A robust scheduling method and system based on virtual generalized multifrontal array

Abstract

The application discloses a kind of robust scheduling method and system based on virtual generalized multifaceted quasi-array, the described and include the following steps: step S1: the parameter of each TCL equipment in heterogeneous TCL group is collected;Step S2: thermodynamic state space model is determined to meet the flexibility set of constraint condition;Step S3: transformation matrix is constructed, and physical variable is mapped to virtual domain;Step S4: boundary function pair is generated based on virtual constraint, and accurate g-multiple surface quasi-array is constructed;Step S5: based on historical error sample, construct statistical feasible uncertainty set, and error is converted into affine disturbance;Step S6: construct hybrid uncertainty set, and realize sample adaptive robust boundary calibration;Step S7: reconstruct sample and carry out adaptive calibration;Step S8: TCL scheduling is modeled as cost minimization or peak minimization optimization problem, using DW decomposition, obtain aggregated power trajectory, each device scheduling column, and carry out application.The application guarantees operation reliability and economic efficiency simultaneously.

Description

Technical Field

[0001] This invention belongs to the field of power system demand-side management and optimal scheduling technology, specifically relating to a robust scheduling method and system based on virtual generalized multifaceted matroid. Background Technology

[0002] In the statistically feasible robust self-dispatch for aggregates of heterogeneous temperature-controlled loads (TCL), self-dispatch refers to the process by which aggregators, as price takers, autonomously optimize their load power trajectories based on externally given electricity price signals in response to electricity market signals.

[0003] Against the backdrop of the global transition to a low-carbon power system, the large-scale grid connection of renewable energy has exacerbated supply and demand fluctuations. Temperature-controlled loads (such as commercial building air conditioning, heat pumps, cold chain equipment, and industrial cooling systems) are an important source of demand-side flexibility due to their widespread deployment and natural thermal inertia. Due to fragmented ownership and limited individual capacity, it is necessary to aggregate and coordinate scheduling to transform heterogeneous TCLs into unified dispatchable entities (virtual power plants or load aggregators).

[0004] The core challenge of TCL scheduling lies in accurately representing the aggregate flexibility set—that is, the Minkowski sum of the feasible power trajectories of all individual devices. Since the number of vertices grows exponentially with the number of devices and in the time domain, directly calculating the exact Minkowski sum is computationally infeasible, making it difficult for existing methods to achieve an effective balance between reliability and cost-effectiveness during scheduling. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a robust scheduling method and system based on virtual generalized multifaceted matroid, while ensuring operational reliability and economic efficiency.

[0006] The objective of this invention is achieved through the following technical solution: a robust scheduling method based on a virtual generalized multifaceted matroid, comprising the following steps:

[0007] Step S1: Collect parameters of each TCL device in the heterogeneous TCL group;

[0008] Step S2: Construct a linear thermodynamic state-space model of the TCL device and determine the set of flexibility that satisfies the constraints;

[0009] Step S3: Construct a transformation matrix to perform virtual coordinate transformation on each TCL device and map physical variables to the virtual domain;

[0010] Step S4: Generate boundary function pairs based on virtual constraints to construct an accurate g-polyhedral matte;

[0011] Step S5: Construct a statistically feasible uncertainty set based on historical error samples, and transform the error into an affine perturbation;

[0012] Step S6: Construct a mixed uncertainty set using historical temperature prediction error samples and implement adaptive robust boundary calibration for the samples;

[0013] Step S7: Reconstruct the sample and perform adaptive calibration;

[0014] Step S8: Model the TCL scheduling as a cost minimization or peak minimization optimization problem, use DW decomposition to obtain the aggregated power trajectory and scheduling columns of each device, and apply them.

[0015] A robust scheduling system based on a virtual generalized multifaceted matroid includes:

[0016] The data acquisition module is used to collect parameters from TCL devices.

[0017] The model building module is used to build a linear thermodynamic state-space model of TCL equipment and determine the set of flexibility that satisfies the constraints.

[0018] The virtual coordinate transformation module is used to construct the transformation matrix, perform virtual coordinate transformation on each TCL device, and map physical variables to the virtual domain;

[0019] The multifaceted matte boundary generation module generates boundary function pairs based on virtual constraints, and constructs an accurate g-multifaceted matte.

[0020] The affine perturbation module constructs a statistically feasible uncertainty set based on historical error samples, transforming the error into an affine perturbation.

