A method and device for constructing a non-intrusive load monitoring mathematical programming model

Abstract

The application is suitable for the field of smart grid, and provides a construction method and device of a non-intrusive load monitoring mathematical programming model. The method uses collected power characteristic data of each electrical appliance, and proposes a target function with two types of linear penalty terms through an integer variable equivalent conversion technology. The two types of linear penalty terms are: an electrical appliance state conversion penalty term and a minimum running state penalty term. Through the introduction of a power variable, power fluctuation constraints and power boundary constraints of the electrical appliance are proposed, and a convex hull expression form of the minimum running time constraints of the electrical appliance is proposed based on the convex hull theory. After other constraints are added, an efficient non-intrusive load monitoring mixed integer programming model is finally obtained. According to the modeling method, an efficient non-intrusive load monitoring mixed integer programming model will be constructed. The model is more compact, and the calculation efficiency is higher.

Description

Technical Field

[0001] This invention belongs to the field of computer technology, and in particular relates to a method and apparatus for constructing a non-intrusive load monitoring mathematical programming model. Background Technology

[0002] Energy is a vital material foundation for human survival and development, a topic of common concern worldwide, and a significant driving force for my country's socio-economic development. However, with the acceleration of industrialization and urbanization, and the continuous upgrading of consumption patterns, my country's energy demand is experiencing rigid growth. Therefore, strengthening the monitoring and management of electricity consumption is of great practical significance for improving my country's energy efficiency, achieving sustainable energy development, building a conservation-oriented society, and alleviating energy pressure.

[0003] Currently, power systems primarily monitor and manage power supply, distribution, and transmission, with less emphasis on monitoring and managing the user end. This results in users not receiving high-quality electricity services, and power grid companies lacking access to more accurate user load information. Therefore, a demand-side power management system platform would significantly improve user satisfaction, while also enhancing grid security and reducing grid consumption.

[0004] Detailed monitoring of electricity user load (hereinafter referred to as load monitoring) is the first step in realizing smart electricity consumption. Load monitoring technology samples and analyzes the total load data of users to monitor the detailed operating status of each electrical appliance within the user's premises, thereby obtaining data information such as the energy consumption and electricity usage behavior of each appliance. In the past, electricity user load monitoring mainly collected total load data for metering. If it is possible to monitor the operating status of each electrical appliance, it will have greater significance for the power grid, users, and even society as a whole.

[0005] Due to technical and economic reasons, my country's power user-side load monitoring technology lags behind the increasingly sophisticated and advanced smart grid. Existing monitoring systems require the installation of numerous devices within the user's premises for induction measurement and data transmission to monitor all electrical equipment online. This not only demands high economic investment and complex management and maintenance, but also, the "intrusive" nature of such monitoring systems leads to brief power outages and disruptions to users' production and daily lives during installation, reducing user satisfaction with smart grid services. Therefore, there is an urgent need to improve the load monitoring technology level in smart grid systems.

[0006] Non-intrusive load monitoring technology, by decomposing and identifying total user load data, can obtain refined data on user-specific load categories and usage status, making it an effective approach to solving the challenges of smart electricity load monitoring. This solution eliminates the need for installing load monitoring devices on the user side or significantly upgrading smart meters. It relies on the existing data acquisition devices and communication networks of the electricity information collection system, employing advanced data communication technology to obtain refined user electricity load data. Then, it utilizes the powerful data processing capabilities of the power cloud platform to run relatively complex and accurate load identification algorithms, achieving non-intrusive load monitoring. This solution offers better economic efficiency and scalability, but several technical challenges remain to be overcome, requiring further research. Summary of the Invention

[0007] The purpose of this invention is to provide a method and apparatus for constructing a non-intrusive load monitoring mathematical programming model, which aims to solve the problems of low accuracy, difficulty in solving existing non-intrusive load monitoring models, and inability to meet the real-time and accuracy requirements of practical applications.

