Large-scale variable frequency air conditioner accurate aggregation method based on external approximation Minkowski sum

Abstract

The invention provides a large-scale variable-frequency air conditioner accurate aggregation method based on external approximation Minkowski sum, which comprises the following steps: building physical models of a variable-frequency air conditioner, including a thermodynamic model, an electrothermal conversion model and a user comfort model; establishing an equivalent virtual battery model; representing an operation feasible region of the equivalent virtual battery model in a convex polytope semi-plane form, and performing aggregation by adopting an external approximation Minkowski sum method to obtain a feasible region of a variable frequency air conditioner cluster; and externally approaching the problem of redundant constraints generated by Minkowski and method aggregation, searching an optimal tangent plane of a feasible region after aggregation based on an auxiliary optimization method of linear programming, identifying and deleting constraints which do not belong to the feasible region, and obtaining an elastic feasible region representation form of the variable frequency air conditioner cluster. According to the method, the complexity of large-scale high-heterogeneity variable frequency air conditioner elastic adjustment feasible region description can be effectively reduced, and the privacy protection problem of a final user is compatible, so that unified management and scheduling of a power grid are facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of power system aggregation optimization, and in particular to a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum. Background Art

[0002] In recent years, with the high penetration rate of new energy sources connected to the grid, the power grid has shown a serious lack of flexibility. Demand-side flexible resources represented by temperature control loads (such as air conditioners, heat pumps, etc.) and electric vehicles can provide high-quality elastic adjustment capabilities to quickly respond to the lack of flexibility in grid dispatching, providing a solution. With the rapid development of the economy, building temperature control loads (TCLs), mainly variable-frequency air conditioners, account for more than 50% and show an increasing trend year by year. However, due to the characteristics of variable-frequency air conditioners, which are mostly small in scale and relatively dispersed in distribution, with different adjustment characteristics and physical parameters and high heterogeneity, it is impractical for grid dispatchers to model each variable-frequency air conditioner when optimizing the dispatch of units, because it will significantly increase the number of variables and constraints, resulting in increased computational burden and compromised tractability.

[0003] At present, there are three architectures that can be used for cluster control: centralized architecture, decentralized architecture, and distributed architecture. Due to its controllability and predictability, the centralized architecture is often used to control devices to participate in demand response scheduling, but it needs to control a large number of devices and requires all devices to pass their parameters and status information to the central controller. Due to the privacy protection of end users or the heavy computing burden of the central controller, the bandwidth and storage requirements of the central controller are extremely high, and centralized control cannot be performed. In order to reduce the computing burden, some studies have used aggregation models to approximate the feasible domain of cluster elastic regulation, such as aggregation models based on Monte Carlo simulation, aggregation models based on state sequences, aggregation models based on Focke-Planck theorem, aggregation models based on population-bin, and aggregation models based on Markov chains, etc., to hierarchically coordinate highly heterogeneous sub-clusters.

[0004] Based on this, it is urgently necessary to aggregate the widely distributed and highly heterogeneous variable-frequency air conditioners through certain aggregation methods to form a cluster external characteristic representation form that can be regulated by the power grid dispatching agency, so as to facilitate unified management and dispatch of the power grid, thereby improving the flexibility and reliability of the power system. Summary of the invention

[0005] The present invention aims to at least solve the above-mentioned technical problems existing in the prior art.

[0006] To this end, the present invention provides a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum.

[0007] The present invention provides a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, comprising:

[0008] Building a physical model of a single variable frequency air conditioner, wherein the physical model of the variable frequency air conditioner includes a thermodynamic model, an electric heat conversion model, and a user comfort model;

[0009] An equivalent virtual battery model is established according to the physical model of the variable frequency air conditioner to characterize the feasible domain of operation of the variable frequency air conditioner; wherein the charge and discharge power and energy boundaries of the equivalent virtual battery model are determined by an optimization method to characterize the characteristics outside the feasible domain of the variable frequency air conditioner;

[0010] The equivalent virtual battery model is characterized in the form of a convex polyhedral half-plane, and its operation feasible domain is represented. The convex polyhedral half-plane forms of multiple variable-frequency air conditioner equivalent virtual battery models are aggregated using the outer approximation Minkowski sum method to obtain the feasible domain of the variable-frequency air conditioner cluster.

[0011] The redundant constraint problem generated by the aggregation of the Minkowski sum method is externally approximated. Based on the auxiliary optimization method of linear programming, the optimal tangent plane of the feasible domain after aggregation is found, the constraints that do not belong to the feasible domain are identified and deleted, and the elastic feasible domain representation form of the variable frequency air-conditioning cluster is obtained.

[0012] The large-scale variable frequency air conditioner accurate aggregation method based on the outer approximation Minkowski sum according to the above technical solution of the present invention may also have the following additional technical features:

[0013] In the above technical solution, the method for building the thermodynamic model includes:

[0014] The equivalent thermal parameter model simulated by the first-order resistor-capacitor circuit is used to simulate the process of variable frequency air conditioning cooling power change, so as to characterize the dynamic change of indoor temperature. The thermodynamic model of variable frequency air conditioning power and indoor temperature change in cooling mode includes:

[0015]

[0016] Where C represents the equivalent heat capacity of the building; T in represents the indoor temperature of the building; t represents the time index; Δt represents the time step; T out represents the outdoor temperature of the building; R represents the equivalent thermal resistance of the building; Q′ represents the heat increment generated inside the building every time step; Q IAC (t) represents the cooling power of the variable frequency air conditioner at time t;

[0017] Wherein, the indoor temperature of the building is limited by user comfort, including:

[0018]

[0019] in, Indicates the upper limit of indoor temperature acceptable to users; Indicates the lower limit of indoor temperature acceptable to users.

[0020] In the above technical solution, the method for building the electrothermal conversion model includes:

[0021] The relationship between the refrigeration power and the power consumption of the variable frequency air conditioner is simulated according to the operating characteristic curve of the performance coefficient of the variable frequency air conditioner compressor. The electric heat conversion model includes:

[0022]

[0023] Where, f represents the operating frequency of the variable frequency air conditioner; k q , μ q , k p and μ p P is the performance coefficient between cooling power and electrical power; IAC (t) represents the power consumption of the variable frequency air conditioner.

[0024] 4. According to the large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum of claim 3, it is characterized in that the method of building the user comfort model includes:

[0025] According to the fact that the more the indoor temperature deviates from the optimal temperature, the faster the body sensation deteriorates, a quadratic function is used to model the user comfort, and the user comfort model includes:

[0026]

[0027] Among them, Comfort(t) represents the user comfort; Indicates the optimum temperature.