[0021] The statistically feasible robust calibration module constructs a mixed uncertainty set using historical temperature prediction error samples and achieves adaptive robust boundary calibration of the samples.

[0022] The sample reconstruction module reconstructs the samples and performs adaptive calibration.

[0023] The decomposition scheduling module models TCL scheduling as a cost minimization or peak minimization optimization problem, and uses DW decomposition to obtain the aggregated power trajectory and the scheduling columns of each device;

[0024] The device execution module is used to perform virtual trajectory inverse transformation and restore the physical power trajectory based on the information obtained from the decomposition scheduling module, and then issue the execution.

[0025] The beneficial effects of this invention are: (1) Accurate flexibility characterization of dissipative TCL based on bijective virtual coordinate transformation: By introducing a device-specific bijective coordinate transformation, the dissipative TCL in the physical domain is dynamically mapped to the lossless virtual domain. In the virtual domain, the flexibility set of each TCL has a model-accurate g-polyhedral matte structure. This transformation is the core technical means to achieve accurate characterization—dynamically transforming dissipative TCL into a pure accumulator in the virtual domain, restoring the time translation invariance required by the g-polyhedral matte theory.

[0026] (2) Virtual boundary function as aggregation oracle and DW decomposition scheduling: Due to the different dissipation factors of different TCLs, the "virtual time" of different devices in the virtual domain is not synchronized, and the aggregation boundary function is not directly equivalent to the physical aggregation set that can be uniformly inversely transformed. This invention uses the aggregation virtual boundary function as a computational oracle to evaluate whether any aggregation power trajectory can be decomposed to the device level; the physical feasibility of the final scheduling is guaranteed by generating the scheduling guarantee through the device-level virtual feasible domain and Dantzig-Wolfe columns.

[0027] (3) "Construction-Refinement" two-stage statistically feasible robust boundary calibration (SRC / ReSRC): The environmental temperature prediction error is transformed into an affine perturbation of the physical boundary vector, and a hybrid uncertainty set (Box+Ellipsoid) is constructed based on historical error samples; the high-dimensional constraints are mapped to one-dimensional quantile estimates using Max-Transformation, providing distribution-independent statistical feasibility guarantees; Stage 2 (ReSRC): The uncertainty set is reconstructed using the safety margin feedback information of the optimal solution of SRC, maintaining reserves in the direction of active constraints and relaxing conservatism in the direction of non-binding, and using independent calibration sample blocks to maintain statistical guarantees.

[0028] (4) Decomposable rolling time-domain self-scheduling architecture: The aggregator generates internal coordinated prices (dual variables) through Dantzig-Wolfe decomposition; after receiving the price, each device independently calculates the optimal scheduling column using its local robust g-polymorphic matrix boundary function and submits it to the aggregator through a greedy algorithm. Closed-loop rolling time-domain execution ensures that the accumulated error is absorbed in the initial conditions of the next window. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0030] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0031] like Figure 1 As shown, a robust scheduling method based on virtual generalized multifaceted matroids includes the following steps:

[0032] Step S1: Collect parameters of each TCL device in the heterogeneous TCL group;

[0033] In step S1, the heterogeneous TCL group refers to a heterogeneous temperature-controlled load group, including multiple TCL devices. The parameters of the TCL devices include thermal resistance. ,capacitance ,efficiency Rated power Set temperature Dead zone and the ambient temperature at time t .

[0034] Step S2: Construct a linear thermodynamic state-space model of the TCL device and determine the set of flexibility that satisfies the constraints;

[0035] S201. Assume a heterogeneous TCL population. It contains N TCL devices, and the heterogeneous TCL group is in a discrete time interval. It has a uniform time step The dynamics of the nth TCL device are controlled by the following thermodynamic equation:

[0036] ;

[0037] in, This represents the indoor temperature at time t. Let be the ambient temperature at time t. Assume that each TCL device uses the same type of cooling equipment. This represents the power consumption at time t; Characterizes the heat dissipation factor of the equipment at each step. , Indicates the thermal characteristics of the equipment;

[0038] set up For a user-defined temperature setting, the nominal baseline power required to maintain this setpoint is:

[0039] ;

[0040] Control input Defined as power deviation, while the state variable Defined as the thermal energy stored relative to a set value:

[0041] ;

[0042] ;

[0043] Substituting into the temperature dynamics equation, we obtain the standard state-space model:

[0044] ;