[0008] This invention is implemented as follows: a method for constructing a non-intrusive load monitoring mathematical programming model, the method comprising:

[0009] Collect electrical characteristic data of electrical appliances, including the number of states of the electrical appliance, the minimum running time of each state of the electrical appliance, the power boundary of each state of the electrical appliance, the power fluctuation amplitude of each state of the electrical appliance, and the transition sequence between each state of the electrical appliance.

[0010] Construct an objective function that considers the state transition penalty term and the minimum operating state penalty term of the appliance by using the equivalent transformation technique of integer variables;

[0011] By introducing power variables, power fluctuation constraints and power boundary constraints for each state of electrical appliances are constructed, and a convex hull expression form for the minimum running time constraint of electrical appliances is established based on convex hull theory.

[0012] Based on power characteristic data, an objective function considering the state transition penalty term and minimum operating state penalty term of electrical appliances, power fluctuation constraints and power boundary constraints of each state of electrical appliances, minimum operating time constraints of electrical appliances, and other constraints, an efficient non-intrusive load monitoring mixed integer programming model is constructed.

[0013] Another objective of this invention is to provide a non-intrusive load monitoring mathematical programming model construction device, the device comprising:

[0014] The data preprocessing unit is used to collect the power characteristic data of each electrical appliance. The power characteristic data includes the number of states of the electrical appliance, the minimum running time of each state of the electrical appliance, the power boundary of each state of the electrical appliance, the power fluctuation amplitude of each state of the electrical appliance, and the transition sequence between each state of the electrical appliance.

[0015] The objective function construction unit constructs an objective function that considers the state transition penalty term and the minimum operating state penalty term of the appliance through the integer variable equivalent transformation technique; and

[0016] The constraint construction unit introduces power variables to construct power fluctuation constraints and power boundary constraints for each state of the electrical appliance, and establishes the convex hull expression form of the minimum running time constraint of the electrical appliance based on convex hull theory.

[0017] Based on power characteristic data, an objective function considering the state transition penalty term and minimum operating state penalty term of electrical appliances, power fluctuation constraints and power boundary constraints of each state of electrical appliances, minimum operating time constraints of electrical appliances, and other constraints, an efficient non-intrusive load monitoring mixed integer programming model is constructed.

[0018] The method for constructing a non-intrusive load monitoring mathematical programming model provided in this invention introduces linear penalty terms (appliance state transition penalty term and minimum operating state penalty term) and power variables to construct a concise linear objective function, power fluctuation constraints and power boundary constraints for each state of the applicator, and minimum operating time constraints for the applicator. This improves the accuracy of non-intrusive load monitoring while reducing the computational difficulty of the model. Model solving using GUROBI 9.1 shows that the non-intrusive load monitoring mixed integer programming model constructed using this invention achieves a load decomposition accuracy of over 94%, and can complete a two-day load decomposition task within 18 seconds. Therefore, the non-intrusive load monitoring mixed integer programming model constructed in this invention can be used to monitor changes in power load to achieve the goals of resource optimization and energy conservation and emission reduction. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a method for constructing a non-intrusive load monitoring mathematical programming model, as provided in an embodiment of the present invention;

[0020] Figure 2 A structural block diagram of a device for constructing a non-intrusive load monitoring mathematical programming model provided in an embodiment of the present invention; Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0022] The efficient, non-intrusive load monitoring mixed-integer programming model construction method provided in this invention introduces linear penalty terms (appliance state transition penalty terms and minimum operating state penalty terms) and power variables to construct a concise linear objective function, power fluctuation constraints and power boundary constraints for each applicator state, and minimum operating time constraints for the applicator. The non-intrusive load monitoring mixed-integer programming model constructed using this invention achieves at least a 10% improvement in computational efficiency and at least a 10% improvement in load decomposition accuracy compared to other advanced models.

[0023] Figure 1 This paper illustrates the implementation flow of a method for constructing a non-intrusive load monitoring mathematical programming model according to an embodiment of the present invention. For ease of explanation, only the parts related to the embodiments of the present invention are shown, and are detailed below:

[0024] like Figure 1 As shown, this embodiment of the invention provides a method for constructing a multi-time period high-dimensional projector group combination model, including steps S102, S104, S106 and S108.