[0028] In the above technical solution, the equivalent virtual battery model is established according to the physical model of the variable frequency air conditioner, including:

[0029] The virtual battery has the properties of charge and discharge power and state of charge, where the charge and discharge power is represented by P VB (t) indicates that P VB (t)>0 indicates virtual battery charging, P VB (t) < 0 indicates virtual battery discharge; due to the working limitation of the battery, P VB (t) Subject to certain restrictions, including:

[0030]

[0031] in, The upper limit of the virtual battery charging and discharging power; is the lower limit of the virtual battery charging and discharging power;

[0032] The charge state of the virtual battery is expressed as E VB (t) is used to describe the energy storage level of the virtual battery; the state of charge of the virtual battery is controlled by the charge and discharge power, including:

[0033] E VB (t+1)=α·E VB (t)+η·P VB (t)

[0034] Among them, α is the energy dissipation coefficient caused by the virtual battery charging and discharging power; η is the virtual battery charging and discharging efficiency;

[0035] The state of charge of the virtual battery is subject to capacity constraints, including:

[0036]

[0037] in, is the upper limit of the virtual battery state of charge; is the lower limit of the virtual battery state of charge;

[0038] The rise and fall of indoor temperature is equivalent to the discharge and charge process of the virtual battery, that is, increasing the cooling power causes the virtual battery to charge, and reducing the cooling power causes the virtual battery to discharge;

[0039] When the indoor temperature reaches the lower limit of the user's acceptable temperature, it means that the current indoor cooling capacity can maintain the energy peak required for the user's comfort, which is equivalent to the virtual battery being fully charged; when the indoor temperature reaches the upper limit of the user's acceptable temperature, it means that the current indoor cooling capacity is difficult to maintain the threshold of the user's comfort, which is equivalent to the virtual battery being exhausted;

[0040] The indoor temperature at time t in the user comfort model is taken as the optimization target. The constraints include the thermodynamic model and the electric heat conversion model. The upper and lower limits of the air conditioning load power consumption when the indoor temperature is at the upper and lower limits of the user comfort level are described, including:

[0041]

[0042] in, Indicates the upper limit of air conditioning load power consumption when the user's comfort level is at the upper limit; Indicates the lower limit of air conditioning load power consumption when the user's comfort level is at the lower limit;

[0043] The energy upper and lower limits of the virtual battery are characterized by the average power of the entire controllable period, including:

[0044]

[0045] in, Indicates that the air conditioning load is equivalent to the energy upper limit of the virtual battery; represents the lower limit of the energy of the virtual battery equivalent to the air conditioning load; α represents the energy dissipation coefficient caused by the charging and discharging power of the virtual battery; represents the reference power of the equivalent virtual battery model; N represents the number of time indexes in the controllable period;

[0046] The equivalent virtual battery model comprises:

[0047]

[0048] in, represents the power of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t represents the energy of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; represents the power upper limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; and represents the power lower limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; η represents the virtual battery charging and discharging efficiency.

[0049] In the above technical solution, the method for calculating the energy dissipation coefficient caused by the virtual battery charging and discharging power includes:

[0050]

[0051] The calculation method of the virtual battery charge and discharge efficiency includes:

[0052]

[0053] In the above technical solution, the equivalent virtual battery model is characterized in the form of a convex polyhedral half-plane, and its operation feasible domain includes:

[0054] The equivalent virtual battery model is used to describe the operating constraints of the variable frequency air conditioner elastic regulation feasible domain, wherein the equivalent virtual battery model is a linear constraint on power;

[0055] The equivalent virtual battery model is summarized as a linear inequality, and its operation feasible domain is characterized in the form of a convex polyhedral half-plane, including:

[0056]

[0057]

[0058] Among them, Z i represents the elastic feasible region of the i-th variable frequency air conditioner; pi represents the operating power of the i-th variable frequency air conditioner; A i b represents the inequality coefficient matrix of the elastic feasible domain of the equivalent virtual battery model of the i-th variable frequency air conditioner; i The column vector representing the elastic feasible region of the equivalent virtual battery model of the i-th variable frequency air conditioner; represents the power constraint of the equivalent virtual battery model, represents the power constraint of the equivalent virtual battery model; E represents the identity matrix, represents the resource coefficient matrix associated with the energy dissipation coefficient α; The column vector representing the power feasible region of the i-th equivalent virtual battery model; represents the column vector of the energy feasible domain of the i-th virtual battery model; n represents the number of variable frequency air conditioners.

[0059] In the above technical solution, the outer approximation Minkowski sum method is used to aggregate the convex polyhedral half-plane forms of multiple variable frequency air conditioner equivalent virtual battery models to obtain the feasible domain of the variable frequency air conditioner cluster, including:

[0060] The elastic adjustment feasible domains of the equivalent virtual battery models of all variable frequency air conditioners whose heterogeneity exceeds the set threshold are aggregated to form the elastic adjustment feasible domain of the cluster. The elastic adjustment feasible domain of the cluster is used to characterize the adjustable power range of the variable frequency air conditioner cluster in response to grid dispatch, including:

[0061]

[0062] Among them, Z Total represents the feasible domain of elastic adjustment of the cluster, M represents the variable frequency air conditioner whose heterogeneity exceeds the set threshold; p M A represents the operating power of the variable frequency air conditioner cluster after aggregation; M b represents the inequality coefficient matrix of the elastic feasible domain of the variable frequency air conditioning cluster after aggregation; b M The column vector representing the elastic feasible region of the aggregated variable frequency air conditioner cluster; represents the Minkowski summation symbol; represents a column matrix composed of M resource coefficient matrices; Represents the unknown parameters, and the inequality needs to be guaranteed to hold as much as possible.

[0063] In the above technical solution, the redundant constraint problem generated by the external approximation Minkowski sum method aggregation is solved by finding the optimal tangent plane of the feasible domain after aggregation based on the auxiliary optimization method of linear programming, identifying and deleting the constraints that do not belong to the feasible domain, and obtaining the elastic feasible domain representation form of the variable frequency air conditioning cluster, including:

[0064] By giving the necessary and sufficient conditions for identifying redundant constraints and comparing the optimal solutions of a series of linear programming problems to determine whether a constraint is redundant;

[0065] Identify and delete the constraints that do not belong to the feasible region. The elastic feasible region representation form of the variable-frequency air-conditioning cluster obtained is:

[0066]

[0067] where, represents the power of the variable-frequency air-conditioning cluster at time t; represents the energy of the variable-frequency air-conditioning cluster at time t; represents the upper power limit of the variable-frequency air-conditioning cluster at time t; represents the lower power limit of the variable-frequency air-conditioning cluster at time t; represents the upper energy limit of the variable-frequency air-conditioning cluster at time t; represents the lower energy limit of the variable-frequency air-conditioning cluster at time t.