[0045] The input coefficients are:

[0046] ;

[0047] This model converts heterogeneous temperature control into a model with a dissipation factor. Virtual energy storage system;

[0048] S202. Determine the set of flexibility conditions that satisfy the constraints:

[0049] (1) The control equipment is constrained by the physical power boundary of the equipment:

[0050] ;

[0051] Among them, the lower boundary upper bound of the boundary ;

[0052] (2) User comfort constraints are determined by temperature range Defined, converted to a symmetric energy capacity limit:

[0053] ;

[0054] The upper boundary is defined as follows: The maximum energy storage capacity is defined as the equivalent energy boundary corresponding to the comfortable temperature range; the lower boundary is defined as... ;

[0055] (3) Flexibility set To satisfy all constraints of the control sequence The set, in Includes ambient temperature The determined boundary parameters, The constraint matrix is ​​formed by the constraints.

[0056] Step S3: Construct a transformation matrix to perform virtual coordinate transformation on each TCL device and map physical variables to the virtual domain;

[0057] Step S3 includes:

[0058] S301. From the initial stage to time t, the cumulative decay of the decay factor is expressed as: It acts as a time-dependent scaling factor, defining the transformation matrix. For diagonal matrices:

[0059] ;

[0060] S302. Define virtual state and virtual control as follows:

[0061] ;;

[0062] This is equivalent to multiplying the control input by at each time step. ;

[0063] S303. Change the virtual state and virtual control Substitute into the physical state equation Divide both sides by The process equation in virtual space is obtained as follows:

[0064]

[0065] Right now:

[0066]

[0067] This equation shows that the dynamics in the virtual domain degenerate into a perfect lossless integrator, restoring the time translation invariance required by g-polyhedral matroid theory.

[0068] Step S4: Generate boundary function pairs based on virtual constraints to construct an accurate g-polyhedral matte;

[0069] S401. Constant physical boundary conditions are mapped to time-varying constraints imposed on these dummy variables, where the power constraint is transformed into:

[0070] ;

[0071] The time-varying virtual boundary is:

[0072] ;

[0073] S402. Limit the state Expanding recursively:

[0074] ;

[0075] Substituting the virtual state definition into the constraint on the cumulative sum of virtual control, we get:

[0076] ;

[0077] The virtual state boundary includes the initial physical Its definition method:

[0078] ;

[0079] S403. In a virtual domain, leverage the flexibility of TCL devices. Constructing an accurate g-polyhedral matte :

[0080] Physical domain flexibility set The virtual coordinates are mapped to the virtual domain after the virtual coordinate transformation in step S3:

[0081] For any ,have Conversely, for any ,have ;because Since it is an invertible diagonal matrix, the set of virtual domain flexibility is... This forms a g-polyhedral matte that is accurate for the model. Its supermode boundary function and submodule boundary function Derived from the virtual power constraints and virtual energy constraints in S401-S402;

[0082] Summation of each TCL device is performed using the algebraic additivity of g-polyhedral matte:

[0083] ;

[0084] g-polyhedral matte defined for the aggregation virtual boundary function, supermode aggregation boundary function Sub-module boundary aggregation function It can be used as a computational oracle to reduce complexity from exponential to O(N);

[0085] In the embodiments of this application, when evaluating candidate aggregated control trajectories Feasibility: If a set of device-level scheduling columns exists satisfy ,and Then the trajectory can be decomposed and realized;

[0086] In the embodiments of this application, in the restricted principal problem (RMP) decomposed by DW (Dantzig-Wolfe), the dual problem of the RMP is solved, and the dual variable is the internally coordinated price signal passed to the equipment subproblem. Each device To generate the optimal scheduling column on the local g-polymorphic matte using a greedy algorithm.

[0087] Because different devices have different dissipation factors In the virtual domain, the virtual timescales of different devices are not synchronized, and the summed virtual aggregation boundary function is not directly equivalent to the physical aggregation set that can be uniformly inversely transformed. Therefore, the aggregation virtual boundary function is mainly used as a computational oracle—to evaluate whether arbitrary aggregation power trajectories can be decomposed to device-level implementation, and to generate the coordination price (dual variable) in the Dantzig-Wolfe decomposition.

