Non-intrusive load monitoring method based on compact mixed integer linear programming

Abstract

The application discloses a non-intrusive load monitoring method based on a compact mixed integer linear programming, and relates to the technical field of power system load monitoring.The application comprises the following steps: collecting aggregate active power, aggregate reactive power and power equipment operation parameters of a total electric meter; constructing a compact mixed integer linear programming model, accurately depicting equipment state transition events by introducing start-up link constraints, relaxing start-up variables into continuous variables to reduce integer complexity, and adopting normalized power variables to improve numerical conditions; calling a mixed integer linear programming solver to solve the model, and obtaining the operation state, start-up events and power consumption of each equipment.Under the premise of maintaining physical interpretability, the application effectively reduces the number of integer variables, improves the calculation efficiency and numerical stability, and provides an efficient and reliable load monitoring tool for power system demand side flexibility evaluation and grid interactive energy management.

Description

Technical Field

[0001] This invention relates to the field of power system load monitoring technology, specifically a non-intrusive load monitoring method based on compact mixed-integer linear programming. Background Technology

[0002] With the deepening of power market reform, accurate load-level information is crucial for demand response, dispatching decisions, and flexibility assessment in industrial and commercial scenarios. Non-Intrusive Load Monitoring (NILM) technology analyzes aggregated electrical measurement data from the master meter to infer the operating status and power consumption of individual electrical devices, avoiding the high cost of deploying dedicated sensors for individual devices, thus becoming an economical and efficient means of obtaining load-level information.

[0003] Currently, NILM methods mainly include Hidden Markov Model methods, machine learning methods, and methods based on Mixed-Integer Linear Programming (MILP). Among them, methods based on MILP are receiving increasing attention due to the development of optimization theory and the advancement of commercial solvers. Although existing NILM methods based on MILP have made some progress in model accuracy, they still face the following technical problems: weak physical interpretability of the initiation variable: In existing methods, the initiation variable is usually associated with adjacent state variables through unilateral constraints. It is impossible to strictly guarantee that the initiation variable takes a value of 1 only when the device state changes from inactive to active. This results in the initiation variable being activated even when the device has not entered the corresponding state, which weakens the physical consistency of the model.

[0004] To address this, the present invention proposes a non-intrusive load monitoring method based on compact mixed-integer linear programming. Summary of the Invention

[0005] The purpose of this invention is to provide a non-intrusive load monitoring method based on compact mixed-integer linear programming to solve the problems mentioned in the background art.

[0006] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: a non-intrusive load monitoring method based on compact mixed-integer linear programming, comprising the following steps: Collect the aggregated active power and aggregated reactive power measured by the main meter at multiple time intervals, and obtain the operating parameters of the electrical equipment within the monitoring range. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. Based on aggregated active power, aggregated reactive power, and operating parameters, a compact mixed-integer linear programming model is constructed, specifically including the construction of the objective function and constraints. The objective function is to minimize the sum of the aggregated power fitting error and the penalty term. The constraints include at least the starting link constraint, the continuous starting variable constraint, the normalized power variable constraint, and the power characteristic constraint. A mixed-integer linear programming solver is used to solve the compact mixed-integer linear programming model, and the output is a non-intrusive load monitoring result, which includes the operating status sequence, start-up event sequence and power consumption sequence of each electrical device.

[0007] Furthermore, the objective function is specifically expressed as: in, This indicates the operating state of device i, j, during time interval t. This indicates that the state is active. This indicates that the state is inactive; It is a continuous variable that represents the operating state of device i at time interval t. This indicates that the state is active. This indicates that the state is inactive; For normalized active power variables, it represents the normalized value of active power of device i in state j during time interval t, with a value range of [0,1]. For normalized reactive power variable, it represents the normalized value of reactive power of device i in state j during time interval t, and the value range is [0,1]. and These are the lower and upper limits of active power for device i in state j, respectively. and These are the lower and upper limits of reactive power for device i in state j, respectively. This represents the number of operating states of device i. , , and These are preset parameters.

[0008] Furthermore, the startup link constraint is used to accurately characterize the logical relationship between the startup variable and adjacent state variables, specifically expressed as follows: in, , , .

[0009] Furthermore, the continuous start-up variable constraint is specifically expressed as follows: Under the influence of initiating link constraints The value of is automatically restricted to 0 or 1, if and only if and ,otherwise .