[0068] In the above technical solution, the method of giving the necessary and sufficient conditions for identifying redundant constraints and comparing the optimal solutions of a series of linear programming problems to determine whether a constraint is redundant includes:

[0069] Let the necessary and sufficient condition of the constraint be Ax < b. Select the k-th row constraint among them and solve the linear programming problems before and after adding this constraint for detection, including:

[0070] ......

[0072] where, I represents the set of non-redundant constraints that have been detected for the constraint A·x ≤ b, and j represents the number of the constraint; means that the k-th row constraint is not included in the set I; if and are equal, the k-th row constraint is redundant; if not, it is not redundant; s.t. represents the constraint condition; LP represents the linear programming objective function.

[0073] In summary, due to the adoption of the above technical features, the beneficial effects of the present invention are:

[0074] The present invention takes the flexible feasible domain aggregation problem of variable frequency air conditioners as the research object, and proposes a large-scale variable frequency air conditioner precise aggregation method based on the outer approximation Minkowski sum, which can effectively reduce the grid dispatch calculation burden and be compatible with the privacy protection issues of end users. This is to facilitate the unified management and dispatch of the power grid, thereby improving the flexibility and reliability of the power system. Specifically, the present invention analyzes the difficulties of the essential problems of variable frequency air conditioner aggregation and the outer approximation Minkowski and technical analysis, and introduces a virtual battery equivalent model to effectively characterize the external characteristics of the variable frequency air conditioner, thereby reducing the complexity of the characterization of the feasible domain of large-scale highly heterogeneous variable frequency air conditioners with flexible regulation.

[0075] Additional aspects and advantages of the present invention will become apparent from the following description or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, in which:

[0077] Figure 1 This is a modeling principle diagram of an equivalent virtual battery model in a large-scale variable frequency air conditioner accurate aggregation method based on an outer approximation Minkowski sum according to an embodiment of the present invention;

[0078] Figure 2 It is a schematic diagram of a two-dimensional feasible domain Minkowski sum in a large-scale variable frequency air conditioner accurate aggregation method based on an outer approximation Minkowski sum according to an embodiment of the present invention;

[0079] Figure 3 It is a schematic diagram of the principle of auxiliary optimization identification of redundant constraints based on linear programming in a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to an embodiment of the present invention;

[0080] Figure 4 It is a schematic diagram of the power feasible domain of the equivalent virtual battery model in the large-scale variable frequency air conditioner accurate aggregation method based on the outer approximation Minkowski sum according to one embodiment of the present invention;

[0081] Figure 5 It is a schematic diagram of the feasible domain of electric energy of an equivalent virtual battery model in a large-scale variable frequency air conditioner accurate aggregation method based on an outer approximation Minkowski sum according to an embodiment of the present invention;

[0082] Figure 6 It is a schematic diagram of the influence of the change of physical parameters on the power feasible domain of the equivalent virtual battery model of a single variable frequency air conditioner in a large-scale variable frequency air conditioner accurate aggregation method based on the outer approximation Minkowski sum according to an embodiment of the present invention;

[0083] Figure 7It is a schematic diagram of the effect of physical parameter changes on the feasible domain of electric energy of an equivalent virtual battery model of a single variable frequency air conditioner in a large-scale variable frequency air conditioner precise aggregation method based on an outer approximation Minkowski sum according to an embodiment of the present invention;

[0084] Figure 8 It is a schematic diagram of the influence of the change of artificial parameters on the power feasible domain of the equivalent virtual battery model of a single variable frequency air conditioner in the large-scale variable frequency air conditioner accurate aggregation method based on the outer approximation Minkowski sum according to one embodiment of the present invention;

[0085] Fig. 9 It is a schematic diagram of the influence of the artificial parameter change on the feasible domain of electric energy of the equivalent virtual battery model of a single variable frequency air conditioner in the large-scale variable frequency air conditioner accurate aggregation method based on the outer approximation Minkowski sum according to one embodiment of the present invention;

[0086] Fig.10 This is a result diagram of the external approximation results and calculation time of the energy boundary aggregation of the variable frequency air conditioner cluster under different aggregation numbers in the large-scale variable frequency air conditioner accurate aggregation method based on the external approximation Minkowski sum according to one embodiment of the present invention;

[0087] Fig.11 This is a result diagram of the external approximation results and calculation time of the energy boundary aggregation of the variable frequency air conditioner cluster at different time scales in the large-scale variable frequency air conditioner precise aggregation method based on the external approximation Minkowski sum in one embodiment of the present invention. DETAILED DESCRIPTION

[0088] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present application and the features in the embodiments can be combined with each other without conflict.

[0089] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the protection scope of the present invention is not limited to the specific embodiments disclosed below.

[0090] Refer to the following Figures 1 to 11 The following describes a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum provided according to some embodiments of the present invention.

[0091] Some embodiments of the present application provide a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum.

[0092] The first embodiment of the present invention proposes a large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, including the following steps S1 to S4.

[0093] S1. Build a physical model of a single variable-frequency air conditioner, where the physical model of the variable-frequency air conditioner includes a thermodynamic model, an electric-heat conversion model, and a user comfort model.

[0094] Specifically, the air conditioning load adopts a liquid-gas cycle mode for cooling and heating, and more for cooling. The present disclosure mainly uses the cooling mode as an example for explanation. That is, when the air conditioner is in the cooling mode, the compressor compresses the low-pressure gas into a high-pressure gas, which becomes a normal-temperature high-pressure liquid after heat dissipation through the condenser (outdoor unit), and then the normal-temperature high-pressure liquid is sent to the evaporator (indoor unit) through a pipeline to be gasified and become a low-temperature gas, thereby absorbing a large amount of heat, making the evaporator cold, and the fan blows the indoor air through the evaporator, and the cold air blown out is cold air, so that the cooling effect can be achieved. The basic structure and basic principle of the variable frequency air conditioner are exactly the same as those of the ordinary air conditioner, and only the frequency converter is installed at the compressor, and its operating frequency can be directly changed by the frequency converter, so as to continuously adjust the cooling / heat and power consumption within a certain range. Considering the influence of the physical environment and human factors (user comfort) on the variable frequency air conditioner, the physical model of the variable frequency air conditioner in the present disclosure mainly includes a thermodynamic model, an electric heat conversion model and a user comfort model.