[0088] Step S5: Construct a statistically feasible uncertainty set based on historical error samples, and transform the error into an affine perturbation;

[0089] Step S5 includes:

[0090] At each scheduling time, based on the prediction of ambient temperature Constructing nominal physical boundaries :

[0091] Define temperature prediction error This error is propagated to the TCL constraint boundary through the baseline power: the power boundary is generated in the predicted baseline coordinates. The level of affine translational perturbation; the time-cumulative perturbation of the energy boundary is:

[0092]

[0093] The random environmental error is represented as an affine perturbation of the physical boundary vector:

[0094] ;

[0095] in For TCL thermal parameters ( The deterministic coefficient matrix determined by the constraint coupling structure, and the affine perturbation form describes the "uncertainty". "How to affect the propagation structure of the physical boundary."

[0096] In step S6, a mixed uncertainty set is constructed using historical temperature prediction error samples, and sample adaptive robust boundary calibration (SRC) is implemented, including:

[0097] S601. Shape Learning: Construction of Hybrid Uncertainty Sets

[0098] Based on historical error sample set Calculate the sample mean and regularized covariance matrix Define Box set and Ellipsoid collection The mixed uncertainty set is the intersection of the two. ,in and The dimensions to be calibrated;

[0099] S602. Size Calibration: Using the Max-Transformation technique, 4T high-dimensional robust feasibility constraints are mapped to an equivalent one-dimensional quantile ranking estimation problem.

[0100] For constrained families Determine the scalar value of the maximum constraint violation in each historical scenario. Sort all K samples in ascending order and take the i-th... This value serves as the robust boundary offset for the constraint; by controlling the confidence level... It provides a distribution-independent statistical feasibility guarantee: the scheduling solution is available out of the sample at a rate not lower than [missing information]. The probability is physically feasible; Constraint matrix The kth row; for The k-th row;

[0101] S603. Based on Robustness boundary is automatically calculated from historical error samples. To meet the target reliability level and confidence level The statistical feasibility of the following.

[0102] Step S7: Reconstruct the sample and perform adaptive calibration;

[0103] Step S7, which implements adaptive robust calibration (ReSRC) for reconstructed samples, includes:

[0104] S701. Execute the SRC step in S6 to obtain the initial robust boundary. Solving the deterministic optimization problem within the robust feasible region yields the first scheduling scheme. ;

[0105] S702. For each constraint k, calculate its safety margin. ,in Constraint matrix The k-th row is used to quantify the degree of constraint activation: This indicates that the constraint still has a margin at the optimal solution. The smaller the value, the closer it is to the constraint boundary;

[0106] S703. Reconstructing the Uncertainty Set Using Safety Margins: Maintaining robust reserves in active constraint directions, and relaxing conservatism in directions with large safety margins.

[0107] like This indicates that the constraint is an active constraint that determines the scheduling quality. When reconstructing the uncertainty set, it is necessary to maintain or even strengthen the robust reserve in this direction, that is, not reduce or appropriately increase the size parameter in the uncertainty projection direction corresponding to the constraint. The preset tension threshold can be set to the lower quantile of the S-value distribution;

[0108] like This indicates that the constraint is far from being activated and there is room for over-conservatism. When reconstructing the uncertainty set, the robustness requirement in this direction should be appropriately relaxed, that is, the size parameter should be reduced in this direction, thereby expanding the feasible region and improving economic efficiency. The preset lenient threshold can be set to the higher quantile of the S-value distribution;

[0109] like The original calibration results remain unchanged;

[0110] S704. Perform final robustness verification using a calibration sample block independent of the SRC stage in step S6: The reconstructed uncertainty set needs to be verified on independent samples to ensure its statistical feasibility is not lower than the target level. If the verification fails, revert to the original SRC result, thus strictly ensuring that the final statistical guarantee is not destroyed by the reconstruction process. The final output robustness boundary is denoted as... .

[0111] Step S8: Model the TCL scheduling as a cost minimization or peak minimization optimization problem, use DW decomposition to obtain the aggregated power trajectory and scheduling columns of each device, and apply them.