[0025] Step S102: Collect the power characteristic data of the electrical appliances. The power characteristic data includes the number of states of the electrical appliances, the minimum running time of each state of the electrical appliances, the power boundary of each state of the electrical appliances, the power fluctuation amplitude of each state of the electrical appliances, and the transition sequence between each state of the electrical appliances.

[0026] Step S104: Construct an objective function that considers the state transition penalty term of the appliance and the minimum operating state penalty term by using the integer variable equivalent transformation technique.

[0027] In this embodiment of the invention, the objective function considering the appliance state transition penalty term and the minimum operating state penalty term is as follows:

[0028]

[0029] Where i represents the appliance number, j represents the appliance status number, t represents the time period, N is the total number of appliances, T is the total number of time periods, and m i Let μ1 and μ2 be the total number of states of appliance i, and μ1 and μ2 be the penalty parameters. Let be the penalty parameter for the j-state of appliance i. Let P be the operating penalty parameter for appliance i in state j during time period t, where P represents active power, Q represents reactive power, and ε is the operating penalty parameter for appliance i in state j during time period t.P,t , ε Q,t As auxiliary variables, x represents the error in active power and the error in reactive power during time period t, respectively. i,j,t This represents the operating state of appliance i in time period t (a 0-1 variable, where 0 represents off and 1 represents on), s i,j,t This represents the on / off state of appliance i in time period t (0-1 variable, 1 represents on, 0 represents otherwise).

[0030] Step S106: By introducing power variables, power fluctuation constraints and power boundary constraints for each state of the electrical appliance are constructed, and a convex hull expression form for the minimum running time constraint of the electrical appliance is established based on convex hull theory.

[0031] In this embodiment of the invention, the power fluctuation constraints and power boundary constraints for each state of the electrical appliance are as follows:

[0032]

[0033]

[0034]

[0035]

[0036]

[0037]

[0038] Where N is the total number of electrical appliances, T is the total number of time periods, and m i Let i be the total number of states of appliance i, where i∈{1,…,N} represents the appliance number, and j∈{1,…,m} i} represents the status number of the appliance, t∈{1,…,T} represents the time period, P i,j,t Q represents the active power of appliance i in state j during time period t. i,j,t This represents the reactive power of appliance i in state j during time period t. P i,j and P represents the lower and upper bounds of the active power in state j of appliance i, respectively. up,i,j and P down,i,j This represents the amplitude of the upward and downward fluctuations in the active power of appliance i in state j. Q i，j and Let Q represent the lower and upper bounds of the reactive power in state j of appliance i, respectively. up,i,j and Q down,i,j x represents the amplitude of the upper and lower fluctuations of reactive power in state j of appliance i. i,j,tThis represents the operating state of appliance i in time period t (a 0-1 variable, where 0 represents off and 1 represents on), s i,j,t This represents the on / off state of appliance i in time period t (0-1 variable, 1 represents on, 0 represents otherwise).

[0039] The minimum operating time constraint for the electrical appliance is:

[0040]

[0041] Where, x i,j,t This represents the operating state of appliance i in time period t (a 0-1 variable, where 0 represents off and 1 represents on), s i,j,t This represents the on / off state of appliance i in time period t (a 0-1 variable, where 1 represents on and 0 represents otherwise). T run,i,j Let $\frac{j}{\frac ... + =max(·,0).

[0042] Step S108: Based on power characteristic data, an objective function considering the state transition penalty term and minimum operating state penalty term of electrical appliances, power fluctuation constraints and power boundary constraints of each state of electrical appliances, minimum operating time constraints of electrical appliances and other constraints, an efficient non-intrusive load monitoring mixed integer programming model is constructed.