[0095] In some embodiments, the method for building the thermodynamic model includes:

[0096] The equivalent thermal parameter (ETP) model simulated by the traditional first-order resistor-capacitor circuit is used to simulate the process of variable frequency air conditioning cooling power change, so as to characterize the dynamic change of indoor temperature. The thermodynamic model of variable frequency air conditioning power and indoor temperature change in cooling mode includes:

[0097]

[0098] Where C represents the equivalent heat capacity of the building; T in represents the indoor temperature of the building; t represents the time index; Δt represents the time step; T out represents the outdoor temperature of the building; R represents the equivalent thermal resistance of the building; Q′ represents the heat increment generated inside the building every time step; Q IAC (t) represents the cooling power of the variable frequency air conditioner at time t;

[0099] Among them, in order to ensure the comfort of people indoors in the building, when the room has good thermal insulation and the frequency conversion capacity is reasonably configured, the indoor temperature should be within the user's acceptable range, that is, the indoor temperature of the building is limited by the user's comfort, including:

[0100]

[0101] in, Indicates the upper limit of indoor temperature acceptable to users; Indicates the lower limit of indoor temperature acceptable to users.

[0102] In some embodiments, the method for constructing the electrothermal conversion model includes:

[0103] The relationship between the refrigeration power and the electric power of the variable frequency air conditioner is simulated according to the operating characteristic curve of the performance coefficient of the variable frequency air conditioner compressor. Specifically, the variable frequency air conditioner can directly change its operating frequency or speed through the inverter, thereby continuously adjusting the refrigeration / heating power and electric power within a certain range, but the performance coefficient of the variable frequency air conditioner compressor is not constant, and its performance coefficient changes with the change of its operating characteristic curve.

[0104] Then the electrothermal conversion model includes:

[0105]

[0106] Where, f represents the operating frequency of the variable frequency air conditioner; k q , μ q , k p and μ p P is the performance coefficient between cooling power and electrical power; IAC (t) represents the power consumption of the variable frequency air conditioner.

[0107] In some embodiments, the method for building the user comfort model includes:

[0108] According to the fact that the more the indoor temperature deviates from the optimal temperature, the faster the body sensation deteriorates, a quadratic function is used to model the user comfort, and the user comfort model includes:

[0109]

[0110] Among them, Comfort(t) represents the user comfort; Indicates the optimum temperature.

[0111] S2. Establish an equivalent virtual battery model based on the physical model of the variable frequency air conditioner to characterize the feasible operation domain of the variable frequency air conditioner; wherein, the charging and discharging power and energy boundaries of the equivalent virtual battery model are determined by an optimization method to characterize the characteristics outside the feasible domain of the variable frequency air conditioner.

[0112] Specifically, like energy storage batteries, virtual batteries also have the properties of charge and discharge power and state of charge, where the charge and discharge power is represented by P VB (t) indicates that P VB (t)>0 indicates virtual battery charging, P VB (t)<0 indicates virtual battery discharge. Due to the working limitation of the battery, P VB(t) is subject to certain constraints, as shown in the following formula:

[0113]

[0114] in, Indicates the upper limit of the virtual battery charge and discharge power; Indicates the lower limit of the virtual battery charge and discharge power.

[0115] The state of charge (SOC) of the virtual battery is expressed by E VB (t) is used to describe the energy storage level of the virtual battery. The state of charge of the virtual battery is controlled by the charge and discharge power, as shown in the following formula:

[0116] E VB (t+1)=α·E VB (t)+η·P VB (t)

[0117] Among them, α represents the energy dissipation coefficient caused by the virtual battery charging and discharging power; η is the virtual battery charging and discharging efficiency.

[0118] The state of charge of the virtual battery is subject to certain capacity constraints, as shown in the following formula:

[0119]

[0120] in, Indicates the upper limit of the virtual battery state of charge; Indicates the lower limit of the virtual battery state of charge.

[0121] The regulation characteristics of the air conditioning load refrigeration system are similar to the battery model. After considering physical characteristics (such as indoor and outdoor temperature, house attributes, etc.) and human factors (user comfort requirements), an equivalent virtual battery model is established to characterize the regulation characteristics of the variable frequency air conditioner, such as Figure 1 On the one hand, the indoor temperature reaching the upper temperature limit is equivalent to the virtual battery being fully charged, and the indoor temperature reaching the lower temperature limit is equivalent to the battery being exhausted; on the other hand, the rise in indoor temperature is equivalent to the discharge process of the virtual battery, and the drop in indoor temperature is equivalent to the charging process of the virtual battery, that is, increasing the cooling power makes the virtual battery charge, and reducing the cooling power makes the virtual battery discharge.

[0122] Taking into account the physical parameters of the variable frequency air conditioner and the user's comfort requirements, an optimization-based method is used to determine the boundaries of the charging and discharging power and energy of the virtual battery model. The charging and discharging power of the virtual battery model is determined by the actual operating power of the variable frequency air conditioner and the power reference value. The upper and lower limits of the actual operating power of the variable frequency air conditioner are further optimized to characterize the feasible domain of the actual operating power of the air conditioning load.

[0123] In a specific embodiment, the indoor temperature at time t in the user comfort model is taken as the optimization target, and the constraints include a thermodynamic model and an electric heat conversion model, and the upper and lower limits of the power when the variable frequency air conditioner is actually running are obtained, including:

[0124]

[0125] Among them, P IAC (t) represents the actual operating power of the variable frequency air conditioner at time t; Indicates the upper limit of the actual operating power of the variable frequency air conditioner; Indicates the lower limit of the actual operating power of the inverter air conditioner.

[0126] Therefore, the range of the actual operating power P(t) of the virtual battery can be expressed as:

[0127]

[0128] In order to better fit the equivalent virtual battery model, it is necessary to determine the power reference value for measuring the battery charging and discharging state, that is, when the actual operating power is greater than the reference power, it means that the virtual battery model is in a charging state, and vice versa, it means that the equivalent virtual battery model is in a discharging state. The power reference value is the power consumed by the air conditioning load when the indoor temperature is at the user-set temperature after considering physical and human factors. The reference power of the equivalent virtual battery model is determined by making the indoor temperature as close to the set temperature as possible. The determination method includes:

[0129]

[0130] in, Indicates the base cooling power of the inverter air conditioner; represents the reference power of the equivalent virtual battery model, T set Indicates the user set temperature.

[0131] Then the charging and discharging power and operating power range of the equivalent virtual battery model can be expressed as:

[0132]

[0133] in, and They are the upper and lower limits of the power when the air conditioning load is actually running.