[0010] Furthermore, the normalized power variable constraint is specifically expressed as follows: Actual active power and reactive power Reconstruct using the following formula: in, and These are the lower and upper limits of active power for electrical equipment in state j, respectively. and These are the lower and upper limits of reactive power for electrical equipment i in state j, respectively.

[0011] Furthermore, the power characteristic constraint is specifically expressed as follows: Among them, the active power fluctuation characteristic is upward. Reactive power upward fluctuation characteristics Active power downward fluctuation characteristics and the downward fluctuation characteristics of reactive power Reconstruct using the following formula: In the formula, and These represent the upward fluctuation characteristics of normalized active and reactive power, respectively. and These represent the downward fluctuation characteristics of normalized active and reactive power, respectively.

[0012] Furthermore, the constraints also include minimum running time constraints, state transition constraints, and state mutual exclusion constraints, wherein: The minimum running time constraint is: in, This represents the minimum power-on time for device i in state j. ; The state transition constraints are: The state mutual exclusion constraint is: In the formula, This represents the number of operating states of electrical equipment i.

[0013] Furthermore, a mixed-integer linear programming solver is used to solve the compact mixed-integer linear programming model, outputting non-intrusive load monitoring results, specifically including: Model Import and Solution Initialization: The objective function, all constraints, and decision variables of the completed compact mixed-integer linear programming model are imported into the commercial mixed-integer linear programming solver Gurobi; the decision variables include 0-1 integer variables representing the start-stop state of each electrical device and continuous variables representing the operating power of each electrical device; the total load observation sequence to be decomposed and the rated power parameters of the electrical devices are used as solution boundary conditions to complete the initialization; Solver parameter configuration: Configure the solver parameters for the Gurobi solver. Specific configuration details include: 1) The solution mode is set to the exact solution mode for mixed-integer linear programming; 2) The relative optimal gap for mixed-integer programming is set to 0.1%; 3) Single-threaded solution; Iterative solution and convergence determination: The solver iteratively solves the compact mixed integer linear programming model based on the branch and bound algorithm. During the iteration process, node pruning is used to reduce the feasible solution space of integer variables. When the relative difference between the obtained objective function value and the theoretical optimal lower bound is less than the preset relative optimal gap, or when the preset maximum solution time is reached, the solution process is terminated and the current optimal feasible solution is output. Results Analysis and Output: The optimal feasible solution output by the solver is analyzed, and the values ​​of the 0-1 start-stop state variables and continuous operating power variables corresponding to each electrical device at each sampling time are extracted. The operating power curves and start-stop event sequences of each electrical device are spliced ​​together according to the time series, which serve as the final non-intrusive load monitoring results.

[0014] According to a second aspect of the present invention, the present invention provides a non-intrusive load monitoring system based on compact mixed-integer linear programming, for implementing the non-intrusive load monitoring method based on compact mixed-integer linear programming described in the first aspect, comprising: The data acquisition module is used to collect the aggregate active power and aggregate reactive power measured by the main meter at multiple time intervals, and to obtain the operating parameters of the electrical equipment within the monitoring range. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. The model building module is used to construct a compact mixed-integer linear programming model based on aggregated active power, aggregated reactive power, and operating parameters. Specifically, it includes the construction of objective function and constraints. The objective function is to minimize the sum of aggregated power fitting error and penalty term. The constraints include at least starting link constraints, continuous starting variable constraints, normalized power variable constraints, and power characteristic constraints. The model solving module is used to solve the compact mixed-integer linear programming model using a mixed-integer linear programming solver, and outputs non-intrusive load monitoring results, which include the operating status sequence, start-up event sequence, and power consumption sequence of each electrical device.

[0015] According to a third aspect of the present invention, a terminal device is provided, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, it employs the non-intrusive load monitoring method based on compact mixed-integer linear programming described in the first aspect.

[0016] This invention has at least the following beneficial effects: 1. This invention introduces a starting link constraint, relaxing the starting variable from a binary variable to a continuous variable. Without changing its physical meaning, it significantly reduces the number of integer decision variables in the model. This makes the originally large-scale and difficult-to-solve mixed integer linear programming problem compact and efficient, and can obtain a feasible solution in a shorter time. It is especially suitable for complex load monitoring scenarios with long time series, multiple devices, and multiple states, and meets the needs of actual power systems for real-time or near-real-time load decomposition.