[0043] In this embodiment of the invention, other constraints include:

[0044] Error constraints:

[0045]

[0046]

[0047] Where N is the total number of electrical appliances, m i Let i be the total number of states of appliance i, where i∈{1,…,N} represents the appliance number, and j∈{1,…,m} i} represents the state number of appliance i, t∈{1,…,T} represents the time period, T is the total number of time periods, and P i,j,t Q represents the active power of appliance i in state j during time period t. i,j,t This represents the reactive power of appliance i in state j during time period t. This represents the total active power collected by the meter during time period t. ε represents the total reactive power collected by the meter during time period t. P,t and ε Q,t It is an auxiliary variable.

[0048] State constraints:

[0049] x i，j，t -x i，j，t-1 ≤s i，j，t

[0050] Where, x i,j,t This represents the operating state of appliance i in time period t (a 0-1 variable, where 0 represents off and 1 represents on), s i,j,t This represents the on / off state of appliance i in time period t (0-1 variable, 1 represents on, 0 represents otherwise).

[0051] Multi-state selection constraints:

[0052]

[0053] Where, x i,j,t This represents the operating state of appliance i in time period t (0-1 variable, 0 represents off, 1 represents running).

[0054] The efficient, non-intrusive load monitoring mixed-integer programming model is constructed as follows:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] x i,j,t -x i,j,t-1 ≤s i,j,t

[0067]

[0068] Where N is the total number of electrical appliances, T is the total number of time periods, and m iLet i be the total number of states of appliance i, where i∈{1,…,N} represents the appliance number, and j∈{1,…,m} i} represents the status number of the appliance, t∈{1,…,T} represents the time period, P i,j,t Q represents the active power of appliance i in state j during time period t. i,j,t This represents the reactive power of appliance i in state j during time period t. P i,j and P represents the lower and upper bounds of the active power in state j of appliance i, respectively. up,i,j and P down,i,j This represents the amplitude of the upward and downward fluctuations in the active power of appliance i in state j. Q i,j and Let Q represent the lower and upper bounds of the reactive power in state j of appliance i, respectively. up,i,j and Q down,i,j x represents the amplitude of the upper and lower fluctuations of reactive power in state j of appliance i. i,j,t This represents the operating state of appliance i in time period t (a 0-1 variable, where 0 represents off and 1 represents on), s i,j,t This represents the on / off state of appliance i in time period t (0-1 variable, 1 represents on, 0 represents otherwise). This represents the total active power collected by the meter during time period t. This represents the total reactive power collected by the meter during time period t, where μ1 and μ2 are penalty parameters. Let be the penalty parameter for the j-state of appliance i. Let ε be the operating penalty parameter for state j of appliance i during time period t. P,t , ε Q,t As auxiliary variables, they represent the errors in active power and reactive power during time period t, respectively.

[0069] In summary, the efficient non-intrusive load monitoring mixed integer programming model construction method provided by this invention constructs a concise linear objective function by introducing linear penalty terms (appliance state transition penalty term and minimum operating state penalty term) and power variables, reducing the complexity of solving the unit model. Furthermore, by introducing power variables, power fluctuation constraints and power boundary constraints for each applicator state are constructed, improving the model's accuracy. Then, minimum operating time constraints for applicators are constructed based on convex hull theory. In addition, solving the model using GUROBI 9.1 shows that the non-intrusive load monitoring mixed integer programming model constructed using this invention achieves a load decomposition accuracy of over 94%, and can complete a two-day load decomposition task within 18 seconds. Therefore, the efficient non-intrusive load monitoring mixed integer programming model constructed by this invention has reduced solution difficulty and high computational efficiency, and can be used to monitor power load to achieve resource optimization and energy conservation and emission reduction goals.

[0070] The following specific examples demonstrate the feasibility of the model constructed by this invention.

[0071] Taking the public dataset AMPds as an example, the accuracy of the model constructed by this invention is shown in Table 5 below.

[0072] electrical appliances dryer refrigerator dishwasher heat pump accuracy 98.43％ 98.21％ 94.47％ 96.96％

[0073] According to the modeling steps described in this invention, an efficient non-intrusive load monitoring mixed integer programming model is established. The model solution based on the GUROBI 9.1 tool shows that the model constructed using the construction method of this invention achieves a load decomposition accuracy of over 94%, and the two-day load decomposition task can be completed within 18 seconds.