[0112] Step S8 includes:

[0113] S801. Optimize the aggregation power trajectory at the aggregator end and solve for the dual variables to generate the internal coordinated price;

[0114] The aggregation power trajectory refers to the aggregator's performance during the scheduling period. Total power sequence for each time period ,in, , representing the sum of power consumption of all TCL devices during time period t; the power vector submitted by each TCL device. Forming an equipment scheduling column;

[0115] S802. Model the scheduling problem of TCL equipment as cost-minimizing scheduling:

[0116] The cost minimization scheduling objective is to minimize the aggregated electricity cost within the scheduling period, and the mathematical model is as follows:

[0117] ;

[0118] Among them, The real-time / day-ahead electricity price for time period t must satisfy constraints including robust power constraints and energy constraints for each device, i.e., robust boundary conditions. And satisfy the consistency constraint between polymerization power and the power of each device:

[0119] ;

[0120] In other embodiments of this application, peak minimization scheduling may also be employed, with the objective of minimizing the maximum aggregate power within a scheduling period. in For the aggregated baseline power vector, For aggregated control trajectories:

[0121] ;

[0122] ;

[0123] The physical meaning of this objective is to minimize the peak load on the transformer / feeder, thereby reducing capacity costs and delaying equipment upgrade investments; in this optimization problem, it is necessary to evaluate candidate aggregated power trajectories. Feasibility: If a set of device-level scheduling columns exists satisfy ,and Then the trajectory can be decomposed and realized;

[0124] S803. Solve the above optimization problem using DW decomposition: Aggregator side (Restricted Master Problem RMP) optimization of the aggregation power trajectory. Solving for dual variables Generate an internally coordinated price and broadcast it to all TCL devices:

[0125] In the restricted master problem (RMP) decomposed by Dantzig-Wolfe, the dual problem of the RMP is solved, and the dual variables are the internally coordinated price signals passed to the equipment subproblem. ;

[0126] The equipment side received the coordinated price Subsequently, in the local robust g-multifaceted matroid The optimal scheduling sequence is independently calculated using a greedy algorithm. Each device To achieve the goal, an optimal scheduling column is generated on the local g-polymorphic matel using a greedy algorithm (the greedy algorithm uses boundary functions to evaluate marginal costs / benefits, sorts by price, and makes decisions accordingly). Then, the virtual scheduling column is... Submit to the aggregator;

[0127] The aggregator updates the RMP and recalculates the coordinated price, repeating the iteration until convergence; each TCL device performs an inverse transformation. Restore the virtual scheduling trajectory to the physical power trajectory, and execute... And form a polymerization power trajectory according to step S801.

[0128] In the embodiments of this application, the above scheme can be executed in a closed-loop rolling manner: closed-loop rolling time-domain execution.

[0129] At each decision point, the process involves: state feedback (reading actual temperature and power) -> updating the nominal boundary based on the latest prediction -> robust calibration (S4-S6) -> device self-scheduling (S7) -> executing only the first step control command of the current window -> inverse transformation to restore the physical power trajectory and issuing it for execution -> proceeding to the next rolling window. Accumulated errors are absorbed in the initial state feedback of the next window.

[0130] A robust scheduling system based on a virtual generalized multifaceted matroid includes:

[0131] The data acquisition module is used to collect parameters from TCL devices.

[0132] The model building module is used to build a linear thermodynamic state-space model of TCL equipment and determine the set of flexibility that satisfies the constraints.

[0133] The virtual coordinate transformation module is used to construct the transformation matrix, perform virtual coordinate transformation on each TCL device, and map physical variables to the virtual domain;

[0134] The multifaceted matte boundary generation module generates boundary function pairs based on virtual constraints, and constructs an accurate g-multifaceted matte.

[0135] The affine perturbation module constructs a statistically feasible uncertainty set based on historical error samples, transforming the error into an affine perturbation.

[0136] The statistically feasible robust calibration module constructs a mixed uncertainty set using historical temperature prediction error samples and achieves adaptive robust boundary calibration of the samples.

[0137] The sample reconstruction module reconstructs the samples and performs adaptive calibration.

[0138] The decomposition scheduling module models TCL scheduling as a cost minimization or peak minimization optimization problem, and uses DW decomposition to obtain the aggregated power trajectory and the scheduling columns of each device;

[0139] The device execution module is used to perform virtual trajectory inverse transformation and restore the physical power trajectory based on the information obtained from the decomposition scheduling module, and then issue the execution.