[0017] 2. The startup link constraint proposed in this invention is a bidirectional equivalence constraint, which can accurately characterize the transition event of the device state from inactive to active. It ensures that the startup variable takes a value of one only when the state actually switches, and takes a value of zero in other cases. This design eliminates the defect that the startup variable may be erroneously activated in the traditional unilateral constraint, so that the startup event sequence output by the model strictly conforms to the actual operating logic of the device, and improves the physical reliability of the load decomposition results.

[0018] 3. This invention uses a normalized power variable to replace the original physical unit power variable, mapping the feasible power domains of all electrical devices of different magnitudes to a unified dimensionless interval. This eliminates the problem of huge differences in coefficient magnitude caused by excessive differences in rated power. This improvement optimizes the numerical conditions of the constraint matrix, reduces the risk of numerical ill-conditioned solvers during iteration, and improves the stability and convergence speed of the solution process. This makes the model applicable to mixed load scenarios that simultaneously include high-power industrial equipment and low-power household equipment.

[0019] 4. While achieving model compactness and numerical optimization, this invention can still accurately express various practical constraints, including power fluctuation limits, minimum continuous operating time, state transition logic, and state mutual exclusion. By combining normalized power variables with power characteristic constraints, this invention can characterize the continuous power regulation behavior of equipment during steady-state operation, rather than being limited to discrete state switching, thus more realistically reflecting the actual operating characteristics of electrical appliances and improving the accuracy of load decomposition.

[0020] Of course, any product implementing this invention does not necessarily need to achieve all of the advantages described above at the same time. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a flowchart illustrating the method described in this invention. Detailed Implementation

[0023] 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.

[0024] Example 1: Please see Figure 1 This invention provides a technical solution: a non-intrusive load monitoring method based on compact mixed-integer linear programming, comprising the following steps: S1. Collect the aggregated active power measured by the main meter over multiple time intervals. and aggregate reactive power It also acquires the operating parameters of electrical equipment within the monitoring range, including the number of operating states. Upper limit of active power in each state and lower limit upper limit of reactive power and lower limit Minimum continuous running time requirement And power fluctuation limiting parameters, including the upward fluctuation characteristics of active power. Reactive power upward fluctuation characteristics Active power downward fluctuation characteristics and the downward fluctuation characteristics of reactive power as well as , , and ; S2. Based on aggregated active power, aggregated reactive power, and operating parameters, construct a compact mixed-integer linear programming model, specifically including the construction of the objective function and constraints; S21. The objective function is to minimize the sum of the aggregate power fitting error and the penalty term: in, This indicates the operating state of device i, j, during time interval t. This indicates that the state is active. This indicates that the state is inactive; It is a continuous variable that represents the operating state of device i at time interval t. This indicates that the state is active. This indicates that the state is inactive; For normalized active power variables, it represents the normalized value of active power of device i in state j during time interval t, with a value range of [0,1]. For normalized reactive power variable, it represents the normalized value of reactive power of device i in state j during time interval t, and the value range is [0,1]. and These are the lower and upper limits of active power for device i in state j, respectively. and These are the lower and upper limits of reactive power for device i in state j, respectively. This represents the number of operating states of device i. , , and These are preset parameters; S22. The constraint conditions are: Startup link constraints are used to precisely characterize the logical relationship between startup variables and adjacent state variables: in, , , ; Consecutive start variable constraints: Under the influence of initiating link constraints The value of is automatically restricted to 0 or 1, if and only if and ,otherwise ; Normalized power variable constraints: Actual active power and reactive power Reconstruct using the following formula: in, and These are the lower and upper limits of active power for device i in state j, respectively. and These are the lower and upper limits of reactive power for device i in state j, respectively; Power characteristic constraints Among them, the active power fluctuation characteristic is upward. Reactive power upward fluctuation characteristics Active power downward fluctuation characteristics and the downward fluctuation characteristics of reactive power Reconstruct using the following formula: In the formula, and These represent the upward fluctuation characteristics of normalized active and reactive power, respectively. and These represent the downward fluctuation characteristics of normalized active and reactive power, respectively. Minimum running time constraint in, This represents the minimum power-on time for device i in state j. ; State transition constraints State Mutual Exclusion Constraint ; S3. A mixed-integer linear programming solver is used to solve the compact mixed-integer linear programming model, outputting non-intrusive load monitoring results. These results include the operating status sequence, startup event sequence, and power consumption sequence of each electrical device; specifically: S31. Model Import and Solution Initialization: Import the objective function, all constraints, and decision variables of the completed compact mixed-integer linear programming model into the commercial mixed-integer linear programming solver Gurobi; the decision variables include 0-1 integer variables representing the start-stop state of each electrical device and continuous variables representing the operating power of each electrical device; the total load observation sequence to be decomposed and the rated power parameters of the electrical devices are used as solution boundary conditions to complete the initialization.