[0134] Generally speaking, the energy stored in buildings exists in the form of heat, and the energy boundary of the virtual battery model is directly related to user comfort. Obviously, when the indoor temperature reaches the lower limit of the temperature acceptable to the user, it means that the current indoor cooling capacity can maintain the energy peak required for user comfort, which is equivalent to the virtual battery being fully charged; when the indoor temperature reaches the upper limit of the temperature acceptable to the user, it means that the current indoor cooling capacity is difficult to maintain the threshold of user comfort, which is equivalent to the virtual battery being exhausted; if the indoor temperature is within the user comfort range, it means that the virtual battery has a certain flexibility at this time, and can adjust the power consumption according to the needs of the grid dispatch without affecting the user comfort requirements. Then, taking the indoor temperature T in the user comfort model as an example, in (t) is the optimization target. The thermodynamic model, the electric heat conversion model, the upper and lower limits of the actual operating power of the variable frequency air conditioner, and the upper and lower limits of the air conditioning load power consumption when the user's comfort level is at the upper and lower limits are the constraints. The upper and lower limits of the air conditioning load power consumption when the room temperature is at the upper and lower limits of the user's comfort level can be described, including:

[0135]

[0136] in, Indicates the upper limit of air conditioning load power consumption when the user's comfort level is at the upper limit; Indicates the lower limit of air conditioning load power consumption when the user's comfort level is at the lower limit;

[0137] The energy upper and lower limits of the virtual battery are characterized by the average power of the entire controllable period, including:

[0138]

[0139] in, Indicates that the air conditioning load is equivalent to the energy upper limit of the virtual battery; represents the lower limit of the energy of the virtual battery equivalent to the air conditioning load; α represents the energy dissipation coefficient caused by the charging and discharging power of the virtual battery; represents the reference power of the equivalent virtual battery model; N represents the number of time indexes in the controllable period;

[0140] Then, the equivalent virtual battery model includes:

[0141]

[0142] in, represents the power of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t represents the energy of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; represents the power upper limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; and represents the power lower limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; η represents the virtual battery charging and discharging efficiency.

[0143] The method for calculating the energy dissipation coefficient caused by the virtual battery charging and discharging power includes:

[0144]

[0145] The calculation method of the virtual battery charge and discharge efficiency includes:

[0146]

[0147] The construction of equivalent virtual battery models of several variable-frequency air conditioners is completed through steps S1 and S2. The methods for describing the elastic feasible domain of cluster resources can be divided into top-down and bottom-up methods. Among them, top-down refers to the direct construction of the elastic feasible domain of the cluster by methods such as data-driven and probability distribution modeling; bottom-up means describing the elastic feasible domain of a single resource and aggregating the elastic feasible domains of multiple independent resources into a unified whole. The present disclosure is based on a bottom-up approach, and the aggregation method for approximate processing of the feasible domain under this approach mainly has two steps: (1) Mainly use equivalent generator models, equivalent energy storage models, and general convex polyhedral models to describe the elastic feasible domain of resources. (2) An approximate linear summation method is used for the elastic feasible domain, which is essentially an addition operation in Euclidean space, namely the Minkowski Sum.

[0148] Among them, the feasible domain of resource elasticity adjustment can be approximated by using the half-plane representation form of convex polytopes, methods based on hypercubes, improved Chino polyhedra, and hyperellipsoids; there are two main types of approximate approximation ideas: (1) internal approximation method. Although the internal approximation method can ensure that there is a feasible solution to the approximate aggregate feasible domain, it will cause a certain degree of loss of the elastic feasible domain space of the aggregate resource cluster. (2) External approximation method, that is, establishing an external approximation model of the original feasible region. Compared with the internal approximation method, the external approximation method has higher computational efficiency, but it will expand the elastic feasible domain space of the aggregate resource cluster. There are a large number of redundant constraints that reduce the optimization performance, and there may be unsolvable problems. Therefore, the present disclosure carries out the following steps S3 and S4.

[0149] S3. Characterize the operating feasible domain of the equivalent virtual battery model in the form of a convex polytope (Polytopes) half plane, and use the outer approximation Minkowski sum method to aggregate the convex polytope half plane forms of multiple variable frequency air conditioner equivalent virtual battery models to obtain the feasible domain of the variable frequency air conditioner cluster.

[0150] Specifically, the equivalent virtual battery model can describe the operation constraints of the flexible regulation feasible region of variable-frequency air conditioners. Through observation, it is found that the equivalent virtual battery model is a linear constraint on power. Therefore, it can be summarized as a linear inequality Ax < b, and its operation feasible region can be characterized in the form of a half-plane of Polytopes, realizing the mapping of the feasible region of the flexible regulation ability of variable-frequency air conditioners, including:

[0151]

[0152]

[0153] Among them, Z i represents the flexible feasible region of the i-th variable-frequency air conditioner; p i represents the operating power of the i-th variable-frequency air conditioner; A i represents the inequality coefficient matrix of the flexible feasible region of the equivalent virtual battery model of the i-th variable-frequency air conditioner; b i represents the column vector of the flexible feasible region of the equivalent virtual battery model of the i-th variable-frequency air conditioner; represents the power constraint of the equivalent virtual battery model, represents the power quantity constraint of the equivalent virtual battery model; E represents the identity matrix, represents the resource coefficient matrix related to the energy dissipation coefficient α; represents the column vector of the power feasible region of the i-th equivalent virtual battery model; represents the column vector of the energy feasible region of the i-th virtual battery model; n represents the number of variable-frequency air conditioners.

[0154] Furthermore, in order to make full use of the excellent regulation ability of variable-frequency air conditioners, multiple independent variable-frequency air conditioners need to be aggregated into a cluster form for unified power grid regulation. Due to the high heterogeneity of variable-frequency air conditioners, the energy dissipation coefficients α of variable-frequency air conditioners are not completely the same. The present disclosure adopts the method based on outer approximation Minkowski sum to aggregate the flexible regulation feasible regions of all virtual battery models of highly heterogeneous variable-frequency air conditioners to form the flexible regulation feasible region of the cluster, and this feasible region characterizes the adjustable power range when the variable-frequency air conditioner cluster responds to power grid dispatching.

[0155] In some embodiments, the highly heterogeneous variable-frequency air conditioners can be screened by setting a threshold and then subsequent calculations can be performed to streamline the calculation process. Of course, this step can also be omitted, and directly aggregate the flexible regulation feasible regions of the equivalent virtual battery models of all variable-frequency air conditioners.

[0156] In a specific embodiment, the elastic adjustment feasible domains of the equivalent virtual battery models of all variable frequency air conditioners whose heterogeneity exceeds a set threshold are aggregated to form the elastic adjustment feasible domain of the cluster, and the elastic adjustment feasible domain of the cluster is used to characterize the adjustable power range of the variable frequency air conditioner cluster in response to grid dispatch, including:

[0157]

[0158] Among them, Z Total represents the feasible domain of elastic adjustment of the cluster, M represents the variable frequency air conditioner whose heterogeneity exceeds the set threshold; p M A represents the operating power of the variable frequency air conditioner cluster after aggregation; M b represents the inequality coefficient matrix of the elastic feasible domain of the variable frequency air conditioning cluster after aggregation; b M The column vector representing the elastic feasible region of the aggregated variable frequency air conditioner cluster; represents the Minkowski summation symbol; represents a column matrix composed of M resource coefficient matrices; Represents the unknown parameters, and the inequality needs to be guaranteed to hold as much as possible.