[0074] Figure 2 This is a structural block diagram of a high-efficiency, non-intrusive load monitoring mixed integer programming model construction device provided by an embodiment of the present invention. For ease of explanation, only the parts related to the embodiment of the present invention are shown in the figure, which are described in detail below:

[0075] See Figure 2 The efficient non-intrusive load monitoring mixed integer programming model construction device provided in this embodiment of the invention includes a data preprocessing unit 210, an objective function construction unit 220, and a constraint construction unit 230.

[0076] The data preprocessing unit 210 is used to collect the power characteristic data of each electrical appliance. The power characteristic data includes the number of states of the electrical appliance, the minimum running time of each state of the electrical appliance, the power boundary of each state of the electrical appliance, the power fluctuation amplitude of each state of the electrical appliance, and the transition sequence between each state of the electrical appliance.

[0077] Objective function construction unit 220 constructs an objective function that considers the state transition penalty term and the minimum operating state penalty term of the appliance through the equivalent transformation technique of integer variables.

[0078] The constraint construction unit 230 introduces power variables to construct power fluctuation constraints and power boundary constraints for each state of the electrical appliance, and establishes the convex hull expression form of the minimum running time constraint of the electrical appliance based on convex hull theory.

[0079] The efficient, non-intrusive load monitoring mixed integer programming model construction method provided in this invention reduces the complexity of solving the unit model by introducing linear penalty terms (appliance state transition penalty term and minimum operating state penalty term) and power variables to construct a concise linear objective function. Furthermore, by introducing power variables, power fluctuation constraints and power boundary constraints for each applicator state are constructed, improving the model's accuracy. Then, minimum operating time constraints for applicators are constructed based on convex hull theory. Model solving using the GUROBI 9.1 tool shows that the model constructed using this invention achieves a load decomposition accuracy of over 94%, and can complete a two-day load decomposition task within 18 seconds. Therefore, the efficient, non-intrusive load monitoring mixed integer programming model constructed in this invention reduces the difficulty of solving the model and has high computational efficiency, making it suitable for monitoring power load to achieve resource optimization and energy conservation and emission reduction goals.

[0080] It should be understood that although the steps in the flowcharts of the various embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the various embodiments may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0081] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0082] 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.

[0083] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for constructing an efficient, non-intrusive mixed-integer programming model for load monitoring, characterized in that, The method includes: Collect electrical characteristic data of electrical appliances, including the number of states of the electrical appliance, the minimum running time of each state of the electrical appliance, the power boundary of each state of the electrical appliance, the power fluctuation amplitude of each state of the electrical appliance, and the transition sequence between each state of the electrical appliance. The objective function, which considers the state transition penalty term and the minimum operating state penalty term of the appliance, is constructed using the equivalent transformation technique of integer variables, as shown below: ， in, Indicate the appliance number, Indicates the status number of the appliance. Indicates time period, The total number of electrical appliances. Total number of time periods For electrical appliances The total number of states, and For penalty parameters, For electrical appliances of The penalty parameter for enabling a state. For electrical appliances of Status in The runtime penalty parameters for the time period, Indicates active power. Indicates reactive power. , As auxiliary variables, they respectively represent Errors in active power and reactive power over a given time period. Indicates electrical appliances of Status in The running status of a time period is represented by a 0-1 variable, where 0 indicates off and 1 indicates running. Indicates electrical appliances of Status in The on / off status of a time period is a 0-1 variable, where 1 indicates on and 0 indicates otherwise. By introducing power variables, power fluctuation constraints and power boundary constraints for each state of the electrical appliance are constructed. Based on convex hull theory, the convex hull expression form of the minimum running time constraint of the electrical appliance is established, as shown below: ， ， ， ， ， ， ， in, The total number of electrical appliances. Total number of time periods For electrical appliances The total number of states, Indicate the appliance number, Indicates the status number of the appliance. Indicates time period, Indicates electrical appliances of Status in Active power during a time period Indicates electrical appliances of Status in Reactive power during a given time period and They represent electrical appliances. of The lower and upper bounds of the active power of the state. and Indicates electrical appliances of The amplitude of the upward and downward fluctuations in active power under the condition. and They represent electrical appliances. of The lower and upper bounds of reactive power in the state. and Indicates electrical appliances of The amplitude of the upper and lower fluctuations of reactive power in the state. Indicates electrical appliances of Status in The running status of a time period is represented by a 0-1 variable, where 0 indicates off and 1 indicates running. Indicates electrical appliances of Status in The on / off status of a time period is represented by a 0-1 variable, where 1 indicates on and 0 indicates otherwise. Indicates electrical appliances of The minimum running time of a state. ; Based on power characteristic data, an objective function considering the state transition penalty term and minimum operating state penalty term of electrical appliances, power fluctuation constraints and power boundary constraints of each state of electrical appliances, minimum operating time constraints of electrical appliances, and other constraints, an efficient non-intrusive load monitoring mixed integer programming model is constructed.

