-stage sub-Bruker model, the process is as follows:

[0149] 1) Determine the constraints

[0150] 1.1) Power balance constraints

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] In the formula, This represents the output power of generator k during time period t. This represents the transmission power between generator k and main bus m during time period t. This represents the power supplied by the primary bus m to the secondary bus during time period t. This represents the transmission power between generator k and main bus m during time period t. This represents the power from the primary busbar m to the secondary busbar j during time period t. This represents the power supplied to the energy storage system by the secondary busbar j during time period t. This represents the power supplied from secondary busbar j to the charging module of the energy storage system during time period t. This represents the power from the secondary busbar j to the discharge module of the energy storage system during time period t. This represents the uncertain load connected to secondary bus j during time period t. This represents the energy transfer efficiency between generator k and main busbar m. α represents the energy transfer efficiency between the primary bus m and the secondary bus j. j,t The binary variable representing the secondary bus bar j in time period t. Represents a time set, Indicates generator set, Let S represent the primary bus set, S represent the secondary bus set, S1 represent the secondary bus set connected to the energy storage system, and S2 represent the secondary bus set not connected to the energy storage system. S = S1 ∪ S2.

[0158] 1.2) Capacity Constraints

[0159]

[0160]

[0161]

[0162]

[0163]

[0164]

[0165]

[0166] In the formula, A binary variable representing the state of generator k during time period t. This represents the minimum power output limit of generator k. This represents the maximum power output limit of generator k. A binary variable representing the connection state between generator k and main busbar m during time period t. This indicates the power transfer limit between generator k and main bus m. This indicates the power limit of the main bus bar m. The binary variable representing the connection state between the primary bus m and the secondary bus j during time period t. This indicates the power transfer limit between the primary bus m and the secondary bus j. U represents the power supplied to the energy storage system by the secondary busbar j. jESS,t A binary variable representing the connection status between secondary busbar j and the energy storage system during time period t. This indicates the power transfer limit between the secondary bus bar j and the energy storage system;

[0167] 1.3) Energy storage constraints

[0168]

[0169]

[0170] In the formula, Δt is the time interval, and SoC ESS,t This indicates the state of the energy storage system during time period t. This indicates the charging efficiency of the energy storage system. This indicates the discharge efficiency of the energy storage system. Indicates the maximum capacity of the energy storage system. SoC ESS Indicates the boundary of the charged state, Indicates the upper bound of the charged state;

[0171] 1.4) Equipment connection constraints

[0172]

[0173]

[0174]

[0175]

[0176]

[0177] In the formula, This indicates the availability of generator k during time period t. This indicates the availability of main bus line m during time period t. This indicates the availability of secondary bus bar j during time period t;

[0178] 1.5) Uncertain load constraints

[0179]

[0180] In the formula, ξ j,t The random variable representing the load forecast error on secondary busbar j during time period t is... This represents the uncertain load connected to secondary bus j during time period t. This represents the expected value of the uncertain load connected to secondary busbar j during time period t;

[0181] 2) Determine the objective function:

[0182] 2.1) Equipment Priority

[0183]

[0184] In the formula, ζ km ζ represents the connection weight between generator k and main busbar m. mj This indicates the connection weight between the primary bus m and the secondary bus j;

[0185] 2.2) Fuel consumption cost

[0186]

[0187] In the formula, c k This represents the fuel consumption cost coefficient of generator k. This represents the cost factor for charging the energy storage system connected to the secondary busbar j. This represents the cost factor for discharging energy from the energy storage system connected to secondary busbar j;

[0188] 3) Obtain the initial energy scheduling model for the more-electric aircraft, as shown in the following formula:

[0189]

[0190] 4) The initial multi-electric aircraft energy scheduling model is reconstructed into a multi-stage sub-Bruker model, as shown in the following formula:

[0191]

[0192]

[0193] C t y t (ξ [t]^ )+D t y t-1 (ξ [t-1]^ )=d t (121)

[0194] W t x t +H t y t (ξ [τ]^ )≤B t ξ [t]^ (122)