[0159] like Figure 2 As shown, two flexible resources with two time periods (d, d+1) with power time coupling characteristics are used to solve the Minkowski sum. Among them, the feasible domains of flexible resource 1 and flexible resource 2 are Z1 and Z2 respectively. The overall feasible domain after aggregation can be expressed as the union of the area swept by the vertex of set 2 along the envelope of set 1 and set 1 itself, recorded as

[0160] S4. Approach the redundant constraints generated by the aggregation of the Minkowski sum method externally, and find the optimal tangent plane of the feasible domain after aggregation based on the auxiliary optimization method of linear programming. Identify and delete the constraints that do not belong to the feasible domain, and obtain the elastic feasible domain representation form of the variable frequency air conditioning cluster.

[0161] Specifically, the outer approximation Minkowski aggregation method is used to ensure computational efficiency, but the process of boundary approximation summation actually expands the feasible domain of cluster flexibility. The selection of will affect the accuracy of the proposed outer approximation Minkowski summation. In order to achieve the best outer approximation effect, the auxiliary optimization constraint reduction method based on linear programming can be used to eliminate redundant constraints. This method gives the necessary and sufficient conditions for identifying redundant constraints and compares a series of optimal solutions of linear programming to determine whether the constraints are redundant, thereby achieving the effect of redundancy reduction.

[0162] Specifically, the auxiliary optimization constraint reduction method based on linear programming includes:

[0163] By giving the necessary and sufficient conditions for identifying redundant constraints, the optimal solutions of a series of linear programming problems are compared to determine whether the constraints are redundant, including:

[0164] Let the necessary and sufficient condition for the constraint be Ax < b. Select the k-th row constraint among them, and solve the linear programming problems before and after adding this constraint respectively for detection, including:

[0165] ......

[0167] Among them, I represents the set of non-redundant constraints that have been detected for the constraint A·x ≤ b, and j represents the number of the constraint; It means that the k-th row constraint is not included in the set I; if and are equal, the k-th row constraint is redundant, and if they are not equal, it is not redundant; s.t. represents the constraint condition; LP represents the objective function of the linear programming.

[0168] As Figure 3 shown, among them, Constraint 1 is a redundant constraint, and Constraints 2, 3, 4, 5, and 6 are non-redundant constraints.

[0169] Based on the above steps, identify and delete the constraints that do not belong to the feasible region, and the obtained elastic feasible region representation form of the variable-frequency air-conditioning cluster is:

[0170]

[0171] Among them, represents the power of the variable-frequency air-conditioning cluster at time t; represents the energy of the variable-frequency air-conditioning cluster at time t; represents the upper power limit of the variable-frequency air-conditioning cluster at time t; represents the lower power limit of the variable-frequency air-conditioning cluster at time t; represents the upper energy limit of the variable-frequency air-conditioning cluster at time t; represents the lower energy limit of the variable-frequency air-conditioning cluster at time t.

[0172] A specific embodiment of the present invention gives a specific example. As follows.

[0173] In this embodiment, the present invention sets the power consumption range of a single variable-frequency air conditioner to be [1, 6] kW, the user comfort range to be [20, 24] °C, and the remaining parameters are randomly distributed within their ranges. For details, see Table 1. Using the typical summer outdoor temperature provided in the main urban area of Chongqing, China, during each time step, the outdoor temperature is used as a fixed value.

[0174] Table 1 Relevant parameters of variable-frequency air conditioners

[0175]

[0176] According to the parameter distribution in Table 1, the variable frequency air conditioner load operation data with different time scales and different numbers are trained. Since there are random numbers in the parameter distribution, the average value is obtained by sampling each result 100 times to prepare for the subsequent equivalent virtual battery model work.

[0177] In order not to involve the privacy information of the terminal users of the variable frequency air conditioner, this embodiment establishes an equivalent virtual battery model of a single variable frequency air conditioner, and obtains the power and energy boundaries through optimization. Therefore, the feasible domain of the variable frequency air conditioner elastic adjustment can be represented by the virtual battery model, such as Figure 4 and Figure 5 It should be noted that in order to reflect the charging and discharging characteristics of the virtual battery model, the reference power is subtracted from the actual power of the original variable frequency air conditioner, so negative power will appear on the power and energy boundary, indicating the discharge power, while positive power indicates the charging power, which does not affect the description of the feasible domain of the variable frequency air conditioner.

[0178] The change trend of the virtual battery power boundary is related to the outdoor temperature and the set indoor initial temperature. During the summer daytime, the outdoor temperature is high and the temperature difference between indoor and outdoor is large. The air conditioner needs to increase the power to meet the user's set comfort cooling demand. At this time, the power downward adjustment elasticity increases and the upward adjustment elasticity decreases; during the summer night, the outdoor temperature drops, the indoor and outdoor temperature difference becomes smaller, and the baseline power required to maintain the user-set comfort temperature is higher. The variable frequency air conditioner needs to reduce the power to meet the cooling demand, so that the power has a larger upward adjustment elasticity and a smaller downward adjustment elasticity. When the indoor temperature is higher than the temperature set by the user, the variable frequency air conditioner power is higher than the baseline power, which is equivalent to charging the virtual battery model, and vice versa, it is equivalent to discharging the virtual battery model.

[0179] It should be noted that this embodiment does not consider the randomness of environmental factors in the process of quantifying the feasible domain of the variable frequency air conditioner. Therefore, the following only analyzes the impact of changes in physical parameters and human parameters on the elastic feasible domain of a single variable frequency air conditioner virtual battery model, while reflecting high heterogeneity, such as Figure 6 , Figure 7 , Figure 8 and Fig. 9 shown.

[0180] The physical parameters are mainly reflected by the thermal capacity and thermal resistance parameters of the building, which reflect the thermal inertia of the house and are collectively characterized as the energy dissipation coefficient. The larger the energy dissipation coefficient of the virtual battery, the better the insulation effect of the user's house. When the other physical parameters and human factors are the same, increasing the energy dissipation coefficient can cause the feasible domain of the virtual battery power to move upward as a whole, increase the flexibility of the virtual battery power to increase, and reduce the flexibility of the virtual battery power to decrease; the energy feasible domain of the virtual battery power will expand as the energy dissipation coefficient increases. Human factors are mainly reflected by the user changing the indoor set temperature, which will affect the indoor comfort and benchmark power, and further affect the energy boundary of the virtual battery. When the physical parameters are the same, as the user sets the temperature, although the upper and lower limits of the power of the variable air conditioner during actual operation are not affected by the set temperature, the feasible domain of the virtual battery power will move upward as a whole, severely compressing the power downward adjustment space; the energy feasible domain of the virtual battery power will expand significantly as the indoor temperature set by the user increases, indicating that as the indoor temperature set by the user increases, the energy supply range that the variable frequency air conditioner can provide increases.