2. A highly efficient, non-intrusive device for constructing a mixed-integer programming model for load monitoring, characterized in that, The device includes: The data preprocessing unit is used to collect the power characteristic data of each electrical appliance. The power characteristic data includes the number of states of the electrical appliance, the minimum running time of each state of the electrical appliance, the power boundary of each state of the electrical appliance, the power fluctuation amplitude of each state of the electrical appliance, and the transition sequence between each state of the electrical appliance. The objective function construction unit constructs an objective function that considers the state transition penalty term and the minimum operating state penalty term of the appliance through the integer variable equivalent transformation technique. The objective function is as follows: ， in, Indicate the appliance number, Indicates the status number of the appliance. Indicates time period, The total number of electrical appliances. The total number of time periods. For electrical appliances The total number of states, and For penalty parameters, For electrical appliances of The penalty parameter for enabling the state. For electrical appliances of Status in The runtime penalty parameters for the time period, Indicates active power. Indicates reactive power. , As auxiliary variables, they respectively represent Errors in active power and reactive power over a given time period. Indicates electrical appliances of Status in The running status of a time period is represented by a 0-1 variable, where 0 indicates off and 1 indicates running. Indicates electrical appliances of Status in The on / off status of a time period is represented by a 0-1 variable, where 1 indicates on and 0 indicates otherwise; and The constraint construction unit introduces power variables to construct power fluctuation constraints and power boundary constraints for each state of the electrical appliance. Based on convex hull theory, it establishes a convex hull expression for the minimum operating time constraint of the electrical appliance. The power fluctuation constraints and power boundary constraints for each state of the electrical appliance are as follows: ， ， ， ， ， ， in, The total number of electrical appliances. Total number of time periods For electrical appliances The total number of states, Indicate the appliance number, Indicates the status number of the appliance. Indicates time period, Indicates electrical appliances of Status in Active power during a time period Indicates electrical appliances of Status in Reactive power during a given time period and They represent electrical appliances. of The lower and upper bounds of the active power of the state. and Indicates electrical appliances of The amplitude of the upward and downward fluctuations in active power under the condition. and They represent electrical appliances. of The lower and upper bounds of reactive power in the state. and Indicates electrical appliances of The amplitude of the upper and lower fluctuations of reactive power in the state. Indicates electrical appliances of Status in The running status of a time period is represented by a 0-1 variable, where 0 indicates off and 1 indicates running. Indicates electrical appliances of Status in The on / off status of a time period is a 0-1 variable, where 1 indicates on and 0 indicates otherwise. Based on power characteristic data, an objective function considering appliance state transition penalties and minimum operating state penalties, power fluctuation constraints and power boundary constraints for each appliance state, minimum operating time constraints, and other constraints, the minimum operating time constraint for the appliance is as follows: ， in, Indicates electrical appliances of The minimum running time of a state. The other constraints include: error constraints, multi-state selection constraints, and state constraints; finally, an efficient non-intrusive load monitoring mixed integer programming model is constructed.

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