[0025] S32. Solver Parameter Configuration: Configure the solver parameters for the Gurobi solver. Specific configuration details include: 1) The solution mode is set to the exact solution mode for mixed-integer linear programming; 2) The relative optimal gap for mixed-integer programming is set to 0.1%; 3) Single-threaded solution.

[0026] S33. Iterative Solution and Convergence Determination: The solver iteratively solves the compact mixed-integer linear programming model based on the branch and bound algorithm. During the iteration process, node pruning is used to reduce the feasible solution space of integer variables. When the relative difference between the obtained objective function value and the theoretical optimal lower bound is less than the preset relative optimal gap, or when the preset maximum solution time is reached, the solution process is terminated and the current optimal feasible solution is output.

[0027] S34. Result Analysis and Output: Analyze the optimal feasible solution output by the solver, extract the values ​​of the 0-1 start-stop state variables and the continuous operating power variables corresponding to each electrical device at each sampling time, and splice them according to the time series to obtain the operating power curve and start-stop event sequence of each electrical device, which serves as the final non-intrusive load monitoring result.

[0028] The technical solution of this embodiment will be further elaborated below with specific simulation experiments: Taking a household's data for one day as an example, this household includes 7 appliances: refrigerator (FRE), heat pump (HPE), dishwasher (DWE), washing machine (CWE), dryer (CDE), living room audio-visual equipment (TV / DVR / amplifier, TVE), and basement socket circuit (BME). First, the aggregated active power and aggregated reactive power measured by the main meter at multiple time intervals are collected, and the operating parameters of the electrical equipment within the monitoring range are obtained. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. Based on the aggregated active power, aggregated reactive power, and operating parameters, a compact mixed-integer linear programming model is constructed, specifically including the construction of the objective function and constraints. The objective function is to minimize the sum of the aggregated power fitting error and the penalty term, and the constraints include at least the starting link constraint, continuous starting variable constraint, normalized power variable constraint, and power characteristic constraint. The objective function, all constraints, and decision variables (including 0-1 integer variables representing the start-stop status of each electrical device and continuous variables representing the operating power of each electrical device) of the completed model are imported into the solver. Initialization is performed using the total load observation sequence to be decomposed and the rated power parameters of the electrical devices as the solution boundary conditions. Subsequently, the Gurobi solver is configured with parameters set to the exact solution mode for mixed-integer linear programming, the relative optimal gap for mixed-integer programming is set to 0.1%, and a single-threaded solution mode is used. After configuration, the solver iteratively solves the compact mixed-integer linear programming model based on the branch-and-bound algorithm. During iteration, node pruning is used to narrow the feasible solution space of integer variables. When the relative difference between the obtained objective function value and the theoretical optimal lower bound is less than the preset relative optimal gap, or when the preset maximum solution time is reached, the solution is terminated and the current optimal feasible solution is output. Finally, the optimal feasible solution output by the solver is analyzed, and the 0-1 variables corresponding to each electrical device at each sampling time are extracted. The values ​​of start / stop state variables and continuous operating power variables are spliced ​​together in time series to obtain the operating power curves and start / stop event sequences of each electrical device, which serve as the final non-intrusive load monitoring results. The accuracy of the decomposition is shown in the table below.