[0181] In this embodiment, the method of the present invention is compared and verified with the comparative method M2, wherein the comparative method M2 also adopts the outer approximation Minkowski sum method, but determines the aggregation energy boundary in the following manner:

[0182] When the number of variable frequency air conditioners reaches a certain scale, the energy dissipation coefficient α in the variable frequency air conditioner cluster can be approximated by the average value of the energy dissipation coefficient α of each variable frequency air conditioner, but this will undoubtedly affect the accuracy of aggregation. At this time, the aggregation feasible domain of N variable frequency air conditioner resources can be expressed by the following formula:

[0183]

[0184] In the formula, It represents the average value of energy dissipation coefficient of multiple variable frequency air conditioners.

[0185] Fig.10 and Fig.11 The effectiveness of the outer approximation Minkowski sum method proposed in the present disclosure for aggregating large-scale high-heterogeneity individual variable-frequency air conditioners is shown. Considering that the degree of approximation of the energy boundary of the aggregation model is affected by the high heterogeneity of the variable-frequency air conditioner (the degree of approximation of the power boundary of the aggregation model is not affected by the high heterogeneity of the variable-frequency air conditioner, so the degree of approximation of the power boundary of the aggregation model is not analyzed), the differences are described by generating random parameters of the normal distribution, and the probability distribution variance of the high-heterogeneity aggregation cluster is defined as twice that of the low-heterogeneity cluster. Due to the existence of random numbers, each result is sampled 100 times and the average is obtained.

[0186] Fig.10 and Fig.11The outer approximation results and calculation time of the energy boundary aggregation of the variable frequency air conditioner cluster under different time dimensions and aggregation numbers are shown. The approximation degree is characterized by the volume of the convex polyhedron formed by the energy boundary. V1 represents the volume obtained by the method M1 of this embodiment, and V2 represents the volume of the comparative method M2. The relative accuracy of the two methods is measured by the volume ratio (V1 / V2). Figure 7 It can be found that, for both high heterogeneity clusters and low heterogeneity clusters, the volume ratio is less than 1, indicating that the external approximation effect of the method M1 of this embodiment is better than the external approximation effect of the comparative method M2. This is because the aggregation model proposed in the present disclosure finds the optimal tangent plane through a series of linear programming problems, which has higher accuracy than the simple averaging of the energy dissipation coefficient before aggregation in the existing method. Secondly, with the increase of the number of aggregations and the time dimension, the external approximation effect of the aggregation model will become worse and worse, but the volume ratio V1 / V2 of method M1 and method M2 will become smaller and smaller, indicating that when the number of aggregations and the time scale are large, the aggregation method proposed in the present disclosure has better approximation effect. In terms of computing time, the method M1 of the present disclosure improves the approximation effect by solving linear programming problems, and the linear programming problem has a polynomial time complexity, and its solution time will basically increase linearly with the increase of the number of aggregations and the time dimension, ensuring the aggregation efficiency of heterogeneous resources.

[0187] In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0188] Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A precise aggregation method for large-scale variable frequency air conditioners based on outer approximation Minkowski sum, It is characterized in that include: Building a physical model of a single variable frequency air conditioner, wherein the physical model of the variable frequency air conditioner includes a thermodynamic model, an electric heat conversion model, and a user comfort model; An equivalent virtual battery model is established according to the physical model of the variable frequency air conditioner to characterize the feasible domain of operation of a single variable frequency air conditioner; wherein the charge and discharge power and energy boundaries of the equivalent virtual battery model are determined by an optimization method to characterize the characteristics outside the feasible domain of the variable frequency air conditioner; The equivalent virtual battery model is characterized in the form of a convex polyhedral half-plane, and its operation feasible domain is represented. The convex polyhedral half-plane forms of multiple variable-frequency air conditioner equivalent virtual battery models are aggregated using the outer approximation Minkowski sum method to obtain the feasible domain of the variable-frequency air conditioner cluster. The redundant constraint problem generated by the aggregation of the Minkowski sum method is externally approximated. Based on the auxiliary optimization method of linear programming, the optimal tangent plane of the feasible domain after aggregation is found, the constraints that do not belong to the feasible domain are identified and deleted, and the elastic feasible domain representation form of the variable frequency air-conditioning cluster is obtained.

2. According to claim 1, the large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, It is characterized in that The method for building the thermodynamic model includes: The equivalent thermal parameter model simulated by the first-order resistor-capacitor circuit is used to simulate the process of variable frequency air conditioning cooling power change, so as to characterize the dynamic change of indoor temperature. The thermodynamic model of variable frequency air conditioning power and indoor temperature change in cooling mode includes: Where C represents the equivalent heat capacity of the building; T in represents the indoor temperature of the building; t represents the time index; Δt represents the time step; T out represents the outdoor temperature of the building; R represents the equivalent thermal resistance of the building; Q′ represents the heat increment generated inside the building every time step; Q IAC (t) represents the cooling power of the variable frequency air conditioner at time t; Wherein, the indoor temperature of the building is limited by user comfort, including: in, Indicates the upper limit of indoor temperature acceptable to users; Indicates the lower limit of indoor temperature acceptable to users.

3. According to claim 2, the large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, It is characterized in that The method for constructing the electrothermal conversion model includes: The relationship between the refrigeration power and the power consumption of the variable frequency air conditioner is simulated according to the operating characteristic curve of the performance coefficient of the variable frequency air conditioner compressor. The electric heat conversion model includes: Where, f represents the operating frequency of the variable frequency air conditioner; k q , μ q , k p and μ p P is the performance coefficient between cooling power and electrical power; IAC (t) represents the power consumption of the variable frequency air conditioner.

4. According to claim 3, the large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, It is characterized in that The method for building the user comfort model includes: According to the fact that the more the indoor temperature deviates from the optimal temperature, the faster the body sensation deteriorates, a quadratic function is used to model the user comfort, and the user comfort model includes: Among them, Comfort(t) represents the user comfort; Indicates the optimum temperature.