[0195] In the formula, X represents x t The feasible region, Y represents y t The feasible region, formula (26) contains formulas (16)-(20); vector y t The uncertain loads constitute all the decision variables in formulas (1)-(15) and (21), corresponding to formulas (27) and (28); c t For the corresponding x in the objective function t The coefficient vector, q t For the corresponding y in the objective function t The coefficient vector, T is the transpose, A and b are the coefficient matrix and vector of formula (26) respectively, C t and D t Let d be the coefficient matrix of formula (27). t W is the coefficient vector of formula (27). t H t and B t For the coefficient matrix of formula (28), define Let t be the vector of uncertain parameters, and let its uncertainty set be Ξ. t N t Let represent the vector dimension of time period t. Then, all revealed uncertainties collected from the beginning to time period t are represented as: in Specifically, ξ = ξ [t＝T]^ Parameter ξ0=ξ 0,0 Set to 1, utilizing its non-degenerate property to set (ξ1,...,ξ) t ) is represented as ξ [t]^ A linear function, For Wasserstein fuzzy sets, Let be the probability distribution function. Let T be the expectation of the worst probability distribution function in the Wasserstein fuzzy set, and T be the scheduling period.

[0196] This method constructs a multi-stage sub-Brussels bar model, which includes various constraints such as power balance constraints, capacity constraints, energy storage constraints, equipment connection constraints, and uncertain load constraints, with the objectives of ensuring equipment connection priority and minimizing fuel consumption costs. Since the multi-stage sub-Brussels bar model contains uncertain loads, it is typically an unsolvable semi-infinite programming problem. This semi-infinite programming problem can be reconstructed into a solvable mixed-integer linear programming problem using piecewise linear decision rules, and then solved using a solver.

[0197] Specifically, uncertain loads are represented as the sum of necessary and unnecessary loads. For example, some important electrical equipment on a multi-electric aircraft, such as navigation equipment and anti-icing equipment, are necessary loads, while some kitchen equipment, such as kettles and microwave ovens, are unnecessary loads. When the electrical system of a multi-electric aircraft fails, necessary loads must be supplied to ensure the safe operation of the multi-electric aircraft. Formulas (1), (3), (5), and (6) provide the energy flow from the generator to the load. Formulas (2) and (4) represent the power supply balance between the power supply end and the downstream main transmission line. Formula (7) is the generator capacity limit, formulas (8) to (11) represent the limitations of different airborne transmission lines, and formulas (12) and (13) limit the energy storage system (ESS) within its charging and discharging range.

[0198] To meet the load demand of the busbars and reduce load shedding, the state of charge (SoC) is introduced to represent the battery dynamics model. Equation (14) represents the remaining capacity constraint of the energy storage at each time period, and Equation (15) represents the maximum / minimum remaining capacity allowed during scheduling. Equations (16), (17), and (19) consider the redundancy of power generation and its distribution. Furthermore, considering the differences in frequency and phase between different power sources, Equation (17) indicates that the main busbar can only be powered by one generator, and Equation (20) indicates that the secondary busbar can only be powered by one main busbar. The nonlinear constraint equations (15) and (18) can be equivalently linearized. Equation (21) further represents the uncertain load. Since equation (21) contains uncertain variables, it cannot be solved directly using solvers such as CPLEX or GUROBI. Furthermore, existing technical solutions such as robust optimization or stochastic programming cannot effectively balance the economy and robustness of decision-making. Therefore, this invention aims to solve this problem by reconstructing the initial multi-electric aircraft energy scheduling model into a multi-stage sub-robust model. The principle is as follows:

[0199] Multi-stage refers to the fact that the decision variables for each stage are made after the load is revealed. Using a multi-stage blobs model essentially follows the unpredictability of the real scheduling process. For a multi-stage blobs model, given a Wasserstein fuzzy set... It includes generating distributions from unknown data. The distribution clusters characterized by certain known properties of y. The partial Bruker optimization problem aims to find the decision y. t To minimize the expected cost in the worst case Furthermore, to accommodate the unpredictability of scheduling, energy management decisions should sequentially follow the realization of uncertainty. Specifically, given a scheduling period T, once decision x... t If so, then the decision y at the current stage... t Will be under uncertain load ξ t After the disclosure, the time window is then rolled forward by one time step, x t+1 The decisions are made sequentially, with all decisions being made as uncertain loads are revealed until termination at time T. Typically, this multi-stage sub-Bruker model is a semi-infinite programming problem that cannot be directly solved using a solver; therefore, decision rules are needed to transform the model into a solvable form.

[0200] S2. Based on the PLDR method and Wasserstein distance, the multi-stage sub-Bruker model is reconstructed into a PLDRO model.

[0201] In one embodiment, the multi-stage sub-Bruker model is reconstructed into a PLDRO model based on the PLDR method and Wasserstein distance, as follows:

[0202] S21. Use lifting operations to obtain a lifted uncertain set.