[0029] In summary, this invention employs a three-level model structure optimization strategy. First, it establishes a strict logical equivalence relationship between the initiation variable and adjacent state variables through initiation link constraints, ensuring that the initiation variable only takes a value of 1 when the device state changes from inactive to active, thus strengthening the physical consistency and logical rigor of the model. Second, based on the strengthened logical structure, the initiation variable is relaxed from a binary variable to a continuous variable, effectively reducing the number of binary decision variables while maintaining the physical interpretation of the initiation event, significantly improving the model's compactness and computational solvability. Finally, a normalized continuous power variable is introduced, mapping the power feasible domain of different devices and states to a unified dimensionless interval, eliminating the difference in coefficient magnitude, improving numerical conditions, and enhancing solution efficiency and stability. This three-level optimization strategy reduces integer complexity and improves numerical conditions while maintaining the physical interpretability of the model. It solves the technical problems of unclear physical meaning of initiation variables, large scale of binary variables, and poor numerical stability in traditional non-intrusive load monitoring models. It significantly improves the solution efficiency and decomposition accuracy of large-scale NILM problems, and provides an efficient and reliable computing tool for demand-side flexibility identification and grid-interactive energy management.

[0030] Example 2: This embodiment provides a non-intrusive load monitoring system based on compact mixed-integer linear programming, used to implement the non-intrusive load monitoring method based on compact mixed-integer linear programming described in Embodiment 1, including: The data acquisition module is used to collect the aggregate active power and aggregate reactive power measured by the main meter at multiple time intervals, and to obtain the operating parameters of the electrical equipment within the monitoring range. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. The model building module is used to construct a compact mixed-integer linear programming model based on aggregated active power, aggregated reactive power, and operating parameters. Specifically, it includes the construction of objective function and constraints. The objective function is to minimize the sum of aggregated power fitting error and penalty term. The constraints include at least starting link constraints, continuous starting variable constraints, normalized power variable constraints, and power characteristic constraints. The model solving module is used to solve the compact mixed-integer linear programming model using a mixed-integer linear programming solver, and outputs non-intrusive load monitoring results, which include the operating status sequence, start-up event sequence, and power consumption sequence of each electrical device.

[0031] Example 3: The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it employs the non-intrusive load monitoring method based on compact mixed integer linear programming described in Embodiment 1.

[0032] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0033] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0034] Example 4: The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the non-intrusive load monitoring method based on compact mixed-integer linear programming described in Embodiment 1.

[0035] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0036] In the description of this specification, the references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0037] The foregoing has shown and described the basic principles, main features, and advantages of this application. Those skilled in the art should understand that this application is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of this application. Various changes and modifications can be made to this application without departing from the spirit and scope thereof, and all such changes and modifications fall within the scope of the claims of this application.

Claims

1. A non-intrusive load monitoring method based on compact mixed-integer linear programming, characterized in that, Includes the following steps: Collect the aggregated active power and aggregated reactive power measured by the main meter at multiple time intervals, and obtain the operating parameters of the electrical equipment within the monitoring range. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. Based on aggregated active power, aggregated reactive power, and operating parameters, a compact mixed-integer linear programming model is constructed, specifically including the construction of the objective function and constraints. The objective function is to minimize the sum of the aggregated power fitting error and the penalty term. The constraints include at least the starting link constraint, the continuous starting variable constraint, the normalized power variable constraint, and the power characteristic constraint. A mixed-integer linear programming solver is used to solve the compact mixed-integer linear programming model, and the output is a non-intrusive load monitoring result, which includes the operating status sequence, start-up event sequence and power consumption sequence of each electrical device.

2. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 1, characterized in that: The objective function is specifically expressed as follows: in, This indicates the operating state of device i, j, during time interval t. This indicates that the state is active. This indicates that the state is inactive; It is a continuous variable that represents the operating state of device i at time interval t. This indicates that the state is active. This indicates that the state is inactive; For normalized active power variables, it represents the normalized value of active power of device i in state j during time interval t, with a value range of [0,1]. For normalized reactive power variable, it represents the normalized value of reactive power of device i in state j during time interval t, and the value range is [0,1]. and These are the lower and upper limits of active power for device i in state j, respectively. and These are the lower and upper limits of reactive power for device i in state j, respectively. This represents the number of operating states of device i. , , and These are preset parameters.

3. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 1, characterized in that: The startup link constraint is used to accurately characterize the logical relationship between the startup variable and adjacent state variables, specifically expressed as follows: in, , , .

4. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 3, characterized in that: The continuous start variable constraint is specifically expressed as follows: Under the influence of initiating link constraints The value of is automatically restricted to 0 or 1, if and only if and ,otherwise .

5. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 4, characterized in that: The normalized power variable constraint is specifically expressed as follows: Actual active power and reactive power Reconstruct using the following formula: in, and These are the lower and upper limits of active power for electrical equipment in state j, respectively. and These are the lower and upper limits of reactive power for electrical equipment i in state j, respectively.

6. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 5, characterized in that: The power characteristic constraint is specifically expressed as follows: Among them, the active power fluctuation characteristic is upward. Reactive power upward fluctuation characteristics Active power downward fluctuation characteristics and the downward fluctuation characteristics of reactive power Reconstruct using the following formula: In the formula, and These represent the upward fluctuation characteristics of normalized active and reactive power, respectively. and These represent the downward fluctuation characteristics of normalized active and reactive power, respectively.

7. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 1, characterized in that: The constraints also include minimum running time constraints, state transition constraints, and state mutual exclusion constraints, wherein: The minimum running time constraint is: in, This represents the minimum power-on time for device i in state j. ; The state transition constraints are: The state mutual exclusion constraint is: In the formula, This represents the number of operating states of electrical equipment i.

8. The non-intrusive load monitoring method based on compact mixed-integer linear programming according to claim 1, characterized in that: A mixed-integer linear programming solver is used to solve a compact mixed-integer linear programming model, outputting non-intrusive load monitoring results, specifically including: Model Import and Solution Initialization: The objective function, all constraints, and decision variables of the completed compact mixed-integer linear programming model are imported into the commercial mixed-integer linear programming solver Gurobi; the decision variables include 0-1 integer variables representing the start-stop state of each electrical device and continuous variables representing the operating power of each electrical device; the total load observation sequence to be decomposed and the rated power parameters of the electrical devices are used as solution boundary conditions to complete the initialization; Solver parameter configuration: Configure the solver parameters for the Gurobi solver. Specific configuration details include: 1) The solution mode is set to the exact solution mode for mixed-integer linear programming; 2) The relative optimal gap for mixed-integer programming is set to 0.1%; 3) Single-threaded solution; Iterative solution and convergence determination: The solver iteratively solves the compact mixed integer linear programming model based on the branch and bound algorithm. During the iteration process, node pruning is used to reduce the feasible solution space of integer variables. When the relative difference between the obtained objective function value and the theoretical optimal lower bound is less than the preset relative optimal gap, or when the preset maximum solution time is reached, the solution process is terminated and the current optimal feasible solution is output. Results Analysis and Output: The optimal feasible solution output by the solver is analyzed, and the values ​​of the 0-1 start-stop state variables and continuous operating power variables corresponding to each electrical device at each sampling time are extracted. The operating power curves and start-stop event sequences of each electrical device are spliced ​​together according to the time series, which serve as the final non-intrusive load monitoring results.

9. A non-intrusive load monitoring system based on compact mixed-integer linear programming, used to implement the non-intrusive load monitoring method based on compact mixed-integer linear programming as described in any one of claims 1 to 8, characterized in that, include: The data acquisition module is used to collect the aggregate active power and aggregate reactive power measured by the main meter at multiple time intervals, and to obtain the operating parameters of the electrical equipment within the monitoring range. The operating parameters include the number of available operating states of each electrical equipment, the upper and lower limits of active power and reactive power for each state, the minimum continuous operating time requirement, and power fluctuation limit parameters. The model building module is used to construct a compact mixed-integer linear programming model based on aggregated active power, aggregated reactive power, and operating parameters. Specifically, it includes the construction of objective function and constraints. The objective function is to minimize the sum of aggregated power fitting error and penalty term. The constraints include at least starting link constraints, continuous starting variable constraints, normalized power variable constraints, and power characteristic constraints. The model solving module is used to solve the compact mixed-integer linear programming model using a mixed-integer linear programming solver, and outputs non-intrusive load monitoring results, which include the operating status sequence, start-up event sequence, and power consumption sequence of each electrical device.

10. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program that can run on a processor. When the processor loads and executes the computer program, it employs the non-intrusive load monitoring method based on compact mixed-integer linear programming as described in any one of claims 1 to 8.

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