5. According to claim 4, the large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum, It is characterized in that The step of establishing an equivalent virtual battery model according to the physical model of the variable frequency air conditioner comprises: The virtual battery has the properties of charge and discharge power and state of charge, where the charge and discharge power is represented by P VB (t) indicates that P VB (t)>0 indicates virtual battery charging, P VB (t) < 0 indicates virtual battery discharge; due to the working limitation of the battery, P VB (t) Subject to certain restrictions, including: in, The upper limit of the virtual battery charging and discharging power; is the lower limit of the virtual battery charging and discharging power; The charge state of the virtual battery is expressed as E VB (t) is used to describe the energy storage level of the virtual battery; the state of charge of the virtual battery is controlled by the charge and discharge power, including: E VB (t+1)=α·E VB (t)+η·P VB (t) Among them, α is the energy dissipation coefficient caused by the virtual battery charging and discharging power; η is the virtual battery charging and discharging efficiency; The state of charge of the virtual battery is subject to capacity constraints, including: in, is the upper limit of the virtual battery state of charge; is the lower limit of the virtual battery state of charge; The rise and fall of indoor temperature is equivalent to the discharge and charge process of the virtual battery, that is, increasing the cooling power causes the virtual battery to charge, and reducing the cooling power causes the virtual battery to discharge; When the indoor temperature reaches the lower limit of the user's acceptable temperature, it means that the current indoor cooling capacity can maintain the energy peak required for the user's comfort, which is equivalent to the virtual battery being fully charged; when the indoor temperature reaches the upper limit of the user's acceptable temperature, it means that the current indoor cooling capacity is difficult to maintain the threshold of the user's comfort, which is equivalent to the virtual battery being exhausted; The indoor temperature at time t in the user comfort model is taken as the optimization target. The constraints include the thermodynamic model and the electric heat conversion model. The upper and lower limits of the air conditioning load power consumption when the indoor temperature is at the upper and lower limits of the user comfort level are described, including: in, Indicates the upper limit of air conditioning load power consumption when the user's comfort level is at the upper limit; Indicates the lower limit of air conditioning load power consumption when the user's comfort level is at the lower limit; The energy upper and lower limits of the virtual battery are characterized by the average power of the entire controllable period, including: in, Indicates that the air conditioning load is equivalent to the energy upper limit of the virtual battery; represents the lower limit of the energy of the virtual battery equivalent to the air conditioning load; α represents the energy dissipation coefficient caused by the charging and discharging power of the virtual battery; represents the reference power of the equivalent virtual battery model; N represents the number of time indexes in the controllable period; The equivalent virtual battery model comprises: in, represents the power of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t represents the energy of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; represents the power upper limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; and represents the power lower limit of the equivalent virtual battery model of the i-th variable frequency air conditioner at time t; η represents the virtual battery charging and discharging efficiency.

6. The large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to claim 5, It is characterized in that The method for calculating the energy dissipation coefficient caused by the virtual battery charging and discharging power includes: The calculation method of the virtual battery charge and discharge efficiency includes:

7. The large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to claim 5, It is characterized in that The equivalent virtual battery model is characterized in the form of a convex polyhedral half-plane, and its feasible operation domain includes: The equivalent virtual battery model is used to describe the operating constraints of the variable frequency air conditioner elastic regulation feasible domain, wherein the equivalent virtual battery model is a linear constraint on power; The equivalent virtual battery model is summarized as a linear inequality, and its operation feasible domain is characterized in the form of a convex polyhedral half-plane, including: Among them, Z i represents the elastic feasible region of the i-th variable frequency air conditioner; p i represents the operating power of the i-th variable frequency air conditioner; A i b represents the inequality coefficient matrix of the elastic feasible domain of the equivalent virtual battery model of the i-th variable frequency air conditioner; i The column vector representing the elastic feasible region of the equivalent virtual battery model of the i-th variable frequency air conditioner; represents the power constraint of the equivalent virtual battery model, represents the power constraint of the equivalent virtual battery model; E represents the identity matrix, represents the resource coefficient matrix associated with the energy dissipation coefficient α; The column vector representing the power feasible region of the i-th equivalent virtual battery model; represents the column vector of the energy feasible domain of the i-th virtual battery model; n represents the number of variable frequency air conditioners.

8. The large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to claim 7, It is characterized in that The outer approximation Minkowski sum method is used to aggregate the convex polyhedral half-plane forms of multiple variable frequency air conditioner equivalent virtual battery models to obtain the feasible domain of the variable frequency air conditioner cluster, including: The elastic adjustment feasible domains of the equivalent virtual battery models of all variable frequency air conditioners whose heterogeneity exceeds the set threshold are aggregated to form the elastic adjustment feasible domain of the cluster. The elastic adjustment feasible domain of the cluster is used to characterize the adjustable power range of the variable frequency air conditioner cluster in response to grid dispatch, including: Z Total =Z 1 ⊕Z 2 ⊕...⊕Z M ={p M |A M ·p M ≤b M } Among them, Z Total represents the feasible domain of elastic adjustment of the cluster, M represents the variable frequency air conditioner whose heterogeneity exceeds the set threshold; p M A represents the operating power of the variable frequency air conditioner cluster after aggregation; M b represents the inequality coefficient matrix of the elastic feasible domain of the variable frequency air conditioning cluster after aggregation; b M The column vector representing the elastic feasible region of the cluster of variable frequency air conditioners after aggregation; ⊕ represents the Minkowski summation symbol; represents a column matrix composed of M resource coefficient matrices; Represents the unknown parameters, and the inequality needs to be guaranteed to hold as much as possible.

9. The large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to claim 8, It is characterized in that The redundant constraint problem generated by the external approximation Minkowski sum method aggregation is solved by finding the optimal tangent plane of the feasible domain after aggregation based on the auxiliary optimization method of linear programming, identifying and deleting the constraints that do not belong to the feasible domain, and obtaining the elastic feasible domain representation form of the variable frequency air conditioning cluster, including: By giving the necessary and sufficient conditions for identifying redundant constraints, we can compare the optimal solutions of a series of linear programming problems to determine whether the constraints are redundant. The constraints that do not belong to the feasible domain are identified and deleted, and the representation form of the elastic feasible domain of the variable frequency air conditioning cluster is obtained as follows: in, represents the power of the variable frequency air conditioning cluster at time t; represents the energy of the variable frequency air conditioning cluster at time t; represents the power upper limit of the variable frequency air conditioning cluster at time t; represents the power lower limit of the variable frequency air conditioning cluster at time t; represents the energy upper limit of the variable frequency air conditioning cluster at time t; Represents the lower limit of energy of the variable frequency air conditioning cluster at time t.

10. The large-scale variable frequency air conditioner accurate aggregation method based on outer approximation Minkowski sum according to claim 9, It is characterized in that By giving the necessary and sufficient conditions for identifying redundant constraints and comparing the optimal solutions of a series of linear programming problems to determine whether the constraints are redundant, it includes: Let the necessary and sufficient condition for the constraint be Ax < b. Select the k-th row constraint among them and solve the linear programming problems before and after adding this constraint respectively for detection, including: ...... Where I represents the set of non-redundant constraints that have been checked for the constraint A·x≤b, and j represents the number of the constraint; Indicates that the k-th row constraint is not included in the set I; if and If they are equal, the k-th row constraint is redundant; if they are not equal, then it is not redundant; st represents the constraint condition; LP represents the linear programming objective function.

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