[0203] In one embodiment, a lifting operation is used to obtain a lifted uncertainty set, including:

[0204] S211. Based on the M load data samples collected from the secondary busbar j during time period t, the load uncertainty set Ξ is obtained. j,t The formula is as follows:

[0205]

[0206] In the formula, ξ is the lower bound of the load data sample of secondary bus j in time period t. j,t Let be the load uncertainty parameter for secondary bus bar j during time period t. This is the upper bound of the load data sample for secondary bus bar j in time period t;

[0207] S212, Definition and And in each uncertain parameter ξ j,t Insert r within the interval j,t A breakpoint of -1 maps uncertain parameters to a high-dimensional space, as shown below:

[0208]

[0209] In the formula, Represents the r-th time interval within time interval t. j,t -1 breakpoints, r j,t Let r be the number of segments in time period t. For ξ0, take r. 0,0 =1;

[0210] S213, Define nonlinear operations Mapping ξ j,t to in Operation It is expressed as follows:

[0211]

[0212] In the formula, q = 1, 2, ..., r j,t ;

[0213] S214. Obtain the improved ξ according to step S213. t Right now Uncertain set Ξ t Represented as a lifting uncertainty set:

[0214]

[0215] In the formula, Let be the lower bound vector of the load during time period t. Let be the upper bound vector of the load during time period t. For the boosted random variable.

[0216] S22. Constructing the equivalent convex hull of lifting uncertain sets.

[0217] In one embodiment, a convex hull equivalent to lifting the uncertain set is constructed. Specifically as follows:

[0218] S221. For any j = 1, ..., N t ,make Define the set of poles in the lift space for:

[0219]

[0220] in,

[0221]

[0222] S222, the convex hull of the secondary bus bar j in time period t. The structure is as follows:

[0223]

[0224] In the formula, Indicates the pole The corresponding coefficients, and

[0225] S223, Based on the convex hull The separability of the property yields: and At the same time, and

[0226] Since the lifted uncertainty set is non-convex and is an open set, it is impossible to reconstruct the multi-stage sub-Brussels bar model based on this lifted uncertainty set. Therefore, it is necessary to construct its equivalent external approximation—the convex hull.

[0227] S23. Obtaining Wasserstein fuzzy sets based on Wasserstein distance.

[0228] In one embodiment, Wasserstein fuzzy sets The formula is as follows:

[0229]

[0230] Among them, Wasserstein distance satisfy:

[0231]

[0232] In the formula, for The marginal distribution represents the true distribution. for The marginal distribution of Π is and The joint distribution of , where ‖·‖ is the norm, For a given boosting support space, Let be the space of the probability distribution function. For random variables under the true distribution, for The differential, for The differential;

[0233] The radius of the Wasserstein sphere is estimated using the following formula:

[0234]

[0235] The Wasserstein sphere radius ∈ and the constant R are calculated as follows:

[0236]

[0237]

[0238]

[0239] In the formula, η is the confidence level. ρ is the mean of the collected load data samples, and ρ is a variable. M represents the number of load data samples collected. For Dirac measurement, To improve the load data sample p in the space, P{·} is the probability.

[0240] S24. Based on the lifting uncertainty set and Wasserstein fuzzy set, the multi-stage sub-Bruker model is reconstructed into a PLDRO model.

[0241] In one embodiment, the multi-stage sub-Bruker model is reconstructed into a PLDRO model based on the lifting uncertainty set and the Wasserstein fuzzy set, as follows:

[0242] S241, y t Mapping to all realized uncertain parameters, the formula is as follows:

[0243]

[0244] In the formula, The vector corresponding to time period t The coefficient matrix, take

[0245] S242, Reconstruct formula (28), as follows:

[0246] S2421. Substitute formula (31) into formula (28) to restate formula (28) as follows:

[0247]

[0248] S2422, Combine formula (32) and Rewritten in matrix form:

[0249]

[0250]

[0251] In the formula, Z t for The corresponding first matrix, for The corresponding second matrix, for The corresponding third matrix, For λ [t]^ The corresponding first matrix, For λ [t]∧ The corresponding second matrix, λ [t]∧ The coefficient vector corresponding to the pole vector. This is the first coefficient vector. This is the second coefficient vector;

[0252] S2423. Based on strong duality theory, formula (33) is expressed as formula (35), thus completing the reconstruction of formula (28):

[0253]

[0254] In the formula, With π t Let T be the dual variable, and T be the transpose.