[0140] The effects of this application are further illustrated below with reference to specific embodiments:

[0141] Example 1 (Cost Minimization): 100 heterogeneous TCL devices, scheduling step size of 1 hour, rolling look-ahead window H = 4, number of uncertain historical samples K = 600, reliability requirement 1 − ε = 95%, confidence level 1 − δ = 95%. PJM market actual historical electricity price and temperature prediction error series are used. Comparison methods include Zonotope / Homothet / General Affine geometric approximation, CCP opportunity constraint, CRO traditional robust optimization, and M-DRO moment-division bluish bar. The method of this invention (ReSRC) achieves an EVR of approximately 3.16% (meeting the ≤ 5% requirement) and an UPR of approximately 15.10% (significantly lower than CCP's 16.08% and CRO's 24.03%), with a computation time of approximately 1.4 seconds per window. This embodiment demonstrates that, in a cost-minimizing scenario with 100 heterogeneous TCLs, the method of the present invention can achieve better economic efficiency (reduced UPR) than traditional opportunity constraint and robust optimization methods while maintaining second-level online computing efficiency, under the premise of meeting preset reliability requirements (EVR≤ 5%).

[0142] Example 2 (Peak Reduction): The objective function is changed to minimizing aggregate peak power:

[0143] ;

[0144] Other settings are the same as in Example 1. The method of this invention (g-poly) achieves a UPR of approximately 0.02% (close to the accurate Minkowski sum and benchmark), with a computation time of approximately 7.0 seconds, which is far superior to the Zonotope method's approximately 75 seconds (UPR approximately 58.95%) and the Homothet method's approximately 0.3 seconds (but with a UPR as high as approximately 79.46%). This example shows that, in peak reduction scenarios, the method of this invention achieves a flexibility capacity utilization rate close to the accurate Minkowski sum (UPR of only 0.02%) through virtual coordinate transformation, significantly reducing the flexibility capacity loss compared to the geometric approximation method (Zonotope UPR 58.95%), verifying the core technical effect of accurate representation of g-poly matte.

[0145] Example 3 (Large-scale expansion): The number of devices is gradually increased from N = 100 to N = 1000, while keeping other parameters unchanged. The computation time of the method of this invention increases approximately linearly (O(N)), verifying the scalability of the algorithm. The average solution time for SRC is about 0.30 seconds, and for ReSRC it is about 1.42 seconds (both can be completed in the second range), meeting the requirements of large-scale fleet online scheduling. This example verifies the complexity advantage of the greedy algorithm in DW decomposition: when the number of devices increases tenfold, the computation time only increases linearly rather than exponentially, indicating that this invention is suitable for large-scale aggregated scheduling scenarios ranging from dozens to thousands of TCLs.

[0146] The foregoing description illustrates and describes a preferred embodiment of the present invention. However, as previously stated, it should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the inventive concept described herein through the foregoing teachings or techniques or knowledge in related fields. Any modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A robust scheduling method based on virtual generalized multifaceted matroids, characterized in that: Includes the following steps: Step S1: Collect parameters of each TCL device in the heterogeneous TCL group; Step S2: Construct a linear thermodynamic state-space model of the TCL device and determine the set of flexibility that satisfies the constraints; Step S3: Construct a transformation matrix to perform virtual coordinate transformation on each TCL device and map physical variables to the virtual domain; Step S4: Generate boundary function pairs based on virtual constraints to construct an accurate g-polyhedral matte; Step S5: Construct a statistically feasible uncertainty set based on historical error samples, and transform the error into an affine perturbation; Step S6: Construct a mixed uncertainty set using historical temperature prediction error samples and implement adaptive robust boundary calibration for the samples; Step S7: Reconstruct the sample and perform adaptive calibration; Step S8: Model the TCL scheduling as a cost minimization or peak minimization optimization problem, use DW decomposition to obtain the aggregated power trajectory and scheduling columns of each device, and apply them.

2. The robust scheduling method based on virtual generalized multifaceted matroid according to claim 1, characterized in that: In step S1, the heterogeneous TCL group refers to a heterogeneous temperature-controlled load group, including multiple TCL devices. The parameters of the TCL devices include thermal resistance. ,capacitance ,efficiency Rated power Set temperature Dead zone and the ambient temperature at time t .

3. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 2, characterized in that: Step S2 includes: S201. Assume a heterogeneous TCL population. It contains N TCL devices, and the heterogeneous TCL group is in a discrete time interval. It has a uniform time step The dynamics of the nth TCL device are controlled by the following thermodynamic equation: ； in, This represents the indoor temperature at time t. Let be the ambient temperature at time t. Assume that each TCL device uses the same type of cooling equipment. This represents the power consumption at time t; Characterizes the heat dissipation factor of the equipment at each step. , Indicates the thermal characteristics of the equipment; set up For a user-defined temperature setting, the nominal baseline power required to maintain this setpoint is: ； Control input Defined as power deviation, while the state variable Defined as the thermal energy stored relative to a set value: ； ； Substituting into the temperature dynamics equation, we obtain the standard state-space model: ； The input coefficients are: ； This model converts heterogeneous temperature control into a model with a dissipation factor. Virtual energy storage system; S202. Determine the set of flexibility conditions that satisfy the constraints: (1) The control equipment is constrained by the physical power boundary of the equipment: ； Among them, the lower boundary upper bound of the boundary ; (2) User comfort constraints are determined by temperature range Defined, converted to a symmetric energy capacity limit: ； The upper boundary is defined as follows: The maximum energy storage capacity is defined as the equivalent energy boundary corresponding to the comfortable temperature range; the lower boundary is defined as... ; (3) Flexibility set To satisfy all constraints of the control sequence The set, in Includes ambient temperature The determined boundary parameters, The constraint matrix is ​​formed by the constraints.

4. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 3, characterized in that: Step S3 includes: S301. From the initial stage to time t, the cumulative decay of the decay factor is expressed as: It acts as a time-dependent scaling factor, defining the transformation matrix. For diagonal matrices: ； S302. Define virtual state and virtual control as follows: ； This is equivalent to multiplying the control input by at each time step. ; S303. Change the virtual state and virtual control Substitute into the physical state equation Divide both sides by The process equation in virtual space is obtained as follows: ； Right now: ； This equation shows that the dynamics in the virtual domain degenerate into a perfect lossless integrator, restoring the time translation invariance required by g-polyhedral matroid theory.

5. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 4, characterized in that: Step S4 includes: S401. Constant physical boundary conditions are mapped to time-varying constraints imposed on these dummy variables, where the power constraint is transformed into: ； The time-varying virtual boundary is: ； S402. Limit the state Expanding recursively: ； Substituting the virtual state definition into the constraint on the cumulative sum of virtual control, we get: ； The virtual state boundary includes the initial physical Its definition method: ； S403. In a virtual domain, leverage the flexibility of TCL devices. Constructing an accurate g-polyhedral matte : Physical domain flexibility set The virtual coordinates are mapped to the virtual domain after the virtual coordinate transformation in step S3: For any ,have Conversely, for any ,have ;because Since it is an invertible diagonal matrix, the set of virtual domain flexibility is... This forms a g-polyhedral matte that is accurate for the model. Its supermode boundary function and submodule boundary function Derived from the virtual power constraints and virtual energy constraints in S401-S402.

6. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 1, characterized in that: Step S5 includes: At each scheduling time, based on the prediction of ambient temperature Constructing nominal physical boundaries : Define temperature prediction error This error is propagated to the TCL constraint boundary through the baseline power: the power boundary is generated in the predicted baseline coordinates. The level of affine translational perturbation; the time-cumulative perturbation of the energy boundary is: ； The random environmental error is represented as an affine perturbation of the physical boundary vector: ； in For TCL thermal parameters The deterministic coefficient matrix determined by the constraint coupling structure.

7. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 1, characterized in that: In step S6, constructing a mixed uncertainty set using historical temperature prediction error samples and implementing adaptive robust boundary calibration of the samples includes: S601. Shape Learning: Constructing a Mixed Uncertainty Set: Based on historical error sample set Calculate the sample mean and regularized covariance matrix Define Box set and Ellipsoid collection The mixed uncertainty set is the intersection of the two. ,in and The dimensions to be calibrated; S602. Size Calibration: Utilizing the Max-Transformation technique to map high-dimensional robust feasibility constraints to an equivalent one-dimensional quantile ordination estimation problem. For constrained families Determine the scalar value of the maximum constraint violation in each historical scenario. Sort all K samples in ascending order and take the i-th... This value serves as the robust boundary offset for the constraint; by controlling the confidence level... It provides a distribution-independent statistical feasibility guarantee: the scheduling solution is available out of the sample at a rate not lower than [missing information]. The probability is physically feasible; Constraint matrix The kth row; for The k-th row; S603. Based on Robustness boundary is automatically calculated from historical error samples. To meet the target reliability level and confidence level The statistical feasibility of the following.

8. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 7, characterized in that: Step S7, which enables adaptive robust calibration of the reconstructed samples, includes: S701. Execute step S6 to obtain the initial robust boundary. Solving the deterministic optimization problem within the robust feasible region yields the first scheduling scheme. ; S702. For each constraint k, calculate its safety margin. ,in Constraint matrix The k-th row is used to quantify the degree of constraint activation: This indicates that the constraint still has a margin at the optimal solution. The smaller the value, the closer it is to the constraint boundary; S703. Reconstructing the Uncertainty Set Using Safety Margins: Maintaining robust reserves in active constraint directions, and relaxing conservatism in directions with large safety margins. like This indicates that the constraint is an active constraint that determines the scheduling quality. When reconstructing the uncertainty set, it is necessary to maintain or even strengthen the robust reserve in this direction, that is, not reduce or appropriately increase the size parameter in the uncertainty projection direction corresponding to the constraint. Preset tension threshold; like This indicates that the constraint is far from being activated and there is room for over-conservatism. When reconstructing the uncertainty set, the robustness requirement in this direction should be appropriately relaxed, that is, the size parameter should be reduced in this direction, thereby expanding the feasible region and improving economic efficiency. This is a preset leniency threshold; like The original calibration results remain unchanged; S704. Perform final robustness verification using a calibration sample block independent of that in step S6: The reconstructed uncertainty set needs to be verified on independent samples to ensure its statistical feasibility is not lower than the target level. If the verification fails, it reverts to the initial robustness boundary, thereby strictly ensuring that the final statistical guarantee is not destroyed by the reconstruction process. The final output robustness boundary is denoted as... .

9. A robust scheduling method based on a virtual generalized multifaceted matroid according to claim 1, characterized in that: Step S8 includes: S801. Optimize the aggregation power trajectory at the aggregator end and solve for the dual variables to generate the internal coordinated price; The aggregation power trajectory refers to the aggregator's performance during the scheduling period. Total power sequence for each time period ,in, , representing the sum of power consumption of all TCL devices during time period t; the power vector submitted by each TCL device. Forming an equipment scheduling column; S802. Model the scheduling problem of TCL equipment as cost-minimizing scheduling: The cost minimization scheduling objective is to minimize the aggregated electricity cost within the scheduling period, and the mathematical model is as follows: ； Among them, The real-time / day-ahead electricity price for time period t must satisfy constraints including robust power constraints and energy constraints for each device, i.e., robust boundary conditions. And satisfy the consistency constraint between polymerization power and the power of each device: ； S803. Solve the above optimization problem using DW decomposition: Aggregator-side optimization for dual variables Generate an internally coordinated price and broadcast it to all TCL devices: In the restricted principal problem decomposed by DW, the dual problem is solved, and the dual variable is the internally coordinated price signal passed to the equipment subproblem. ; The equipment side received the coordinated price Subsequently, in the local robust g-multifaceted matroid The optimal scheduling sequence is independently calculated using a greedy algorithm. Each device To achieve the goal, generate the optimal scheduling column on the local g-polymorphic matel using a greedy algorithm, and then... Submit to the aggregator; The aggregator updates the RMP and recalculates the coordinated price, repeating the iteration until convergence. Each TCL device undergoes inverse conversion To restore the virtual scheduling trajectory to the physical power trajectory, execute: ； And form a polymerization power trajectory according to step S801.

10. A robust scheduling system based on a virtual generalized multifaceted matroid, wherein the method described in any one of claims 1 to 9 is characterized in that: include: The data acquisition module is used to collect parameters from TCL devices. The model building module is used to build a linear thermodynamic state-space model of TCL equipment and determine the set of flexibility that satisfies the constraints. The virtual coordinate transformation module is used to construct the transformation matrix, perform virtual coordinate transformation on each TCL device, and map physical variables to the virtual domain; The multifaceted matte boundary generation module generates boundary function pairs based on virtual constraints, and constructs an accurate g-multifaceted matte. The affine perturbation module constructs a statistically feasible uncertainty set based on historical error samples, transforming the error into an affine perturbation. The statistically feasible robust calibration module constructs a mixed uncertainty set using historical temperature prediction error samples and achieves adaptive robust boundary calibration of the samples. The sample reconstruction module reconstructs the samples and performs adaptive calibration. The decomposition scheduling module models TCL scheduling as a cost minimization or peak minimization optimization problem, and uses DW decomposition to obtain the aggregated power trajectory and the scheduling columns of each device; The device execution module is used to perform virtual trajectory inverse transformation and restore the physical power trajectory based on the information obtained from the decomposition scheduling module, and then issue the execution.

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