[0255] S243, Reconstruct formula (27), as follows:

[0256] S2431. Substituting formula (31) into formula (27), formula (27) is reconstructed as follows:

[0257]

[0258] In the formula, Q t for The corresponding matrix;

[0259] S2432. According to formula (36), let Q t The g-th action d t The g-th action get:

[0260]

[0261] S2433, For any convex hull Usually by r j,t A non-degenerate simplex consisting of +1 poles. Therefore, construct r j,t ∑_(i=1)^n linearly independent vectors as the convex hull The linear representation of the convex hull, and utilizing the separability of the convex hull, the convex hull is... structure linearly independent vectors To express, for For a vector of all 1s within a given space, formula (37) is expressed as:

[0262]

[0263] In the formula, and e and A vector, e, is a completely one vector, satisfying... and Then formula (36) is equivalent to:

[0264]

[0265] S244, Reconstruct formula (25), as follows:

[0266] S2441. Under formula (31), the function Represented as Therefore, the part of the blue rod in formula (25) It can be represented as a finite convex programming approach, with the following formula:

[0267]

[0268] In the formula, λ and s p z p All are introduced variables, where ∈ is the radius of the Wasserstein sphere and M is the number of collected load data samples. For the observed sample of the random variable, ||·|| * Denotes the dual norm;

[0269] S2442. Substituting formula (31) into formula (40), the only constraint in formula (40) containing an uncertain variable is expressed as:

[0270]

[0271] S2443. Based on the strong duality theorem and combined with the convex hull... Representing formula (41) as follows:

[0272]

[0273] In the formula, and π T,p Let be the dual vector of sample p in time period T. For time period T The corresponding first matrix, For time period T The corresponding first matrix, For time period T The corresponding coefficient vector, for The coefficient vector corresponding to time period T, For time period T The corresponding second matrix, For time period T The corresponding second matrix;

[0274] Combining this with formula (40), we get:

[0275]

[0276] S245. Combining formulas (35), (39) and (43), the PLDRO model is obtained. The PLDRO model is as follows:

[0277]

[0278]

[0279] After constructing the multi-stage sub-Brussels bar model, the constructed multi-stage sub-Brussels bar model is reconstructed into a PLDRO model (represented as a MILP model) based on the PLDR method and Wasserstein distance, specifically:

[0280] First, the uncertain set is lifted to a higher-dimensional space to construct the lifted uncertain set. Second, a Wasserstein fuzzy set is constructed. Finally, based on the constructed lifted uncertain set and Wasserstein fuzzy set, the multi-stage sub-Bruker model is reconstructed. The principle of the PLDR method is to lift the original multi-stage sub-Bruker model to a higher-dimensional space through a lifting operation, and then apply the LDR method to the lifting problem, thereby balancing the optimality and scaling of the decision rule. Specifically, this invention uses the LDR method to map adaptive decision y. t This extends to the uncertain parameters of all realized lifts. This lift-based LDR method is called the PLDR method. For an example of the PLDR method, refer to existing technology: A. Georghiou, W. Wiesemann, and D. Kuhn, “Generalized decision rule approximations for stochastic programming via liftings,” Math. Program., vol. 152, no. 1, pp. 301–338, 2015. Subsequently, a fuzzy set based on Wasserstein distance is introduced to reconstruct the multi-stage sub-Brussels model of lifts into a MILP model.

[0281] S3. Acquire historical load data of multi-electric aircraft and monitor equipment availability in real time.

[0282] S4. Based on the load history dataset, equipment availability status, and preset energy management parameters, the PLDRO model is solved using a solver. In the scheduling cycle of the multi-electric aircraft, based on the rolling scheduling method, after observing uncertain loads, energy management decisions are calculated and executed according to the solution results of the PLDRO model, thereby realizing the energy scheduling of the multi-electric aircraft.

[0283] In one embodiment, the solver is a GUROBI solver or a CPLEX solver. It should be noted that the solver can also be other solvers in the prior art used for solving mixed-integer linear programming problems, and this is not limited thereto.

[0284] Specifically, energy management parameters (such as...) are set according to the actual operating conditions of multi-electric aircraft. Based on historical load datasets (i.e., load configuration data, etc.) and equipment availability status (i.e., availability of generators, main busbars, secondary busbars, etc.), the solver solves the PLDRO model to generate integer variables and coefficient matrices. In the energy management cycle (i.e., scheduling cycle T) of a multi-electric aircraft, based on the rolling scheduling method, after observing the uncertain load, formula (31) is used through the coefficient matrix. Calculate and execute energy management decisions to achieve energy scheduling for multi-electric aircraft.

[0285] To further understand the present invention, the technical solution of the present invention will be further described below in conjunction with the accompanying drawings and experiments.

[0286] This invention references typical multi-electric aircraft architectures such as Figure 2 As shown, the multi-electric aircraft consists of two main generators, Gen1 (G1) and Gen2 (G2), one APU Gen (G3), two main buses (Left 115VAC / 360-800Hz Bus and Right 115VAC / 360-800Hz Bus respectively), three secondary buses (two DC buses, a 270VDC Bus and a 28V LVDC Bus, and one AC bus, a 115VAC / 400Hz Bus respectively), two energy storage systems (ESS, connected to the DC buses), and also includes motors and actuators, primary AC loads, non-critical AC loads, critical AC loads, non-critical DC loads, critical DC loads, solid-state power controllers (SSPCs), and a transformer rectifier. Units such as TRU (Transformer Unit) and Auto-Transformer Rectifier Unit (ATRU) were used. Load configuration during a certain cruise phase of the multi-electric aircraft was taken as historical data, and a Gaussian distribution with relative standard deviation (RSD) was used to represent the disturbance data to indicate prediction error. The confidence level was set to 95%, and the total load was evenly distributed between unnecessary and necessary loads. Specific parameter settings are shown in Table 1.

[0287] Table 1

[0288]

[0289]

[0290] In Table 1, N G N represents the number of generators. MB Number of main bus lines, N SB N represents the number of secondary bus lines. ESS N represents the number of energy storage systems. Load For the number of loads, SoC ESS,0 This represents the state of the energy storage system during time period t (t=0), i.e., the initial state of the energy storage system.

[0291] To analyze the statistical characteristics of the PLDRO model, Tables 2 and 3 compare the operating costs of scheduling models optimized using multi-stage robust optimization, stochastic programming, and robust optimization methods (corresponding to the PLDRO, SAA, and RO models, respectively). Table 2 shows the total cost for different sample sizes when RSD equals 1. Table 3 shows the total cost for different RSDs when the sample size is 40. Tables 2 and 3 show that the cost of the PLDRO model used in this application is lower than the RO model but higher than the SAA model. Table 2 reveals that as historical data increases, the RO model incurs higher costs due to the integration of more boundary information, while the PLDRO and SAA models focus more on the distribution characteristics of historical data, making it difficult for a small number of boundary samples to influence the overall decision. Furthermore, the PLDRO model aims to find the worst distribution in the distribution cluster; therefore, its cost is not lower than that of the SAA model. In Table 3, when load fluctuations are greater, the PLDRO model produces more conservative decisions compared to the SAA model, resulting in higher costs. In summary, the PLDRO model combines the advantages of both the SAA and RO models.

[0292] Table 2

[0293]

[0294] Table 3

[0295]

[0296] Figure 3 This further illustrates the relationship between the PLDRO, SAA, and RO models. It can be seen that as the Wasserstein sphere radius increases, the cost of the PLDRO model consistently falls between that of the SAA and RO models. When the Wasserstein sphere radius is 0, it only contains the empirical distribution, thus its cost is consistent with the SAA model. Similarly, when the Wasserstein sphere radius is very large, its cost approaches that of the RO model. It is easy to see that the SAA and RO models can be considered two special cases of the PLDRO model.

[0297] To evaluate the good approximation performance achieved by the proposed PLDRO-based model, the PLDRO model (the multi-stage distributionally robust model based on the piecewise linear decision rule, PLDRO) is compared with a typical LDR-based model (the multi-stage distributionally robust model based on the linear decision rule, TDRO). Figure 4 The costs of the PLDRO and TDRO models are shown under different RSDs. It can be seen that the cost difference between the two models increases with increasing RSD, indicating that the proposed model can achieve lower costs without sacrificing conservatism under conditions of greater load fluctuations. Figure 5 The expected costs were compared for different Wasserstein sphere radii. It can be seen that as the Wasserstein sphere radius increases, the optimal values ​​of both models approach the optimal value of the robust optimization. However, the cost of the PLDRO model is no greater than that of the TDRO model for the same Wasserstein sphere radius, demonstrating the good approximation performance of the PLDRO model.

[0298] Finally, to demonstrate the excellent adaptive scheduling capability of the PLDRO model, this invention considers several typical scenarios (it should be understood that these typical scenarios are only used to explain this invention and are not intended to limit the invention), as shown in Table 4. First, the RSD is set to 0.1, the sample size is 40, and the historical load dataset and equipment availability status are fed into the solver to generate integer variables and a coefficient matrix. Secondly, four typical scenarios are generated using a scenario reduction algorithm. Finally, under formula (31), a deterministic scheduling decision is obtained based on the rolling scheduling method. Figure 6The scheduling results are shown under different scenarios. In Scenario 1, under normal conditions, the two main generators G1 and G2 supply all power demand, while G3 is shut down according to a predefined priority. In Scenario 2, when generator G1 fails at t=10, generator G2 and the energy storage system ESS supply all uncertain load demand. In Scenario 3, G1 fails at t=5, and both G1 and G2 fail at t=8. According to the predefined safety level (priority), G3 supplies all necessary loads. At the same time, the main bus bar Right 115VAC / 360-800Hz Bus fails at t=12. Due to the set redundancy path, the load can still be powered. The same situation occurs in Scenario 4, where the 28V low-voltage DC bus bar (28V LVDC Bus) fails, the 115V AC bus bar (115V AC / 400Hz Bus) supplies the necessary loads of the 28V DC bus bar, and the energy storage system ESS connected to the 28V low-voltage DC bus bar is shut down.

[0299] Table 4

[0300]

[0301]

[0302] This method establishes an energy dispatch model for multi-electric aircraft (MEA) while considering equipment availability and priority. This model not only improves the reliability and safety of MEA energy dispatch systems but also reduces fuel consumption during MEA operation, achieving lower carbon emissions. It also considers the unpredictability of MEA fault decision-making and dispatch processes in real-world applications. Utilizing a Wasserstein distance-based bibliometric optimization method and piecewise linear decision rules, it adapts to the load uncertainty in the MEA power system, exhibiting good economic efficiency and robustness. While maximizing power supply, it allows decision-makers to flexibly adjust the bibliometric optimization dispatch scheme based on dispatch requirements by changing the Wasserstein sphere radius. Furthermore, this method fully follows the actual dispatch process; as uncertain loads are revealed sequentially, the MEA power system energy dispatch scheme is executed in a rolling manner, respecting the unpredictability of the real dispatch process.

[0303] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0304] The embodiments described above are merely specific and detailed examples of the embodiments described in this application, and should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the appended claims.

Claims

1. A multi-electric aircraft energy scheduling method based on distributed bar optimization, wherein the multi-electric aircraft includes at least one generator, a main busbar, a secondary busbar, and an energy storage system, characterized in that: The energy scheduling method for multi-electric aircraft based on distributed bar optimization includes the following steps: S1. Construct a multi-stage sub-Bruker model, the process is as follows: 1) Determine the constraints, which include power balance constraints, capacity constraints, energy storage constraints, equipment connection constraints, and uncertain load constraints; 2) Determine the objective function: 2.1) Equipment Priority ； In the formula, Indicates generator With the main busbar The connection weights, Indicates the main bus bar With secondary busbar The connection weights, Indicates the generator during time period t With the main busbar Binary variables representing connection state. Indicates the main bus bar during time period t With secondary busbar Binary variables representing connection state. Represents a time set, Indicates generator set, Indicates the main flow set, Represents a secondary bus set; 2.2) Fuel consumption cost ； In the formula, Indicates generator fuel consumption cost coefficient Indicates the generator during time period t 'output power' Indicates connection to secondary bus bar The cost factor of charging an energy storage system. Indicates connection to secondary bus bar The cost factor of discharging energy storage systems This represents the power supplied from secondary busbar j to the charging module of the energy storage system during time period t. This represents the power from the secondary busbar j to the discharge module of the energy storage system during time period t. This represents a secondary bus set connected to an energy storage system; 3) Based on the constraints, the initial energy scheduling model for the more-electric aircraft is obtained according to equipment priority and fuel consumption cost, as shown in the following formula: ； 4) The initial multi-electric aircraft energy scheduling model is reconstructed into a multi-stage sub-Bruker model, as shown in the following formula: ； ； ； ； In the formula, , X represents The feasible region, Y represents feasible domain, Indicates the generator during time period t binary variables of state Indicates the secondary busbar in time period t Binary variables relating to the connection status of the energy storage system. Indicates the generator during time period t With the main busbar Transmission power, Indicates the main bus bar during time period t The power supplied to the secondary busbar, Indicates time period t from the main busbar To secondary bus power, Indicates the secondary busbar in time period t The power supplied to the energy storage system This indicates that time period t is connected to the secondary bus bar. Uncertain loads; For the corresponding objective function The coefficient vector, For the corresponding objective function coefficient vector, For transpose, and The coefficient matrix and vector of formula (26) are shown in sequence. and The coefficient matrix of formula (27) is... Let be the coefficient vector of formula (27). , and For the coefficient matrix of formula (28), define for The time-period uncertain parameter vector has the following uncertainty set: N t represent The vector dimension of the time period is from the beginning to the end. All revealed uncertain loads collected during the time period are represented as ,in Special ,parameter Set to 1, utilizing its non-degenerate property to Represented as A linear function, For Wasserstein fuzzy sets, Let be the probability distribution function. Let T be the expectation of the worst probability distribution function in the Wasserstein fuzzy set, and T be the scheduling period. S2. Based on the PLDR method and Wasserstein distance, the multi-stage sub-BLRO model is reconstructed into a PLDRO model; S3. Acquire historical load data of multi-electric aircraft and monitor equipment availability status in real time; S4. Based on the load history dataset, equipment availability status, and preset energy management parameters, the PLDRO model is solved using a solver. In the scheduling cycle of the multi-electric aircraft, based on the rolling scheduling method, after observing uncertain loads, energy management decisions are calculated and executed according to the solution results of the PLDRO model, thereby realizing the energy scheduling of the multi-electric aircraft.

2. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 1, characterized in that: The specific constraints are as follows: 1.1) Power balance constraints ； ； ； ； ； ； In the formula, Indicates generator With the main busbar Energy transfer efficiency, Indicates the main bus bar With secondary busbar Energy transfer efficiency, Indicates the secondary busbar in time period t binary variables, This represents a secondary bus set that is not connected to an energy storage system. ; 1.2) Capacity Constraints ； ； ； ； ； ； ； In the formula, Indicates generator The minimum power output limit, Indicates generator The maximum power output limit, Indicates generator With the main busbar Power transmission limitations, Indicates the main bus bar Power limitations, Indicates the main bus bar With secondary busbar Power transmission limitations, Indicates secondary bus bar The power supplied to the energy storage system Indicates secondary bus bar Power transfer limitations of energy storage systems; 1.3) Energy storage constraints ； ； In the formula, For time intervals, This indicates the state of the energy storage system during time period t. This indicates the charging efficiency of the energy storage system. This indicates the discharge efficiency of the energy storage system. Indicates the maximum capacity of the energy storage system. Indicates the boundary of the charged state, Indicates the upper bound of the charged state; 1.4) Equipment connection constraints ； ； ； ； ； In the formula, Indicates the generator during time period t Availability, Indicates the main bus bar during time period t Availability, Indicates the secondary busbar in time period t Availability; 1.5) Uncertain load constraints ； In the formula, Indicates the secondary busbar in time period t Random variables of load forecasting error This indicates that time period t is connected to the secondary bus bar. Uncertain loads, This indicates that time period t is connected to the secondary bus bar. The expected value of the uncertain load; The constraint condition is then expressed as: And formula (26) contains formulas (16)-(20); vector The uncertain loads constitute all the decision variables in formulas (1)-(15) and (21), which correspond to formulas (27) and (28).

3. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 2, characterized in that: The multi-stage sub-Brook bar model is reconstructed into a PLDRO model based on the PLDR method and Wasserstein distance, as detailed below: S21. Use lifting operations to obtain a lifted uncertain set; S22. Constructing the equivalent convex hull of lifting uncertain sets. ; S23. Obtaining Wasserstein fuzzy sets based on Wasserstein distance. ; S24. Based on the lifting uncertainty set and Wasserstein fuzzy set, the multi-stage sub-Bruker model is reconstructed into a PLDRO model.

4. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 3, characterized in that: The method of obtaining a lifted uncertainty set by lifting operations includes: S211, According to the secondary bus bar of time period t Collected from above The load uncertainty set is obtained from a sample of load data. The formula is as follows: ； In the formula, For secondary busbars in time period t The lower bound of the load data sample. For secondary busbars in time period t Uncertain parameters of the load, For secondary busbars in time period t The upper bound of the load data sample; S212, Definition and And in each uncertain parameter Insert within the interval Breakpoints, which map uncertain parameters to a high-dimensional space, are represented as follows: ； In the formula, Represents the first time interval within time period t. One breakpoint, Let t be the number of segments in time period t. ,Pick ; S213, Define nonlinear operations , mapping to ,in Operation It is expressed as follows: ； In the formula, ; S214, The improved version obtained according to step S213 Right now Uncertain set Represented as a lifting uncertainty set: ； In the formula, Let be the lower bound vector of the load during time period t. Let be the upper bound vector of the load during time period t. For the boosted random variable.

5. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 4, characterized in that: The construction lifts the convex hull of the uncertain set. The details are as follows: S221, For any ,make Define the set of poles in the lift space. for: ； in, ； S222, the convex hull of the secondary bus bar j in time period t. The structure is as follows: ； In the formula, Indicates the pole The corresponding coefficients, and ; S223, Based on the convex hull The separability of the property yields: , and At the same time, order , and .

6. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 5, characterized in that: The multi-stage sub-Bruker model is reconstructed into a PLDRO model based on the lifting uncertainty set and Wasserstein fuzzy set, as detailed below: S241, will Mapping to all realized uncertain parameters, the formula is as follows: ； In the formula, The vector corresponding to time period t The coefficient matrix, take ; S242, Reconstruct formula (28), as follows: S2421. Substitute formula (31) into formula (28) to restate formula (28) as follows: ； S2422, Combine formula (32) and Rewritten in matrix form: ； ； In the formula, for The corresponding first matrix, for The corresponding second matrix, for The corresponding third matrix, for The corresponding first matrix, for The corresponding second matrix, The coefficient vector corresponding to the pole vector. This is the first coefficient vector. This is the second coefficient vector; S2423. Based on strong duality theory, formula (33) is expressed as formula (35), thus completing the reconstruction of formula (28): ； In the formula, and As dual variables, For transpose; S243, Reconstruct formula (27), as follows: S2431. Substituting formula (31) into formula (27), formula (27) is reconstructed as follows: ； In the formula, for The corresponding matrix; S2432. According to formula (36), let... The g-th action , The g-th action ,get: ； S2433, For any convex hull ,structure ∑_(i=1)^n linearly independent vectors as the convex hull The linear representation of the convex hull, and utilizing the separability of the convex hull, the convex hull is... structure linearly independent vectors To express, for For a vector of all 1s within a given space, formula (37) is expressed as: ； In the formula, and In order and The vector, Let be a vector of all ones, satisfying and Then formula (36) is equivalent to: ； S244, Reconstruct formula (25), as follows: S2441. Under formula (31), the function Represented as Therefore, the part of the blue rod in formula (25) It can be represented as a finite convex programming approach, with the following formula: ； In the formula, , , Both introduce variables. Let M be the radius of the Wasserstein sphere, and M be the number of collected load data samples. For the observed samples of random variables, Denotes the dual norm; S2442. Substituting formula (31) into formula (40), the only constraint in formula (40) containing an uncertain variable is expressed as: ； S2443. Based on the strong duality theorem and combined with the convex hull... Formula (41) can be reformulated as follows: ； In the formula, , and for Samples in The dual vector of the time period, For time period T The corresponding first matrix, For time period T The corresponding first matrix, For time period T The corresponding coefficient vector, for The coefficient vector corresponding to time period T, For time period T The corresponding second matrix, For time period T The corresponding second matrix; Combining this with formula (40), we get: ； S245. The PLDRO model is obtained by combining formulas (35), (39) and (43), and the PLDRO model is as follows: ； 。 7. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 3, characterized in that: The Wasserstein fuzzy set The formula is as follows: ； Among them, Wasserstein distance satisfy: ； In the formula, for The marginal distribution represents the true distribution. for marginal distribution, for and The joint distribution For norm, , For a given boosting support space, Let be the space of the probability distribution function. For random variables under the true distribution, for The differential, for The differential; Wasserstein sphere radius The following estimation formula is used: ； Wherein, the radius of the Wasserstein sphere The constant R is calculated as follows: ； ； ； In the formula, For confidence level, ρ is the mean of the collected load data samples, and ρ is a variable. M represents the number of load data samples collected. For Dirac measurement, To improve the load data sample in the space , Let be the probability.

8. The multi-electric aircraft energy scheduling method based on distributed bar optimization as described in claim 1, characterized in that: The solver is either the GUROBI solver or the CPLEX solver.

Images